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http://www.nursingresearch.co.nz/refbase/search.php?sqlQuery=SELECT%20author%2C%20title%2C%20type%2C%20year%2C%20publication%2C%20abbrev_journal%2C%20volume%2C%20issue%2C%20pages%2C%20keywords%2C%20abstract%2C%20thesis%2C%20editor%2C%20publisher%2C%20place%2C%20abbrev_series_title%2C%20series_title%2C%20series_editor%2C%20series_volume%2C%20series_issue%2C%20edition%2C%20language%2C%20author_count%2C%20online_publication%2C%20online_citation%2C%20doi%2C%20serial%20FROM%20refs%20WHERE%20serial%20%3D%201618%20ORDER%20BY%20created_date%20DESC%2C%20created_time%20DESC%2C%20modified_date%20DESC%2C%20modified_time%20DESC%2C%20serial%20DESC&client=&formType=sqlSearch&submit=Cite&viewType=&showQuery=0&showLinks=1&showRows=15&rowOffset=&wrapResults=1&citeOrder=creation-date&citeStyle=APA&exportFormat=RIS&exportType=html&exportStylesheet=&citeType=LaTeX&headerMsg= | nursingresearch.co.nz | CC-MAIN-2019-35 | application/x-latex | application/x-latex | crawl-data/CC-MAIN-2019-35/segments/1566027314959.58/warc/CC-MAIN-20190819201207-20190819223207-00438.warc.gz | 289,049,823 | 1,345 | %&LaTeX
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\bibitem{Brown2019} Brown, J. (2019). \textit{Thorn in the flesh: the experience of women living with surgical mesh complications}. Master{\textquoteright}s thesis, University of Otago, Dunedin. Retrieved August 20, 2019, from https://www.nzno.org.nz/resources/library/theses
\end{thebibliography}
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http://theanarchistlibrary.org/library/benjamin-tucker-tolstoyism-gone-to-seed.tex | theanarchistlibrary.org | CC-MAIN-2020-29 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2020-29/segments/1593655924908.55/warc/CC-MAIN-20200711064158-20200711094158-00361.warc.gz | 142,478,806 | 3,121 | \documentclass[DIV=12,%
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\title{“Tolstoyism Gone to Seed”}
\date{November 25, 1927}
\author{Benjamin Tucker}
\subtitle{}
% https://groups.google.com/d/topic/comp.text.tex/6fYmcVMbSbQ/discussion
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{\usekomafont{title}{\huge “Tolstoyism Gone to Seed”\par}}%
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{\usekomafont{author}{Benjamin Tucker\par}}%
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{\usekomafont{date}{November 25, 1927\par}}%
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\par
November 25, 1927
Dear Mr. Schumm:
I wrote you of the proposition of the National Institute for the Blind regarding ‘The Ego and His Own.’ It turns out to be a bit less encouraging than the first letters to Fifield indicated. Not bad, though, after all. What it amounts to is this; a copy is to be cut in raised type, by hand, by a volunteer, for Helen Keller, and a duplicate is to be put in the general library of raised type for the blind. I suppose, then, that Helen Keller is interested, or, if not, that some enthusiastic person hopes to interest her.
One sees now in Russia the perfect realization of “peace at any price,’ a land that knows not hate, the flowering of the gospel of universal love, Tolstoyism gone to seed. What a spectacle does that unhappy country present today! Simple, stupid, sodden; reeking, rotting, rampant; a deliquescent nest of life that crawls and creeps, she melts, she sprawls, she slops, she stinks! A gigantic Camembert, in the last disgusting stage.
Yours sincereley,
Benj R. Tucker
c\Slash{}o Munroe \& Co.
4 rue Ventadour
Paris, France
% begin final page
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The Anarchist Library
\smallskip
Anti-Copyright
\bigskip
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\bigskip
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\strut
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\begin{center}
Benjamin Tucker
“Tolstoyism Gone to Seed”
November 25, 1927
\bigskip
Retrieved on 2016-10-28 from http:\Slash{}\Slash{}marxists.architexturez.net\Slash{}archive\Slash{}tucker\Slash{}1927\Slash{}tolstoyism.htm
Source: Benjamin R. Tucker Papers, New York Public Library; Transcribed: by Mitchell Abidor, 2009.
\bigskip
\textbf{theanarchistlibrary.org}
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|
http://release-notes.trms.com/tex/199 | trms.com | CC-MAIN-2023-14 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2023-14/segments/1679296945376.29/warc/CC-MAIN-20230325222822-20230326012822-00021.warc.gz | 41,103,228 | 1,286 | \section{Carousel 5.1.3 Release Notes}
\begin{description}
\item[{\color{red}
\textbf{3119} \textbf{Configuration window nesting problem}
\textbf{Added a missing target attribute to the "main menu" link in the error screen.}
\item[{\color{red}
\textbf{3159} \textbf{Possible crash when the DisplayEngine displays many zones}
\textbf{Fixed issue where the DisplayEngine was not allocating enough memory for its internal zone list which could potentially corrupt memory and crash with a large number of zones.}
\item[{\color{red}
\textbf{3163} \textbf{5.1.2's DisplayEngine won't launch on some systems}
\textbf{Fixed issue where the DisplayEngine required runtime libraries that weren't available on some systems.}
\end{description}
|
https://www.math.bgu.ac.il/en/teaching/fall2021/courses/linear-algebra-for-biotechnology.tex | bgu.ac.il | CC-MAIN-2022-49 | text/tex | application/x-tex | crawl-data/CC-MAIN-2022-49/segments/1669446710900.9/warc/CC-MAIN-20221202082526-20221202112526-00737.warc.gz | 913,946,389 | 2,397 | \documentclass[oneside,final,11pt]{article}
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\usepackage{polyglossia}
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\begin{document}
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\begin{center}
\huge{The Department of Mathematics}\\[0.1\baselineskip]
\Large{2020--21--A term}\\[0.2\baselineskip]
\end{center}
\begin{description}
\item[Course Name]
Linear Algebra for Biotechnology
\item[Course Number]
\LRE{201.1.9551}
\item[Course web page]\mbox{}\\
\url{https://www.math.bgu.ac.il//en/teaching/fall2021/courses/linear-algebra-for-biotechnology}
\item[Lecturer]
Dr. Natalia Gulko,
\nolinkurl{<gulko@post.bgu.ac.il>},
Office מינוס 108
\item[Office Hours]
\url{https://www.math.bgu.ac.il/en/teaching/hours}
\end{description}
\section*{Abstract}
\section*{Requirements and grading\footnote{Information may change during the first two weeks of the term. Please consult the webpage for updates}}
\section*{Course topics}
Complex numbers.Systems of linear equations. Solving linear systems: row reduction and echelon forms. Homogenous and inhomogenous systems.Rank of matrix.Vector spaces. Linearly independent and linearly dependent sets of vectors. Linear combinations of vectors.Inner (dot) product, length, and orthogonality. The Gram - Schmidt process.Matrices: vector space of matrices, linear matrix operations, matrix multiplication, inverse matrix. An algorithm for finding inverse matrix by means of elementary row operations.Rank of matrix and its invertibility. Solving systems of linear equations by means of inverse matrix.Determinants. Condition detA=0 and its meaning. Tranposed matrix.Eigenvectors and eigenvalues. The characteristic polynomial and characteristic equation. Finding of eigenvectors and eigenvalues.Diagonalization and diagonalizable matrices. Symmetric matrices.
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% vim: ft=eruby.tex:
|
https://www.freehaven.net/doc/fh-related-pubs.tex | freehaven.net | CC-MAIN-2019-13 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2019-13/segments/1552912203326.34/warc/CC-MAIN-20190324043400-20190324065400-00344.warc.gz | 742,883,580 | 12,899 | \section{Publication Services}
There are a number of projects and papers which discuss anonymous publication
services.
We start this section by providing an overview of some of the related projects
and papers. After this overview, we examine in detail the amount of anonymity
and privacy protection that each project offers.
\subsection{The Eternity Service}
Ross Anderson's paper on the Eternity Service \cite{eternity}
is the motivation
for this entire project. It includes a wonderful vision of how the
world might work in the future, in terms of data havens and distributed
decentralized data storage. The overall goal is to build a system that
provides highly available data: as Anderson phrases, it ``[t]he basic
idea is to use redundancy and scattering techniques to replicate data
across a large set of machines (such as the Internet), and add anonymity
mechanisms to drive up the cost of selective service denial attacks.''
A publisher would upload a document and some digital cash, along with a
requested file duration (cost would be based on document size and desired
duration). In the simple design, a publisher would upload the document to
100 servers, and remember ten of these servers for the purposes of auditing
their performance. Because he does not record most of the servers to whom he
submitted the file, there is no way to identify which of the participating
eternity servers are storing his file. Document queries are done via broadcast,
and document delivery is achieved through one-way anonymous remailers.
On the other hand, it relies on a stable
digital cash scheme, which is certainly not available today. Further, it has a strong
correlation between ability to store data into the system and amount of real-world
capital available. While our proposal does have a loose correlation between available
resources and amount of influence over the servnet, the correlation is not nearly as direct.
There are also a number of contradictions and other issues which are not addressed in
his brief paper: for instance, if documents are submitted anonymously but publishers
are expected to remember a random sample of servers so they can audit them, what do they do when
they find that some server is cheating? Since publishers are anonymous, it would seem that they
have no power at all. Anderson passes this responsibility on to the digital cash
itself, so servers do not receive payment if they stop providing the associated service. He
does not elaborate on the possible implications of this increased accountability to the anonymity of
the authors.
Another problem is that there is no consideration at all to maintaining a dynamic
list of available servers and allowing servers to smoothly join and leave.
He proposes that a directory of files in the system should itself be a file in the system.
However, without a mechanism for updating or revising files, this would appear very difficult
to achieve.
\subsection{The {\tt .cz} implementation}
A team of students at Charles University in Czechoslovakia decided to implement their
version \cite{eternitycz}
of Anderson's
idea. They use a mixnet and made overall reasonable design decisions.
Tonda Bene wrote his PhD
thesis \cite{benethesis}
on this design, and provided many more
concrete explanations of the details that Anderson skips over in his
original paper. However, there
are a number of issues that we have with their implementation:
\begin{itemize}
\item They implement everything they need by themselves. They do not exist in a
vacuum -- for example, the world already has `good enough' loose time
synchronization applications such as xntpd, so there is no need to implement a new
API and designs. This leads to code bloat and too
many layers of abstraction, which makes verifying security very difficult.
\item Almost all of their files are binary. It would be easier to examine or modify
their configuration files if they were in a human-readable and human-writable format.
\item BSD-limited. Their code is not ported to Linux yet, much less other platforms.
First of all, the port is probably
difficult if they have not yet successfully ported it to another platform. Secondly,
a well-designed system (whether in perl, C, or
Java) should be extremely portable already -- this does not bode well.
\item A centralized (single or few) trusted bank system is assumed.
\end{itemize}
\subsection{Eternity Usenet}
Adam Back proposed \cite{eternityusenet}
a simpler implementation of the Eternity Service, using the existing Usenet
infrastructure to distribute the posted files all around the world. This is an
excellent idea, but on the other hand this limits the participating servers to systems
which already host Usenet news. Further, news administrators much specifically choose to
participate in this variant of the eternity service, and so they may well choose not
to carry the `alt' groups that
comprise the service.
Eternity Usenet uses normal Usenet mechanisms for retrieval, posting,
and expiring, so publishers may not have control over the expiration time or
propagation rate of their document.
To achieve anonymity in publishing, Eternity Usenet employs cypherpunks
type I and type II (mixmaster) remailers as gateways from email to newsgroups.
Publishers PGP-sign documents which they wish to publish into the system:
these documents are formatted in html, and readers make http search or query requests to
`Eternity Servers' which map these requests into NNTP commands either
to a remote news server or a local news spool. With the initial implementation,
the default list of newsgroups to read consists only of
{\tt alt.anonymous.messages}. The Eternity Server effectively provides an interface
to a virtual web filesystem which posters populate via Usenet posts.
Back treats Usenet as an append-only file system. His system provides support
for replacing files (virtual addresses) because newer posts signed with the same
PGP key are assumed to be from the same publisher. Addresses are claimed on a
first-come first-served basis, and PGP signatures provide linkability between an
initial file at a given address and a revision of that file. However, he does not appear
to provide an explanation of conflict resolution that might arise from two addresses
being claimed at the same time -- since Usenet posts may arrive out of order, it
would seem that there might be some subtle attacks against file coherency if two
different Eternity Servers have a different notion of who owns a file.
Also, while the system is not directly `censorable' as we usually consider it,
the term `eternity' is misleading.
Usenet posts expire based on age and size. Back does not provide an analysis of how
long a given document will survive in the network. The task of making a feasible
distributed store of Eternity documents is left as a future work.
Four public-access Eternity Servers are listed at the end of the article; none of
these servers is still available. This indicates that active work on Eternity Usenet
is not ingoing.
%so anonymity might not be as strongly preserved on either side of the
%transaction. Additionally, people can post data to the service, and then
%prove that a specific server was hosting that data (since all of them are).
%This is crucial for laws where mere possession of the data is illegal.
%\subsection{India Project}
%While the India Project{\footnote {\tt http://www.eecs.harvard.edu/\~{}india/}} has no
%real anonymity measures and is designed with efficiency (high bandwidth reads) in mind,
%it includes an implementation of Rabin's information dispersal algorithm; this might be
%able to be lifted entirely and reused for our project.
% \subsection{Internet Memory Project}
% It, uhm, exists. We should look it up. I bet it doesn't address anonymity.
\subsection{Napster}
The Napster service\cite{napster} is a company based around
connecting people who are offering MP3 files to people who want to download them.
While they provide no real anonymity and disclaim all legal liability, a very important
thing to note about the Napster service is that it is highly successful. Thousands of
people use Napster daily to exchange music; if there were greater security (and comparable
ease of use), we suspect that many thousands more would participate. The existence of
Napster presents a
very clear argument that the Internet community wants a service like this, at least
for music.
%The response to the Metallica suit\cite{metallica} --- in particular,
%the continued use of Napster for trading of illegal MP3 files ---
%indicates that the Internet community is willing to continue use of
%this service even knowing that it could have negative legal
%consequences.
\subsection{Gnutella}
Gnutella\cite{gnutella} is a peer-to-peer Napster clone. It was
developed by a subsidiary company of AOL, and once it went public it
was immediately shut down by AOL (presumably since AOL has interests
in not disrupting the music and movie industries).
Development is proceeding via a widely scattered group of open-source contributors.
Gnutella depends on the ``Small Worlds'' model to maintain a connected
network; see Subsection \ref{subsec:smallworlds} for a more detailed description
and analysis of this idea.
According to the new developers' web site:
\begin{quotation}
Gnutella puts a stop to all those shenanigans. When you send a query
to the GnutellaNet, there is not much in it that can link that query
to you. I'm not saying it's totally impossible to figure out who's
searching for what, but it's pretty unlikely, and each time your query
is passed, the possibility of discovering who originated that query is
reduced exponentially. More on that in the next section.
In short, there is no safer way to search without being watched.
A big however, however. To speed things up, downloads are not
anonymous. Well, we have to make compromises. But again, nobody's
keeping logs, and nobody's trying to profile you.
\end{quotation}
There is a strong contradiction between their bold statement about
perfection and their warnings that users concerned about maintaining
anonymity really should avoid using the system. Behind the media hype,
it is clear there are a number of aspects of their protocol
\cite{gnutellaprotocol}
that help to reveal identities of users.
The header of a Gnutella packet contains a number of fields. Two of
these fields are the `TTL' (time to live: the number of additional hops
after which the packet should be dropped) and `Hops taken' (the number
of hops this packet has made since its creation). The TTL is started at
some default value based on the expected size of the network, and the
Hops value is effectively an inverse of the TTL during the travel of
the packet. Because the Hops value is 1 when the packet is initially
sent, it is clear when a given server is generating a query (assuming
it is playing by the protocol, which for the vast majority of users is a
reasonable assumption). Even if there were no Hops value, the fact that
the TTL itself has a default value for most client programs is sufficient
to make a server originating a request distinguishable from another
server in the system, in the mathematical sense presented in Chapter 2.
Further, the Gnutella network is not so well distributed as they might
lead users to believe. While the protocol is designed for a user to
set up connections with his `friends', there is no infrastructure in
place for easily building such a set of friends. Instead, the Gnutella
site offers a `default' set of friends with which users can start. Most
users will never change this file if the service is functional. This
means that the actual network is built not as a flat network but rather
as a hierarchical system, as shown in their pictures of the Gnutella
network topology \cite{gnutellamaps}. There are a small number of
central nodes which would be ideal targets for government agencies or
other organizations collecting information about users.
%If the TTL and Hops fields aren't enough, every message in the system is
%stamped with a Globally Unique Identifier (GUID). This identifier is used
%to recognize messages which have already been seen, so they are not passed
%on redundantly. This prevents the Gnutella network from an exponential
%explosion of messages, since the default TTL is typically as high as 25.
If the TTL and Hops fields aren't enough to reveal identities, it turns out that
only the queries have any
semblance of anonymity protection. The actual downloads are done by
point-to-point connections, meaning that the IP addresses of server
and reader are both revealed to each other. This is done for reasons
of efficiency.
Sites such as the Gnutella Wall of Shame\cite{gnushame}, which attempts
to entrap child pornographers using the Gnutella service, show that the
direct file-transfer portion of the Gnutella service has been demonstrated
to not adequately protect the anonymity of servers or readers.
Gnutella is not designed to be an anonymous communications or publication
network. Gnutella is a network designed to provide {\em availability} for
data from one user to the next, and it does a relatively good job of this.
%http://gnutella.wego.com/go/wego.pages.page?groupId=116705&view=page&folderId=118398&pageId=118400
%http://capnbry.dyndns.org/gnutella/protocol.html
%http://www.rixsoft.com/Knowbuddy/gnutellafaq.html
\subsection{Freenet}
The Freenet project \cite{freenet} is
one of the most popular related works. Like Gnutella, Freenet proposes
an interconnected network of nodes, each acting as both client and
server. When a user wishes to request a document, she hashes the name of
that document (where she gets this name is outside the scope of Freenet)
and then queries her own server about the location. If her server does not
have it, it passes the query on to a nearby server which is `more likely'
to have it. Freenet clusters documents with similar hashes nearby each
other, and uses a complex routing protocol to route queries `downhill'
until they arrive at the desired document.
Freenet is similar to Gnutella in that its main purpose is to provide
highly {\em available} data to its users. There are also a number of
differences between Freenet and Gnutella. First of all, Freenet caches
data near requestors. Specifically, when a request is answered over a
given path, all servers along that path cache that document. This means
that future queries for that document will be answered very quickly,
assuming the copies of that document haven't expired from the nearby
caches. This introduces another important feature: persistence of
data. Because nodes cache documents as they are requested, the documents
do not disappear from the system when the server offering those documents
disappears. This is a key improvement over Napster and Gnutella.
Freenet bases document lifetime on the popularity of the document:
frequently requested files get duplicated around the system, whereas
infrequently requested files live in only a few places or die out
completely. While this is a valid choice for a system that emphasizes
availability, it precludes certain uses of the system. For instance,
I can see circumstances where a file has a 12 month lifetime but only
becomes popular in the last few months of its lifetime. Examples
include photos of JFK Jr.\ saluting his father, or a (timestamped) Idaho
phone book that has those ten extra names that the FBI might one day be
accused of `erasing'. Indeed, this is already happening --
\cite{yugo} describes a case where Yugoslav phone books are being collected ``to
document residency for the close to one million people forced to evacuate
Kosovo.''
Freenet takes some steps to increase anonymity. Their goals include both
sender and reader anonymity, as well as plausible deniability for servers
-- the notion that a server does not know the contents of documents it
is storing. They provide this last, which we clarify as isolated-server
document-anonymity (as opposed to connected-server), by referencing
and storing files as $H(name)$ and having users encrypt the documents
themselves with $name$ before inserting them. This means that anybody who
knows the original $name$ string can decrypt the document, but the server
storing the document is unable to invert $H(name)$ to determine $name$.
However, they have the same flaw with publisher- and reader-anonymity
that Gnutella does, due to the presence of the TTL and Depth (comparable
to Hops) fields in the Freenet message headers. Because the document
requests are also sent through the network (rather than peer-to-peer
as they are in Gnutella), there's room for a little bit more anonymity
than Gnutella provides. However, nodes nearby a reader still have a
greater than even chance of being able to identify that reader. Further,
statistical attacks similar to those described in the Crowds \cite{crowds}
paper might work to pinpoint the location of a given reader or publisher;
however, the caching does provide some protection against this since
the network topology for a given document changes dramatically after
each request. This needs to be analyzed further.
Another attack to consider is that simply doing a request from a strict
political environment will cause a copy of the data to migrate into that
jurisdiction, giving law enforcement more reason to shut those servers
down. On the other hand, it may well be that such environments will close
down servers without requiring `sufficient cause', so the political and
legal arguments are meaningless.
It might even be that a less anonymous system is more likely to be
accepted in more parts of the world. This will have to be explored simply
by trying it. However, because Freenet provides weaker anonymity than
Free Haven, it is currently unsuitable for use by those who are truly
concerned about maintaining their privacy, such as political dissidents
or other whistleblowers. (See Chapter 4 for more details about these issues.)
\subsection{Graduated Mirroring}
The `Graduated Mirroring' proposal \cite{gradmirroring} was introduced
by Ron Rivest in response to our initial proposals about a buddy system
and other accountability measures that greatly increase the complexity
of the system. In short, this idea involves a group of servers, each
controlled by a person called the `manager', which all sign up to receive
documents published to the service. Each published document arrives at
each server; the manager manually peruses the document and decides how
important or valuable he believes it to be. Based on this evaluation,
he chooses how many shares of the document to store. For each share,
he basically chooses a random share number and generates that share
via some information dispersal algorithm -- this share generation is
implemented by evaluating a polynomial which describes the overall
document at a number of random values.
Server managers can modify their support for a given document. If they
want to support the document less, they simply throw out some of their
shares. If they want to support the document more, they retrieve the
document and generate some new shares.
When a document no longer has enough support for readers to be able to
reconstruct it, that document has effectively expired; server managers
still holding information about that document may then decide to throw
away whatever they have about the document -- this effectively replaces
the notion of a publisher-chosen expiration date with a much simpler
notion of server-popularity. This notion of popularity is similar to the
notion that Freenet uses, but the duration of a document is based on
how much the {\em servers} like the document rather than on how much the
readers like the document.
While this system has some excellent features, including simplicity first
and foremost, we have a number of issues with it. The first issue is that
it is not what we want to build: the fact that only popular data would get
mirrored is counter to our design goal of content-neutrality. We believe
that it does not capture the essence of what we want from a data haven.
Indeed, it also goes against our basic assumptions about computing: we
have a lot of hardware, and very few people. This trend will get more
pronounced as time goes on. Having a person hand-sort and consider each
item really cuts down on the number of people who would be willing to
host a server. Overall, we believe that paving the way for an automated
robust data haven based on privacy of publisher and data is going to
have more of an effect in the long run.
%\subsection{Anon}
%http://www.inf.tu-dresden.de/\~{}hf2/anon/
\subsection{Intermemory}
The Intermemory Project \cite{GY98} \cite{CEGGSY98} is an initiative at NEC
Research aimed at producing an archival system which makes use of
spare space on the Internet. The goal is high availability and high
persistence of information. Intermemory uses information dispersal
to mitigate the consequences of server failure, and spends much time
addressing systems issues such as synchronization of information
between many different servers.
Servers join Intermemory and donate a certain amount of space
temporarily in return for the right to store some small fraction of
that space in the system forever. The ``economic'' viability of the
Intermemory design depends on the assumption that tomorrow's storage
will be cheap and plentiful enough to meet the obligations incurred
today.
At present, Intermemory exists as a prototype implementation within NEC.
The public papers on Intermemory do not even address security, much
less anonymity, and it is not clear how the system reacts in the
presence of malicious adversaries. We therefore do not formally compare
Intermemory to the other systems listed here. Instead, we mention it
as an example of a publication and archival system which is designed
without the severe constraints necessary to ensure anonymity.
\subsection{Publius}
Publius attacks the problem of anonymous publishing from a different angle.
Rather than trying to come up with a routing protocol like Gnutella and
Freenet, Publius simply employs some one-way anonymous channel to transfer
documents from publishers to servers. The Publius protocol is designed to
maintain availability of documents on these servers.
In this system, a publisher generates a key $K$ for her document, and encrypts the document
with this key. She performs Shamir's secret-sharing algorithm to build a set
of $n$ key shares, any $k$ of which is sufficient to reconstruct $K$. From
there, she chooses some $n$ of the Publius servers and anonymously delivers
the encrypted message plus one share to each of these $n$ servers.
In this way, the document is replicated over each server, but the key is split
over the $n$ servers. Document reading is implemented by running a local web proxy
on the reader's machine; the $n$ addresses chosen as servers are concatenated into
a URL which is presumably published or otherwise remembered. (Publius provides no
description of how a directory service
might be built, or any other mechanism for remembering URLs after documents are
inserted.)
The URL used to retrieve the document specifies all $n$ servers at which the document
was stored. This means that to retrieve a given document, the local proxy fetches
each document independently, reconstructs the original key $K$, and then decrypts
the document.
The Publius system provides strong publisher-anonymity, because a one-way
channel is sufficient for communications to the servers. In addition,
because a cryptographically strong secret-sharing protocol is used and
each server only receives one share, Publius provides both computational
and also information-theoretic isolated-server document-anonymity:
a given server is not able to determine anything about a document that
it is helping to store.
On the other hand, there are a number of limitations beyond those the
authors of the paper enumerate. For instance, the entire scheme is based
on a static, system-wide list of available servers. Since these servers
are permanent, there is no support for adding new servers or purging dead
ones. Perhaps more importantly, however, there is no support for recognizing
misbehaving servers and removing from them the list of available servers.
Another point is that readers cannot determine if a share is corrupt
simply by examining it: the reader must request all of the shares and attempt
to reconstruct in order to determine the integrity of a share. Providing a
mechanism for self-evident share integrity checking might provide significant
robustness to the system.
Publius is by far the strongest related work in terms of our notions of
anonymity. The paper is very well-written and goes into considerable detail
on various attacks and counters to those attacks.
\subsection{An analysis of anonymity}
Many of these related works offer their own variant of `anonymity' for some
of the agents in the system. In this section, we analyze this anonymity that
each work provides in the context of the definitions and formalizations
proposed in Chapter 2.
% \begin{center}
\begin{table}[htc]
\begin{tabular}{|c|ccccc|}
\hline
Project & Publisher & Reader & Server & Document & Query \\
\hline
Gnutella & & & & & \\
\hline
FreeNet & & & & \cm & \\
\hline
Eternity Usenet& \cm & & & & \\
\hline
Publius & \cm & & & \cm & \\
\hline
Free Haven & \cm & \cm & \cm & \cm & \\
\hline
\end{tabular}
\caption{Overview: Computational Anonymity}
\label{table:comp-anon-pub}
\end{table}
% \end{center}
This first table provides an overview of the protections
for each of the broad categories of anonymity against computationally-limited
adversaries.
Informally, for polynomially-bounded adversaries who have passive access
to some of the edges between agents, a \cm on this table indicates that the
adversary has less than a polynomial + $\frac12$ chance of correctly
guessing the identity of one of the individuals involved in any given
transaction.
Gnutella fails to provide publisher-anonymity, reader-anonymity, or
server-anonymity because of the peer-to-peer connections for actual
file transfer. Because Gnutella servers start out knowing the intended
contents of the document they are offering, they also fail to provide
document-anonymity.
Freenet achieves document-anonymity because servers are not unable to
reverse the hash of the document name to determine the key with which
to decrypt the document. However server-anonymity is not provided because
given a document, it is very easy to locate a server that is carrying
that document -- querying any server at all will result in that server
carrying the document! Because of the TTL and Hops fields for both reading
and publishing, Freenet also fails to achieve publisher- or reader-anonymity.
Eternity Usenet provides publisher anonymity via the use of one-way anonymous
remailers. Reader anonymity is not protected, and it is clear that a Usenet
service that offers Eternity files is carrying the Eternity feed. Because
each downstream host gets its only entire copy of the feed, there is no
document-anonymity in Eternity Usenet.
Publius achieves document-anonymity because
the key is split between the $n$ servers, and without sufficient shares
of the key a server is unable to decrypt the document that is stores.
Because documents are published to Publius through a one-way anonymous
remailer, it provides publisher-anonymity. However, it provides no support
for protecting readers, and the servers containing a given file are clearly
marked in the URL used for retrieving that file.
Free Haven achieves publisher-anonymity via an anonymous remailer channel.
Similarly, reader-anonymity is provided because the responses are directed
through a mixnet to a temporary address that the reader provides. Server
anonymity is maintained because document requests are performed via broadcast,
and the results arrive out of a one-way channel.
Free Haven achieves document-anonymity because the document itself is
split; assuming a wide enough dispersal of documents, a given server will
never see enough shares of a document to be able to reconstruct it. Certainly
a server that is not actively trying to rebuild a document (for instance, by
doing a request for the other shares) will not have the document available,
since it is broken into shares before publication.
\begin{table}[htc]
%\begin{center}
\begin{tabular}{|c|ccc|ccc|ccc|cc|cc|}
\hline
Project & \multicolumn{3}{c}{Publisher} & \multicolumn{3}{c}{Reader} \vline & \multicolumn{3}{c}{Server}
\vline & \multicolumn{2}{c}{Document} \vline & \multicolumn{2}{c}{Query} \vline \\
& C & I-T & P-F & C & I-T & P-F & C & I-T & P-F & C & I-T & C & I-T \\
\hline
Gnutella & & & & & & & & & & & & & \\
\hline
FreeNet & & & & & & & & & & \cm & & & \\
\hline
Eternity Usenet & \cm & \cm & \cm &&&& &&& && & \\
\hline
Publius & \cm & \cm & \cm & & & & & & & \cm & \cm & & \\
\hline
Free Haven & \cm & \cm & \cm & \cm & & \cm & \cm & & & \cm & & & \\
\hline
FH + ideal mix &\cm&\cm&\cm & \cm & \cm & \cm & \cm & \cm &\cm & \cm & & & \\
\hline
\end{tabular}
\caption{Anonymity Properties of Publishing Systems}
\label{table:real-anon-pub}
\end{table}
%\end{center}
This second table provides a more detailed view of the different publishing
systems which we examined. There are a number of interesting points that
become clearer once we increase the resolution of the table.
First of all,
we see that the secret sharing algorithm which Publius uses provides a stronger
form of document-anonymity, since an isolated server really can learn nothing at all
about the contents of a document that it is helping to store. Secondly, we
see that those systems which provide publisher anonymity tend to provide a
very strong form of it -- namely, computational, information-theoretic, and
also perfect-forward publisher anonymity. This is because the publishers can
make use of one-way communications channels, effectively removing any linkability;
removing the need for a reply pseudonym on the mixnet means that there is
`nothing to crack'. Thirdly, we note that Free Haven achieves perfect-forward
reader anonymity: this is because readers make up a new pseudonym for every
document request, so there is no linkability.
The most important line by far in this table is the last line, though. The
fact that it implies that Free Haven is part of the reason it achieves
this much anonymity is slightly misleading: it really is the ideal mix
which is providing the first nine aspects of anonymity. Assuming a robust
ideal mix network like that described in Chapter 2, there would be no
linkability between transactions, and mere computational ability on the
part of the adversary would be insufficient to identify the parties in a
transaction.
This would mean that we could in fact relegate most of the anonymity to the
communications channel itself, and provide a simple back-end file system or
equivalent service to transfer documents between agents. Thus the design of
the back-end system could be based primarily on addressing other issues such
as availability of documents, protections against flooding and denial of
service attacks, and accountability in the face of this enforced anonymity.
Unfortunately, the design and deployment of such an ideal mix network is
a very challenging task, and one for our future works chapter. Until then,
we focus on providing increased anonymity with a combination of more
conventional mix networks and a publication system tailored for the mixnet.
|
http://dlmf.nist.gov/6.16.E2.tex | nist.gov | CC-MAIN-2014-10 | application/x-tex | null | crawl-data/CC-MAIN-2014-10/segments/1394010650250/warc/CC-MAIN-20140305091050-00004-ip-10-183-142-35.ec2.internal.warc.gz | 56,116,574 | 666 | \[S_{n}(x)=\sum_{{k=0}}^{{n-1}}\frac{\mathop{\sin\/}\nolimits\!\left((2k+1)x%
\right)}{2k+1}=\frac{1}{2}\int_{0}^{x}\frac{\mathop{\sin\/}\nolimits\!\left(2%
nt\right)}{\mathop{\sin\/}\nolimits t}dt=\tfrac{1}{2}\mathop{\mathrm{Si}\/}%
\nolimits\!\left(2nx\right)+R_{n}(x),\] |
http://mirror.math.ku.edu/tex-archive/graphics/pgf/contrib/braids/braids.sty | ku.edu | CC-MAIN-2014-49 | text/x-tex | null | crawl-data/CC-MAIN-2014-49/segments/1416931009551.23/warc/CC-MAIN-20141125155649-00159-ip-10-235-23-156.ec2.internal.warc.gz | 202,740,165 | 3,600 | %%
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\title{2010 Anarchist Survey}
\date{December 2010}
\author{Lucien van der Walt}
\subtitle{Notes for a critical assesment}
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\par
Recently, an “Anarchist Survey” was run online, with the results appearing around August 2010.
This is a very interesting, indeed important, initiative – let me stress that. However, it is let down by some important flaws in research design and data analysis. The use of the internet to deliver the survey also some inherent problems. Because of these issues, the survey cannot be considered representative and it cannot be considered a solid basis from which to draw conclusions about anarchism today.
Regarding \textbf{administration}, participation is entirely self-selected, as people were invited to participate. This means there are no controls for representivity, and no way to judge response rates. Moreover, it would overrepresent people who like filling out forms on the internet. There is no way to measure to ensure that people don’t vote twice, thrice or whatever.
The invitation was through internet networks, mainly linked to anarchism. Obviously people outside of those networks are not included, and, since the authors defined anarchism very loosely (see below), the invitation also went out to networks of people whose links to anarchism are tenuous at best.
The internet, of course, is an extremely cheap delivery platform with an amazing coverage, but it is shaped by language, heavily biased towards some regions and its demographics are not representative in terms of age, class or race. Its hardly surprising that only 17.6 percent of those who responded are over 36 – what does \emph{not} follow is that this is an accurate reflection of anarchism\Slash{} syndicalism \emph{as a whole.}
In effect, a survey in English, on the internet, will be affected by factors outside of its control: the overwhelming weight of the US internet audience, the overrepresentation of middle class people, the massive underrepresentation of regions like India and Africa; all of these factors will also shape the contours of the networks which were drawn into the survey. In the case of even Anglophone Africa,the internet is profoundly dominated by South Africa, a country in which internet access is itself tied directly to class and race.
Consequently, it is not surprising that less than 10\% of respondents are from Africa, Asia and Latin America. Most are from North America and Europe (just short of 90\%), and North America means almost only Canada and the US, not Mexico; Europe here, given language, really mainly means the UK and Ireland.
Obviously this has a large impact on the data generated, and on the ability of the survey’s administrators to answer some of the questions that they hoped to answer e.g. “whether or not anarchism was in fact appealing to a significant number of non-whites (sic.)”. The authors themselves concede in the report that most respondents are “white straight men between the ages of 16 and 45” [but then try explain this away:] “Then again, this is also the dominant group of Internet users\dots{}” [Actually, this is the “dominant group of Internet users that a survey like this will \emph{attract\dots{}} so] this not quite true; \dots{} the[y[ should qualify [this] with the statement “\dots{}\emph{in the US and UK}“; it is simply not true globally.
There are serious problems with the \textbf{design}. The survey uses categories that cause problematic results. There are problems with the language used (such as the term “non-white”, considered pejorative in many countries).
While trying to get a sense of the racial categories of respondents, the designers left out major categories, such as Latinos\Slash{} Hispanic, now the largest US racial “minority”, not to mention Latin American categories like \emph{mestizo} and Indian.
The analysis of the data apologises for this omission, but seems to think it is addressed by the category “indigenous”. However, “indigenous” is a much larger category and could include e.g. aboriginals in Australia [and would not include a great many Latin Americans]. Moreover, the US construct Latinos\Slash{} Hispanic applies to \emph{all} Latin Americans, white, black, \emph{mestizo}, \emph{pardo}, Indian etc., but these categories are clearly differentiated in Latin America. Meanwhile, in the survey “white” (dubbed Caucasian, an Americanism) is separated from “semitic”, although Jews (who would presumably fit here) are considered white in almost all countries.
The authors then go on to worry, in their analysis, that the data suggests that the movement has an “ostensible lack of appeal [\dots{}] for non-whites [that] warrants further discussion.” [But] since the survey tells us more about who could (or bothered to) respond, it does itself not demonstrate an “ostensible lack of appeal” in general. (This is not to say that there isn’t an issue here – simply that such a conclusion cannot be drawn from the data set that this survey constructs).
As noted earlier, the definition of anarchism used is rather loose and questionable, so questionable groups like “anarcho-capitalists” and “primitivists” and “Christian anarchism” are included as types of anarchism, while categories like “revolutionary syndicalism” and “anarchist people of colour” are not. Authors listed as “anarchists” included people who have nothing to with anarchism, like John Zerzan, the “primitivist” crank, Steve Best, the animal rights extremist etc.
Rather than use anarchist or Marxist definitions of class, it uses marketing survey-type class categories like “lower middle class,” [and] distinguishes “working class” from “poor\Slash{} unemployed”. No definition is given of these categories, so what it means to be in (say) “lower middle class” [is unclear]. Where a “working class” person who earns a minimum wage would fit in is unclear [- are they “poor,” “working class,” “lower middle class”?].
In discussing “work sector”, there are some peculiar design decisions. The question here slips between [economic] sectors (e.g. education), specific occupations that cut across sectors (e.g. “art”), and types of work (e.g. manual labour). Where an electrician at a university, for example, goes is unclear.
Strikingly, the main economic sectors are entirely absent: defence\Slash{} war, manufacturing, mining, agriculture, and most of the service sector e.g. transport, security, cleaning, finance.
That pretty much excludes 80\% of everyone employed in most countries. On the other hand, “art”, hardly a site of mass employment, is listed.
Similar issues arise with other questions. For instance, on the issue of whether “violence” can be used by anarchists, has overlapping, imprecise and leading options like “violence should only be used as a form of defence” and “violence will unfortunately be part of the revolution”. The mainstream anarchist position is that violence should only be used for “self-defence” and \emph{this is why} it would be “part of the revolution” since the ruling class will not quietly. Throwing in “unfortunately” implies a judgement against violence which goes against this basic logic. Meanwhile, violence as a \emph{strategy,} as insurrectionist anarchism, is not covered.
In short, interesting results but of an anecdotal quality only.
Even so, interestingly, responses to question 25 showed that most people [who responded] disagreed that “anarcho-capitalists,” “individualists,” “lifestyle anarchists” (and its sub-category, so-called “Crimethinc”), “primitivists” and “Christian anarchists” etc. are anarchists in the first place.
Equally, it is interesting that responses to question 20 showed the most common anarchist “labels” people used were the traditional, red anarchist ones: anarchist-communist, libertarian socialist, social anarchist and anarcho-syndicalist.
Question 27, on favourite anarchist thinkers, was dominated by actual anarchists and syndicalists, with the exception of Bookchin, and in question 45 (favourite book ), Kropotkin dominated, with Bakunin, Berkman, Chomsky, Goldman, Rocker and \emph{Black Flame} (!) all coming out towards the top.
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The Anarchist Library (Mirror)
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Anti-Copyright
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\begin{center}
Lucien van der Walt
2010 Anarchist Survey
Notes for a critical assesment
December 2010
\bigskip
Retrieved on 8\textsuperscript{th} September 2021 from \href{https://lucienvanderwalt.com/2011/01/15/2010-anarchist-survey-notes-for-a-critical-assesment/}{lucienvanderwalt.com}
(minor edit Feb 2013, marked with [])
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\textbf{usa.anarchistlibraries.net}
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http://lions-wing.net/lessons/publish/tex-examples/examex.tex | lions-wing.net | CC-MAIN-2022-27 | text/x-tex | application/x-tex | crawl-data/CC-MAIN-2022-27/segments/1656103669266.42/warc/CC-MAIN-20220630062154-20220630092154-00265.warc.gz | 32,802,845 | 3,156 | \documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\pagestyle{plain}
\oddsidemargin 0cm
\textwidth 16cm
\topmargin -1cm
\parindent 0cm
\textheight 22cm
\parskip 3mm
\def\E{\mathbb{E}}
\def\bS{\mathbb{S}}
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\date{ }
\title{{University of Manchester Institute of Science and Technology}\\ \vspace*{2cm}
{\small UA351: Pure Topics II \hfill UA351}}
\author{\hspace*{-14cm}For candidates taking:\hfill \\DEGREE OF MMath\\
DEGREE OF BSc\\
FINAL EXAMINATION in HONOURS SCHOOL OF \\
PURE MATHEMATICS AND COMPUTATION\\ MATHEMATICS AND LANGUAGE STUDIES\\
MATHEMATICS\\ MATHEMATICS STATISTICS AND OPERATIONAL RESEARCH\\
MATHEAMATICS AND MANAGEMENT SCIENCES}
\begin{document}
\maketitle
\vspace*{3cm}
Date: ???????? \hfill Time: ????
\vspace*{3cm}
\begin{center}
{\large\bf Answer Three Questions}
\end{center}
\newpage
{\large\bf 1.}\\
{\large\bf (i)} Given that the set of all $3\times 3$ orthogonal
real matrices with determinant $+1$
forms a group $SO(3)$ under matrix multiplication, prove that $SO(3)$ has a
subgroup $R_Z$ consisting of rotations about the $z$-axis. Write down without proof
the definitions of two other subgroups, $R_X, \, R_Y,$ of $SO(3),$ corresponding
to rotations about the $x$-axis and $y$-axis respectively.
{\large\bf (ii)} Prove that the map
$$g:[0,2\pi]\times [-\pi/2,\pi/2]\rightarrow \E^3 :
(u,v) \mapsto (\cos v \cos u, \cos v\sin u, \sin v)$$ provides a parametrization
of the standard unit sphere $\bS^2.$
{\large\bf (iii)} Prove that $R_Z$ defines an action on the
standard unit sphere $\bS^2$ by the map $$\rho:R_Z\times \bS^2
\rightarrow \bS^2 : ([A_{ij}],[p_j]) \mapsto
[\sum_{k=1}^{k=3}A_{ik}p_k]$$ and find its orbits. Prove also that
this action is effective but neither free nor transitive.
{\large\bf (iv)} Find a parametric equation for the equator curve on $\bS^2$ in the form
$$e:[0,2\pi]\rightarrow \bS^2$$
and find the parameter value $t_0\in [0,2\pi]$ such that
$$e(t_0)=(\frac{1}{\sqrt 2},\frac{1}{\sqrt 2},0) = p, \ {\rm say}.$$
Find a parametric equation for the great circle $\gamma$ through $p$ and inclined at
angle $\pi/6$ to the equator, so that $\gamma(t_1)=p$ for some $t_1$ in the domain
of $\gamma$ and $\gamma'(t_1)$ makes an angle $\pi/6$ with $e'(t_0)$ at $p.$
What is the torsion of $\gamma?$
\newpage
{\large\bf 2.}\\
Let $\alpha :(a,b)\rightarrow \E^3$ be a regular curve with positive curvature $\kappa,$
torsion $\tau$ and a Frenet-Serret frame field $(T,N,B).$
Denote by $s:(a,b)\rightarrow \R$ the arc length function and suppose that
$\hat{\alpha} :(c,d)\rightarrow \E^3$ is a unit speed reparametrization of $\alpha.$
Denote by $\hat{\kappa}$ and
$\hat{\tau}$ the curvature and torsion respectively of $\hat{\alpha},$ and
by $(\hat{T},\hat{N},\hat{B})$ the Frenet-Serret frame field of $\hat{\alpha}.$
{\large\bf (i)} Write down without proof
the Frenet-Serret equations for $\hat{\alpha}$ and use the definitions
\begin{eqnarray*}
\kappa(t) &=& \hat{\kappa}(s(t)) \\
\tau(t) &=& \hat{\tau}(s(t)) \\
T(t) &=& \hat{T}(s(t)) \\
N(t) &=& \hat{N}(s(t)) \\
B(t) &=& \hat{B}(s(t))
\end{eqnarray*}
to obtain the Frenet-Serret equations for $\alpha.$
{\large\bf (ii)} Prove that $\alpha$ has acceleration
$$\alpha'' = s''T+(s')^2\kappa N$$
with curvature
$$\kappa = \frac{||\alpha' \times\alpha''||}{||\alpha'||^3}$$
and torsion
$$\tau = \frac{\alpha' \times\alpha''\cdot \alpha'''}{||\alpha'\times \alpha''||^2}.$$
{\large\bf (iii)} Find the curvature and torsion of the twisted cubic curve
$$\alpha: (0,1) \rightarrow \E^3 : t \mapsto (t,t^2,t^3).$$
\newpage
{\large\bf 3.} \\
Let $\Phi:M_1\rightarrow M_2$ be a local isometry between two
regular surfaces $M_1$ and $M_2$ in $\E^3$ with Gaussian curvatures
$K_1,K_2,$ respectively. A famous theorem of Gauss states
that then
$$K_1=K_2\circ\Phi.$$
Prove by counterexample that the converse is false by considering the funnel
surface $M_1$ with patch map
$$(u,v)\mapsto (v\cos u,v\sin u, \log v)$$
the helicoid $M_2$ with patch map
$$(u,v)\mapsto (v\cos u,v\sin u, u)$$
and the diffeomorphism
$$\Phi:M_1\rightarrow M_2:(v\cos u,v\sin u, \log v)\mapsto (v\cos u,v\sin u, u).$$
Do this by showing that this $M_1$ and $M_2$ have the same curvature at corresponding
points under $\Phi,$ but $\Phi$ is not an isometry.
You may use without proof the Weingarten result that the determinant of the shape
operator $S$ is given by
$$\det S = \frac{eg-f^2}{EG-F^2}$$
when the arc length formula is
$$ds^2=Edu^2+2Fdudv+Gdv^2$$
and, for a unit normal field $\hat{n}$ and a patch map $x,$ the second fundamental form
has components given by
$$e=\hat{n}\cdot x_{uu}, \ \ f=\hat{n}\cdot x_{uv}, \ \ g=\hat{n} \cdot x_{vv}.$$
\newpage
{\large\bf 4.}\\
{\large\bf (i)}
Draw a projection of an oriented trefoil knot $T,$ and number the overcrossings. From
your drawing, write down without proof
a matrix from which the Alexander polynomial ${\cal A}(T)$
may be found as the monic factor of a determinant. Find ${\cal A}(T).$
{\large\bf (ii)}
Take an identical pair of oriented trefoil knots and by joining them together
form an oriented sum knot, $R;$
take two more oriented trefoil knots, one the mirror image of
the other, and join them to form a different
summand oriented knot, $G;$ do this in such a way that $R$ and $G$ each have
a projection with six overcrossings. [In fact, one of your summands should be
the square knot and the other should be the granny knot.]
Find suitable
such projections, number the overcrossings and then compute for $R,G$ without proof
the Alexander polynomials ${\cal A}(R)$ and ${\cal A}(G).$
{\large\bf (iii)}
Write down an equation relating the three polynomials,
${\cal A}(T),$ ${\cal A}(R)$ and ${\cal A}(G).$
\end{document}
|
http://chadmusick.wdfiles.com/local--files/knots/k11a237c.tex | wdfiles.com | CC-MAIN-2019-51 | text/x-tex | application/x-tex | crawl-data/CC-MAIN-2019-51/segments/1575540482284.9/warc/CC-MAIN-20191205213531-20191206001531-00530.warc.gz | 27,429,233 | 1,059 | \documentclass{standalone}
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http://www.lpi.usra.edu/meetings/templates/latex2e.tex | usra.edu | CC-MAIN-2017-30 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2017-30/segments/1500549423769.10/warc/CC-MAIN-20170721102310-20170721122310-00602.warc.gz | 483,575,334 | 2,482 | \documentclass{article} % Do NOT delete this line
\usepackage{lpiabstr_2e} % Do NOT delete this line
\usepackage{times}
% This is the macro file to use with LaTeX version 2e. It is written to
% work with the accompanying style file lpiabstr_2e.sty.
% NOTE: The style file lpiabstr.sty requires access to the Times
% font package; if you do not have these fonts on your system, the
% template and style file will not work. The font package can be
% retrieved from any CTAN (Comprehensive TeX Archive Network) site;
% go to
%
% http://www.ctan.org/
%
% and click on "CTAN mirror" for a listing of the site nearest you.
\begin{document} % Do NOT delete this line
% Type your title in the argument below, using upper- and lower-case letters:
\title{Global Evolution of Solids in Viscous Protoplanetary Disks}
% Type your authors as shown in the example below, listing each author in
% a separate author argument, with affiliation given in the affiliation
% argument as needed:
\author{J. R. Dotson}
\affil{Lunar and Planetary Institute, Houston TX 77058-1113, USA,
(dotson@lpi.usra.edu)}
\author{D. Hilbert}
\author{S. L. Hokanson}
\author{L. Tanner}
\affil{Department of Astronomy, University of Houston-Clear Lake,
Houston TX 77058, USA}
\author{A. Wiles}
\author{S. Lee}
\affil{Geology Department, University of Illinois, Chicago IL 60637, USA}
% If your abstract is two pages long, type your running head in the argument
% below:
\runningtitle{GLOBAL EVOLUTION: J. R. Dotson et al.}
\titlemake % Sets the title, author information; do NOT delete
\begin{abstracttext}
This macro will format your abstract for the volume.
You will have retrieved this template file and the macro file lpiabstr\_2e.sty
from the meeting Web site. The macro file lpiabstr\_2e.sty can be placed
in the same directory as your abstract, or in any of the standard LaTeX
input directories. The macro file assumes that you are running LaTeX 2e;
if you are running LaTeX 2.09, you should use the 2.09 macros instead.
If your LaTeX system does not have a macro called ''times'' to configure
the use of PostScript Times Roman fonts, your system will complain that
it cannot find times.sty. Read the commented note found at the top of this
file for directions on where you can retrieve the Times Roman font package.
Insert the title of your abstract as the argument of the ``title'' macro,
just after the ``begin{document}'' macro. Insert all author names and
affiliation names in the ``author'' and ``affil'' commands. You should
list all the authors by institution, listing all the authors for the first
institution, then that institution, then all the authors for the second
institution, followed by the second institution, and so forth. If you
cannot group all the authors by affiliation, you will have to repeat
the affiliation for each separate occurrence. The example given in this
file shows the correct way to enter authors and affiliations (be sure to
remove all the samples when you prepare your abstract!).
If the abstract is more than one page, you will need a running head for the
second page, abbreviating the title and author list as in the sample.
Remember that the length of your abstract cannot exceed the length requirement
stated in the announcement text. If you
do not input the correct information for YOUR running head, the one used
in the sample will appear on the second page of your abstract.
You should then type your abstract between the command lines
``begin{abstracttext}'' and ``end{abstracttext}.'' Remember to remove
ALL the sample text that currently exists between these two lines.
After you run the LaTeX processor on your abstract, use dvips (or the dvi
processor on your system) to produce a PostScript output file. You will
submit the PostScript file (and NOT the LaTeX file) to the LPI. (However,
depending on which meeting your abstract is for, the LPI may request your
source files separately.)
You will notice that macros are not given for internal formatting (headings,
etc.). The macros and style file merely define the page dimensions, format
of title and author lines, two-column text format, and running head
placement. Formatting of tables, equations, headings, captions,
references, etc., are at your discretion. Keep in mind that your text
columns are only 3 inches (7.5 cm) wide, so plan the size of your tables,
equations, and figures accordingly.
\end{abstracttext}
\end{document}
|
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\title{Vitamin B12 Malabsorption and Pseudo-Thrombotic Microangiopathy in an
Adolescent.}
\author[1]{Simone Chang}%
\author[2]{Mercia Gondim}%
\author[3]{Michael Angelo Huang}%
\affil[1]{University of Louisville School of Medicine}%
\affil[2]{Norton Children's Hospital}%
\affil[3]{University of Louisville}%
\vspace{-1em}
\date{\today}
\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup
\selectlanguage{english}
\begin{abstract}
Thrombotic microangiopathies (TMAs) are a group of rare disorders that
can be considered life threatening. The hallmark of this disease is a
microangiopathic hemolytic anemia with an associated thrombocytopenia
which could be congenital or acquired. Acquired vitamin B12 deficiency
is overlooked in developed countries but can mimic a TMA. We report the
case of 17-year-old male with malabsorption of vitamin B12 with
development of pseudo-TMA. When faced with a clinical presentation of a
TMA in a child or an adolescent patient, physicians must be aware of the
possibility of vitamin B12 deficiency especially in patients at risk for
malabsorption.%
\end{abstract}%
\sloppy
\textbf{Abstract}
Thrombotic microangiopathies (TMAs) are a group of rare disorders that
can be considered life threatening. The hallmark of this disease is a
microangiopathic hemolytic anemia with an associated thrombocytopenia
which could be congenital or acquired. Acquired vitamin B12 deficiency
is overlooked in developed countries but can mimic a TMA. We report the
case of 17-year-old male with malabsorption of vitamin B12 with
development of pseudo-TMA. When faced with a clinical presentation of a
TMA in a child or an adolescent patient, physicians must be aware of the
possibility of vitamin B12 deficiency especially in patients at risk for
malabsorption.
\textbf{Introduction}
Thrombotic microangiopathies (TMAs) are a group of rare disorders that
are characterized by microangiopathic hemolytic anemia and
thrombocytopenia with thrombosis of the microvasculature. This is often
associated with organ dysfunction and encompass congenital and acquired
etiologies{[}1{]}. Distinguishing between these disorders is important,
as many TMAs are life-threatening.
Acquired B12 deficiency is overlooked because of its rarity in developed
countries{[}2{]}. Hematologic manifestations of B12 deficiency can
include pancytopenia because of ineffective hematopoiesis. Defective red
blood cells (RBCs) undergo phagocytosis in the marrow and as a result
mimic an intravascular hemolytic process.
We describe the case of a 17- year-old male who had a history of
intestinal resection and celiac disease which lead to a pseudo -- TMA
through malabsorption of vitamin B12.
\textbf{Case Description}
A 17-year-old male with history of intestinal resection secondary to
gastroschisis at birth was referred to the emergency room for shortness
of breath, fatigue, and lightheadedness for a week. His history was
significant for celiac disease, iron and B12 deficiency with symptomatic
anemia in the past, requiring transfusions. It had been at least a year
since he had taken his last supplements and he had not adhered to a
gluten-free diet. He denied constitutional symptoms, fevers, bleeding,
or recurrent illnesses. His physical examination was significant for
weight below the third percentile, pallor, mildly icteric sclerae and
hepatosplenomegaly. He was alert and oriented with no noticeable
neurological deficits.
His complete blood count (CBC) was significant for pancytopenia with a
WBC: 2.42 x 10\^{}3/uL, Hb: 5.9 g/dL, MCV: 95.4 fL, Plt: 111 x
10\^{}3/uL and a reticulocytopenia of 0.6\%. Review of his peripheral
smear was significant for anisocytosis, microcytosis, poikilocytosis and
schistocytes. Routine chemistries were suggestive of hemolysis with an
elevated LDH of \textgreater{}50 000 U/L, an unconjugated
hyperbilirubinemia of 3.7 mg/dL and an undetectable haptoglobin. His
synthetic liver function was unremarkable with normal coagulation
studies despite a notable transaminitis. A liver ultrasound showed
diffuse echogenicity with likely fatty infiltration but no evidence of
portal hypertension. He had a negative direct coombs, iron studies were
unremarkable and a B12 \textless{}109 pg/mL. His renal function was also
unremarkable. He was transfused two units of packed red blood cells,
which allowed for stabilization of his hemoglobin and he was started on
oral iron and B12 supplementation.
The differential included a pancytopenia secondary to B12 deficiency
with a superimposed hemolytic process as well as concern for a malignant
bone marrow infiltrative process given his pancytopenia and
hepatomegaly. Paroxysmal nocturnal hemogobinuria testing was negative. A
bone marrow biopsy and aspirate displayed no changes consistent with
myelodysplasia or malignancy. There was evidence of erythroid
hyperplasia and megaloblastic maturation along with hypersegmented
neutrophils consistent with his B12 deficiency as shown in Fig. 1. His
liver biopsy showed non-alcoholic steatohepatitis attributed to his
uncontrolled celiac disease and the decision was made to convert his
oral B12 to an intramuscular formulation.
Repeat B12 and LDH were 525 pg/mL and 503 U/L respectively showing
resolution of his symptoms. Despite not being included in the initial
differential, a hemolytic anemia in the presence of a progressive
thrombocytopenia warrants the consideration of a TMA. However, given the
resolution of his symptoms with B12 supplementation the diagnosis of
pseudo-TMA secondary to B12 deficiency was made.
\textbf{Discussion}
B12 deficiency is the leading cause of megaloblastic anemia and in
developed countries is often overlooked. It is more common in the
elderly but the estimated prevalence is around 6\% in people younger
than 60 years in the United Kingdom and United States {[}2{]}. Causes of
severe of B12 deficiency generally involve disruption of some aspect of
the physiologic pathway for B12 absorption comprising intrinsic factor
and the cubam receptor in the terminal ileum {[}3{]}. In the reported
case, there are several factors that could have contributed to B12
deficiency, his history of intestinal resection and his uncontrolled
celiac disease. Despite not being frequently reported, B12 deficiency in
patients with celiac disease has a prevalence of between 8\% and 41\%
{[}4, 5{]}.
Hematologic manifestations consist of all blood elements being affected
by this ineffective megaloblastic hematopoiesis. Initially, the cell
content and size of RBC usually precede the onset of anemia. Nuclear
hypersegmentation of neutrophils is another common early manifestation.
Neutropenia and thrombocytopenia can infrequently follow as late
features with a resulting pancytopenia that can ultimately become severe
enough to mimic a severe aplastic anemia.
Hematopoietic precursor cells produced in the bone marrow are defective
in B12 deficiency. As a result, they undergo cell death in the marrow
and are phagocytosed before they can exit into the blood as
reticulocytes. This intramedullary hemolysis manifests itself with
increased markers of cell turnover such as LDH and markers of increased
hemoglobin breakdown such as indirect hyperbilirubinemia and decreased
or absent haptoglobin. As a means of compensating, erythropoietin levels
rise and the bone marrow becomes more hypercellular (as shown in Fig.
1), however the reticulocyte count fails to rise {[}6{]}.
In our case, his pancytopenia and reticulocytopenia were evident and
consistent with a megaloblastic picture. However, his LDH seemed to be
elevated out of proportion to the degree of hemolysis he experienced.
When compared to patients with thrombotic thrombocytopenic purpura
(TTP), No\selectlanguage{ngerman}ël et al showed that patients who had pseudo-TMA had
significantly higher LDH levels, platelet counts and lower reticulocyte
counts in the adult population {[}7{]}. Hyperhomocysteinemia has also
been implicated (not checked in our patient) in increasing the risk of
hemolysis in vitamin B12 in vitro in addition to causing endothelial
damage leading to intravascular hemolysis and RBC fragmentation {[}8{]}.
This combination of intramedullary and intravascular hemolysis could
potentially account for the degree of LDH elevation seen in this case.
There have been three other cases of reported pediatric pseudo- TMA
secondary to B12 in the literature {[}9-12{]}. These cases all occurred
because of decreased intake and our case highlights the need to follow
patients with malabsorptive syndromes. Because many of the cases were
initially thought to have thrombotic thrombocytopenic purpura (TTP),
they received plasma exchange with gradual improvement of their
symptoms. This improvement is thought to be due to B12 contained in the
infused plasma during the exchange{[}13{]}.
The PLASMIC score has served as prediction tool for severe ADAMTS13
deficiency{[}14{]} but has not been evaluated in differentiating TTP
from a pseudo-TMA. While it is well recognized as a helpful adjunct in
the adult population, few studies have looked at its utility in children
and adolescents. Linder et al showed retrospectively that the PLASMIC
score was able to accurately identify pediatric patients at highest risk
for severe ADAMTS13 deficiency with a sensitivity of 100\% and a
specificity of 78.1\% {[}15{]}. In evaluating the PLASMIC scores of
pediatric cases in the literature; 75\% of the patients with B12 induced
pseudo-TMA would have been placed in a low risk category (TABLE 1). This
may prove to be a helpful adjunct to physicians when faced with this
clinical presentation.
The treating team deduced that his initial pancytopenia had been
secondary to his B12 deficiency given his history. This case posed a
diagnostic challenge and highlights to pediatric hematologists this
unusual presentation of B12 induced TMA and that it should be considered
in the differential with a patient presenting with a TMA syndrome.
References
1. Kottke-Marchant, K., \emph{Diagnostic approach to microangiopathic
hemolytic disorders.} Int J Lab Hematol, 2017. \textbf{39 Suppl 1} : p.
69-75.
2. Hunt, A., D. Harrington, and S. Robinson, \emph{Vitamin B12
deficiency.} Bmj, 2014. \textbf{349} : p. g5226.
3. Green, R., \emph{Vitamin B(12) deficiency from the perspective of a
practicing hematologist.} Blood, 2017. \textbf{129} (19): p. 2603-2611.
4. Dahele, A. and S. Ghosh, \emph{Vitamin B12 deficiency in untreated
celiac disease.} Am J Gastroenterol, 2001. \textbf{96} (3): p. 745-50.
5. García-Manzanares, A. and A.J. Lucendo, \emph{Nutritional and dietary
aspects of celiac disease.} Nutr Clin Pract, 2011. \textbf{26} (2): p.
163-73.
6. Orkin, S.H., D.E. Fisher, and D. Ginsburg, \emph{Nathan and Oski's
hematology and oncology of infancy and childhood} . 2015, Philadelphia
(Pa.): Elsevier Saunders.
7. Noël, N., et al., \emph{Hemolysis and schistocytosis in the emergency
department: consider pseudothrombotic microangiopathy related to vitamin
B12 deficiency.} Qjm, 2013. \textbf{106} (11): p. 1017-22.
8. Ventura, P., et al., \emph{A role for homocysteine increase in
haemolysis of megaloblastic anaemias due to vitamin B(12) and folate
deficiency: results from an in vitro experience.} Biochim Biophys Acta,
2004. \textbf{1739} (1): p. 33-42.
9. Asano, T., et al., \emph{Neglect-induced pseudo-thrombotic
thrombocytopenic purpura due to vitamin B12 deficiency.} Pediatr Int,
2015. \textbf{57} (5): p. 988-90.
10. Delbet, J.D. and T. Ulinski, \emph{Thrombotic microangiopathy and
breastfeeding: where is the link? Answers.} Pediatr Nephrol,
2018.\textbf{33} (6): p. 987-989.
11. Delbet, J.D. and T. Ulinski, \emph{Thrombotic microangiopathy and
breastfeeding: where is the link? Questions.} Pediatr Nephrol,
2018.\textbf{33} (6): p. 985-986.
12. Dimond, A., J.N. George, and C. Hastings, \emph{Severe vitamin B-12
deficiency in a child mimicking thrombotic thrombocytopenic
purpura.}Pediatr Blood Cancer, 2009. \textbf{52} (3): p. 420-2.
13. Green, R., \emph{Anemias beyond B12 and iron deficiency: the buzz
about other B's, elementary, and nonelementary problems.} Hematology,
2012. \textbf{2012} (1): p. 492-498.
14. Bendapudi, P.K., et al., \emph{Derivation and external validation of
the PLASMIC score for rapid assessment of adults with thrombotic
microangiopathies: a cohort study.} Lancet Haematol, 2017.\textbf{4}
(4): p. e157-e164.
15. Linder, G.E., et al., \emph{Assessment of the Plasmic Score Utility
for Classification of Pediatric Thrombotic Microangiopathies.} Blood,
2019. \textbf{134} (Supplement\_1): p. 1075-1075.
Figure Legend
Table 1: WBC: white blood cell count, Hb: hemoglobin, MCV: mean
corpuscular volume, Plt: platelet count,
ANC: Absolute Neutrophil Count, Retic: reticulocyte count, LDH: lactate
dehydrogenase.
\textbf{Hosted file}
\verb`Table 1.docx` available at \url{https://authorea.com/users/346736/articles/472627-vitamin-b12-malabsorption-and-pseudo-thrombotic-microangiopathy-in-an-adolescent}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Bone-marrow-aspirate-showing-erythroid-hyperplasia-and-megaloblastic-changes-of-nuclei/Bone-marrow-aspirate-showing-erythroid-hyperplasia-and-megaloblastic-changes-of-nuclei}
\end{center}
\end{figure}
\selectlanguage{english}
\FloatBarrier
\end{document}
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Summary: Sets are one of the most fundamental concepts in mathematics but we can not calculate with set operations and set relations on the ClassPad. On the other hand we can write in the text mode with special symbols of the set theory in the ClassPad, e.g. $\in,\not\in,\cup,\cap,\setminus, \subset,\subseteq,\ne,\dots$ Thus some students of informatics tried to introduce the set theory in the operating system version 3.05 (published 2010). They followed two ways of solution: 1. Create a so called Add-In for ClassPad to calculate with sets of real numbers. 2. Create a Basic-program for ClassPad to calculate with finite sets of numbers or words.
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Project Gutenberg's The Iron Boys on the Ore Boats, by James R. Mears
This eBook is for the use of anyone anywhere at no cost and with
almost no restrictions whatsoever. You may copy it, give it away or
re-use it under the terms of the Project Gutenberg License included
with this eBook or online at www.gutenberg.org
Title: The Iron Boys on the Ore Boats
or, Roughing It on the Great Lakes
Author: James R. Mears
Release Date: June 23, 2012 [EBook \#40067]
Language: English
Character set encoding: ASCII
*** START OF THIS PROJECT GUTENBERG EBOOK THE IRON BOYS ON THE ORE BOATS ***
Produced by Dianna Adair, Stephen Hutcheson, Rod Crawford,
Dave Morgan and the Online Distributed Proofreading Team
at http://www.pgdp.net
The Iron Boys on the
Ore Boats
OR
Roughing It on the Great Lakes
By
JAMES R. MEARS
Author of The Iron Boys in the Mines, The Iron Boys as Foremen,
The Iron Boys in the Steel Mills, \textit{etc}.
Illustrated
PHILADELPHIA
HENRY ALTEMUS COMPANY
COPYRIGHT, 1913, BY
HOWARD E. ALTEMUS
Illustration: Both Boys Were Hurled Forward
CONTENTS
CHAPTER PAGE
I. TO THE INLAND SEAS 7
II. THE IRON BOYS AS CARGO 20
III. A SURPRISED SKIPPER 31
IV. THE BOYS STAND THE TEST 42
V. TROUBLE IN THE STOKE HOLE 54
VI. THE FIRST STEP UPWARD 63
VII. THE IRON BOYS ON DECK 70
VIII. THE CRASH IN THE FOG 82
IX. A TRAGEDY OF THE LAKES 93
X. TOSSED UP BY THE WAVES 104
XI. BY PLUCK ALONE 113
XII. ON THE ROAD TO CONNEAUT 122
XIII. IN THE GRIP OF A GIANT SHELL 129
XIV. STEVE SAVES THE CAPTAIN 135
XV. AT THE WHEEL 151
XVI. THROUGH THE ROCKY CUT 163
XVII. THE BLOW IN THE DARK 172
XVIII. VISITORS ON THE ``RICHMOND'' 181
XIX. IN THE GRIP OF THE WAVES 190
XX. AN EXCITING RESCUE 202
XXI. A NEW HAND AT THE WHEEL 210
XXII. LEADING A LIVELY CHASE 219
XXIII. THE WIRELESS MESSAGE 223
XXIV. CONCLUSION 245
The Iron Boys on the Ore Boats
CHAPTER I
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\gutchapter{TO THE INLAND SEAS}
``What are we to do?''
``The first duty of an inspector is to inspect, I should say,'' answered Steve Rush, with a soft laugh, in answer to his companion's question.
Bob Jarvis made a wry face.
``You think you are very smart this morning, seeing that you have been complimented by the president of the mining company,'' grumbled Jarvis. ``I don't know whether I like this new job or not. We were making pretty good money in the mines and we were bosses at that. Are we going to do any bossing when we get on the lakes?''
``I think not. We shall be ordinary seamen. Somebody else will do the bossing in this instance and we shall be the victims. Mr. Carrhart will tell us all about it in a minute. He is arranging for our work now. It will be a great change, and while we shall be working pretty hard we shall be adding to our store of knowledge, Bob. We are lucky to possess so fully the confidence of our superiors. Let's try to show that we are worthy of their confidence in our new places.''
``When do we start?''
``I don't know. Mr. Carrhart is looking that matter up now.''
The lads were sitting in the private office of the president of the mining company, whither they had been summoned from their work at the mines. Mr. Carrhart, the president, stepped briskly into the office at that juncture.
``Well, lads, I have arranged for your transportation.''
``May I ask on what ship we are to sail, sir?'' questioned Steve.
``The `Wanderer.' She is not one of our newest ships, but she is a staunch old vessel with about as many conveniences as are to be found on the newer and more modern boats. I sometimes think we are getting further away from what a ship should be---but then, I am not a sailor. I am not supposed to know anything about ships,'' laughed the president.
``When do we sail?''
``Some time to-night. The `Wanderer' is not yet in. She passed the Soo nearly forty hours ago and should dock some time this afternoon. She is coming up light this time, for a change.''
``How long does it take to load the ship with ore?'' asked Steve, his active mind already in search of knowledge along the line of their new calling.
``Eight hours or so.''
``That is quick time,'' nodded Jarvis.
``It strikes me as being a long time,'' remarked Rush.
``That is the point exactly,'' agreed Mr. Carrhart. ``If you boys can find a way to shorten the loading time you will have served your purpose well. That is exactly why we are sending you out on this inspecting tour---that is, it is one of the reasons. We want to know where we can save money and time in the shipment of ores to the furnaces.''
``But, sir, we know nothing about this branch of the business,'' protested Steve. ``Are there not others better qualified than ourselves?''
``They think they are,'' answered the president reflectively. ``We have tried them out. Most of them are wedded to old methods. What we want is new methods as well as new blood. Besides, you lads have expressed yourselves as being anxious to learn everything about the mining and steel business. I am taking you at your word. You are thoroughly posted on the mining end. I do not believe you could be much more so were you to spend three years more underground. The shipment of the ore is the next step. You have followed the ore down from the mines to the shipping point, here in Duluth. Now I am going to have you spend a few months on the Great Lakes.''
``That will be a fine experience, sir.''
``I think so.''
``Is the purpose of our going to sea on the lakes known, or is it not to be known to any one outside of ourselves?''
``Certainly not. The mission might fail of its purposes were such to be the case. To all intents and appearances, you two boys will be plain, everyday sailors. You will find many hardships in the life of a Great Lakes sailor, but then, if I know you, I do not believe you will mind these very much,'' added Mr. Carrhart, with an indulgent smile.
``We certainly shall not,'' answered Rush, with emphasis. ``The harder the work the better it seems to agree with me.''
``But not with me,'' retorted Jarvis.
The president laughed.
``That doesn't agree with what the reports show. For industry and attention to duty you are a close second to your friend Rush. I presume, Rush, that we shall be losing you one of these days?''
``What do you mean, sir?''
``You will wish to go on to the mills, eh?''
Steve thought briefly.
``Yes, sir; that is our ambition.''
``I thought so. You may depend upon me to use my influence to further your ambition, though I shall very much dislike to lose you.''
``You are very kind, sir.''
``What I hoped you would do was to remain with the mining end of our business, where one of these days you would rise to the grade of general superintendent. Perhaps after you have had your experiences at the other end of the line, you will decide to come back. If I am still president of the mining company you will be well taken care of, should you return.''
``Thank you, sir; perhaps we shall be back sooner than you think.''
``And now for the subject at issue. Here is a letter to the master of the `Wanderer,' Captain Simms, stating that you are to be taken on board his ship as seamen. He does not know that it is your first cruise, but I have an idea that he will learn the truth soon enough.''
There was a grim smile on the face of the president.
``You will find Captain Simms a gruff old seadog. He is one of our oldest and most trustworthy masters, and after you come to know him I am sure you will like him very much. You have a fairly clear idea of what is expected of you by the company. You boys are both keen and resourceful and I expect a great deal from you. I know that you will see all there is to be seen, and no doubt will see some things that have been overlooked by older heads than yours.''
``Have you any further directions to give before we leave you, sir?'' inquired Steve.
``None whatever. I wish you success, which I am sure you will have. You need not go to the ore docks until this evening, unless you wish to, as you probably will have some things to do in town.''
After bidding the president good-bye, the boys took their leave. It seemed only a few weeks since Steve Rush had first entered the office of the president of the mining company looking for a job. The same office boy with whom he had had trouble at the start of his career was on guard at the door, but Steve had grown away from him. Steve, who with his companion, Bob Jarvis, will be recognized at once as one of the Iron Boys, was tall for his age and muscular. His manner of life had done much for his physical well-being, and he was not the same boy who had fought his way into the president's office, the account of which is set forth in ``\textit{The} \textit{iron} \textit{boys} \textit{in} \textit{the} \textit{mines}.''
It was there that Steve Rush and Bob Jarvis first became friends, after they had met and fought a battle in a lonely drift in the Cousin Jack Iron Mine; it was there that both lads proved their heroism by saving the president and several other officials of the company, when the entire company was threatened with death from a burning bag of dynamite.
It was in the Cousin Jack Mine that Steve and his newly found friend saw the need of and invented a new tram railroad system, by which the mining company was saved many thousands of dollars a year.
Again in ``\textit{The} \textit{iron} \textit{boys} \textit{as} \textit{foremen},'' was told how the lads proved themselves by saving the powder magazine from blowing up while the mine was burning and the flames were creeping toward the deadly explosives. It will be recalled that it was mainly through the heroic efforts of the Iron Boys that the Red Rock Mine was saved from almost total destruction, and that through their further efforts many lives were undoubtedly saved. From then on they continued to distinguish themselves, playing a conspicuous part in the great strike, in the end exposing and unmasking a wicked and unscrupulous man who was leading the miners on to commit deeds of violence.
They were the same boys who were now starting out on a new career for the same company. In this instance the lads were to become sailors on the inland seas, known as the Great Lakes. The lads were taking up this new calling for the twofold purpose of learning still another branch of the great corporation's business and they fondly hoped their work would prove of importance to their employers.
The office of the president was located in Duluth, many miles from the Iron Range where the boys had been working for the last two years.
Their first act after leaving the offices was to make their way down to the water front to the ship canal, leading from the harbor out to Lake Superior. Steve pointed out the aeerial bridge to his companion. This was a car carried through the air suspended from a giant truss over the river, by which passengers were transferred across to Superior on the other side. Bob had never seen this wonder before and was deeply interested in it. To Steve Rush it was of particular interest, for he had acquired no slight knowledge of engineering during his experience in the mines up on the range.
Boats were moving in and out, huge lake freighters, ore boats and passenger ships, for the lake traffic was in full cry now. After strolling about for a time, Steve took his companion home with him, and the rest of the afternoon was spent with Steve's mother. Supper finished, the lads decided that they would get down to the ore docks, as the ship would likely be in by that time.
Darkness had set in when they reached the docks. These docks, as those who have had the misfortune to have to make their way over them are aware, consist of tiers upon tiers of trestle. Over the tops, high in the air, ore trains rumble in by day and by night, discharging their cargoes of red ore into huge hoppers, from which the ore is loaded into the boats, or Great Lakes ore carriers, as they are called.
Neither boy had ever been out on one of these trestles before, and the task looked to be rather formidable.
``How are we going to do it?'' demanded Bob, surveying the great structure apprehensively.
``I guess the only way will be to keep going until we get somewhere or fall off. I don't see the ship, but we shall see it when we get to the top of the trestle.''
Both boys narrowly missed being run down by an ore train as it was shunted out on the trestle. The lads were in a dangerous place, but they did not feel at all disturbed about it. Men were flitting about in the dim light of half a dozen electric globes distributed along the top of the trestle that loomed all of seventy-five feet above the water.
``There's a ship down there,'' cried Steve.
``Yes, and there's one on the other side,'' answered Bob. ``Why, there are ships at all of the docks along here. Are you sure we have hit the right dock?''
``I am not sure of anything, except that we are likely to break our necks if we don't look sharp,'' answered Rush, with a laugh. ``We will ask the first man we meet where the `Wanderer' is. There comes some one now.''
Rush hailed the man, a foreigner. The latter neither answered nor paid the slightest attention to the question put to him.
``Thank you,'' murmured Rush.
``Mighty sociable lot of men up here,'' jeered Bob. ``But then I suppose they have to keep their minds on their work or fall off the trestle. I prefer to work underground. In the mines, there's no danger of falling down.''
Ore was being shot down through the chutes into boats on each side of the great trestle. There was the roar as of a great cataract as the red dirt went hurtling down into the hold of the ships many feet below.
``Let's get down on one of the other levels, Steve. Then we'll drift over to the heading at the other end.''
``Anybody'd think you were down in a mine. These aren't levels; they are tiers. You remind me of one of our miners who came down here to Duluth. He went to a hotel, and in telling some of the boys about it, he said: 'We got in a swell cage with looking glasses all around the inside. The cage tender jerked us up to the sixteenth level. We went along this till we came to a crosscut; then they led us into a swell drift an' we struck the heading and sat down.' What do you think of that?''
``That sounds like a lumber-jack more than it does a miner. He must have had a sky parlor. I wonder what hotel he got into.''
Suddenly a great shouting was set up far below where the boys were standing, and further on toward the end of the trestle.
``Now what's the matter?'' wondered Steve. Two long blasts of a steamship's whistle sounded.
``There goes a ship. They're pulling out. I'll bet that's the `Wanderer,''' shouted Bob.
``If if is, she will pull out without us. No, it can't be the `Wanderer,' for she did not come in until after sundown and it is not possible that the ship could be loaded by this time. We'll simply have to find our way down through the trestle somewhere and locate our ship. If we knew which side the boat lay it would be easier for us. Can you see which boat is leaving, Bob?''
``I think it is a boat from one of the other piers. I don't see anything going away near us.''
``Suppose we move out toward the end. Then we shall be able to see where we are and what we are doing.''
``And fall off?''
``Certainly not. We will walk along by the side of the track. There is a railing here. No danger at all of falling.''
The boys had their suit cases in their hands. They carried little baggage, having been informed that there was no room on board for trunks or luggage. Besides, the lads needed few clothes outside of several suits of underwear.
As they stepped along, walking side by side, Steve pointed up at a bright star.
``I wonder if we had better lay our course by that one------Grab me, Bob---I'm falling!'' suddenly cried Steve Rush.
Jarvis stretched out a quick hand, fastening upon Steve's collar. But the movement threw Jarvis off his balance. He, too, toppled forward.
Rush had stepped into an open chute through which the red ore was roaring down into the hold of the ship seventy-five feet below them. Steve struggled valiantly to prevent himself from going in, and Bob tried his best to keep from going in after.
``Let go, Bob; you'll go in, too!''
The warning came too late. Steve shot out of sight, leaving a fragment of his coat collar in the hand of his companion. Then Bob went in, head first.
Neither lad uttered a cry. They were not of the crying kind, and even had they uttered a shout their voices would have been drowned in the roar of the ore thundering into the hold of the big ship awaiting it down in the slip.
\gutchapter{CHAPTER II}
\section*{\raggedright THE IRON BOYS AS CARGO}
\textit{Through} some fortunate twist of his body, Jarvis righted himself while
going through the big hopper into which the ore was shooting. He landed
feet first at the bottom of the hopper.
In the meantime Steve Rush, with a few seconds' start of his companion,
had gone on down through the hopper. He hit the long wooden ore chutes
that led down into the ship; he struck the chute with a heavy bump and
then went on at a speed that took his breath away. Steve was in a
sitting posture. Jarvis followed him at the same rate of speed, lying
flat on his back.
There was ore on all sides of them; in fact, they were riding on the
swift-moving ore; all about them was darkness, and even had there been
lights it is doubtful if the Iron Boys would have seen them, because of
the speed at which they were traveling.
Steve's mind was working with its usual rapidity. Had he known exactly
what awaited them below he might have been able to plan with more
certainty. He did reason, however, that they would probably have to pass
through a small opening when they reached the bottom of the chute. In
this he was wrong, though right across the chute where it entered the
ship was a heavy iron brace dividing the chute in half, which was placed
there to give the ship more rigidity.
``Lie flat!'' shouted Rush, with quick instinct, himself dropping on his
back. He did not know whether Bob were following him or not. Jarvis was,
but he was in no need of the admonition to lie flat. He was as flat as
it was possible for him to be and he could not have straightened up had
it been to save his life.
Jarvis was close enough, however, to hear the warning cry. He opened his
mouth to answer, getting it full of red ore as a result. The ore got
down in his throat, sending him into a paroxysm of choking, sneezing and
growling that was lost in the noise about him.
Suddenly Steve felt himself shooting through space. He realized, in that
instant, that he had left the chute. A few seconds more and he struck
heavily on his feet, bounded into the air, then plunged forward head
first.
The lad landed on his stomach, slipped down a conical pile of ore to the
bottom, his head striking the side of the ship, doubling him up and
leaving him stunned and unconscious.
Jarvis, who was not far behind him, went through very much the same
experience, save that he turned a somersault when he left the chute,
landing flat on his back on the pile of ore. His feet drove against the
side of the ship with the force of a battering-ram, backed by the full
weight of the lad's body. The effect was nearly the same as it had been
in the case of Rush. Bob was stunned. He, too, lay still, after curling
up against the vessel's side.
``Hey, what's that?'' a voice had shouted as the boys disappeared through
the hatches.
``What's what?''
``I thought I saw something besides ore go through the chute in number
seven hatch.''
``You're seeing things!''
``Maybe I am.''
``Close number seven hatch!'' shouted the second mate, and the two deck
hands, after the chute had been hoisted a little above the deck, slid
the heavy hatch cover into place. All the ore that was needed had gone
in through that hatch. The ship was nearly loaded. All that was now
required was a few car-loads at the ends to trim the ship properly,
after which she would be ready to sail.
Within the next ten minutes the rest of the ore had been shipped. With
loud crashings, interspersed with hoarse shouts, harshly-uttered
commands and an occasional toot of warning from the ship's whistle, the
hatch-covers were put in place and the ship made ready for her journey
down the Great Lakes.
There followed a moment of inactivity; then came a blast of the whistle
fully a minute in duration. It was the signal that the ship was about to
back out of her slip, warning all other craft to keep clear.
The propeller began to churn the waters of the harbor and the ore
carrier, with its cargo of ten thousand tons of iron ore, backed slowly
out into the stream.
Bob Jarvis rolled over until he was practically standing on his head and
shoulders. He toppled over on his back with a jolt that woke him up. The
lad gave a kick and some one grunted.
``Hey, there, take your foot out of my stomach, whoever you are. Is that
you, Bob?''
``I---I don't know. Hello, Steve, that you?''
``I guess it's both of us. Ugh! My mouth is so full of ore that I can
hard---hardly talk.''
``I've got a dark red taste in my own mouth. I've swallowed enough ore to
make a steel rail. Do you know where we are?''
``We have fallen into the hold of a ship, and we are lucky that we are
not dead.''
``Maybe we are and don't know it,'' jeered Jarvis, pulling himself up. He
tried to get to his feet, but the ore slipped from under him, leaving
him at the bottom against the side of the vessel again.
``Quit it!'' shouted Steve. ``Are you trying to bury me?''
The latter was on his feet too, brushing the dirt from mouth, eyes, nose
and ears. Bob had sent a quantity of it sliding down the chute.
``I can't help it. What's the matter with you? What do you think about
this business?''
``I don't think, I know. We are in a nice fix.''
``Think so?''
``I told you I didn't think,'' retorted Steve in a tone of slight
irritation.
``Glad you admit it.''
``We have been dumped into the hold of an ore vessel. I don't know
whether or not there is any way to get out, and it is sure that the
hatches will not be opened again until the vessel reaches her
destination.''
``How long will that be?''
``That depends upon where they are going. If they are bound for any of
the Lake Erie ports I should imagine it would take a week or more.''
Bob groaned.
``I'm going to yell.''
``Yell, if you can. I've too much ore in my mouth to make much of a
noise.''
Jarvis raised his voice in a shout. It did not seem to attract any
attention. The lad shouted again and again. By this time the ship was
trembling from stem to stern under the jar of the propeller that was
beating the water at many hundred revolutions a minute.
``Nobody on this ship, I guess,'' muttered Bob. ``Come, suggest something.
You've always got something to say,'' urged Jarvis.
``I was about to say that you might as well save your breath. No one can
hear us through the thick decks; in fact, I presume every one has turned
in except those on watch forward, and the engine room crews at the rear
end of the ship.''
``Then I am going to lie down and go to sleep,'' declared Jarvis.
``Don't do anything of the sort. The ore is likely to slide down and bury
you. The less disturbance we make here the better it will be for us.''
``Why didn't you think of that before we fell in? I suppose we are pretty
deep down in the ship, aren't we?''
``About as close to the bottom as we can get without drowning. We will
keep as quiet as possible until we can plan some way of helping
ourselves out of this predicament.''
Bob grunted unintelligibly. For some time after this the Iron Boys
leaned against the side of the ship, Steve trying to plan some way out
of the difficulty, Bob growling inwardly over the hard luck that had
befallen them.
All at once the ship gave a quick, sudden lurch. Jarvis lost his
balance, falling over on his face. The ore came down in a deluge,
covering him from head to feet before he had sufficient time to scramble
out of the way. Steve, bracing himself against the side of the ship,
stooped over and helped his companion to his feet.
``The old tub's going to tip over,'' gasped Jarvis. ``What's the matter
with her?''
``Nothing is wrong. We have gotten out of the ship canal and into the
open water of Lake Superior. There must be considerable sea. Don't you
hear the waves smashing against the sides of the ship?''
``It isn't what I hear, but what I feel,'' answered Bob faintly. ``I feel
queer. My head's spinning like a top. Is yours?''
``No; I can't say that it is. Are you getting seasick?''
``How do I know? I have never been seasick. How does it feel to be that
way?''
``I have heard that when people are seasick they don't care very much
whether they live or die.''
``Then---then---I wish I could die right here, if it would make me forget
that awful goneness under my belt. Ugh!''
Bob settled down against the side of the ship, moaning.
``Don't be a baby. Get up and be a man.''
``I---I don't want to be a man. I---I'd rather be a wooden image, then I
wouldn't care what happened. In case the ship went down I could float
and------''
Bob's words were lost in an anguished moan. Steve felt far from
comfortable, but he set his teeth and made a resolve not to give up.
``The sea is coming up, Bob,'' announced Rush after a long period of
silence.
``The---the sea------? It's my opinion that something else will be coming up
soon if things don't stop moving around the way---the way they are doing
now.''
Steve laughed.
``Remember, Bob, that we are not likely to get anything in our stomachs
for some days. Be careful.''
Bob groaned.
``If I ever get anything solid under my feet I'll take it out of you for
that! That's a mean trick to play on a fellow when he's in the shape I'm
in at this minute. How long do you suppose the noise outside will keep
up?''
``I don't know. Probably all the way down Superior.''
``And how far is that?''
``Let me see. I think Mr. Carrhart said the trip to the---the Soo took
thirty-six hours.''
``Help!'' muttered Jarvis faintly.
``Now, I want you to brace up. Come on, get up. If you don't I'll trounce
you and make you forget your troubles.''
``Yes, you can talk, but if you felt as badly as I do, you wouldn't spout
that way. You; couldn't without---without------''
``Perhaps I \textit{do} feel badly, but I may have the will power to fight it
out.''
Steve reached down and pulled Jarvis up beside him. The latter
protested, but it did him no good, for he was apparently unable to offer
any resistance. Rush threw an arm about his companion and began talking
about other subjects in order to divert Bob's mind from his sufferings,
for his was a real case of seasickness.
In the meantime the sea seemed to be rising, though as a matter of fact
there was little sea on. The short, sharp waves of the lake were moving
the big, flat-bottomed steamer almost as roughly as they would have
moved a little row boat, for the ore carriers are proverbial rollers.
After a time Jarvis began to feel easier, and the lads, lulled by the
motion of the ship, grew sleepy. Steve did not dare allow himself to go
to sleep. He knew, full well, that such a thing would be dangerous. A
lurch of the vessel might cover their heads with dirt and smother them
to death before they were able to extricate themselves. Then again, they
might be buried too deeply to dig their way out at all.
``Lean up against me, Bob. No need of our both standing here suffering
for sleep. If you get too heavy I'll let you drop; then I guess you will
wake up.''
Bob leaned heavily on his companion. He would have done so in a moment
more at any rate, for his eyelids seemed to weigh a ton. The lad was
asleep almost instantly. After a time Steve's eyelids also drooped. He
could hold them up no longer. Then he went to sleep, braced against the
wall of the hull, his companion sleeping soundly in his arms.
There could be but one result of this. They had been asleep but a few
moments before, in a lurch of the ship, Rush toppled over with Jarvis on
top of him, a ton or more of ore banked up about them.
``Get up! Get up!'' shouted Steve, as soon as he was able to get his mouth
free of the red ore.
Jarvis muttered, and Steve was obliged to push his companion off by
sheer force. The lad pinched and pounded himself, to awaken his dulled
senses thoroughly, then he began to punch Jarvis about with his clenched
fists.
``Leggo! Quit that, or I'll------''
Bob tried to strike Steve, but instead, he measured his length on the
ore pile.
``I'm trying to get you awake, and if you don't want to be roughly
handled you'd better pull yourself together,'' warned Steve.
``I'll get even with you for this one,'' growled Jarvis. ``What's the use
in trying to keep awake?''
``I've answered that question already. Besides, I am going to try to find
some way out of this hold.''
``You'll have a nice time doing it,'' growled Jarvis.
``I expect to have. But I know there must be some way. You keep close to
me.''
``What are you going to do?''
``Feel my way along the side of the ship to see if I can get hold of a
ladder or something that we can climb up.''
``I couldn't climb a step ladder without falling off, the way I feel
now,'' objected Jarvis.
\gutchapter{CHAPTER III}
\section*{\raggedright A SURPRISED SKIPPER}
``\textit{No} use!'' groaned Jarvis. ``There isn't a ghost of a chance of our
getting out of this until the old tub gets to some place or other. We're
done for, this time. I wish I had stayed in the mines, where I belong,
instead of following along after you. You can get into more trouble than
any other fellow I ever knew.''
``Never mind,'' laughed Steve. ``We're the Iron Boys. Why shouldn't we
travel as part of the iron ore cargo? The only thing that troubles me is
that we have lost our ship. The `Wanderer' will sail to-night with two
men short, and---but I care more about what Mr. Carrhart will think when
he hears that we missed our boat. He will think us a couple of stupid
boys, and he will be justified in so thinking.''
``I don't care what he thinks,'' growled Bob. ``What's bothering me now is
my stomach, and the thought of how I'm going to get out of this.''
Steve did not reply. An idea had occurred to him. Gathering up a handful
of soft ore he tossed it up over His head. Some of the stuff showered
down over Bob Jarvis, causing that young man to protest vigorously. A
large portion of the stuff, however, did not come down. Steve heard it
drop on metal, roll a little way then stop.
``Quit that, now,'' protested Jarvis. ``What on earth are you trying to do?
I can't appreciate a joke to-night.''
``This is not a joke,'' answered Steve, gathering up another handful. ``I
am saving your life.''
``Huh! Pleasant way you have of doing the trick.''
Several large chunks of ore were tossed up with the same result. They
did not roll back into the hold.
``I've got it, Bob,'' exulted the Iron Boy.
``You're wrong there. I got most of it myself.''
``Listen! There is a platform or passageway running along this side of
the ship above our heads. I suspected there must be something of the
sort, for surely they have to get into the hold occasionally------''
``Above our heads, you say, eh?''
``Yes.''
``Precious lot of good that will do us,'' grunted Bob.
``That depends upon whether or not you have any spunk left.''
``I guess I've got as much of that kind of stuff as you have. But I'm
sick---I'm a sick man, Steve Rush!''
``Forget it, and then you'll be a brave man. At all events I'll tell you
what I want you to do.''
``Go ahead. I can't be any worse off than I am.''
``I am going to brace myself here against the side, and I want you to
climb up to my shoulders. You ought not to have any difficulty in
standing on them, when once you get up, for you will have the side of
the hull to lean against.''
``Can't do it; can't do it at all. Why don't you do it yourself, instead
of trying to make me do so when you know how sick I am?''
``All right, if you want me to stand on your neck. I am offering you the
easiest part of the plan.''
``I guess you won't stand on my neck! All right; I'll be the goat. What
am I to do when I get up to where I can stand on \textit{your} neck?''
``Reach up for the platform. If you can get it, all you have to do is to
pull yourself up. Then, after you are once up you can, perhaps, reach
over and give me a hand.''
``Fine, fine!'' jeered Jarvis. ``I wish I could talk as easily as you. Why,
I'd hire out to spout in a political campaign and------''
``Don't waste breath. I am ready.''
Feeling his way in the darkness, Bob finally got hold of his companion.
It was not a difficult task for him, strong and athletic as he was, to
climb to Rush's shoulders. The difficulty was in staying on the
shoulders after he once got there.
Bob didn't stay long. He toppled over backwards with a quick roll of the
ship, landing high up on the ore pile, sliding down to the bottom,
protesting and growling at the boy who had been the cause of his
downfall.
``Do it yourself!'' Jarvis shouted after getting to his feet once more.
``Come on, now! You're all right.''
After a little urging Jarvis succeeded in reaching his chum's shoulders
once more.
``Now, be careful! I will try to hold you,'' said Steve grasping his
companion's ankles.
``I've got hold of it. I've got the platform. It's only a little above my
waist. Leggo my legs.''
Steve stepped out from under so suddenly that Jarvis was left dangling
in the air.
The latter was too busy in trying to pull himself up, to enable him to
make any retort. He scrambled to the passageway or platform, out of
breath and dizzy. For a few moments Bob lay flat on the support beneath
him, groaning.
``Don't be a tenderfoot. What's the matter?'' called Steve.
``Everything's the matter. I'm all shot to pieces---I'm all falling apart
inside------''
``Take your time. When you feel able give me a hand. Is there any railing
around the walk?''
``Yes; how did you know?''
``I just guessed it, that's all.''
``All right; come on.''
Bob leaned as far over as he could, without falling, and tried to reach
the upraised hands of his companion.
``Can't make it. You've got to grow a little first,'' Jarvis jeered.
``We are going to make it. I'm going to back up on the ore and take a
running jump. You stand by ready to catch me. Better twist your legs
about a railing post if there is such a thing handy.''
``I'm waiting for you. I hope you bump your nose until it bleeds.''
But Steve Rush did not bump his nose. He took a running jump, nearly
losing his foothold in starting. By a lucky chance he landed half way
up the side of the hold, right against Bob's hands. Bob grasped him
about the waist.
``Now, pull me up,'' commanded Rush.
``I can't. I'm a sick man, I tell you.''
``Fudge! Just hang on and I will do the rest, but for goodness' sake
don't let go and fall off.''
``Why should I let go? You don't think I am so anxious to get down there
as all that, do you?''
Steve climbed nimbly up the body of his companion until he found himself
able to reach the rail with one hand. It was then but the work of a
moment to pull himself up to the platform.
``There, now we're all right,'' exclaimed Rush triumphantly.
``No, we're all wrong. I tell you I'm a sick man,'' protested Jarvis.
``If I hear you say that again, I am likely to throw you off. You make me
sick.''
``Hope I do. Then you'll know how I feel.''
``This is better than I had hoped for,'' said Steve, not heeding his
friend's ill-natured remark. ``They've got to get up early in the morning
if they want to down the Iron Boys, I tell you,'' he chuckled.
``It strikes me that we downed ourselves pretty thoroughly. Well, are we
going to get out of here to-night?''
``We are going to make an effort to do so at once. Keep hold of the rail
and follow me. Look out where you step. We don't want to take any more
tumbles, or------''
``Oh, that's all right. I couldn't feel any worse if I fell off from a
house or the top of a mine shaft.''
The two moved along cautiously, Steve feeling his way with feet and
hands. They were going toward the stern of the ship, though they were
not aware of the fact. The passageway, constructed for the purpose of
getting about on the inside of the hull, was narrow, built of metal, but
without anything on it to bar their progress.
They made their way around the stern, which, inside the ship, was next
to the engine room. Rush felt the throb of the engines near him and knew
then that they were near the stern. They were separated from the engine
room by a bulkhead and there was no opening into the engine compartment
from the cargo-carrying part of the hull.
``We shall have to work our way to the other end,'' Steve said.
The boys, with Steve in the lead, continued their cautious creeping
around the ship until finally they had reached the forward end. Steve's
hands came in contact with a door.
``Oh, pshaw, it's locked,'' he cried. ``This is too bad.''
``Kick it in,'' suggested Bob, as the most practical way out of the
difficulty.
``I can't; it's locked.''
``And after all the trouble we have been put to!''
``At least, Bob, we have found a place where we shall be able to lie down
and go to sleep in safety. That is surely worth all the trouble we have
been put to, as you call it.''
``That's so. I hadn't thought of it in that light before. And I'm such a
sick------''
``You know what I told you.''
Jarvis did not complete what he was saying.
``Good night.''
Bob threw himself down on the hard floor and went to sleep. Steve
decided that this was the best thing they could do, so he, too, lay down
and was sound asleep at once. Neither lad awakened for hours. Steve
finally opened his eyes and yawned. A ray of light that had penetrated
between a thin joint between a hatch cover and its frame, hit his left
eye squarely.
``Wake up, Bob,'' he cried.
``Go 'way! Don't bother me. I'm having my beauty sleep.''
Steve sprang up, shaking the other boy roughly.
``It's daylight. Come on; we've got to make a break to get out of here
now, if we do it at all. I just heard some one tramping along the deck
overhead.''
Bob sat up rubbing his eyes sleepily. He would much have preferred to
sleep longer, but he knew full well that, if he tried it, Steve Rush
would fall upon him and make life miserable for him for the next few
minutes. So Jarvis got up, grumbling.
``Where does that door lead to?'' he demanded, pointing to a door that
Steve had not yet seen.
A faint light in the hold made it possible to see a short distance away.
Steve glanced at the door, then sprang toward it.
``Hurrah, it is unlocked!''
``And don't forget that I found it. I can see like an owl, even if I am
sick------''
Steve had jerked the door open, revealing a dark chamber. It proved to
be the chain and anchor room where odds and ends of the ship were
stored.
After a little groping about in this chamber, they came upon a
companion-way, up which they hurried. There they met with another door,
but this one too was unlocked. Rush opened it and stepped into the full
light of day.
For the moment the light blinded both. The boys stood there, rubbing
their eyes, blinking, and breathing in the fresh air of the lake.
``Great!'' exclaimed Steve.
The ship was rolling gently. They glanced about them, but there was no
land in sight. Everything was a sea of green, with white-capped combers
tracing long lines of white against the deep green.
``Beautiful, isn't it, old chap?''
``It might be, if there were some land in sight. Where's everybody?''
``I don't know, but we will find out.''
Smoke was rolling from the funnel of the steamer, a ribbon of white
steam from the exhaust pipe trailing off astern and losing itself in the
black smoke.
``This is a beautiful sight, even if we have lost our boat and gone to
sea on an unknown craft,'' exclaimed Rush, his eyes glistening.
``Pshaw!'' grunted Jarvis.
``I guess it is about time we looked up some one and found out whether we
are headed for the Soo, or------''
``Or the North Pole,'' added Jarvis.
``Well, who are you?'' demanded a gruff voice just behind the lads.
The Iron Boys wheeled sharply.
They found themselves facing a thick-set man, whose face, from exposure
to wind and sunshine, was almost fiery red. He was surveying the boys
from head to foot with a look of stern disapproval.
Steve and Bob, with their torn and soiled clothes, \textit{did} present a most
disreputable appearance. Their hair was unkempt and full of red ore,
while their linen, white and clean when they left home on the previous
day, now also partook of the color of the iron ore in which they had
wallowed for several hours.
``May I ask who you are, sir?'' questioned Steve politely.
``I am the captain of this ship, and, unless you answer my question
pretty lively, I'll have you ironed and thrown into the hold.''
``We have just come from there, sir,'' interrupted Bob.
``That is quite evident from your appearance. You are stowaways, eh?''
``No, sir; we got into the ship by accident, last night, and could not
get out. We tried to attract attention, but were unable to do so.''
``What were you doing around the ship?''
``We were to ship on the `Wanderer.' We lost our way on the docks and
fell into the hold of this ship. We had a hard time getting out, but
here we are, hoping to get to our ship as soon as we get to the next
stop.''
It was the captain's turn to look astonished.
\gutchapter{CHAPTER IV}
\section*{\raggedright THE BOYS STAND THE TEST}
``\textit{You} want to get on board the `Wanderer,' eh?''
``Yes, sir.''
``What for?''
``I have told you we were to ship on her---we were to work on board.''
``What were you to do on board?''
``We were to work at whatever we were set at.''
``Hm-m-m!'' mused the red-faced skipper. ``Had your breakfast?''
``No, sir; we have not had anything to eat since we ate luncheon
yesterday noon.''
``Hm-m-m-m. Come with me.''
The captain led the way aft over the decks, along a walk at the side of
the hatches, which the lads observed were snugly battened down. Their
conductor passed on by the engine house, clear to the stern of the
vessel, where he entered the door of the deck-house.
``Jake!'' he called sharply, poking his head into the room.
A white-capped, white-aproned man suddenly made his appearance.
``Vat iss?'' demanded the ship's cook.
``Give these boys some breakfast.''
Jake surveyed the boys critically before replying.
``\textit{Ja},'' he said, turning back into his kitchen.
``Sit down at the table. When you have finished eating come forward and I
will talk with you.''
``Thank you. Where shall we find you, sir?'' asked Rush.
``If I'm not in the wheel house I'll be somewhere else.''
``I hope you won't take it into your head to meet us in the hold,''
interjected Jarvis. ``We have had hold enough to hold us for the rest of
our lives.''
``Don't get smart, young man,'' snapped the master, turning and leaving
the room.
``I wouldn't get funny with the captain, were I in your place,'' warned
Steve. ``He evidently doesn't appreciate your jokes. Smell that
breakfast?''
``You bet I do, but smelling won't help much.''
Jake soon brought in a satisfying meal, to which the boys helped
themselves liberally. The cook stood about watching them questioningly
for a time, but, as the boys seemed too busy to open a conversation with
him, he turned back to his galley with a deep grunt of disapproval.
After having finished their meal the Iron Boys went out on deck, where
for a time they stood leaning over the rail looking down into the
foaming water slipping past the side of the ship.
``We had better be going forward, Bob,'' suggested Steve.
On the way forward they passed several deck hands at work. Some were
sweeping, others washing down the decks with a hose and a scrub brush.
``That's going to be our job, I guess,'' grinned Bob.
``Then, it's me for the mines, Steve Rush!''
Inquiring for the captain, they were told that he was in his cabin just
under the pilot-house. They hurried there, and, knocking, were told to
enter. The captain's quarters they found, to their surprise, to be
luxurious. There was an observation room extending across the ship, with
eight windows in front, looking out on the sea ahead of the ship. Off
from this observation room and to the rear of it were two handsome
bedrooms, furnished with brass bedsteads and hung with silk draperies.
Bob looked around for a mat on which to wipe his feet.
The captain, seated at a desk, turned around in his chair, surveying the
boys critically.
``You certainly are not very handsome to look at,'' was his comment,
uttered in a gruff tone.
``No, sir, not very,'' admitted Steve, flushing as he looked down at his
soiled clothes.
``Do we have to dress up on this ship?'' demanded Jarvis, with some heat.
``You will have to do one thing---preserve a respectful attitude toward
the commanding officer, and take orders without giving any back talk,''
replied the master, eyeing the boy sternly.
``We aren't working on this ship.''
``Perhaps you think you are not, but you are.''
``We are working, or going to work, on the `Wanderer,''' answered Bob.
``That is what I am saying. This is the `Wanderer.'''
``The 'Wanderer'?'' exclaimed the lads.
``Yes.''
``Then we did fall into luck, after all.''
``It looks that way, though you may change your minds before you've been
aboard long. Which of you is which?''
``I am Steve Rush. This is Bob Jarvis.''
``Glad to meet you, young gentlemen.''
They could not tell if the captain intended the words to be sarcastic,
or whether he meant to be polite to them. They were rather inclined to
the former opinion.
``When do we go to work?'' demanded Jarvis.
``Now; at once. We don't have any lazybones on board this ship. Are you
men strong?''
``Yes, sir; I think so,'' replied Steve, smiling.
``Can you shovel coal?''
``We can shovel anything that we are able to lift.''
``Very well, then; I'll put you in the stoke hole.''
``What kind of a hole is that?'' questioned Jarvis.
``That is the place where the black-faced gang shovel the fuel under the
boilers to make the ship move along.''
``Oh, you mean the firemen?''
``That's the scientific name. The common name is stoker. I'll send you
down to the chief engineer, and he will give you a trick. You'll have to
work like sixty, and if you don't you'll get off at the Soo and foot it
back home,'' continued the skipper gruffly.
If Steve were disappointed, or objected to the work that had been
assigned to them, he made no comment. Jarvis, however, made no secret of
his displeasure. He grumbled under his breath, despite the warning looks
directed at him by Steve Rush.
Captain Simms pushed a button, and a few minutes later a short man,
clean shaven, red of face like the captain, entered.
``This is Mr. Major, the first mate. He is next in rank to the master. He
will take you to the chief engineer for your assignment.''
``Where do we sleep?'' asked Jarvis.
``I had nearly forgotten that. You will show the boys their cabin, Mr.
Major.''
The first mate nodded. His was a surly face, and the lads did not
approve of him at first. However, upon gaining the deck the first mate
spoke to them in a tone that was kind and helpful.
``This is your first time out, isn't it, boys?'' he asked.
``Yes, sir,'' replied Steve.
``Well, you'll get along all right. Do your work well and you will find
that Captain Simms will take to you all right. You will have enough time
off to rest and sleep, though the work is pretty steady on the lakes.
You will find this is the case when we are in port, even more than when
on the move. The loading and unloading keeps all hands at their
stations. You have been in the mines, have you not?''
``Yes, sir.''
``We were foremen,'' interjected Bob.
The mate glanced at them in surprise.
``I should think you would have stayed there, then. The pay is better and
the hours more regular.''
``We wished to learn this end of the business,'' answered Steve somewhat
shortly.
A few minutes later they were introduced to Mr. Macrae, the chief
engineer, in whose department they were to begin their work on a lake
steamer. The chief was a man of few words, these words always to the
point. The mate explained to him the disposition Captain Simms wished
made of the boys.
``Ever fire any?'' demanded the chief.
Steve shook his head.
``Nothing more than a cook stove,'' spoke up Jarvis, with a twinkle in his
eyes, at which the chief's face threatened for a few seconds to relax
into a smile. Instead, it drew down harshly and his lips set more firmly
together.
``Humph! Nice couple to send me, and short-handed in the stoke hole, as
it is. Well, you'll fire all right, and you'll find it ain't no six-day
stove-firing, either.''
``When do we go on?'' asked Rush.
``I guess now is as good a time as any. Where's your jumpers?''
Steve glanced at his companion quizzically.
``Did we leave our bags down in the hold, Bob?''
``I guess that's where we left them, sure enough.''
The mate sent a deck hand for the bags of the boys, after which they
retired to the cabin set aside for them at the stern of the ship, and
began preparing for their new work. They went on duty at nine o'clock,
being told that they would take a six-hour trick, with a six-hour
lay-off, after which they would report for duty again.
The chief took the boys below, introduced them to the foreman of the
fire room, then stood about while the foreman instructed them in their
duties. These consisted in keeping the fire up under two boilers. They
were obliged to throw the coal in many feet under the boiler, which
required both skill and strength.
When the fire doors were closed, the heat was still stifling, but when
the doors were thrown open waves of white hot heat leaped out enveloping
the stokers. The first time that Jarvis essayed the feat he burned his
eyebrows off by getting too close to the door and facing it full.
Bob sprang back with a growl that was half howl. As soon as he could get
the door closed he ran to the water barrel, sticking his head clear
under. The stoke-room gang howled uproariously.
``A lubber, eh?'' laughed one of the stokers. ``You'll get all the hotness
you want before you get out of this hole. How about you, pretty boy?''
turning to address Steve.
``You look out for your own furnaces, old man; I'll attend to mine, and
if I get stuck I'll ask somebody who knows.''
The gang laughed at this, and the fellow whom Rush had answered so
sharply, glared angrily at the tall, slender lad who was throwing coal
into the white-hot mouth of the furnace. He was doing his work almost as
methodically as though he was used to it, save that his aim was not
quite as sure as in the case of the more experienced men.
After having watched the boys at work for a few minutes, Mr. Macrae
nodded to himself, then climbed up the ladders to the deck. He met the
master soon after.
``Get those boys to work?'' demanded Captain Simms.
``Yes.''
``Any good?''
``Pretty likely pair. They have the strength of yearling bulls. Where did
they come from? I didn't see them when we came out.''
``No, they came out of the hold,'' grinned Captain Simms.
``Out of the hold?''
``Yes; funny thing about that. They boarded the ship with a load of ore.''
The captain went on to explain how the boys came to be on board.
``Doesn't it strike you as peculiar that they are sent down here in this
way?''
``Not at all, Mac. They want to learn the business. Mr. Carrhart sent me
a line yesterday explaining the case. Said they were a fine pair, and he
wanted to see them get along.''
``Then why put them in the hole?''
``Don't you think that will try them out as quickly as anything else?''
said the captain.
``I guess that's right,'' admitted the chief engineer. ``And we need them
just now, too. I'm glad they are on board, even if they are green hands.
But young Rush is going to be a winner, and no mistake.''
``What's the matter with the other one?''
``Nothing, except that he is a little fresh at times.''
``So I already have observed. You will take that out of him, Mac.''
``I'll do that all right, or break his back in the trying. The stoke hole
isn't any place for weaklings, as you and I know.''
``Keep me posted. I want to know about them. If they make good maybe I'll
change them, giving them a berth on deck.''
``We'd better give them a good try-out first,'' advised the chief.
``Certainly.''
In the meantime the subjects of this discussion were toiling with might
and main far down below the water level. The ship seemed much steadier
down there, and there was scarcely any roll perceptible. Had it not been
for the terrific heat the youngsters would not have minded the work so
much. However, as the day drew on they began to feel the strain.
The gong, announcing the change of watch, sounded loud and startling.
They did not give it any heed, but kept right on shoveling.
``Well, are you fellows going to work right through the next trick?''
asked the foreman.
``Have we finished?'' questioned Bob innocently.
``Until nine o'clock to-night.''
The lads put down their shovels with a sigh of relief.
``Is there such a thing as a bath room that we can use?'' questioned Rush.
``What? Do you fellows ever wash?'' demanded the stoker who had had the
words with Steve earlier in the day.
``That depends upon the company we have been in,'' answered the lad
sharply. ``Did you tell me about the bath room, sir?''
The foreman could not repress a grin. He pointed up the companion
ladder.
``You will find one on the deck above this. First door to the right.''
``Thank you, sir.''
Steve began climbing up the ladder, followed by Bob and, a few rungs
behind, by the surly stoker who had sought to have fun with the Iron
Boys and had got the worst of the argument in each case.
Their first trick on board an ore carrier had been gotten through
successfully, but it was about the hardest six hours the lads remembered
ever having put in. They hurried out into the air before taking a bath.
Never had fresh air smelled so sweet as it did that day. The lads were
black, the coating of soot on their faces being streaked with
perspiration, and their clothes could have been no wetter had they just
come up from the sea.
``This is about the limit!'' laughed Bob Jarvis. ``Here I am, without any
eyebrows and half my beautiful locks burned away, all because you and I
have ambitions to get on in the world. Honestly, Steve, is it worth it?''
``You know it is, Bob Jarvis,'' answered the Iron Boy, gazing straight
into the inflamed, soot-framed eyes of his companion.
\gutchapter{CHAPTER V}
\section*{\raggedright TROUBLE IN THE STOKE HOLE}
``\textit{I'll} put you to sleep one of these fine days, young feller,'' greeted
the stoker with whom Steve had had the words. The boys had just turned
to go to their bath, Bob already having entered the deck house.
``Are you addressing me?'' demanded Steve coldly.
``I'm talking to you.''
``Forget it,'' said the lad, brushing past the soot-begrimed stoker and
hurrying in to his bath.
That was the beginning of it. Surely Steve had not tried to make an
enemy of the man, but he had done so just the same, and an enemy whom he
was to hear from ere many days had passed.
Meeting the first mate later in the day Steve asked who the man was.
``The name he gave on coming aboard was Smith. I don't know anything
about him. He has never sailed with us before, but I understand he knows
his business---that is, he is a good stoker and has been on ships before.
Why do you ask?''
``I wondered,'' answered Steve evasively.
``Has he been bothering you?''
``Oh, no; I am not very much bothered,'' answered the lad, with a smile.
The boys' cabin was on the starboard or right side of the ship. It was a
pleasant little room, commanding a view out over the water. There were
two berths in the cabin, a little desk and a couple of steamship
pictures, the door of the cabin opening out to the deck.
They felt very much at home in their new quarters, and after the first
good sleep there they were ready for anything that might be required of
them.
The new stokers took their evening trick, each determined to hold up his
end of the work with the rest of the men. And each did. Not a man in
that hot, fiery pit shoveled more coal on that watch, or shoveled it to
better advantage than did the Iron Boys.
The man Smith shoveled at the furnace door next to Steve Rush, and the
former lost no opportunity to hurl rough jokes and taunts at the Iron
Boy. These were, in most instances, greeted with howls of delight by the
other stokers, who seemed to take the keenest pleasure in seeing the two
boys humiliated.
Steve took it all good-naturedly, but Jarvis had to exercise great
self-restraint to keep himself in check. He could hardly resist taking
it out of the big bully.
Smith was tall and angular, his small, beady eyes setting more closely
together than was good to look upon. In addition to this there was a
slight slant to them, giving him almost the appearance of an Oriental.
Steve shrewdly came to the conclusion that Smith was a bad man, and
furthermore, the boy decided in his own mind that the man had a past,
for Rush was a keen observer, few things passing him unobserved.
All at once, Smith's shovel slipped, showering Steve with coal from head
to foot. The sharp edges of the chunks of coal cut the boy's head and
one cheek until the blood came.
Rush calmly brushed himself off, wiped the blood from his head and face
amid the jeers of the stokers. Then he turned to the grinning Smith.
``Did you do that on purpose?'' demanded the lad coolly.
``I reckon it was an accident, kid. What would you do if it wasn't?''
``I am not making any threats, but I hope it will not happen again.''
``He did it on purpose,'' volunteered Bob.
``Never mind, Bob; keep out of this. Mr. Smith had a dizzy spell and he
couldn't see where he was tossing the coal. He isn't wholly responsible
for what he is doing.''
Smith uttered a growl.
``You making sport of me?'' he demanded, in a surly tone.
``Oh, no; I couldn't think of that, because I don't see anything funny
about you. You are the most serious proposition I ever set eyes on.''
Smith was not grinning now. His face had drawn down into harsh, menacing
lines, his chin settling close to his chest, his eyes narrowing to mere
slits. Rush was watching him as the boy carelessly tossed a shovel of
coal into the furnace.
Smith drew a long breath, grabbed up his shovel and began firing once
more. The critical stage had been passed for the moment, but Rush knew
that sooner or later there would be a clash of some sort, and he knew,
too, that when it did come the tough stokers would side with their own
companion.
Nothing more of a serious nature occurred in that watch, though the boys
kept on the lookout for trouble.
It was in the early morning watch, however, when the ship's company was
sleeping, all save those who were on watch at the time, that there came
a renewal of the trouble---when the threatened disturbance came to a
head.
The boys had arranged that when the back of either was turned to the
stoker the other should keep his eyes open. This arrangement they had
carried out faithfully until four o'clock in the morning arrived. Day
was breaking, but the toilers down in the depths of the stoke hole could
not see the coming of the day. They would not have noticed it had they
been able to for the reasons that their minds were wholly absorbed with
other matters.
Suddenly a second shower of coal rained over Steve Rush from the shovel
of the man Smith.
Steve turned sharply, fixing his eyes on Jarvis. The latter nodded,
meaning that Smith had thrown the coal deliberately.
``That's the time you did it on purpose, Mister man,'' said Steve in his
usual calm voice.
``Well, supposing I did? What you going to do about it?''
``This!''
Whack!
The Iron Boy's fist smote the stoker a powerful blow in the face. Smith
toppled over against the hot boiler. Rush saw at once that the fellow
would be seriously burned. Leaping forward he dragged the man away,
dropping him on the coal heap.
For the moment the stokers were so amazed at the exhibition of strength
and skill on the part of Steve Rush that they could do no more than
gape and gaze.
The knocked-out stoker struggled to his feet. His eyes were bloodshot
and his face distorted with passion.
``I would suggest that we put off our dispute until we have nothing else
to do,'' suggested Steve. ``You mustn't forget that we are on duty now,
and the captain will discipline us if we have trouble here.''
With a bellow of rage, Smith rushed his young antagonist. The blow that
he got this time spun the fellow around, landing him on his face on the
coal heap. The blow had reached him before his own fists were fairly up
in position. Steve knew that what was to be done must be done quickly.
He loathed such fights, but he was among rough men. He had been among
rough men ever since he had started out in the mines, and it was a case
of fighting one's battles or going down with serious injuries, or
perhaps worse. Experience had told him that the quicker such affairs
were ended the better for all concerned, and that the man who landed the
first effective blow was more than likely to win the fight.
Steve usually did land first.
Bob was dancing about with glowing eyes.
``Please somebody hit \textit{me}!'' he begged. ``I've got to get into the row.
I've got to punch some of you wooden heads, or you'll never be
satisfied; neither will I.''
``Give them the coal. Bury them!'' roared a voice.
Smith leaped to his feet, and stretching out a hand threw open a furnace
door.
``I'll give the little fiend a toasting!'' he howled.
``No, no---the coal!'' protested the others.
The Iron Boys saw at once that matters had taken a more serious turn
than they had looked for. The lads slowly backed up against a bulk head,
their hands resting easily on their shovels.
``I would suggest that you men had better get to work,'' said Rush. ``The
steam will be going down in a minute or so, then you'll hear from the
chief engineer.''
He had hoped to call them back to their duty, and thus avoid what was
before them.
``The coal, the coal!''
With one accord the stokers thrust their shovels into the coal pile.
Ten shovels of hard coal were hurled at the Iron Boys with unerring aim
and at almost projectile speed.
``Down!'' shouted Rush.
Both lads dropped to the floor of the fire room, the black chunks of
coal passing harmlessly over their heads.
``Let 'em have another! Throw low!''
The stokers sent the next black volley straight out from their hips,
which should have reached the mark had the boys adopted their former
tactics.
``Dodge between!'' commanded Steve.
Jarvis obeyed instantly. In fact, in an emergency, he always looked to
his companion for orders.
When they saw that their second attempt had failed the stokers uttered a
yell of rage.
``Bat them over the head with your shovels!'' advised one.
But Rush had anticipated the suggestion. He was already leaping forward,
his shovel cutting the air. He brought its flat side against the side of
a stoker's head. The man toppled over, unconscious, and before the men
could recover from their surprise two more of their number had fallen
victims to the Iron Boy's shovel.
Bob had leaped into the fray by this time. He was swinging his own
shovel, uttering a shout each time it came in contact with a head.
``Give ground, Bob!'' shouted Rush. ``I'll fix them. Just watch out that
they don't land on you, or they'll cut your head off with those
sharp-edged things.''
``I'll hold them! Come on, you black ruffians!''
Steve had sprung to one side of the fire room, where he began tugging at
a wheel, from which he unrolled a long, dark object. One end of this he
quickly connected to a four-inch pipe, turned a shut-off and sprang out
into the middle of the fire room, carrying one end of the object in his
hands.
``Quick! Back off, Bob!''
Bob did so. He saw at once what Rush intended to do.
``Give it to them!'' he shouted.
\gutchapter{CHAPTER VI}
\section*{\raggedright THE FIRST STEP UPWARD}
\textit{The} Iron Boy held a three-inch fire hose in his hands. A powerful stream
leaped from the nozzle. The first man it hit was bowled over like a
nine-pin, the man uttering a choking yell as he went down.
Another leaped at Steve with upraised shovel. He shared the fate of his
companion. One after another of them went down under the force of the
stream from the fire hose.
It was a kind of warfare that none of those tough customers had ever
engaged in before. In a moment the men were yelling wildly, now and then
Bob Jarvis's voice raised above the hubbub in a howl of joy. The heat in
the fire room quickly turned the water to steam, a dense gray cloud
hanging over all, obscuring everything in the room. It was with
difficulty that the boy could make out the forms of his enemies.
The men were making desperate efforts to break through and escape by the
door, to which Rush had slowly backed. As soon as a man sprang forward
Steve would let him have the full force of the stream from the hose
squarely in the face. The stoker would be on his back instantly; then
Rush, would play the stream on the others, swinging the hose from side
to side to keep the crew back.
All the fight had been taken out of them, but the relentless stream
still played on and over them with terrific force.
``Quit! We've got enough!'' howled a voice.
``I can't hear,'' answered Steve, playing the hose from one end of the
cringing line to the other. ``I'm going to turn on the hot water soon, I
don't believe this cold water will take all the dirt off.''
``Skin them alive!'' jeered Jarvis.
There came an interruption. The howls of the men, having reached the
upper deck, had attracted the attention of the chief engineer. He had
come running down the companion ladder, believing something serious had
happened in the engine room. He was met by a cloud of steam.
``What's going on here? Have you blown out a tube?'' he shouted.
``No; I'm blowing off some rowdies, that's all. Bob, shut off the water.
The fun's all over.''
Macrae grasped Rush by the collar.
``What does this mean? I'll discharge you at the end of the cruise.''
``I am sorry, sir; but those men attacked us and we had to fight them the
best way we could. I thought a shower bath would do them more good than
anything else, and cool them off quicker.''
``Get to work there, you lazy lubbers. Your steam is twenty pounds below
the mark. I'll fine the lot of you. Rush, come up to the deck, I want to
talk with you.''
``I would suggest, sir, that you hear what the men have to say first.''
``How did this row start?'' demanded the chief engineer.
``He turned the hose on us, jest because he got a grouch on against us.''
``That's a lie!'' exclaimed Jarvis.
Mr. Macrae motioned for Steve to accompany him. The boy followed up to
the deck where the chief led the way to his office and cabin.
``Now, I'll listen to the story. You have done a very serious thing; you
have imperiled the safety of the ship and laid yourself liable to arrest
and ironing. What have you to say?''
``I acted purely in self defense. It was a case of defend yourself or get
my head knocked off. I chose the former. I am sorry I was the cause of
the steam going down, but we can put on more steam in a few minutes. I
couldn't do the same for my head.''
``Tell me exactly what occurred.''
Rush did so, omitting the name of the stoker who had been the real cause
of the uprising. Mr. Macrae listened with grave face until the story of
the trouble had been told.
``Who started it?''
``I would rather not say. I do not think he will start anything else very
soon. He got about all that was coming to him.''
``I should say he did. However, this is a matter that will have to be
laid before Captain Simms. Go back to the fire room. I will accompany
you and see that matters are straightened out.''
This the chief did.
``The next man who starts any disturbance here will be put in irons!''
said Mr. Macrae sternly. ``This applies to every one of you. I shall lay
the matter before the captain, as it is. He will act as he thinks best,
but it is my opinion that the whole gang of you ought to be thrown off
the ship at the first stop. You may be, at that.''
As soon as the captain rose, the chief told him the story of the battle
in the stoke hole.
``What, those two boys did up the whole crew of ten men down there?''
exclaimed the master.
``That's about what it amounted to.''
``Most remarkable thing I ever heard of! But I will guarantee they never
started the row.''
``No, I think not. Both boys refuse to say who did.''
``Good for them. I knew they had the right kind of stuff in them. Pity we
haven't got more like them.''
``What do you think best to do, sir?''
Captain Simms reflected for a moment.
``Being convinced that the stokers are wholly to blame, I shall fine each
of them a day's pay. You may so inform them.''
``And the two boys also?''
``No. Why should they be fined? You can't blame them for defending
themselves. What time do the boys come off watch?''
``Nine o'clock.''
``Tell them to report to me after they get fixed up.''
``Very good, sir.''
Captain Simms went to his cabin, where he related to the first mate the
story of the fire room row. Both officers laughed heartily.
``I would have given a month's wages to have seen that fuss,'' laughed the
mate. ``I guess the black-face gang has come to the conclusion that it
has picked up a couple of Tartars. Evidently it isn't the first time
those lads have been called upon to take care of themselves.''
Before the stoke hole watch knocked off the captain made it his business
to go below and look over the men. Every man save the Iron Boys wore a
sullen, revengeful look on his face. But this was not all. There was
blood on several of the faces, and the men's clothes and hair still bore
traces of the shower bath that Steve Rush had given them.
Neither lad paid any attention to the captain. They went on with their
work as steadily as though he were not present, or nothing out of the
ordinary had occurred.
The captain turned away rather hastily and left the compartment. He felt
that, if he remained a second longer, he would have to laugh. That would
not do at all. And laugh he did, after he had gotten far enough away
from the fire room to make wise such a proceeding.
``I'll get even with you for that!'' snarled Smith in Rush's ear, after
the departure of the master.
Steve made no reply.
``You'll wake up one of these fine mornings wetter than I was after you
turned the hose on me, you whelp!''
Smith drove his elbow into the Iron Boy's side with considerable force.
Rush slowly faced him.
``Look here, you loafer, I'll knock you down if you do that again. Or,
if you prefer it, I'll give you another bath. You are trying to pick a
fight with me. I am not looking for it, but if you insist I'll give you
what you want. Fight or stop!''
Smith glanced uneasily at the door leading from the fire room, muttered
something unintelligible to the others and began shoveling coal into his
furnace.
Shortly after that the watch ended. Steve hurried through his bath.
After putting on his clean clothes he called on the captain. The latter
looked over the slim, well set-up young lad quizzically.
``I didn't think it of you, Rush.''
Steve flushed painfully.
``You wish to see me, sir?''
``Yes. Be careful. In this instance let me say very frankly that I am
glad you cleaned out that lot. The only trouble is that you ought to
have thrown the whole gang overboard. We can't spare them, or I might
have done it myself before this. I'm going to take you two boys off the
stoke hole watch.''
``What do you wish us to do, sir?''
``I will promote you to the deck.''
\gutchapter{CHAPTER VII}
\section*{\raggedright THE IRON BOYS ON DECK}
\textit{The} lads began their work above decks on the following day. It was a
welcome relief to be out in the open air, with the wind blowing over
them, the soft odors of the inland seas mingling with the faint perfume
of the land drifting out from the unseen shores.
The first work of the Iron Boys was to remove the hatches that the sun
might penetrate the hold and dry out the ore, which had been put in very
damp. Ore in that condition did not handle easily, taking up time and
costing considerably more to handle than when dry. Steve pondered over
this all during his first forenoon's work. Here was something that ought
to be remedied. His fertile brain was at a loss to solve the problem. He
talked the matter over with Jarvis after luncheon, that day, and asked
his companion's opinion.
``That's easy,'' answered Bob promptly. ``Put a stove in.''
``Where?''
``In the ore pockets on the trestles.''
``That would be fine,'' grinned Steve. ``But you have given me an idea. I
will think it over. There is a point that it will pay us both to think
over very carefully. Have you seen anything of our friends from below
decks this morning?''
``No; I guess they must be sleeping.''
``Look out, Bob. We haven't heard the last from Smith. He is a vengeful
fellow and he will try to get even with us. I hope he doesn't ship with
us on the return trip.''
``I'll punch his head for him if he gets funny with me.''
``I don't like the man's looks at all. It is my opinion that he is a
desperate character.''
``Well, so are we, for that matter,'' replied Jarvis with a mirthless
grin.
``I am beginning to think so myself, old chap. It seems almost impossible
for us to keep out of trouble. I, for one, am going to stop it. Next
time any rough argument is started I'm going to run.''
Jarvis laughed uproariously.
``I think I see you doing it! Why, you wouldn't run if you saw a herd of
elephants charging you. No, sir---not Steve Rush!''
At about four o'clock in the afternoon the boys were ordered to assist
in replacing the hatches to make all snug for the night. The vessel was
slipping down Lake Huron, now, at an eleven-knot gait. There was a
gentle roll on the sea, but neither lad minded that. Neither would
suffer further from seasickness, they felt sure.
The hatches having been made secure there was nothing more to be done
for the rest of the afternoon. The lads were free to go where they
pleased and do as they pleased. They repaired to their cabin, where they
remained until supper time. They now ate with the ship's officers, the
stokers and oilers having a mess-room by themselves. The officers'
mess-room was a roomy apartment at the extreme stern of the ship, and
the food served there was excellent. The boys did not remember ever to
have had better.
Mr. Major, the first mate, occupied the lower end of the long table,
while the captain sat at the head. There was little conversation. The
principal business was eating, sailors having a habit of shoveling in
their food as fast as possible when it is placed before them.
The result was that Steve and Bob, being accustomed to eat slowly and
chew their food well, were not half through when the others rose from
the table.
``Going to eat all night?'' demanded the captain, with the suspicion of a
smile on his face.
``Oh, no,'' laughed Rush. ``Not quite so long as that, I hope.''
``How about you?'' questioned the master, nodding at Jarvis.
``Well,'' answered Bob reflectively, ``as nearly as I can figure it I am
about amidships between soup and pie. If I don't fall through the centre
hatch before I reach the pie end I'll be on deck about seven o'clock.''
The officers laughed heartily.
``Do we go on duty this evening, sir?'' questioned Rush.
``Certainly,'' replied the captain. ``You take your regular tricks just the
same. You two will take the forward watch at nine o'clock.''
They had never been on watch before, and did not know what their duties
were to be. So, after finishing their supper, they hunted up Mr. Major
and asked him to explain their duties to them. He told them that all
they had to do would be to watch out for lights ahead and either side of
the ship, ring the hours on the ship's bell just forward of the bridge,
at the same time glancing back at their own ship's running lights to see
if all were burning brightly. The mate told them how to report this,
giving them some other suggestions at the same time.
``This is fine,'' glowed Bob. ``We're going to walk the bridge at midnight,
aren't we?''
``Rush will have the bridge watch,'' explained Mr. Major. ``You will take
the deck just forward of and under the bridge. It is not hard work in
good weather, but it gets to be rather lonesome at times. I shall be on
duty in the pilot-house during your trick. If you are in doubt at any
time be sure to call out to me.''
Both promised that they would. It was with keen anticipation that the
lads made their way forward from their cabins a few minutes before nine
o'clock.
``Second watch changed,'' called the watch who was on the point of
retiring.
``Aye, aye,'' answered the officer in charge in the pilot-house. All was
dark in there so the men could see ahead, the windows of the captain's
cabin having the shades pulled tight so that not a single ray of light
could shine out ahead to blind the eyes of the lookouts.
``All clear ahead. Steamer heading up the lake off the starboard bow.''
``All right,'' answered Steve as he took his place at the rail of the
bridge. ``I guess she won't run into us.''
``Watch for that steamer's red light off to starboard,'' warned a
business-like voice from the blackness of the pilot-house.
``I will,'' replied Steve.
``Say, `aye, aye, sir.'''
``Aye, aye, sir.''
``That's right. We observe all the forms on board these ships just the
same as they do on the high seas.''
``What's all that talk about up there?'' called Bob Jarvis, from his post
in the bow on the deck below.
``You are to keep watch of that fellow off to starboard,'' answered Rush.
``Starboard? Let's see---that's the left side, isn't it?''
``No, the right.''
``Oh, I guess that's right.''
``Tell the watch below to 'tend to his business,'' warned the mate in the
pilot-house.
``Forward watch, knock off talking,'' called Steve.
``Don't get funny up there or I'll come up and straighten you out.''
``Bob,'' called Steve softly, ``the officer will be down there in a moment
if you don't stop your nonsense. This is business. Keep your eyes on the
water and call out whenever you see a light. I------''
``Ship, ho!'' sang out Jarvis suddenly, interrupting what Steve was
saying.
``Lower watch reports a ship, sir,'' sang out Steve.
``Where away?'' demanded the mate.
``Where away?'' repeated Steve.
``Oh, 'bout a mile off the right-hand side,'' answered the lower watch
nonchalantly.
``He means the vessel off to starboard, sir,'' Rush informed the officer
in charge.
``Has that wooden-head just discovered the ore carrier over there?''
``I guess so, sir.''
``Pshaw! You keep your eyes open.''
``He will be all right after he gets settled down to it, sir,'' said Steve
apologetically.
``We're likely to be sent to the bottom before that time, if we wait for
him to keep us out of trouble.''
The ship sailed on. Now and then Steve's keen eyes would sight a green
or red or a white light, and under the instruction of the mate he
quickly learned to determine the position of the boat from her lights,
enabling him to say instantly which way the other ship was traveling.
After a while the captain entered the pilot-house.
``Who's on the forward watch?'' he demanded.
``Rush on the bridge, Jarvis in the forward peak.''
``Keep a sharp lookout. They are new men.''
``Aye, aye, sir. Rush is all right. He has eyes like an owl at night.
Trust him for not letting anything------''
``Red light dead ahead,'' called Rush.
``What do you make of her?''
``Nothing more, sir.''
``That's one of the Wyckoff coal fleet,'' announced the captain, leaning
from the pilot-house window. ``She's headed for Shoal Island.''
``How in the name of all that's good does he know all that?'' muttered the
boy on the bridge. ``I can't see a thing but the red light, and that
means that her port beam is almost across our bow. I don't see anything
else.''
``I suppose you are wondering how I know that, eh?'' chuckled the captain,
nodding to the lad pacing the bridge just below him.
``Well, yes, sir; I was wondering,'' admitted Rush.
``Do you make out her white lights!''
``No, sir.''
``That's where I have you. There is a bank of fog or mist settling over
the lake. If you will raise your eyes a little to the right of the red
light you will make out two faint blurs------''
``I see them, sir.''
``Those are her masthead lights. I know the set of the masts of the
Wyckoff boats, that's all. So will you, after you have been at sea long
enough. It is all a matter of experience. I have been drilling up and
down these lakes for the past thirty years. I ought to know a few
things about them and the fellows who are navigating them. It's going to
storm.''
``Yes, sir,'' agreed the lad, but he did not see any signs of rain. The
stars were bright overhead and the moon was shining brightly. ``I see I
have a few things to learn about the weather,'' he muttered.
A few minutes later Steve discovered that the moon and the stars had
suddenly disappeared. The captain knew they would, for the wind had
veered to the southeast and he had seen the fog bank settling down since
the first moment he entered the pilot house. The rain started in shortly
afterwards in a thin drizzle.
``Hey, up there, it's getting wet down here!'' shouted Bob. ``Hand me down
an umbrella or something.''
``Keep a sharp lookout, lads,'' warned the captain. ``Remember we've got a
load of coal across our bows.''
``Aye, aye, sir,'' answered Steve. ``I think I can see quite a way ahead of
us.''
``That is a mistake. You can't see a ship's length ahead. Keep your eyes
open.''
``I will, sir.''
``Where is your raincoat?''
``I am afraid I have none. I never thought to bring one with me.''
``Tell your friend Jarvis to go to my cabin and ask the steward for two
coats.''
Steve did so, and a few minutes later the lads were well protected from
the storm, which was now upon them in full force. The rain was coming
down in blinding sheets by this time, beating into the faces of the Iron
Boys.
Suddenly Steve leaned over the edge of the bridge, shading his eyes with
his hand. Something that he thought he had observed in Bob's position
had attracted his attention. He gazed more keenly, then uttered a little
gasp. Jarvis was standing with his head down, facing away from the storm
toward the stern of the ship. He looked very comfortable and contented.
``Bob!''
Steve's tone was stern.
``Bob!''
``What do you want?''
``Turn around and be quick about it!'' Steve was speaking too low for the
officers in the pilot-house to hear. ``Don't you know that the safety of
the ship depends largely on our watchfulness at this minute, and------''
``Clang, clang, clang, clang, clang clang,'' interrupted the ship's clock
in the pilot-house.
Steve grasped the cord attached to the clapper of the big bell in front
of the bridge, giving it six steady jerks.
``Six bells, eleven o'clock. All lights are burning brightly, sir,'' Rush
called in the singsong voice of the sailor.
``Aye, aye,'' answered the deep voice of the mate from the darkness of the
pilot-house.
``Reduce speed to one-half,'' commanded the captain, in a low voice. He
usually gave his commands calmly, no matter how great the stress or
emergency. ``Do you see anything of that coal carrier, Rush?''
``No, sir; she must be some distance away from us by this time.''
``She ought to be, but she isn't.''
``May I ask how you know that, sir?''
``I get her smoke.''
``I don't make it out, sir.''
``Neither do I, by sight, but I see it through my nose. I smell it.''
``Well, doesn't that beat all!'' muttered Rush.
He bent every energy toward piercing the black bank ahead. For the first
time Steve Rush experienced a sense of uneasiness, and for the first
time he realized what the perils of the sea meant. Before, it had seemed
to him that, unless a ship were laboring in a great storm, there could
be little danger. Once a minute the siren far back in the darkness, near
the engine superstructure, would wail out a long, dismal blast which, a
moment later, was answered by the ship out there somewhere ahead. The
sound of the other boat's siren did not seem to Steve Rush to be getting
any nearer, but to the experienced ears of Captain Simms quite the
contrary was plain.
``Look steady, down there!'' he warned in a sharp tone which told Rush
there was something that he did not know about was likely to happen.
``Look sharp!'' he repeated to Bob Jarvis.
``I'm looking. I'm------''
Steve Rush's voice cut in quick and sharp, though there was little trace
of excitement in it.
``Sheer off! Ship dead ahead!''
``Hard a-port!'' commanded the captain, at the same time sounding a long
wailing blast on the siren.
A deafening crash followed almost upon the command.
\gutchapter{CHAPTER VIII}
\section*{\raggedright THE CRASH IN THE FOG}
\textit{Steve} was thrown flat on his face on the bridge, while Bob Jarvis
doubled up, wedged into the forepeak of the boat on the deck below.
``Full speed astern!'' roared the captain.
The chains of the pilot-house telegraph rattled ominously and the
propeller, nearly six hundred feet aft of the bridge, began whirling the
other way at tremendous speed.
``Hey! What---what---what's happened?'' shouted Bob Jarvis. ``Have we hit the
shore?''
``Close the water-tight bulkheads!'' commanded Captain Simms. The mate
threw over the electric switch that gave the signal for the closing of
all water-tight doors and bulkheads.
``Sound the general alarm!''
Gongs began to ring all over the ship.
``Order the engine and stoke room crews to stand by their tricks. I'll
give them warning in time in case we have been badly hit.''
The mate obeyed quickly and without a single lost motion. By this time
Steve had leaped to his feet. Ahead of him, it seemed almost on top of
them, loomed a great black hull. Lights shone dimly through the heavy
pall of fog. He understood without having to be told what had happened.
The ``Wanderer'' had come into collision with another ship, presumably the
same one whose lights the bridge watch had been watching off to
starboard earlier in the evening. Even in the excitement of the moment
Rush did not understand how this thing could have happened, if the other
boat had held to the courses she was on when he last saw the other boat.
``Make ready the lifeboats!'' commanded the captain of the ``Wanderer.''
Then, raising his megaphone to his lips, the master bellowed through it:
``Are you hard hit?''
``We have a hole punched in our side big enough for you to go through.
Stand by until we can find out whether we'll float or not.''
``Aye, aye, we'll stand by. We want to find out how much of a smash \textit{we}
have got. Mr. Major, get down there and examine the nose of our boat,
and see how much of a bang we got. It's lucky for us that we hit the
other craft in the position we did.''
The mate hurried down to where Bob was still on watch. Even after the
crash had come, and he had picked himself up, Jarvis stuck to his post,
though he believed the ship to be sinking. And, besides, Bob being
right at the point of the collision, so close in fact that woodwork from
the other boat showered over him in a perfect rain, got the full force
of it. He was bruised and battered, he had lost his hat and he was
greatly shaken up by the terrific impact.
The ``Wanderer'' had backed away to a safe distance, and the first mate
was now making an examination of her wound.
``We've broken our nose off,'' he called up to the bridge.
``Is she taking in any water?''
``Yes, sir; but I think the bulkhead will hold it so we won't go down.''
``Good! Ahoy, coal carrier there.''
``Aye, aye,'' came the reply from the deck of the stranger.
``Who are you?''
``The `James Macomber,' coal laden, bound for Shoal Island.''
``Well, I must say you are doing some fine steering. What are you doing
over here?''
``We got out of position in the fog.''
``I should say you did. How are you?''
``Listing badly to port and settling by the stern.''
``Better get your boats over while you have the time. Shall we put over a
boat?''
``No; we can manage to get away if she goes.''
``I tell you, you're going down! Get away while you've got the time.''
``All right; stand by.''
``Can I do anything, sir?'' asked Steve.
``Yes; go aft and take two men with you. Take the boat and cast off. Lay
well away from the ship and give me a hail, so I'll know where you are.
Stand by and, mind you, don't drift away and get lost. We'll never pick
you up in this fog if you do. Understand?''
``Yes, sir.''
``Order Jarvis up to the bridge.''
``Bob, come up here. The captain orders you to take the bridge.''
Steve ran down the ladder to the forward deck, then on down to the main
deck, where all hands not otherwise engaged had assembled. They were
leaning over the side peering into the darkness to see what had
happened. Steve was beset by questions. He explained briefly what had
happened, repeating the captain's orders for himself and two men to man
the life-boat and put off to pick up any one needing assistance.
The second mate, then in charge of the deck, assigned two strong oarsmen
to go with Rush. The latter was to be in charge of the boat, so the
captain had said, though Steve was dubious about his ability to fill
that office. Of course he was interested in boats, but he was much more
familiar with drifts and levels than he was with navigation of the
lakes.
``Man the boat,'' ordered the second mate.
The men took their places in the life-boat, which already had been
hauled up ready for launching, the Iron Boy taking his place in the
stern by the tiller.
``Are you ready?''
``All ready.''
``Cast off!'' came the hoarse command from the second mate.
Steve instinctively grasped the gunwales of the life-boat as the craft
dropped toward the water. He thought the boat had broken loose from the
davits and was falling into the sea, so swift was its descent. Yet he
might have known from the sound of the groaning, creaking block and
tackle that he and his companions were still safe.
The life-boat struck the water with a loud splash, rocking perilously as
Steve, still gripping the sides, stood in a crouching position ready to
jump should the boat tip over. Then the little craft righted itself,
though it lay rising and falling, rolling and tossing perilously on the
long lake swell. Rush had no idea that the water was so turbulent.
``Cast off!''
The two oarsmen quickly unhooked the blocks from the rings at the
extreme ends of the small boat.
``Are you ready?'' they asked.
``Yes,'' said Steve, though he was not certain whether he was ready or
not. His mind worked with its usual quickness, however. He knew that he
was expected to get off somewhere near the steamer ``Macomber.''
``Give way!'' he commanded.
The sailors pushed the life-boat away from the side of the ship with
their oars; then, placing the oars in the locks, fell to pulling
steadily. Steve turned the tiller the wrong way the first thing. The
nose of the life boat hit the hull of the ``Wanderer'' with such force as
to throw the three men to the bottom of their boat.
``Lubbers!'' bellowed the second mate from the deck of the ship. ``What are
you trying to do---run us down?''
Steve's face was burning with mortification. Fortunately the night was
too dark for any one to see this.
``What's the matter with you?'' demanded one of the oarsmen.
``I turned the tiller the wrong way,'' answered Rush truthfully. ``Pull
away.''
The men growled as they fell to their oars once more. A few swift
strokes and they were clear of their ship, Rush this time handling his
tiller with more skill than before. He tried the rudder cautiously and
found that it responded readily to the least movement of the tiller.
``Now I'm all right,'' he muttered. ``That is if I don't run something else
down.''
Swinging out in a wide circle the lad steered around the bow of the
``Wanderer,'' heading for the spot where he thought the distressed ship
lay.
``Lifeboat there!'' bellowed the captain through his megaphone.
``Aye, aye, sir.''
``Where you heading?''
``For the other ship.''
``No you're not. You're heading for the shore. Pull to port a little
more. There, that's better. Look where you are going, now.''
The captain's tone was stern and commanding. Steve leaned well forward,
peering into the thick fog ahead. He could not make out the other ship
as yet, though he could hear the shouting and the hoarsely uttered
commands on her deck. It was a scene such as he had never imagined
before, and it thrilled Steve Rush through and through. He felt that he
was ready for deeds of valor if he should only get the chance to perform
them.
``Steady, men,'' the boy warned. ``We must be near the other ship now. I
can hear their voices more plainly. It is curious we can't see their
lights, though.''
``That's because of the fog, cap'n,'' volunteered one of the sailors at
the oars.
``They're------''
``Look out! We're under the stern of the ship now!'' cried Rush, throwing
his tiller hard to port.
The life boat hit the stern of the ship, far down under her counter,
with a resounding crash. There followed the sound of breaking woodwork,
as the gunwale of the lifeboat crashed in. The little craft shipped a
heavy sea, drenching all hands.
The sailors had dropped their oars and were preparing to jump.
``Sit down!'' commanded the young skipper.
``We're sinking!''
``Well, if we are, let's get in a better place to do it. We don't want to
be floundering in the water under the stern of this sinking ship, do we?
Get to your oars and pull away!''
The Iron Boy's voice had assumed a tone of command. The men, recognizing
that he was not alarmed, bent themselves to their oars and pulled
quickly from their present dangerous position.
``Have we anything in the boat with which to bail it out?''
``No.''
``Then we will sit in the water. I guess we can't be much wetter than we
are.''
The men grumbled.
``Lay to, till I find out how badly we are injured.''
A brief examination of the side of the boat that had come in contact
with the ship, showed that the gunwale had been smashed in, but the gash
did not extend far enough down to place the little boat in great danger
unless perhaps the sea rose high enough to wash over the side. As yet
the lake was rolling lazily as is usually the case in a fog, for a
breeze would quickly dispel the heaviest bank of fog and drive it away.
``We're all right,'' decided the young coxswain. ``Pull around slowly.''
Standing up in the stern of the life-boat with the tiller between his
legs, Steve hailed the disabled ship.
``Ahoy, there!'' he called.
``Ahoy! Who are you?''
``Life-boat from the `Wanderer.' If you want any help, sing out.''
``We'll need it all right.''
``Are you sinking?''
``We don't know. We're settling some.''
``Got much water aboard?''
``More'n we need to drink. Come in closer, so we can get you if we need
to.''
``How about your own boats?''
``Life boat smashed in the collision. Ship's raft is safe. That'll carry
most of us, perhaps all of us, if necessary.''
``Better get it ready, then, in case anything happens,'' advised the lad,
who was rapidly becoming a seasoned sailor. ``Pull in a little closer,
boys, but look sharp because we may have to get out in a hurry, in case
anything happens over there.''
The boat drifted slowly in toward the injured ship. This time the little
craft had worked around abeam of the coaler, the latter's lights showing
dimly in the thick fog.
``Keep your siren going to warn off other ships, why don't you?'' shouted
Rush.
The suggestion was a good one. It was instantly acted upon by the master
of the ``Macomber.'' Then the ``Wanderer'' started her siren going, the
hoarse voices of the whistles sounding dull and unreal through the fog.
Steve grinned appreciatively.
``At least I have made one good suggestion,'' he muttered. ``There will be
no excuse for any other ship hereabouts running into us. That would be a
nice mess.''
Suddenly there arose a commotion on board the damaged coaler. The shouts
grew louder. The crash of a steel hatch falling into place could be
heard here and there. A loud splash sounded between the life-boat and
the ship.
``Somebody's overboard!'' cried Steve. ``Pull in!''
``Life-boat there!''
``Aye, aye!''
``We're sinking by the stern!''
``Pull in quick, lads!'' commanded Steve Rush.
\gutchapter{CHAPTER IX}
\section*{\raggedright A TRAGEDY OF THE LAKES}
\textit{There} followed a sound as though the wind were suddenly rising. The
sound grew to the roar of a gale.
Rush did not understand the meaning of it. He did understand, however,
that there was a man in the water near by, and that there was a human
life to save.
``Where are you?'' he called.
``Here! Be quick!''
Rush had the fellow by the collar, in short order, and with some
difficulty, hauled the man into the life-boat.
``The ship's going down. Get out of here!'' cried the rescued sailor.
``Pull out, boys!'' commanded Rush, grasping the tiller and swinging the
bow of his boat about.
``There she goes!'' shouted the sailor from the ``Macomber.''
The huge coaler's lights suddenly went out as the sea flooded her dynamo
room. The hatches began blowing off with loud explosions as the water
was forced up under them.
``What is it?'' cried Steve.
``The hatches.''
Boom!
``There goes the main bulkhead. It's all up with her now.''
Yells and cries rent the air. Men were leaping into the sea from the
doomed ship, and though the men in the life-boat could not see, they
could hear.
``I can't stand this!'' gritted the Iron Boy, jamming the tiller hard
over.
``What are you going to do?'' demanded one of the sailors.
``I'm going in there after those men,'' answered Steve Rush.
``It's sure death!''
``We'll go, just the same.''
``No we won't; we'll pull out of here like lightning.''
Steve grabbed up a boat hook.
``Pull, I tell you; pull for all you two are worth, or I'll knock your
heads off with this hook. Now---\textit{go}!''
The oarsmen pulled. They were used to obeying orders, and they realized
that the young coxswain of their craft was no weakling. He meant exactly
what he had said. Besides the men, after all, were as anxious to save
those of their own calling, now struggling in the water, as Steve could
possibly be.
The bow of the life-boat sent the water spurting into the air as the
craft cut through the sea. Another man was hauled aboard.
``Where's the rest of them?'' demanded Rush.
``The water's full of them,'' gasped the rescued sailor.
``Ahoy, there, men---swim this way if you can. We're waiting for you.
We'll------''
With a sickening roar that Steve Rush would never forget as long as he
lived, the ``Macomber'' dived stern first under the surface of the water.
Her engine and boiler rooms, being at the stern, were flooded instantly.
Then came a report as if the universe had been suddenly rent in twain,
an explosion that seemed to rend the air, the earth and the sea.
``The ship's blowing up!'' cried one of the men in the boat. He knew what
the sound meant. Steve did not, but he caught his breath sharply when he
heard the words.
``Pull out!''
Instead, the life-boat was lifted out. It seemed to rise right up into
the air, and when the Iron Boy at the helm sought to throw the rudder
over there was not water to push against---only thin air.
``Hang on! We're going over!'' shouted the boy.
Cries for help were heard on all sides of the life-boat now. But Steve
was powerless to aid the drowning ones. He was concerned with saving
himself and those with him just at this time.
The boat continued to go into the air; then, suddenly, it swung bottom
side up, spilling its human freight into the lake.
As the men of the life-boat fell into the water they were caught by the
suction of the sinking ship and borne struggling about in the great eddy
that swirled with the speed of a mill-race.
Steve fought valiantly to save himself by trying to swim out of the
whirlpool, but even his great strength was not equal to the task. He was
tossed to the centre of the eddy; then he felt himself being drawn
downward by some invisible force. Even then the Iron Boy did not lose
his presence of mind. He caught and held his breath as the waters were
closing over him.
Down and down shot the body of Steve Rush until he believed he must be
near the bottom of Lake Huron. Hours seemed to have been occupied in the
descent, whereas it had been a matter of seconds only. He had made no
resistance, calmly deciding to save his strength until action would
count for something.
Steve had no thought of giving up. While his heart was filled with a
great dread he was not excited, because he would not permit himself to
be.
``I'll die game, if I do die,'' he kept repeating to himself.
At last the pull from beneath seemed to be lessening a little. There was
not the same terrific force tugging at his feet. Steve kicked out and
the effort, he thought, raised him a little.
Thus encouraged he began kicking with all his strength, treading water
and working his hands as fast as he could. There could be no doubt about
it now. He was shooting toward the top at a good speed.
Suddenly he gave a great gasp as he felt the warm, damp air strike his
face. His lungs were almost at the bursting point, and he felt that he
could not have held his breath a second longer.
Steve lay over on the water, on his back, moving his hands listlessly to
help keep him afloat. Thus far he had had no thought of the ship to
which he belonged. He was too much exhausted to do more than lie still,
which he did, drawing in long, deep breaths of the fresh air. Nothing
had ever tasted so sweet to Steve Rush and he felt an overpowering
desire to go to sleep.
All at once he threw himself over on his stomach as the long, shrill
blast of a steamer's whistle smote his ears.
``It's the 'Wanderer'!'' he cried. ``And they must be miles away.''
The ship was not very far away. It was the blanket of fog that had
smothered the sound of the whistle and made it seem many miles off to
port of him.
Rush raised his voice and shouted. His voice, of course, carried for a
very short distance, for the same reason that had made the ship's
whistle sound a long way off. Again and again did he shout, but not a
response did he get, save the long wail of the siren. Not a light was to
be seen anywhere, nor were there any signs of the other men who had been
in the life-boat with him at the time it was lifted from the water and
turned bottom side up.
A great feeling of lonesomeness came over the Iron Boy when he realized
that he was far out in the lake alone. He, of course, did not know how
far they were from shore, but he believed it to be at least twenty
miles.
He reasoned that his ship would not sail away without him unless the
captain were reasonably certain that Steve had been drowned. The lad
decided to swim in the direction from which the whistle sound had come.
He had taken but a few strokes when he became entangled in a mass of
wreckage. At first he thought he was going to drown before he could
extricate himself, then he discovered that he could not if he tried.
Illustration: Steve Clung to the Door.
Pieces of floating wood were all about him, some of them the lad
recognized as part of a deck house. He fastened to a door that had been
split in half, probably by the explosion, and stretching out full length
upon it, lay still to rest. He was reasonably safe now, though, of
course, unless he were rescued very soon he would become chilled and
slip off into the sea.
The wind began to stir up out of the southwest a little. Steve took
courage from this.
``It will blow me toward the ship,'' he exclaimed. ``That is, if the ship
is where I think it is.''
He began paddling with might and main, steering with his feet as well as
he could, shifting his weight this side and that from time to time as a
swell threatened to upset him.
The siren blew several long blasts.
``That's queer,'' muttered Steve. ``She seems to be getting farther and
farther away from me all the time.''
The reason for this was that Rush was getting farther and farther away
from the ship. He was propelling himself along in the wrong direction.
As the fog began to race on ahead of him he took a look over the waters
that now showed white ridges as far as the eye could penetrate. Not a
light could he see, save one bright light dead ahead of him. The light
winked, went out, then suddenly appeared after a few seconds interval.
``There's the ship!'' he cried. ``But, oh, how far off it seems to be.''
What Steve could not understand, was that he did not see more than one
light. Both masthead lights, at least, should have shown. He decided
that the side light, the red and the green, were too low down for him to
catch a glance at over the tops of the rising waves.
``I'll swim for it anyway,'' he decided, settling to his work with all the
strength that was in him. It would be useless to waste breath in
calling, because those on the ship could not hear him at that great
distance.
Suddenly the wind abated, the fog rolled back over the lake, again
enveloping the swimmer in a dense black mantle. The sea was still
running with him, however, and would continue to do so for some time to
come, thus helping him along.
After a couple hours of paddling and drifting, during which Rush made
considerable headway, the lad realized that he was getting tired.
Further than this he was cold and chilled. The chills extended from his
head to his feet.
``This won't do,'' Steve cried, confusedly. ``If I get much colder I shall
fall off my ship and drown.''
He began paddling with renewed vigor, but, work as he would he seemed
unable to throw off the chill. He realized, too, that his body was
getting numb. The Iron Boy fought desperately, but the more he fought
the more drowsy did he become. His efforts grew less and less and his
progress slower.
Steve wrapped both arms about the door and with cheek pressed close to
it, resigned himself to what he thought would be a few minutes' rest.
His heavy eyelids closed slowly; his breathing grew regular, but faint
and his legs stretched out full length, being in the water up to his
knees.
Steve had given way to the languor that was creeping over him. He was
adrift and alone far out on the treacherous water of the great lake.
\gutchapter{CHAPTER X}
\section*{\raggedright TOSSED UP BY THE WAVES}
\textit{The} light that Steve Rush had seen, the winking, twinkling light came
from the lighthouse on North Point. The North Point light was a
revolving affair, which accounted for its vanishing and then reappearing
at stated intervals.
A few hours passed, though they were as seconds to the unconscious boy
on the slender raft. At last he began to feel a glow spreading over his
benumbed body. He moved a little, took a long breath then settled back
into his former stupor. But the warmth continued to spread. Steve felt a
sense of being on fire. After a while he realized that the support under
him was no longer moving, though he could hear the roar of the waves in
his ears. He found himself dimly wondering why they did not break over
him and drench him and chill him to the marrow.
Steve tried to raise one hand to his head, but the hand was pinioned so
that he could not move it. His curiosity was becoming aroused. Rush
opened his eyes. Before him and above him was a rocky, precipitous
coast. Then in a rush of understanding he realized that he was lying on
the rocky shore of the lake coast. Both hands were still under the door,
which accounted for his inability to raise one of them a few minutes
since.
The sun was beating down hotly, warming the Iron Boy's blood, sending it
more rapidly through his veins.
With a cry of thankfulness Steve Rush got unsteadily to his feet. He was
so stiff that he could hardly stand, though the numbness of a few hours
since was fast passing away.
``I have been carried to the shore and I'm saved!'' he shouted. ``This is
the most wonderful thing that ever has happened to me. But I wonder
where I am.''
It was early in the morning, that was certain. He judged the hour must
be about seven o'clock. His watch had stopped at midnight. Turning
quickly the lad glanced out over the green waters of the lake that
sparkled in the morning sunlight, a gentle ripple ruffling the surface.
Here and there a huge ore carrier was observed, working its way up or
down the lake. Far in the offing thin ribbons of gray smoke told where
other vessels were steaming along.
``I wonder if any of those ships is the 'Wanderer'?'' mused the Iron Boy.
``And I wonder something else, too---I wonder whether I am going to get
any breakfast or not. It is useless for me to try to signal a ship in
here. They probably would not come in even if they saw me, as I imagine
this is shoal water all around here. There must be some one living about
here somewhere. I'll start on a little exploring tour for breakfast.''
Steve turned away and began climbing up the rocks. This being his first
passage over the lakes, he was not at all familiar with the coast and
consequently had no idea where he was.
In the meantime the ship had sailed away. The ``Wanderer'' had lain to
until the first gray dawn of the morning. A few of the men had been
saved, including two of the sailors in the boat Steve had set out in.
All the others in that craft had been lost, as were the greater part of
the crew of the lost steamer. The men rescued from the life-boat were of
the opinion that Steve Rush had gone down with the others.
Bob Jarvis said not a word. His face was pale and drawn. He went about
his duties methodically, speaking to no one, but listening to every word
that was said about the tragedy.
After cutting wide circles for a full two hours the ``Wanderer'' was put
about on her interrupted course.
``South south-west one half,'' announced the skipper in a low tone.
The words meant to all who heard them, that he had abandoned the
search---that the missing men had been given up for lost. Their names
would be added to the list of fifty thousand souls who have lost their
lives on the Great Lakes during the last fifty years.
Captain Simms' face was grave. He had taken a great liking to Steve
Rush. He had lost, as he thought, three men, the first loss of life on a
ship commanded by him since he had been in the service of the company as
a sailing master.
``Mr. Major, you will report the accident and the loss of the men as soon
as we reach the St. Clair River,'' he said.
``Aye, aye, sir.''
Captain Simms left the pilot-house, from which point of vantage he had
been sweeping the waters of the lake with his glasses, and went down to
his own cabin to turn in for a few hours' sleep.
* * * * *
In the meantime the object of the thoughts of nearly every man on board,
Steve Rush, was climbing to the top of the rocks that lined the coast.
Reaching there he sought the highest point attainable and looked about
him.
``I am on an island!'' he exclaimed. ``From the looks of things I am the
only person here. Well, this \textit{is} cheerful, but it is much better than
being out yonder,'' he added with a gesture toward the rippling waters of
Lake Huron.
Rush decided to investigate his island the next thing he did. So he
climbed down to the beach again and began following the coast line. As
he went on he found traces indicating that some one had been there.
There were chicken bones and the charred embers of a recent fire in one
spot. Steve came to the conclusion that fishermen had been on the island
not long since. If this were so there were hopes that they or some of
their kind would visit the place again. Steve walked the greater part of
the day. On one side of the island he saw a large bay. Across a point of
what he judged to be the mainland, he could see another bay and beyond
that a cloud in the sky that looked like smoke.
``There must be a large town or a city over yonder, but I don't know what
it is. I do not even know whether I am in the United States or Canada.''
All day long the lad tramped. When night came he was hungry, stiff and
weak. Had it not been for his splendid constitution and great endurance
he would have given up long before that.
Just before dark he caught sight of a small sailboat slipping easily
along, headed, he thought, for the larger bay on beyond the narrow
point of land.
Steve hailed the craft. One man in the stern of the boat stood up and
gazed shoreward through a glass. Rush swung his arms and shouted that he
wanted to be taken off the island. The man in the stern calmly closed
his glasses and sat down, while the boat held steadily to her course.
Steve sat down, too. He was not so much discouraged as he was angry and
disgusted.
``Why couldn't he have sailed somewhere so I wouldn't have seen him,
instead of drifting by so tantalizingly near me?'' he cried.
There being no answer to the question, Rush began looking about for a
place to sleep. The best he could do was a spot just under a ledge of
rock. The boy went down to the beach and brought back his life raft, the
piece of a deck house door on which he had floated ashore. This he
carried up to his bedroom under the ledge and stood it against the
rocks.
``That will do very well, in the absence of something better,'' he decided
grinning as broadly as the drawn muscles of his face would permit him to
do.
Then Steve crawled under this rude shelter, drawing his coat as closely
about him as possible and went sound asleep.
Steve was exhausted bodily and mentally, and it was not to be wondered
at considering what he had gone through in the last twelve hours.
Besides this he had had nothing to eat since supper on the previous day.
The following morning Rush did not awaken until the sunlight warmed his
bedroom. He crawled out, rubbed his eyes and looked about him.
``Well, if it isn't morning! But maybe it's the next morning; maybe I
slept a day and a night.''
He had now lost all track of time. Steve sat down to think matters over
calmly. His position was a serious one and he understood that full well.
``If I remain here another day I shall be unable to get away,'' he mused.
``Then I shall in all probability starve to death. That won't do. I don't
propose to give up as long as I have any strength left in me, and I
guess I have a little, even after what I have passed through.''
Rush sat studying the narrow stretch of water separating him from the
slender neck of land that he had observed the day before.
``It can't be more than three miles across there. If I had had a good
meal this morning I believe I could swim across to the other shore. That
looks to me like the mainland. There is surely something on beyond
there several miles away. I wonder if I dare try to swim it?''
A little reflection convinced the lad that such an attempt could end but
one way---he would drown before he reached the neck of land.
His eyes roved about, after a while resting reflectively on the piece of
deck-house door that had served his purpose so well after the sinking of
the steamer. A look of new-found intelligence gradually grew in his
eyes.
``The very thing! Hurrah!'' he cried, springing up and dancing about,
forgetful for the moment, that he needed all the strength he had left.
``I swam on the door all night. Surely I can stand a few hours more on it
in the bright sunlight. Why didn't I think of it before?''
Rush lost no time in acting upon the suggestion that had come to him. He
grabbed up the cabin door and began staggering down the rocks with it.
The door was heavy and he was weak. Once he stumbled and fell. The door
went clattering down over the rocks, Steve bringing up in a heap some
distance above it.
``There, I'll bet it's broken. If it is I'm done for.''
But the door was not broken. It was tough enough to stand the hard usage
to which it had been subjected. Steve was after it with a shout as soon
as he saw that it had not been split.
After that he proceeded more carefully; within a few minutes he reached
the beach with his burden. There the lad paused to think over the best
way to go about his own rescue. He took off his coat slowly, folded and
placed it on the door, then removing his suspenders he tied the coat
fast to his raft.
``There, I think that's all I had better take off or I shall get chilled
again.''
After a final, sweeping glance at the sea, the lad shoved the raft, or
rather one end of it, into the water and sat down on the beach to rest
and gather courage for the great undertaking before him.
``It beats all what a man will do for the sake of a meal,'' he grinned. ``I
might stay on this island all summer, and have a pretty good time, were
it possible for me to get along without food. But, no; I've got to eat
or I'll die. Well, here goes.''
He shoved the door out into the water, pushing it along ahead of him
until the water was up to his shoulders. Rush then slid his body up on
the raft and began paddling with his hands and kicking his feet, pushing
himself along, heading around a curve of the island, for the extreme
narrow point of land jutting out into the lake.
\gutchapter{CHAPTER XI}
\section*{\raggedright BY PLUCK ALONE}
\textit{After} half an hour of steady paddling, Rush shoved his coat up for a
pillow and lay flat on the slender raft to rest himself. He was
breathing hard from his exertions; in fact, he was well nigh exhausted.
But the Iron Boy's pluck was of the same quality as ever. Nothing could
weaken that, no matter how dire his predicament.
``I could make better time swimming,'' he mused, raising his head a little
and gazing longingly at the shore that now seemed farther off than
before, ``if I only dared. I don't mean that; I do dare, but it would not
be prudent. I want to get to the mainland, and I think my present method
is the best one to get me there. Well, I must start the engines going
again,'' decided the lad, grinning at his own humor.
Had any one chanced to be looking in his direction from the shore, that
person probably would have thought he was gazing upon some strange
creature from the deep, for Steve was making the water foam all about
him. His head and the end of the board were all that were visible above
the surface. Once he paddled so fast as to cause him to lose his
balance. His raft turned turtle, landing Rush on his back in the water.
Laughing almost gleefully at his own misfortune, the lad, in a few swift
strokes, regained the door.
``That was just so much effort wasted,'' he remarked. ``I must remember
that I am not running a race. I ought to be in pretty good trim for one,
though; if I get through with this one I shall be fit for most any kind
of an old race that I come across.''
For the rest of the journey Steve made no attempt to spurt. He paddled
along steadily, making slow but sure progress toward the goal on which
his eyes were continually fixed.
The sun was at its zenith when, slipping from the board, he found solid
rock under his feet. Steve tried to shout, but he was too worn to raise
his voice. He clung to the door until it grounded with a grating sound
on the beach. Steve lay there for a few minutes. Then he staggered to
his feet, making his way up the beach a few feet from the water, there
to throw himself on the ground exhausted.
For nearly two hours he lay resting, having fallen into a deep sleep.
Then he awakened, sat up, resting his head in his hands for one last
little wink, the wink that was to give the lad the strength and courage
to take up his journey.
``Hello, what's the matter?''
Rush started up suddenly. He saw before him a boy somewhat younger than
himself, dressed in rough clothes. The boy was carrying part of a fish
net.
``Say, I'm glad to see you, and don't you forget it,'' exclaimed the Iron
Boy, striding forward and grasping the hand of the other lad, much to
the latter's astonishment. ``Who are you?''
``I'm Billy Trimmer. I am a fisherman---me and my father.''
``Do you live near here?'' asked Steve eagerly, with visions of a meal
before him.
``Nope. We live over yonder,'' pointing to the cloud of smoke that was now
much more plainly in evidence than before.
``Is that a town over there?''
``Yes.''
``What is the name of the town?''
``Alpena.''
``Oh! And what do you call that little island over yonder?''
``That one with the stones sticking up all over it like a porcupine's
back?''
``That describes it. Some of them are sticking into me yet.''
``That's Little Gull Island.''
``How far is it to Alpena?'' questioned Rush.
``'Bout ten miles.''
Steve uttered a long, low whistle.
``What's the easiest way to get there?''
``Hoof it. Ain't no other way.''
``That's too bad. Is there a house anywhere near here where I could buy
something to eat?''
``Nary a house. But you kin git all you want over to Alpena.''
``Thank you very much. I think I will be going.''
``Say, where'd you come from?''
``From the lake---out of the lake. I was drowned out there last night, or
pretty nearly drowned. A steamer went down and I was carried under------''
``A steamer?''
``Yes.''
``Which one?''
``The `Macomber,' I think it was. Coal laden and------''
``I must tell Pa,'' and the fisher boy was off on the run.
Steve gazed after the lad reflectively.
``I'd give a ten-dollar bill to anybody who would tell me how to run like
that now. Poor Bob, I'll bet he's eating his big heart out for sorrow
over my disappearance.'' Steve paused. ``They think I'm drowned, of
course, they do, and I ought to be. It must have been intended that I
should be, but somehow I didn't arrive on schedule time.''
Chuckling to himself, the lad started on toward the city, ten miles
away. He tried to make himself forget his weariness by whistling and
singing. Coming to some willow bushes, he cut the stiffest small branch
he could find, from which he trimmed the nubs, then started on, whipping
his legs with it.
This seemed to start the circulation, and at the same time to take his
mind from his own weariness. After a time the wet, swollen shoes began
to chafe his heels, and it was not very long before the skin had been
worn from both heels. Then a blister suddenly bobbed up on the ball of
the right foot.
The boy took off his shoes and tried to doctor the sore spots, but there
was nothing he could do save tear up his handkerchief and bind up the
affected parts.
``A boil on my nose, now, would just about complete my misfortune,'' Rush
grinned. ``I'm going to carry my shoes in my hands.''
This did not work very well, for Steve's feet were sore and the rocks
over which he was walking made his feet more tender than ever, so he put
the shoes on again. They had shrunk, of course, and the putting on was
attended with a great deal of pain. Steve Rush did not even grunt. He
drew them on almost roughly, stamped in them and jumped up and down.
``There, I guess that'll fix that blister, anyway. I wish I could jump on
the sore spots on my heels and cure them as easily.''
He started, and kept on without another stop until three o'clock in the
afternoon, when Rush halted for a drink of water at a little creek that
crossed his trail.
It was a sore and very much dilapidated young man who crawled into the
town just before supper time that evening. Realizing that his appearance
was far from prepossessing, Rush sought the back streets, following them
in so far as possible, keeping an eye out for a hotel that he thought
might be respectable.
He found such a place after some searching about, during which the
policemen he passed had eyed him suspiciously.
Steve entered the place, which proved to be a farmers' hotel, and asked
if he could get supper and lodging there. The man behind the desk eyed
the lad narrowly.
``You've made a mistake young fellow,'' said the clerk.
``How so?'' inquired Steve innocently.
``You should go out and see the hostler. Maybe he'll put you up. We don't
keep your kind in here.''
Several bystanders laughed at the boy's expense. But Rush never
flinched.
``Oh, I beg your pardon, sir; I thought I was in the stable. This must be
where you herd the other lower animals. I see they are all here.''
Before any one could recover his wits sufficiently to make a retort,
Steve had stepped out of the place.
Next the boy tried a restaurant. He got no further than the desk when he
was held up by the proprietor.
``Hold on; where are you going?''
``I wish something to eat,'' answered the boy politely.
``You're in the wrong place, and------''
``No, I am not. That's what the fellow told me the last place I called
at. They can't both be the wrong place, so this must be the right one.''
The proprietor of the place stepped out from behind his desk, laying a
firm hand on Steve Rush's shoulder. A peculiar glint shot into the eyes
of the Iron Boy, but he stood still.
``We can't serve you here. This is a gentlemen's restaurant. Perhaps you
will find something that will suit you down on the south side.''
``I have money, sir. I am willing to pay for what I get. I have been in a
shipwreck and am not very presentable------''
``I can't help it; you'll have to get out.''
``See here, sir, I shall not get out until I have had my supper. I have
had nothing to eat in twenty-four hours, and I'm hungry.''
``Go on, go on; don't raise any disturbance here.''
Steve walked over and laid a five-dollar bill on the desk.
``There's your money in advance. Give me the change after I have finished
my supper------''
``I said I couldn't serve you here. I------''
``Oh, yes you can, and what's more you're going to.''
``I'll call a policeman and have you put out.''
``Look here, Mister Man, unless I get some supper here quickly, I'll have
the law on you. You are keeping a public house, and you have no right to
turn me out.''
Steve didn't know whether he were right or not, but he took a long
chance. He saw at once that he had made a good point, so he pressed it
further.
``I am going to sit down at that table over there, and I shall expect to
be served at once.''
The proprietor's hand fell from the Iron Boy's shoulder as the latter
strode to the nearest table and seated himself. A waiter stepped up to
him asking what he would have, at the same time thrusting a bill of
fare on the table in front of the boy.
``I think I'll take about five dollars' worth of ham and eggs,'' answered
Rush without a trace of a smile on his face.
\gutchapter{CHAPTER XII}
\section*{\raggedright ON THE ROAD TO CONNEAUT}
\textit{Steve} had no further difficulty at the restaurant, though he noticed
that the proprietor of the place was watching him and scowling at him
all through the meal.
``I usually get what I go after,'' thought the boy. ``In this case it is
food.''
After paying his bill he hunted up a clothing store, where he fitted
himself out with a new suit, shirt, necktie, straw hat and a suit of
underwear, for everything that Steve had on was practically ruined.
This, with a pair of shoes purchased at another store, made him look
quite like his usual self.
Arrayed in his new suit Steve had no difficulty in getting into one of
the best hotels in the city. He left a call for six o'clock that he
might catch a train to Detroit, where he hoped to catch the ``Wanderer.''
He nearly missed the train next morning, because of his longing for a
cat nap. Arriving at Detroit he visited a newspaper office and inquired
if the ship had been sighted.
``Passed down during the night,'' was the discouraging answer.
``Where for?'' questioned the boy, as the ships usually got their
destination orders when they passed Detroit.
``Conneaut. See here, you are not one of the men who were on that ship
are you?'' questioned the newspaper man.
``Thank you, sir. I will be going. Can you tell me what time I can get a
train for Conneaut?'' answered Rush, avoiding the question.
Steve felt that he would be called upon to make a report of his share in
the disaster, and his good judgment told him that he should not make a
first statement to any one outside the company.
The next train out did not leave until late in the afternoon, so Rush
employed the time in going about the city. He visited all the places of
interest, getting his luncheon at a large hotel on the hill. The hotel
was named after a famous Indian Chief, but the prices asked for the
luncheon made Steve gasp.
``My wages would keep me here about three days,'' he muttered.
Later the lad boarded a train and hurried toward his destination. He did
not know whether he should find his ship in port or not, reasoning that
the craft would have to proceed under reduced speed the rest of the way
down on account of the smashed-in bow.
Shortly after dark the boy arrived. Inquiring his way to the ore docks,
he hurried down toward the inlet. This was a narrow canal, leading up
into the lower part of the town for some distance. Ships were packed in
the inlet, side to side, like sardines in a box. Most of them were lying
with anchor lights up; others with their running lights still lighted,
showing that they had just arrived in port. On either side of the inlet
loomed the dark trestles, from some of which the rattle and roar of
unloading machinery arose in a deafening chorus.
``This is about all a man's life is worth to face,'' decided Steve, as he
dodged a swiftly moving car that towered above him loaded with ore. Then
he narrowly missed being ground under a traveling crane that was in
operation unloading a ship.
``Can you tell me, sir, if the `Wanderer' has arrived?'' asked the boy of
a yard policeman who approached the lad to find out what he was doing
there.
``She's outside the harbor now. I heard her whistling for a tug a few
minutes ago. But we don't allow strangers in the yards here. It is too
dangerous.''
``I belong on the `Wanderer,''' explained Steve.
``Oh, you do, eh?''
``Yes.''
``Then what are you doing here?''
``Waiting for her.''
``When did you leave her?'' questioned the officer suspiciously.
``A couple of days ago, somewhere about the middle of Lake Huron. I went
down when the wreck occurred.''
The story of the wreck and the sinking of the coaler had by this time
been spread all over the country. The policeman gazed at the boy with
wondering eyes.
``You don't say?''
``Yes, sir.''
``Tell me about it.''
``I am sorry, but I think I had better say nothing until I have talked
with Captain Simms. Do you know where the `Wanderer' is going to berth?''
``See that pig there, just shifting her position?'' referring to a
whaleback, the latter style of boats being known to sailors on the lakes
as ``pigs,'' because of their pig-like bow.
``Yes.''
``The ship you want is coming into that berth. See, there's a crowd of
reporters waiting around there now to interview the captain.''
``I guess I'll keep out of their sight, then,'' laughed the lad.
Steve paced up and down the dock keeping well in the shadow, watching
the channel with eager eyes. He could hardly wait until the ship got in,
so anxious was he to relieve the anxiety of his companion, Bob Jarvis.
``There she comes,'' announced the policeman.
Steve shaded his eyes and gazed intently. Yes, sure enough it was the
``Wanderer.'' He could make out her broken nose now and the peculiar set
of her sticks. The lad had never before realized the size of the ship.
She seemed to loom up in the air higher than any of the buildings on the
opposite side of the inlet. All was dark on board her, no light save her
running lights showing; but up there in the darkened pilot-house Steve
knew, keen, cautious eyes were watching out for the safety of the boat
as well as for the safety of others in the harbor.
Rush heard the rasping sound of the bridge telegraph as the signal was
given to reverse. The spring-rope came whirling through the air and a
moment later the big hawser struck the water with a splash, being
quickly drawn to the dock by the dock hands.
All this was very interesting to Steve Rush, for it will be remembered
that he had never watched the docking of an ore boat before. The figure
of Mr. Major, the first mate, was faintly outlined at the rail, looking
down and giving orders to the men on the dock in a sharp, business-like
tone.
``Put out the ladder!'' the mate commanded.
The ladder came over the side, and was let down carefully until it
rested on the dock. Before any of those on board had an opportunity to
go over the side Steve had sprung to the ladder, up which he ran nimbly,
swinging over the rail to the deck of the ``Wanderer.''
``See here, young fellow, what do you want?'' demanded the mate. Then he
leaned forward, gazing keenly at the newcomer.
``Wha---what------''
``Steve!'' screamed Jarvis, rushing across the ship and throwing his arms
about young Rush. Jarvis was so overcome with emotion that for the
moment he found himself unable to utter another sound.
``Rush!'' cried the mate, fairly pulling the boy away from his companion
and wringing both Steve's hands. ``Why, why, we thought you went down
with the coaler.''
``I did. I guess I'm too tough to die. I surely have had plenty of
opportunity to do so.''
``Wait till I get through docking the ship, and then tell me all about
it.''
``I must see the captain first. Is he up in the house?''
``No; I think he just went down to his cabin.''
``Were any of our men lost?''
``Two of them. Jarvis here leaped overboard and saved four men from the
other ship, who were drowning while trying to swim out to us.''
``Good boy, Bob,'' said Steve as he patted his companion affectionately.
``You must tell me all about it when we get to our cabin, by and by. I
have had some experiences, too, some that will make you laugh.''
Others of the crew were pressing forward to shake the hand of the plucky
Iron Boy, for both boys were popular with all hands save the stoke-hole
crew.
``I must see the captain, Bob. I'll be back in a few minutes.''
Steve hurried up to the forward deck, rapped on the door and was bidden
to enter. Captain Simms looked, then blinked rapidly as his eyes fixed
themselves on the boy framed in the cabin doorway.
``Hello, is that you, Rush?''
``Yes, sir.''
``I thought there wasn't water enough in Huron to drown your kind.''
``No, sir.''
``Come in and sit down. I want to talk to you.''
\gutchapter{CHAPTER XIII}
\section*{\raggedright IN THE GRIP OF A GIANT SHELL}
\textit{Before} Captain Simms would permit the lad to leave him, he had to hear
the story of Steve's experiences. The story was frequently interrupted
by grunts of approval on the part of the skipper. The latter was not an
emotional man, as was evidenced by his greeting of Rush after the boy
had, as it were, risen from the lake.
Rush's story finished, he asked the captain to tell him all about what
had occurred after the accident.
``It isn't what did occur so much as what's going to happen,'' answered
the master gloomily.
``What do you mean, sir?''
``I shall lose my license.''
``What, and you not to blame? Impossible.''
``Yes, but how am I going to prove that I am blameless?''
``The authorities will believe what you say, will they not?''
``They have just as good a right to believe the captain of the other
boat. He will say it was my fault, and perhaps I shall say it was his
fault, and there you are. Both of us will lose out in the end. The other
skipper was saved and I am glad of it. It seems too bad that, after all
these years on the lakes without a blemish on my record, I have to be
knocked out at this time. My wife and little girl will be heart-broken.''
``Perhaps it will not be so bad as you think, sir. Of course, we are all
deeply grieved over the loss of life. That cannot now be helped. It is
our business to find out where the blame is and fix it there, no matter
whom it hits. I know one whom I am pretty sure it will not hit.''
Captain Simms squinted at the lad.
``Who?''
``Yourself.''
``Rush, you're a fine fellow. I like you,'' announced the skipper, with
something approaching enthusiasm in his voice as he stepped forward and
grasped the hands of his deck man in a grip of iron. Steve thought he
had a pretty good grip himself, but his own was as nothing compared with
that of the captain of the ``Wanderer.''
``I reported the accident from Detroit, and was ordered to proceed to
destination if able. I haven't heard anything from headquarters yet. I
shall hear something in the morning, as soon as our arrival here is
reported.''
``When do we unload?''
``They begin in about an hour.''
``Then I must get into some old clothes and get ready for work.''
``You need not go on duty to-night, unless you wish to.''
``I prefer it. You see, I have been idle for a couple of days and I shall
get out of practice,'' replied the boy, with a good-natured laugh.
``Idle! Humph! After swimming half way across Lake Huron, being drowned
into the bargain, walking almost across the state of Michigan, going
without food for twenty-four hours, not to speak of a few other little
things---then to talk about being idle. Go back and tell the cook to set
up the best on the ship. After you have had a good meal you may go to
work, if you wish. I suppose you'll not be satisfied unless you do. Go
on with you. Tell the first mate I want to see him.''
An hour later found Steve in his working clothes. The cranes for
unloading were just being moved into place when he reached the deck.
These were huge affairs, each provided with a giant scoop that gulped a
little mouthful of some fifty tons of ore every time its iron jaws were
opened.
There was a rattle and a bang as the hatch covers were being ripped off
and cast to the far side of the deck; men on the trestles were
shouting, whistles were blowing in the harbor, gasoline launches
conveying ship's officers to and from the other side of the inlet, were
exhausting with vicious explosions. Steve thought he had never seen such
confusion before, yet he knew full well that there was in reality no
confusion about it. Everything was being worked out in keeping with a
perfectly arranged system.
``Rush, you get down in the hold and take charge of the unloading,''
ordered the mate.
Steve hurried below. The hold was dimly lighted by an electric light at
either end. He did not know exactly what he was expected to do. The
great scoop dived down, swallowed a mouthful of ore and was out with it
like some huge monster, almost before Rush realized what was going on.
``Whew! That's going some!'' he exclaimed. ``There comes the thing again.
Hello, up there!'' cried the boy, with hands to mouth. ``Hadn't you better
take out some from the other end so as to unload the boat evenly?''
``Yes, that's what we've got you down there for, to watch things,''
shouted a voice from the deck. ``You're all right. Keep it up!''
``I don't know whether I am, or not,'' muttered the boy making his way
over the ore to the stern of the hold. ``This strikes me as being a
dangerous sort of spot.''
He watched the huge steel lips of the scoop as it felt about like the
lips of a horse gathering the oats from its manger, quickly grabbing up
its fifty tons of ore then leaping for the trestle some fifty feet
above, where it dropped its burden into cars waiting to transfer the ore
to the furnaces.
Load after load was scooped up. The rattle and the bang of the unloader
was deafening. It made the Iron Boy's ears ache.
``According to the speed at which we are unloading, now, we should be
finished in about four hours,'' he said. ``This is the most wonderful
mechanism I ever saw!''
There came a lull, during which the ship was moved further astern, in
order that the unloader might pick up ore from the forward part of the
hold. By the time this had been done, and the huge crane shifted to its
new position, nearly an hour had been lost.
The boy pondered over this for some time. It seemed to him like an
unnecessary loss of time.
``Why, so long as they have one crane at an unloading point, should they
not have more?'' he reflected. ``This is worth looking into.''
He thought he saw where a great improvement could be made, and he
decided to think it over when he had more time. Perhaps he could
suggest something to the officials that would be of use to them after
all.
Steve and his companion, while working as ordinary seamen, were drawing
the same fine salaries that they had received in the mines. Therefore
the boys felt it was their duty to earn the money being paid to them by
doing something worth while. They were getting three times as much as
was paid to the other men doing similar work.
As Rush was thinking all these things over the lights in the hold
suddenly went out, leaving the place in absolute darkness.
``Lights out!'' he shouted.
A rush of air fanned his cheek. He raised a hand to brush away some
object that seemed to be hovering over him. It was as if invisible hands
were groping in the dark, feeling for the Iron Boy's face to caress it.
Steve instinctively crouched down as low as he could on the ore. There
was little of it beneath him, the greater part having been removed by
the giant shell of the unloader.
Suddenly with a groan and many creakings the object whose presence he
had dimly felt now closed over him.
``The unloader!'' cried Steve. ``It's caught me! It's caught me!''
\gutchapter{CHAPTER XIV}
\section*{\raggedright STEVE SAVES THE CAPTAIN}
\textit{Fortunately} for Steve Rush the load scooped up by the unloader, chanced
to be a light one, only a few tons being in the scoop itself. That left
him head room so that he was not crushed against the upper side of the
giant shell. Still, his quarters were cramped and the sensation was, if
anything, more trying than had been that when he found himself alone in
the waters of Lake Huron.
``I'm done for this time, I guess. Hello, there! Stop the machine! I'm
caught!'' he shouted.
In the groaning and creaking of the great crane his cries for help were
unheard. Steve felt himself being borne swiftly through the air. Up, up
swung the great shell, swaying dizzily from side to side after it left
the deck of the ship. As it passed out of the hold Steve uttered a shout
louder than the others. He was not frightened, but, as was quite natural
under the circumstances, he wanted to get out of his unpleasant
predicament.
Bob Jarvis, who was at the rail, heard the cry. He divined the truth
instantly. Springing to an open hatch he leaned over, bellowing out the
name of his companion into the hold. There was no response. Bob did not
believe there would be.
``Stop it! Stop it!'' he shouted.
It is doubtful if the crane man heard, and if he did he failed to
understand, for the big shell kept on mounting to the top of the
trestle.
``What's the matter!'' demanded the mate. ``You're enough to raise the
dead.''
Jarvis did not stop to answer. He sprang for the side of the ship,
leaped over the rail, and, catching the sides of the ladder, shot down
to the pier without touching a single rung of the ladder. The instant
his feet touched the pier the lad darted off to the trestle. A cleat
ladder extended up the side of the trestle to the top. Bob ran up it
like a real sailor and rushed over the ties to the place where the train
was being loaded for the furnaces.
In the meantime, Steve Rush had been hoisted to the top. He knew what
was coming. The lad braced his feet and shoulders against opposite sides
of the scoop, hoping thereby to hold himself in place. He had forgotten
that the shell would open up at the proper moment in order to discharge
its load---would open up so wide that not even a fragment of anything
would be left within it.
Suddenly the great jaws of the shell opened with a crash and a bang.
There followed the roar of rushing iron ore as it dropped into the
waiting ore car on the track.
Rush dropped like a stone. He landed in the railroad car, half buried
under the ore, dazed and bleeding from the sharp pieces of ore that had
hit him on the head during his descent.
``Hey there, stop it, stop it!'' shouted Jarvis, running toward the spot
as the crane was swinging the scoop off toward the ship for another
load.
``Stop what?'' demanded the foreman of loading.
``You've dumped a man from that scoop! Which car was it?''
The foreman laughed easily.
``I guess you must be crazy.''
``Which car is it, I say? Answer me quick. He may be killed, or------''
``That's the car right there, the last one filled and------''
But Bob was bounding toward the place with desperate haste.
``Steve! Steve!''
``Ye-yes, I'm \textit{it} again,'' answered a muffled voice, dragging himself from
the ore, shaking the dirt from him.
``Look out for the shell! It'll be on you again before you know it,''
warned Jarvis. He had heard the creaking and groaning of the machinery,
sounds, which told him the big scoop was on its way upward again with
still another load of the red ore.
Rush staggered to the edge of the car.
``Jump!'' commanded Bob.
Steve did so, not knowing where he would land, but with perfect
confidence in his companion's presence of mind. No sooner had the lad
cleared the car than a load of ore was dumped on the spot where he had
been standing but a few seconds before.
Bob grunted as the heavy body of Steve Rush landed full in his arms,
causing the former to sit down heavily on the trestle with the dirt from
the dumping shell, showering over them.
``Good for you, Bob! You saved my life. Let's get out of this place.''
``I am perfectly agreeable to that. How do we get down?''
``There are two ways. One is to jump off and the other is to go down the
ladder. The latter is the way I'm going. Perhaps you prefer the other,
judging from your past performances as the horsemen would say. You have
made some pretty good records as it is.''
Bob made for the ladder, followed by Steve. When the two boys climbed
over the rail to the deck of the ship, the first mate gazed at them in
astonishment.
``I thought you were down in the hold, Rush.''
``So I was,'' laughed the boy.
``What did you come out for?''
``I couldn't help myself. I went up in the scoop, which caught me when
the lights went out down there. Something is the matter with your
electric arrangements down there, I guess.''
Mr. Major gasped.
``You don't mean you went up in that thing?''
``I guess I do.''
``He got dumped on an ore car,'' added Jarvis by way of explanation. ``And
he lives to tell the tale.''
``Get down in the hold. The ship is listing to port. They are taking too
much out on that side. Jarvis, you run back and tell the engineer to
have his electrician find out what is the matter with the lights in the
hold. Look out for yourself, Rush, this time. I am beginning to think
you are a hoodoo.''
``And I am beginning to hold the same opinion,'' answered the Iron Boy.
``If you keep on we won't be able to get a sailor to ship on the same
craft with you.''
``I don't know that I should blame them much for feeling that way.
Trouble is tied to my heels, but somehow I manage to get through on a
pinch,'' laughed the boy, hurrying for the stairway that led down into
the entrance to the ore hold.
The ship was fully unloaded at midnight. All hands were dirty, dusty and
tired when they started aft to wash up and get ready for bed.
``Where's that soogy barrel?'' yelled one of the deck hands, meaning the
receptacle holding hot water, well soaped, from which the men filled
their basins for washing.
``It's down in the engine room being steamed out. There's another one
down in the lazaret. We'll fetch it up and have it filled before those
lubbers down below get the old one ready.''
``We'll help,'' cried Steve. ``Come along, fellows. I guess the whole crew
ought to be able to get the barrel up without calling any of the dock
hands to help us.''
They started away, laughing, and the barrel was hoisted from the lazaret
or storeroom near the stern of the vessel, quickly filled from a
hot-water pipe and a good portion of the contents distributed among the
men.
In another hour all hands save the anchor watch were sound asleep, the
captain with the stoicism of the sailor, sleeping as soundly as the
rest, notwithstanding the fact that he might wake up in the morning
shorn of his command, a disgraced man.
Instead, on the following morning the ``Wanderer's'' master received a
message from Duluth ordering him to report immediately for a hearing. He
was instructed to bring with him certain men of his crew. There was no
time to be lost. Without waiting for breakfast the captain ordered Mr.
Major, the first mate, the Iron Boys and the wheelman on duty at the
time of the collision to make ready to accompany him to Duluth at once.
The message further stated that the ship would be taken to Duluth for
survey and repairs by a master who was then on the way to Conneaut.
The party got away within a few minutes, the second mate being left in
charge, and thirty minutes later they were on their way to the north.
The examination took place that evening immediately after the arrival of
the officers and men from the ``Wanderer.''
The examination was to be a strictly company examination, but the
government officers in charge of the licensing of pilots on the Great
Lakes were on hand to listen to the testimony and to decide whether
further investigations were necessary. Mr. Carrhart and the
superintendent of the line of steamships belonging to the company were
present to take an active part in the investigation.
Captain Simms was the first witness called. He gave his version of the
accident, explaining the position of the ship, the course it was sailing
on at the time and all other facts in his possession. The fact that he
was on duty at the time, and that the ship was sailing under reduced
speed, was a point in his favor, though it did not by any means serve to
relieve him of the responsibility for the accident.
``Who was on the bridge at the time of the accident?'' asked Mr. Carrhart.
``Stephen Rush. Jarvis was on watch in the forepeak.''
``We will hear Rush next,'' said Mr. Carrhart.
The Iron Boy was called in from an adjoining room, where the witnesses
had been placed. When a witness finished his testimony he was permitted
to sit down in the room and listen to the proceedings. This Captain
Simms did. Steve took his place in the witness chair.
``You were on the bridge watch on the night that the `Wanderer' collided
with the `Macomber,' were you not?'' asked the superintendent, who was
conducting the examination.
``Yes, sir.''
``State what occurred.''
Steve, in a clear, firm voice that carried conviction with it, related
briefly and tersely all that he knew of the collision. He omitted his
experience in drifting ashore, but a few questions from Mr. Carrhart
served to draw out that most interesting recital. All hands listened
attentively.
Each face, as the narrative proceeded, expressed silent admiration for
the wonderful pluck and endurance of the Iron Boy. But his hearers did
not feel surprised at what he had accomplished after they had studied
the firm set of the lips, the square-cut jaw and the clear, steady eyes.
``You had sighted the side lights of the `Macomber' some time before the
collision, had you not?''
``Yes, sir; about half an hour before the crash came, I should say,
roughly speaking.''
``What was the position of the two ships?''
``I don't know that I can explain it so that you would understand. I can
draw a diagram of it if you wish.''
``Do so.''
Rush quickly outlined the position of the two ships on a pad of paper
and handed it to his questioner.
``Do you know what the course of your ship was?''
``Not so that I could name it. I would know if I had a compass---I mean I
could point it out.''
The superintendent called for a compass card, which a clerk brought from
his office. Steve studied it a moment, turning the card around until he
had placed it in the desired position.
``This is where we were, up to the time the fog came down and we couldn't
see anything more,'' he said, placing a finger on a point on the card.
``But you were on the bridge. How could you know this?'' demanded the
questioner.
``I was watching the bridge compass, trying to learn something about it.
You see, this is my first experience on a ship and I was anxious to
learn all I could.''
``Then your course was south-south-west-one-half?''
``I don't know, sir. The little mark on the compass rim was on the point
that I have indicated, previous to the time the fog settled.''
Thus far the lad's testimony had corroborated all that the captain had
said.
``Have you had any talk with Captain Simms as to what you should testify
to?'' interrupted one of the government representatives.
``Certainly not, sir,'' answered the boy flushing. ``Captain Simms is not
that kind of man. He expects me to tell the truth, and that is what I am
trying to do.''
``We understand that, Rush,'' interposed Mr. Carrhart, soothingly. ``You
are giving us some valuable information. The gentlemen merely wish to
get at all of the facts.''
``Now, Mr. Rush, let me understand this clearly. You say that the course
was south-south-west-one-half just before the fog settled?''
``Yes, sir, if that is the course indicated by that point,'' again placing
his finger on the compass card.
``Am I to infer then that the course was changed after the fog came
down?''
``Yes, sir.''
``Ah!''
The spectators straightened up at this. Their faces were grave. An
important piece of evidence had been brought out. It might be against
Captain Simms, or it might be in his favor. All depended upon the boy's
further testimony.
``What was the course after the change?''
Steve again pointed to the card.
``We swung over to this point.''
The superintendent and the government representatives examined the point
indicated by Steve very carefully.
``South-south-west flat?''
``If that is it, yes sir.''
``Captain, you may answer where you are. Did you change your course as
indicated by Rush?''
``I did. The boy is right. He hasn't eyes in his head for nothing. He
sees more than any one else on my ship does.''
``Did you think what the reason for that change of course was?'' demanded
the superintendent, again turning to Steve.
``I thought it was to make sure that we should clear the other ship.''
``Yes; according to the position of both vessels, the `Macomber' had the
right of way,'' interjected the captain. ``I changed the course to clear
them, and I should have done so. I don't understand, yet, why I did
not.''
``Why did you not tell us of this in your testimony?''
``I did not think of it.''
``Even though it was in your favor?''
The captain nodded.
The captain of the lost ``Macomber'' was called in.
``What course was your ship steering when the collision occurred?'' he was
asked.
``I supposed it was the course as indicated on the report made by me.''
``You were in your cabin asleep?''
``Yes, sir.''
``Who was on duty in the pilot-house?''
``The mate and the wheelman.''
``They were lost?''
``They were.''
``You know of no reason why they should have changed their course so as
to throw your ship squarely in front of the 'Wanderer'?''
``No earthly reason.''
``They were thoroughly capable and experienced men?''
``Yes, so far as my observation went.''
``You admit that the course of your ship was changed, do you not?''
``If what the young man and Captain Simms say is true, our course must
have been changed. I cannot but think the mate must have lost his head,
or else failed to note the position of the compass while he was busy
peering ahead. That is probably the explanation, the wheelman forgetting
himself in looking ahead also. He knew there was a ship under their
bows; both knew it and they were naturally anxious.''
``You would not have mentioned this had not the young seaman Rush brought
it out?''
``I might not have, because I did not know it. It puts the matter in an
entirely new light.''
``You admit, then, that your vessel was in the wrong?'' interposed one of
the government officials.
``I am obliged to, granting that the statements we have heard are
correct, and I have no idea that they are not. While I am responsible
for the safety of my ship, I do not see how I can be held accountable
for the disaster. I did not know there was a fog and no word was brought
to me to that effect. A man must get sleep at some time, and what better
time than when the skies are fair and the sea is calm?''
The officials cleared the room, after which they went into executive
session with the government men. Their discussion lasted little more
than half an hour. The two captains were then sent for, the witnesses
being allowed to enter the room also.
``Captain Simms,'' announced the superintendent of the steamship line, ``we
find you free from all blame in this matter. You did all that you could.
You let your ship swing off sufficiently to have cleared the `Macomber';
you were under reduced speed, and you were at your post where you should
have been under the circumstances. Besides this, you and your crew did
heroic service in rescuing the men of the ill-fated ship. You lost two
of your own men in so doing and nearly lost a third. Especial credit is
due to Seaman Robert Jarvis, who bravely saved several lives at the risk
of losing his own. As for you, Captain,'' he added, addressing the master
of the ``Macomber,'' ``I am sorry to say that we shall have to lay you off
for sixty days. While you were not physically responsible for the loss
of your ship, you are morally responsible. Had you been at your post,
and had there been no errors of judgment on your part, you would have
been freed from blame. At the expiration of your suspension you will no
doubt be assigned to another ship. The government officials here concur
in both decisions. They agree that Captain Simms is wholly blameless for
the disaster.''
Captain Simms did not smile. His face was grave. He was sincerely sorry
for the other captain. He knew how easy it was for a man to lose his
place in the line through no immediate fault of his own. Simms himself
might have been in the position of the other man had it not been for one
keen, honest, observant boy.
``Gentlemen, I wish to say a word,'' announced Mr. Carrhart, rising. ``I
wish to say that this board owes a vote of thanks to Seaman Stephen
Rush.''
``We do,'' assented several voices at once.
``I know Mr. Rush and his friend Jarvis very well, and I have watched
their careers for the last two years. They always do well whatever is
set before them to do. Had it not been for Rush's very explicit
testimony---for his keen observation, we probably should not have gotten
at the facts, and a great injustice might have been done to Captain
Simms, though that would have been largely his own fault. Captain Simms,
you will proceed to Detroit in the morning and take charge of the
`Richmond,' our new steel, ore-carrying steamer, which is ready to go
into commission at once. I presume you will take these two young men
with you on the new boat?''
``I certainly shall if they will ship with me,'' answered Captain Simms
promptly. ``I wish I had some more men like them. Even half as good men
would do very well.''
The captain stepped across the room and grasped Steve by the hand.
``I owe this whole business to you, Rush, and you bet I won't forget
it!''
\gutchapter{CHAPTER XV}
\section*{\raggedright AT THE WHEEL}
``\textit{Isn't} she a beauty!'' said Steve admiringly, as, with Jarvis and Captain
Simms, he stood on the dock at the shipyards in Detroit, gazing up at
the new steamer, the finest ship of her kind plying the lakes.
``She is,'' agreed the master proudly, ``but I'm not forgetting that I
might not have had her if it hadn't been for you. Let's go aboard and
look her over.''
All hands climbed the ladder to the deck. Besides the usual two
deck-houses, fore and aft, there was another house just aft of the
forward house. This was the guest or passenger dining room where the
guests of the line would be served with their meals. After admiring this
the men went forward. The captain's quarters were handsomer than
anything the men ever had seen before.
``The only trouble with this outfit up here is that it's bigger and I'll
be lonesome up here,'' laughed the captain.
``We'll come up and visit you,'' returned Jarvis.
``I hope you will, at that,'' answered the skipper heartily. ``I don't
know of any men I would rather have in my cabin. I'll tell you what you
do. You both come in every evening when we are not otherwise engaged,
and I will teach you navigation.''
``Thank you very much, sir,'' replied Rush. ``That is exactly what I wish
to learn. Of course, I cannot learn it all while I am on the lakes, but
I shall be able to get a general idea of it.''
``You will learn it quickly enough. After you have been on these lakes
one season you'll know more about these waters than a whole lot of men
who have been drilling up and down here for the greater part of their
lives. We will go back and look over your quarters now.''
The room assigned to the boys was even more attractive than had been
their quarters on the old ship. The room was large and cosily furnished,
and the Iron Boys were delighted with it.
The next thing was the selection of a crew. Captain Simms, with the
authority of the officials of the line, decided to ship his old crew,
which was done as soon as the ``Wanderer'' reached Detroit on the
following day. The new ship was under orders to proceed to Duluth for a
cargo of ore.
The up trip was uneventful, the efforts of all hands being devoted to
shaking the new vessel down and getting acquainted with her. The
``Richmond'' proved herself to be all that was expected of her. She
handled easily and well.
During the three days' trip up the lakes, the boys began their study of
navigation. Their first work was to learn to box the compass; that is,
name every point on the compass. Steve, with his usual aptness,
committed the card to memory in one night. Bob was not very far behind
him. Then they took up the study of the theory of navigation, working
out positions by moon, stars and sun, all requiring more or less
mathematical proficiency. Rush proved himself an apt pupil, and he had
made a good start by the time they reached the ore docks in Duluth.
The lads found a few hours time in which to run home to see Steve's
mother, and at daylight on the following morning the ``Richmond'' backed
from her slip and turned her trim bow toward the waters of Lake Superior
once more.
``I am going to put you two men on the wheel,'' announced the master, on
the morning of the second day out.
``Steering the ship?'' questioned Jarvis.
``Yes. You will find it easy work, but you will have to pay strict
attention to business.''
The eyes of the Iron Boys glowed with pleasure. They took a trial watch
early that forenoon under the direction of the captain, who first
explained the operation of the wheel. Unlike the old style steering
wheels, this one was operated by crude petroleum instead of by ropes and
chains running over pulleys. Turning the wheel forced the oil through a
little half-inch pipe. The pressure thus obtained opened a valve in the
engine room and set the steam steering gear at work. The ship, by this
modern method, could be steered with a single finger.
``Wonderful, wonderful!'' exclaimed the boys, when they fully understood
the operation. Their knowledge of it was not complete until they had
made a journey back to the engine room to watch the steam steering gear
work there as the wheel was turned in the pilot-house.
Then there was another wonder that they were instructed in, the
electrical equipment of the ship. All the running lights were lighted by
electricity from the pilot-house. Then there were three methods of
blowing the whistle situated aft of the pilot-house. First, there was
the usual whistle cord; then there was a lever some two feet in length,
that pulled the wire attached to the whistle valve. But the most
remarkable of all was an electric button whistle. A pressure on this
blew the steam whistle. A long pressure blew a long blast and a quick
pressure a short blast.
``Electricity plays an important part in the world's affairs to-day,''
said Captain Simms, noting their keen interest. ``You see we have
wireless equipment, too.''
``Why isn't it working?''
``It will be when we get some one to operate it. I understand that the
line is going to ship an operator at the Soo. I don't know whether it is
a good thing or not. Too handy for the officials to say, 'Why did you do
that?' or `Why didn't you do this?' Well, it's always possible that the
thing won't work when you want it to. I guess we can see to that.''
The boys nodded. Steve was at the wheel. He soon got the knack of
keeping the vessel on her course, but found that watching the compass
card so steadily made his head ache. Still, it was fascinating work. The
helmsman sat on a high stool, both arms resting on the wheel between the
spokes, his eyes looking over the wheel and down into the binnacle. A
glance up showed miles of sea ahead with the gently rising and falling
bow of the ship in the foreground. There was a consciousness of power as
the helmsman gently turned the wheel this way or that. The great ship
obeyed his slightest pressure. Glancing back through the rear windows of
the pilot-house the stern of the ship swung in response to the turn of
the wheel with a crack-the-whip motion.
The skipper, noting Steve's glance at the swinging stern, nodded.
``That is what you must look out for when in close quarters. You see, you
are so far forward here that you can scarcely believe what a wide circle
that other end will make---I should say sweep. It doesn't necessarily cut
circles. In entering harbors you must measure your distance with your
eyes and know how far you can turn your wheel without having the stern
of the ship smash into a breakwater, or crash in the side of some other
vessel to the right or left of you.''
``There is much to learn. I can see that.''
``Sailing the lakes is done by instinct largely. If a man's cut out for
the business he makes a go of it. If he isn't, some dark night he misses
his way and lands on a hidden reef somewhere. Then, presto, he's out of
a job, and maybe worse.''
``When do we reach the Soo?'' interrupted Jarvis.
``This evening. Rush will be at the wheel about that time, and you had
better be up here, too, Jarvis. You can't become too familiar with the
ports and the lights. Do you know how to read buoys?''
``No, sir,'' answered the boys.
``It is very simple. When you are entering port red buoys, with even
numbers, are left to your right hand or starboard. Black buoys with odd
numbers are left to the left hand or port. That's the rule the world
over.''
``But,'' objected Jarvis, ``suppose it's night and you can't see the buoys.
What are you going to do then?''
The captain laughed heartily.
``Lights, my boy. Channels are lighted at night, so you can't go wrong;
but a good navigator will take his ship through any place without a
light to guide him. I want you boys to learn every one of the
ranges------''
``What is a range?'' interrupted Bob.
``Guide lights,'' spoke up Steve quickly. ``They are the lights on shore,
either lighthouses or buoys, to show you how to lay your course.''
``That is the idea,'' agreed Captain Simms. ``Let's hear you box the
compass while we are here alone, Jarvis.''
Bob went over, taking a look at the compass.
``Why do you do that?''
``I wanted to see whether we were at the north pole or the south pole.''
``I guess you would know it if you were---that is, you would be pretty
certain that you weren't navigating the Great Lakes. Go ahead now.''
Jarvis shut his eyes and began reading off the points of the compass,
making only one error in his reading.
``That is fine,'' announced the skipper. ``I'll guarantee there isn't a man
in the ship's crew, outside of the first mate, who can do it so well. Of
course, I am excepting Rush and myself. Rush does everything well.''
That night Steve took his regular trick at the wheel at eight o'clock.
Of course, Jarvis was there, too, as were the captain and the first
mate. They were nearing the Soo, as they could see from the lights.
``Let's see, you boys have not been through here, have you?''
``We were below decks the other time, sir.''
``Oh, yes, I remember. We will take the Canadian locks this time. The
Canadian locks are on the left and the American locks on the right, but
the latter are too short to hold a boat as long as this one, so we are
obliged to take the Canadian side.''
``Why do we have to lock through?'' questioned Jarvis.
``To get around the rapids, and for the further reason that Huron lies
lower than Superior. This is Whitefish Bay. The light that we have just
dropped to starboard is Whitefish Point Lighthouse. Rush, do you see
that red light yonder?''
``Yes, sir.''
``Point on it.''
``I can't see the bow of our boat so as to tell whether I am pointing on
the light or not.''
``I'll fix that.''
The captain pressed a button and a ray of dull, ghostly light appeared
just beyond and over the bow.
The lads uttered exclamations of amazement.
``What is it? How did you do it, sir?''
``That, lads, is a guide light on the end of the pole that answers for
the bowsprit. The light is there for the purpose of giving you a guide
to steer by in narrow places.''
Lights began to spring up ahead, until there was such a confusion of
them that neither boy could make anything out of them, but the steady
eyes of the captain picked out the lights that he wished to find without
the least difficulty.
``Do you hear the roar of the rapids in the St. Mary's River?''
``Yes; we hear them.''
``Those green lights way over yonder are on the American locks. Now port
your helm and steer for that white light standing high above the rest.
Are you on it?''
``On the mark, sir,'' answered Steve.
They continued on this course for ten or fifteen minutes, when the
captain ordered the wheelman to starboard his wheel. This threw the bow
to the left, sending the boat across the bay on a diagonal course.
``Why don't you go straight in?'' asked Jarvis.
``We should land high and dry on the rocks if we did,'' answered the
skipper, with a short laugh. ``Others have tried that very thing. The
hulls of some of their ships are down there under the water now.''
The boys began to realize that navigating the Great Lakes required a
great deal of skill and knowledge.
``There is a ship in the locks now,'' announced Captain Simms.
Both boys gazed into the night, but they could see no ship. The master
signaled the engine room to slow down, explaining, at the same time,
that they would have to drift in slowly and stop until the other boat
got out.
The channel began to narrow as the master directed the wheel this way
and that until they found themselves in a walled-in channel that led
directly to the locks themselves.
``Snub her!'' commanded the captain, leaning from the pilot-house window.
A ladder was shoved over the side of the moving ship, a man on either
side of it on deck pushing it along so that it might not be dragged.
Quick as a flash a sailor sprang on the ladder, and, grasping the side
pieces, shot down to the dock on that side, a distance of some twenty
feet. Following came others, all getting down in the same manner. It was
a dangerous thing to do and excited the wonder and admiration of the two
boys in the pilot-house.
``If I were to try that I would be in the water,'' laughed Rush. ``It is a
good thing for me that I am at the wheel, for I wouldn't be able to
resist trying that experiment.''
Hawsers were cast over from the deck, and these, the men who had gone
over the side, twisted about snubbing posts. At the same time the ship's
propeller began reversing slowly at a signal from the captain. The ship
came to an easy stop. The skill with which it had all been done, made a
deep impression on the Iron Boys.
A few moments later the gates of the locks opened and the other steamer
moved slowly out. So close did they pass the ``Richmond'' that some of the
men reached out and shook hands across the gulf, while the two captains
held a brief conversation. Then the ``Richmond'' let go her moorings and
moved slowly into the Canadian locks. The gates swung to behind them,
the water began rushing from the other end of the locks and the ship
rapidly settled until her decks were level with the dock beside which
she stood. The men who had gone over the side now stepped aboard and
hauled in the hawsers after them.
``Marvelous!'' breathed the Iron Boys.
``Slow speed ahead,'' commanded the skipper. ``We are now on the Huron
level. Here comes your relief. I hope you boys get a good night's
sleep.''
``Thank you, sir; good night,'' answered the lads, starting for their
cabin. It had been a most interesting evening for them.
\gutchapter{CHAPTER XVI}
\section*{\raggedright THROUGH THE ROCKY CUT}
FOUR long and two short blasts roared from the whistle of the
``Richmond.''
It was the private signal of Captain Simms. The ship was bearing down on
Port Huron and was at that moment at the mouth of the St. Clair River.
The skipper stepped to the door of the pilot-house with megaphone in
hand.
``This is where I live,'' he explained. ``My wife always comes out to see
me as we pass. See the light there, in that cottage on the river bank?
Well, that's where I live when I'm not steamboating. There she comes.''
Through the moonlight Steve saw a woman running down to the edge of the
water.
``How are you, John?'' called her pleasant voice through a megaphone.
``I'm well; how are the folks?''
``They're all well.''
``Any news?''
``Nothing except that Betty has six pretty white chickens and she's
terribly cross.''
``Put her in the soup,'' suggested the captain.
Just then a little white-robed figure appeared at an upper window of the
captain's home. In her hand the little one also held a megaphone. It
was the captain's twelve-year-old daughter, Marie, the apple of his eye.
``H-e-l-l-o P-Pa-pa-a-a,'' came the greeting in a childish treble.
``Hello, Marie!'' bellowed Bob Jarvis from the rail aft of the bridge.
``Who are you? I don't know your voice.''
``I'm Bob Jarvis, but you don't know me.''
``Hello, Bob. Yes, I do. My papa wrote to me about you. Where's Steve?''
There was a laugh that rippled from one end of the deck to the other.
``Never mind him; he is steering the ship. When are you coming out with
us? Come along and we'll have a lot of fun.''
``I don't know. When Papa says I may. When may I come, Papa? And you
haven't said a word to me yet. You'll be gone in a minute.''
``How could I? You haven't given me a chance to get a word in edgeways.
Port your helm a little,'' he added, in a lower voice to Rush.
``Port a little,'' answered Steve.
``When, Papa?''
``Perhaps the next trip. I will send you a letter from down the line.
Jennie, can you go back with us if I stop for you on the up trip?''
``I'll see. If I can do so I'll run up the red flag on the staff. If you
see that you may stop. If not, you will know we can't get away that
trip. I've got to attend to my early canning, you know.''
Captain Simms grumbled something outside the megaphone, that sounded
something like, ``Shoot the canning!''
``Good-bye,'' came two voices, sounding faint and far away on the soft
night air, one being a woman's voice, the other the thin, childish
treble of a little girl.
``Head on that bright light low down there,'' directed the skipper, with a
last lingering look back toward his home. ``That's the worst of this
business. A fellow gets about a five-minute look at his home and family,
once a month or so. I'd rather be sitting on my front porch to-night
than steering a ship through this rocky river.''
``Is that a light-house that I am steering for?''
``No; that's an inspector's cabin. Starboard some.''
``Starboard some,'' repeated the helmsman.
``All ships have to report as they go by. You will hear him call when we
get abreast. Those fellows never seem to sleep.''
``It must be a lonely life for a man out there.''
``It is, and------''
``Ship ahoy. What ship is that?'' bellowed the inspector through his
megaphone.
```Richmond' from Duluth with ore.''
``The what?''
``'Richmond'!'' roared Bob from the lower deck.
``I don't catch it.''
``Six o'clock,'' howled Jarvis with his hands to his mouth, at which there
was a loud laugh from the ship's company.
``Steamer `Richmond,''' shouted the captain. ``Why don't you open your
ears? Think we can stand here yelling like wild Indians all night?''
The inspector did not answer. From past experience he realized the
futility of an argument with a lake captain.
``This is the most dangerous navigating of any place on the lakes, Rush,''
said the skipper. ``The bottom of our ship is only three feet from the
bottom of the cut at this minute. Swerving six feet either to the right
or left out of our course would put us hard and fast on the rocks. We
should block the channel besides running the risk of breaking the ship's
back. Steady!''
``Steady, sir.''
``Remember, I am talking to the rudder. I keep that rudder in my mind
every second of the time. I can see its every movement. I don't know
there is such a thing as a steering wheel when I'm navigating like this.
Port a little.''
``Port a little, sir.''
``Now head for that range light up on the hill there. This cut, known as
Rock Cut, was built by the government at great expense. Hold your course
as you are until you round the bend in the cut there, then head on a red
light that you will see high up on the rocks. Get your funnel back there
in range with the white light on the hill you see to the left. You will
be exactly in the channel then. Keep in the middle. I have to go to my
cabin for a moment. I think I can trust you. Remember, the channel is
narrow and you must keep well within it.''
``I will, sir.''
Steve was left alone in the pilot-house. As he was steering by range
guides alone, now, he did not have to watch the compass. All the windows
of the pilot-house had been let down so that he had an unobstructed view
all around.
``I'm running the ship,'' breathed the lad. ``I don't know who's taking the
biggest chance, myself or the captain.''
Though the Iron Boy felt the responsibility of his position, he could
not help the little thrill of triumph that ran through him. He was far
up in the air with no one save the watch down in the forepeak near him.
The night was bright and glorious, the most peaceful scene he had ever
gazed upon. But Rush did not devote much thought to the peacefulness of
his surroundings. His mind was too thoroughly centred on his work.
The ``Richmond,'' sailed majestically around the bend in the cut, Steve
glancing back over the decks to see that his funnel was coming in line
with the range indicated by the captain. As Rush looked ahead through
the open pilot-house window again his heart fairly leaped into his
throat. Two eyes, one red the other green were blinking at him right in
his path dead ahead.
``It's a ship!'' he exclaimed. ``I don't dare pass it here. I don't know
whether there's room or not. What shall I do?''
The Iron Boy's quick mind solved the problem in a flash. Springing to
the pilot-house telegraph he swung the indicator over to the words,
``Half speed astern.''
The ship began to tremble under the impact of the reversing propeller.
Grasping the whistle lever Steve blew five short, sharp blasts, then
taking his place at the wheel he calmly kept the vessel in her course,
the other ship bearing down on him whistling as if the whistle lever had
been wired down.
The reversing of the propeller had not been lost on Captain Simms. He
knew instantly what it meant when he felt the trembling of the vessel.
Then came the danger signal---five sharp blasts on the whistle.
The captain was out of his cabin on the run taking the stairway to the
bridge three steps at a time. By this time Rush had thrown the telegraph
indicator over to ``full speed astern.'' He was watching the stern to see
that it did not swing out of the channel, then turning to see what the
vessel ahead of him was doing.
What had caused him to so suddenly reverse the propeller was not so much
the narrowness of the channel, but rather a light that was placed well
out from the shore line on his side. It was a white light, and, while he
did not understand the meaning of it, he knew that it had been placed
there as a warning to ships to keep well outside of it.
The other boat was coming to a stop also, but by the time Captain Simms
reached the pilot-house the bows of the two ships were so close together
that it seemed as though they might crash together. One swift,
comprehensive glance told the captain everything. He noted that his
vessel was reversing, that the pilot was keeping her in the channel and
that the other ship was coming to a stop.
Without a word to Steve he grasped his megaphone and sprang to the
window.
``Choke her down, you fools! Do you want to run us under?''
``Get out of the way yourself! Why didn't you blow your whistle? You saw
that buoy there. You have seen it for the last half hour. You knew you
ought to have given warning before you got into the cut here.''
``What does that buoy mean?'' demanded Captain Simms.
``A coal barge was sunk there this morning.''
The two vessels met with a heavy bump that set everything rattling on
board both ships, but the shock was not sufficiently severe to do any
damage to either.
``Back up, you fellows, unless you want us to push you out!'' commanded
Captain Simms.
In the meantime, after the shock, Steve had stepped to the telegraph and
swung the indicator to the word ``Stop!''
The two captains hurled language at each other for the next two minutes,
but the other skipper grew tired of it first. He gave the order to
reverse propeller. The up-bound boat began to retreat slowly.
``Slow speed ahead,'' commanded Captain Simms.
The master was leaning from the pilot-house window, megaphone in hand,
ready to roar at the other skipper at the first opportunity. But there
was no good excuse for him to do so. After backing down stream
sufficiently to make passing safe, Captain Simms gave his whistle lever
a jerk, sounding one sharp blast, meaning that he would meet and pass
the other vessel on its port side.
The ``Richmond'' slipped by at a little higher speed than was safe, her
sides scraping the paint off the other boat in spots.
``I ought to report you, you lubber!'' roared Captain Simms in passing.
``You ain't fit to command a mud scow. I've got a kid on this boat who's
a better captain, after half a cruise, than you'll be if you cruise all
your life.''
The captain jerked the telegraph indicator to ``three-quarter speed
ahead'' with such violence that it threatened to tear the indicator
chains from their hooks. Then he turned to Rush.
``Steve, much obliged,'' he said. ``That's the second time you saved the
ship. I owe you another one for that. Unless I am greatly mistaken,
you'll be trotting around with a master's license in your inside pocket
by the time you are twenty-one. Steady there.''
``Steady, sir,'' answered the boy at the wheel.
\gutchapter{CHAPTER XVII}
\section*{\raggedright THE BLOW IN THE DARK}
\textit{They} had passed out through Lake St. Clair as eight bells rang out.
Steve relinquished the wheel to the next watch and bidding good night to
the captain started back toward his quarters.
The lad made his way back over the deck, strolling slowly along,
enjoying the night and thinking over the events of the evening. As he
reached the after deck-house he halted, leaning against it looking
forward and watching the gentle rising and falling of the upper works
forward.
``It is almost fascinating enough to make one want to spend his life on
board a ship,'' mused the Iron Boy. ``Well, I must turn in. I------''
He did not finish what he was about to say. A crushing blow was dealt
him on the back of the head, coming from the deep shadows on the
starboard side of the after deck-house.
Steve staggered forward, then fell face downward on the steel deck of
the ``Richmond.''
Sailors found him there, half an hour later, unconscious. No one knew
what had happened. The captain was notified at once and he, after an
examination of the boy, decided that Steve had fallen against a steel
hatch and had given his head a severe bump. They worked over the lad for
nearly an hour before getting him back to consciousness. He had been put
to bed, and Bob was detailed to sit by and watch his companion, which he
did with solemn face. Steve fell into a deep sleep from which he did not
fully awaken until morning.
He was lame and sore from head to feet. Bob was asleep on the edge of
the berth and the ship was rolling heavily. Without waking his
companion, Rush got up after much effort, dressed himself, and,
supporting himself by keeping his hands on the woodwork, made his way
outside. Day was just breaking.
Steve leaned against the deck-house in the same position that he had
been occupying on the previous night when he was struck.
The captain, at that juncture, came along on his way to breakfast.
``Hello, Rush,'' he greeted, halting. ``How do you feel?''
``All knocked out.''
``That's too bad. Come in and have some breakfast. You will feel better
after that.''
``I do not think I want any breakfast, sir.''
``Pshaw! Come along. By the way, you had a nasty fall last night, didn't
you?''
``I should say I did.''
``How did you happen to slip?''
``I didn't slip, captain.''
``You didn't?''
``No, sir.''
``Then how did you happen to crack your head on a hatch cover?''
``How was I lying when you found me?''
``They said you were lying on your face.''
``If that was the case, I couldn't very well have bumped the back of my
head on a hatch cover, could I?''
``That had not occurred to me before. See here, didn't you lose your
balance or stumble and fall?''
``I fell, but it was through no fault of my own.''
``Will you tell me what did happen?'' questioned the captain with a
puzzled expression on his face.
``I think I was struck,'' answered Rush calmly.
``Knocked down?''
``Yes, sir.''
``Impossible! Who---what------?''
``I do not know any more about it than you do, sir. I was standing here
just as I am now, when I got a terrible blow on the back of my head. I
didn't know it was a blow then, but as I think it over I remember very
well. Everything grew dark about me. The next I knew I was in my cabin,
with you and Jarvis working over me.''
``What you are telling me is a very serious matter, Rush.''
``It was serious enough for me at the time.''
``Who was on the deck at the time?''
``No one, so far as I observed.''
``But, it would have been impossible for any one to approach close enough
to hit you, without your either hearing or seeing him.''
``It would seem so. Yet the fact remains that I was hit. It takes
considerable to knock me out, sir, but I got enough last night.''
``Do you suspect any one?''
``Not a person. I cannot understand it at all.''
``Well, you just keep your eyes open. If you find out who struck that
dastardly blow I'll deal severely with him. He won't be in condition to
strike any one else for some time to come.''
``I think I shall be able to take care of the man myself when I meet him
and know him,'' replied the lad, with a faint smile. ``I shall report for
duty on time this morning, so please do not put any one in my place.''
``Very well; perhaps it will do you good to be busy. Well, I'm going to
breakfast. Let me know if you get a line on this mystery.''
Steve did not answer. He stood leaning against the after deck-house,
thinking. Finally he turned with a sigh intending to go forward. As he
did so a man came out of the stokers' dining room and started to go
below. Rush halted sharply.
``Hello, Smith,'' he said. ``When did you come aboard the 'Richmond'?''
``When did you think I came aboard?''
``That's what I am asking you.''
``Mebby I'm a fish and swam out,'' answered the stoker. Smith was the man
with whom Steve had had the trouble on the first disastrous cruise.
``I shouldn't be surprised. You are equal to most anything that's out of
the ordinary. Where were you last night?''
``Stoking from six to twelve---eight bells. But------'' Smith checked
himself.
``So you came off at twelve, eh?''
``I did. But how's that your business?''
``Perhaps it may be my business. At least, I am going to make it my
business.''
``See here, young feller, be you trying to pick a row with me?''
``No; one doesn't have to pick a quarrel with you. You're always
quarreling. If I wanted to have a fight with you all I should have to do
would be to look at you and the fight would be on. I'm looking at you
now, Smith.''
The stoker uttered a half-suppressed growl of anger, started toward the
Iron Boy, then halted, opening and closing his fingers nervously.
``I'll---I'll------''
``Out with it. You will feel better after you have said it,'' urged Steve
in an encouraging voice.
``I'll break your blasted head for you------''
Smith made a jump for the Iron Boy.
Steve stepped lightly to one side, putting out his foot as the stoker
shot by him. Smith's head hit the edge of a hatch, then he sprawled
forward on the deck.
``So you're the fellow who gave me that blow in the dark last night, are
you?'' demanded the lad in a stern voice.
``I---I'll kill you for this!'' roared the stoker, raising a vengeful face
to the Iron Boy.
``You'll do it some dark night, then. You haven't the courage to face a
man in broad daylight and meet him man to man---no; I won't put it that
way, for you are no man. You're just a common tough, that's what you
are. Now get up and take your medicine, for you're going to get a
walloping that ought to last you longer than the hose bath did.''
Smith sprang to his feet and rushed at his young antagonist. He did not
reach Steve, however. The fellow suddenly received a blow under the ear
that sent him spinning and tumbling over among the hatches that extended
above the deck some two feet at their highest point.
But Steve had not delivered the blow. He had not even raised his hands,
though he was standing in position ready to meet the charge of the tough
stoker.
``Get up, you hound!'' roared Captain Simms.
It was he who had delivered the blow. He had emerged from the mess room
just in time to see the stoker's enraged face over Steve Rush's
shoulder. The captain understood instantly what Smith was about to do.
The skipper took two quick strides forward and his powerful fist smote
the other man a terrific blow.
The stoker leaped to his feet and went for the captain, now enraged
beyond all control. But he had reckoned without his man. The skipper
knocked the angry stoker down almost before the latter could raise his
fists.
``Never mind, Captain; I can take care of him,'' urged Steve.
``Stand back! This is my circus. What was he going to hit you for?''
``I was to blame. I goaded him into it. I------''
``Wait a minute. He hasn't got enough yet. He's coming for me.''
The captain suspended conversation long enough to give Smith a right and
left swing on either side of the head that sent the fellow to the deck
with all the fight knocked out of him, and which put him out of business
for the next ten minutes.
Captain Simms turned calmly to Rush.
``Now, what was it you were saying, my lad?''
Rush could not repress a smile.
``Nothing very much. You know Smith and myself had some trouble on the
last cruise?''
``Yes, I remember.''
``He never has gotten over being angry at me. He began saying
disagreeable things to me, and I suppose I helped the matter along by
tantalizing him. I was as much to blame as Smith was. But---but I'm sorry
you didn't let me give him what he was spoiling for.''
``He got it, that's all that is necessary,'' growled the master. ``See
here, Rush, he isn't the fellow who hit you last night, is he?'' demanded
the captain suddenly, shooting a quick, suspicious glance into the face
of the Iron Boy.
``I didn't see who hit me,'' answered Steve, truthfully even if somewhat
evasively.
``Call the first mate!''
Rush did so.
``Put that man in irons and keep him on bread and water until he is ready
to go to work and mind his own business. I've half a notion to turn him
over to the authorities for mutiny,'' said the skipper reflectively.
``Don't you think he has had punishment enough, sir?'' urged Steve.
``Yes, I suppose he has at that. Iron him, Major. It will do him good.''
The stoker woke up just as the steel bracelets were being snapped on his
wrists. Protesting and threatening, he was dragged to the lazaret, where
he was destined to remain for the next twenty-four hours in solitary
confinement, with nothing more substantial to live on than bread and
water.
\gutchapter{CHAPTER XVIII}
VISITORS \textit{on} \textit{the} ``\textit{Richmond}''
\textit{The} ugly stoker was liberated on the following day after having promised to behave himself in the future. But he held his head low when showing himself on deck, which was seldom. He never permitted his shifting eyes to meet those of Steve Rush, nor did Steve make any effort to address the man. The lad was confident, in his own mind, that Smith was the man who struck him that night by the after deck-house, but the drubbing that Captain Simms had given the fellow made Rush feel that they were now even.
On the way back the ship picked up Mrs. Simms and little Marie at Port Huron. The ``Richmond'' was on its way to South Chicago with a cargo of coal. This took them around into Lake Michigan, and many were the happy hours spent by the captain's little daughter and the Iron Boys. They played games on deck between watches, as though all three were children. Rush and Jarvis had constituted themselves the special guardians of the little girl, and she queened it over them, making them her willing subjects.
At South Chicago the ship was held up for a week because the company to which the coal was consigned was not ready to receive it. Steve considered this to be bad business policy on the part of the steamship people, and another memorandum went down in his book, to be considered in detail later on.
While at South Chicago the lads made frequent trips into the city, which they had never visited before. One afternoon they took the captain's wife and daughter to a matinee, then out to dinner at a fashionable restaurant.
It made a pleasant break in the lives of each of the four, and helped to cement the friendship between little Marie and her new-found friends.
At last the coal was unloaded. After filling the tanks with water ballast, the ``Richmond'' started away for the northward to take on another cargo of ore and once more to drill down the Great Lakes.
The water ballast did not draw the ship down to its load level, with the result that she rolled considerably.
``The glass is falling,'' announced the captain as the craft swung into Lake Superior two days later. ``I shouldn't be surprised if we had quite a jabble of a sea before night.''
``We don't care, do we?'' chirped Marie, to whom a rolling ship was a keen delight.
``Not as long as the dishes stay on the table,'' answered Bob, with a merry laugh. ``When are you going to bake that long-promised cake for me?''
``Just as soon as the cook will let me. He's always cooking something for the night watch when he isn't getting the regular meals. My, but that night watch must have an awful appetite!'' she chuckled.
``Yes, I've noticed that,'' agreed Bob. ``But you can't lay it to me. I've a feather-weight appetite. I didn't have any at all when I first went aboard an ore carrier. It beats all how quickly a fellow will lose all interest in life the first time out.''
The wind blew hard all the way up Superior, raising, as the captain had promised it would, ``quite a jabble of a sea.'' But the blow was nothing like a heavy gale. It was just a sea, a nasty, uncomfortable sea. The boys and Marie were in great good humor all the way up. Marie's mother was ill in her stateroom and the assistant cook had had an unexpected attack of seasickness.
``Nice crew of lubbers,'' growled the captain, when informed of the assistant cook's indisposition.
The ship reached Duluth at night and immediately was shunted into the slip at the ore docks for loading. After the hatches were down a huge crate was hoisted aboard with a crane. A section of the deck was opened up and the crate was let down into the lazaret. The crate was consigned to one of the company's officials in the East. No one paid any attention to the crate, and it is doubtful if any one save the captain and the first mate knew what the contents of the crate were.
Hatches were battened down and long before daylight the ``Richmond'' was on her way again. By this time the ``jabble'' had increased to a full gale. No other ship ventured out, but Captain Simms was not a skipper to be held back by the weather. He knew his ship was seaworthy and he knew full well how to handle her safely in any sea that the lakes could kick up. A full northwester was raging down from the hills and the glass was falling all the time. The ``glass'' is the sailor's name for barometer.
Steve took the wheel as they passed out, and he was obliged to give up the wheelman's stool because he could not keep it right side up under him. He dragged a platform over to the wheel. It was made for the purpose, having cross-cleats on it to enable the helmsman to keep his footing when the ship was cutting up capers.
``There,'' he announced, ``I'll stick here until the wheel comes off.''
Waves broke over the vessel continuously, striking the deck with reports like those of distant artillery. Superior was a dreary waste of gray and white. The air seemed full of the spume of the crested rollers, while the clouds were leaden and threatening.
``Look at the rainbow!'' cried Bob, pointing off to the westward.
``That ain't a rainbow you landlubber,'' jeered a companion.
``Well, if it isn't I never saw a rainbow.''
``No, it's a dog.''
``A what?''
``Sundog.''
``Bob, you certainly are a lubber,'' laughed Mr. Major. ``Didn't you ever see a sundog before?''
``Never. What are they for?''
``I don't know what they are for. I know what they do---they bring gales and storm and trouble all along the line. That's what the dogs do.''
``I think the other ships saw it before we did, for there doesn't seem to be another boat on the lake.''
``No; at least, the little fellows have taken to harbors along the coast. It wasn't the sundog, however, but the glass that warned them. You know the glass has been falling for the past twenty-four hours. We know what to expect when that happens, but we don't know what to expect when the storm strikes us. These lakes are the most treacherous bodies of water in the world. Twenty miles beyond here is the graveyard of Superior, where the hulls of more than fifty ships lie rotting on the bottom. Some of them went down in weather no worse than this. This is bad enough.''
Bob listened attentively.
``Do you ever get seasick in any of these storms?''
``Always,'' answered the first mate, in a matter of fact tone. ``If this keeps on you won't see me at mess to-day noon. You'll have to eat your dinner standing up, but not for me.''
The weather grew more tempestuous as the forenoon wore on. The scuppers were running rivers of green lake water and there was not a dry spot on the decks; even the upper works standing high in the air, were dripping with the spray that had been showered over them.
``Let her off three points,'' commanded the captain.
Almost instant relief from the incessant pounding was noticeable. The waves came aboard only occasionally, though the sea was running the same as before and the ship was rolling almost down to her rails.
``That is better,'' nodded Steve, his voice echoing in the silence of the pilot-house.
``Did it make you dizzy?'' smiled the skipper.
``No, sir. I got all over that after I fell in the hold that time. It isn't a comfortable feeling to have the floor rolling around beneath one's feet, but I am getting so that I do not mind it much. Is that a boat ahead of us there?''
``Yes,'' replied the captain, placing the glasses to his eyes. ``It's a pig, and she's having a pretty hard time of it. All you can see of her is a smother of foam in the place where the ship is. The smoke from her funnel seems to come right out of the lake.''
``Are those whalebacks safe, Captain?'' asked the pilot.
``Yes. I commanded one for two seasons. They are perfectly safe, so long as nothing happens to them.''
Steve laughed.
``That goes without saying.''
``But they are the wettest boats in the world, as you can judge by watching that fellow beating his way against the sea. They have a very thin skin and the least puncture will go through. Next thing you'll hear the hatches blowing off, and down she goes like a meteorite shot from above.''
``I don't believe I should care for them. I prefer to be high above water like this, rather than under it all the way down the lakes. If I wanted to travel on a submarine I'd ship on a real one.''
The gale was playing tunes on the braces, and the life-span running from the forward to the after deck-house was swaying back and forth. Steve gazed at it a moment then turned to the skipper.
``I never could see the use of those life-spans. If the ship goes down, I don't understand how a life-span from one end of the ship to the other, is going to help any.''
``They haven't been on long. A good many lives would have been saved if they had been. You see, the span is a rope on which travels a little swing just large enough to hold a man. Then there is a free rope running through a ring in the top of the swing by which to pull one's self along.''
``Yes, I have figured that out.''
``Then suppose that to-night, in the darkness, we were to miss our way. The compass might go bad, we might be driven out of our course and all that sort of thing, you know---and all of a sudden we might drive our bow full speed on one of those low-lying Apostle Islands!''
``Yes, sir.''
``The stern of the ship would sink low and there she would pound to pieces. That's where the men astern would find use for the life-span. By it they would be able to pull themselves to the bow of the boat and perhaps make their escape before the stern finally went down under water. They are a good thing, and you should see to it that the spans are always in working order. I have those on my ship examined every day. I------''
The captain was interrupted in what he was saying by a yell from the deck. The skipper took a quick look aft through the pilot-house windows, then sprang to the pilot-house telegraph.
``Full speed astern!'' crashed the message to the engine room.
\gutchapter{CHAPTER XIX}
\section*{\raggedright IN THE GRIP OF THE WAVES}
``\textit{Somebody} overboard!'' said the captain sharply.
``Who?'' demanded Steve, in an equally sharp tone as his relief took the
wheel from his hands.
``I don't know.''
Just then the figure of a man was seen to leap from the top of the after
deck-house into the raging sea.
Bob Jarvis had been clinging to a ladder that the chief engineer was
holding up against the whistle pipe, the valve of the whistle having
worked loose. The engineer had asked Bob to help him as a favor, which
the lad was glad to do, though that was not his department. It was a
ticklish position in which to work, and at any moment a lurch of the
ship might throw the ladder over and throw the Iron Boy into the sea. He
gave no heed to the danger of his position, for he was rapidly becoming
a true sailor.
Suddenly, as though some instinct had told him to do so, Bob turned his
head and glanced over the deck to the forward deck-house. As he did so
he uttered an exclamation. Little Marie had just descended the steps
from her father's quarters, and was already on the main deck. In her
arms she carried several parcels.
``Go back!'' roared Jarvis.
The words were driven back down his throat by the wind, and if the child
understood his gestures she did not heed them.
Bob groaned.
``Let me down, quick! The child is trying to get aft and she'll never
make it.''
With rare presence of mind, Jarvis gave the whistle lever five quick,
short jerks, sending forth as many blasts, the signal of danger.
Instantly some one shouted a sharp warning.
By this time the lad had slid down the ladder and was making for the
edge of the deck-house to drop down to the deck. He halted all of a
sudden. Bob tried to cry out, but the words would not come. He felt a
sickening sensation sweep over him, and a sudden dizziness took
possession of him.
A white-crested wave had risen up out of the sea right alongside of the
big steel ore carrier. For a moment it hung trembling over the ship like
an avenging monster. Then suddenly it swooped down. It reminded Jarvis
of a steam clam shell scooping up ore. He was thinking calmly now, and
he was planning what he should do an instant later.
The green scoop dipped, lifted the little Marie clear of the deck, then
raised her high above the steel hatch covers.
A faint cry floated back to where the Iron Boy was standing as the
captain's daughter was carried over the opposite side of the ship and
dropped into the sea.
A great shout escaped Bob Jarvis. Lifting himself to his toes he took a
long curving dive from the deck-house. He cleared the ship's rail with
plenty of room to spare, entering the water head first just at the base
of a huge swell.
In an almost incredibly short time his hatless head bobbed up on the
other side of the swell, leaving him struggling alone on the rough
waters. The ship had slipped quickly by. But already her propeller was
beating the water with all the force of the steam power behind it,
turned on full, in an effort to start the ship going astern.
Steve had rushed out on deck the instant he was relieved. Unmindful of
the seas that were again breaking over the deck as the ship shifted her
position, he dashed aft, drenched to the skin and battered this way and
that by the angry combers as they roared curling aboard.
A sailor ran panting up the stairs to the pilot-house.
``It's the little girl!'' cried the sailor. ``Your daughter's overboard
and Jarvis has gone after her. They'll both be drowned!''
``Port your helm a little,'' said the skipper in a calm, steady voice, as
he turned to the wheelman. ``Steady!''
Springing to the telephone he called up the after deck-house.
``Have boat Number 6 manned and swung out ready for launching. Have men
stand by with life-lines and rings ready to cast if we come up with
them. You stand by and watch out astern.''
The commands were delivered in quick, sharp accents, but there was no
trace of excitement either in the captain's tone or on his features. He
was every inch the commander, cool, calm, resourceful. Years of
commanding had taught him that to be a master of others one must first
be the master of himself and of his own emotions.
``Where are they? Do you see them?'' shouted Rush, as he dashed to the
after rail of the ship where a number of men were standing with pale,
frightened faces.
A hand pointed astern where, a second or so later, Steve caught sight of
the bobbing head of his companion.
``Has he got the child?'' Rush cried.
``Yes. Leastwise, he had a minute ago. It was a lucky chance. You see, he
jumped just in time and the girl was fairly swept into his arms.''
``It was not chance,'' retorted Steve. ``Bob knew what he was doing.''
Steve was pacing up and down the after deck, scarcely able to restrain
himself from leaping into the sea and going to his companion's
assistance. He knew, however, that the chances were that he would never
be able to reach the struggling figure off there. At any rate the ship,
which was now beating its way astern at a very fair rate of speed, would
get to the spot before he could possibly hope to do so, even if he were
able to make it at all.
Far up above the decks in the pilot-house with glasses to his eyes,
stood the skipper, calm, stern, alert, now and then giving a brief
command to the man at the wheel in a voice in which there was still no
hint of nervousness or excitement.
The first mate gazed at his commander in wonder. There were Iron Boys in
that ship's company and there was a master who was also iron.
``I think you had better go aft, Mr. Major,'' directed the skipper. ``Take
charge back there. We are going to have difficulty in getting them
aboard, even if they keep up until we get to them. The boy is making a
great fight of it.''
``Aye, aye, sir. Has he the girl still?''
``Yes. He is trying to keep her head above water until we get to him, but
I'm afraid she'll drown before we can help them.''
The first mate hurried from the pilot-house, starting aft at a run. He
began shouting out his orders before he reached the stern. He found
Steve Rush with coat and shoes off, poised on the rail of the plunging
stern, the water dashing over him as he clung with one hand to a
stanchion.
``You are not going to try to go over, Rush?'' he shouted.
``There's no need now,'' answered the boy, not for an instant taking his
eyes from the two figures off there in the water.
The ship was drawing near and it was observable that Jarvis was not
battling as strongly as he had before. They knew that he was becoming
exhausted from his desperate struggle with the great seas that were
sweeping him.
``Man boat Number 6 and put it over!'' commanded the mate.
``No use to do that,'' called Rush. ``It will not live. Better put over the
lines at the proper time.''
``No; it is the captain's orders to launch Number 6 boat. I want two
men.''
Nearly every man there stepped forward. They glanced at Rush. He was
still on the rail. He had made no effort to volunteer for the dangerous
service. They wondered at it, but they knew the boy's courage too well
to think for a moment that he had been deterred from offering to go out
in the life-boat through fear. There were those present who would have
resented such an imputation.
Steve cast a disapproving glance at the mate who was then superintending
the launching of the craft. The men who were to go out in it already had
taken their places in the boat, that had been provided with ropes, life
rings and life preservers.
At command the boat was swung out, the men standing up and steadying
their craft by pressing their oars against the sides of the ship itself.
``Careful that you do not fall out!'' warned Mr. Major. ``I will give the
command to let go. When I do so drop to your seats and out oars.''
``Aye, aye, sir.''
``Shut off!'' shouted Rush. ``You'll run them down!''
The mate made a signal to the captain, but the latter had timed the
progress of his vessel too well to need the signal. Already the
propeller had ceased revolving and the captain was giving his directions
to the wheelman so as to throw the stern to one side of the struggling
boy.
Captain Simms' plan was to drift down on Jarvis and the child, with the
sea. Perhaps it was not the best thing to do, but it was the quickest
and seconds were golden at that critical moment.
``Let go!'' roared the mate.
The life-boat struck the water with a splash. Instantly it was picked up
on the crest of a giant roller, lifted high in the air, and hurled
against the side of the ship with terrific force.
With a sickening crash the life-boat was crushed into splinters,
precipitating the crew into the rough sea.
Rush leaped from the rail to the deck. He had been ready to do so when
he saw what the mate proposed to do. He foresaw the end of the
life-boat, and perhaps of the men who were manning her, even before they
made a start to obey the orders of the mate.
Grasping a life ring to which a long line had been attached, Steve
hurled it over the side of the ship.
``Grab the line!'' he shouted to one of the men next to him. ``Watch out
and haul in when you get your man hooked.''
Another life ring dropped over the side of the ship and the line to this
Steve passed to another man. Both struggling sailors in the water
fastened to the life rings that had been dropped within easy reach of
them, thanks to the careful aim of the Iron Boy.
Steve saw that the two were reasonably safe; then, grabbing up another
ring, he sprang to the rail on the port side.
Bob Jarvis and the girl were drifting in, buffeted this way and that by
one huge wave after another. The girl's head was drooping over Bob's
left shoulder.
``Can you make it?'' bellowed Rush.
``I don't know.'' Bob's voice sounded far away.
Steve was watching him with keen, steady eyes. The lad felt sure that
they never would get aboard without at least serious injury.
``Kick the ship ahead a couple of turns!'' shouted Rush in a tone of
command.
The word was transmitted to the captain in the pilot-house by gestures.
The captain gave the signal, but not quite quickly enough to accomplish
what Rush had hoped for. He wanted the ship advanced a few feet so that
Jarvis and his burden would drift past the stern where they could be
pulled up without the danger of being crushed against the side of the
ship.
Before the propeller had made one complete revolution the stern of the
``Richmond'' was hit by a giant wave and then by another. The vessel it
seemed was literally lifted from the water and thrown to one side. That
was the side where Bob Jarvis was struggling to save himself and the
captain's daughter.
Illustration: Another Figure Dived from the Rail.
Bob saw what was going to happen. The plucky lad held the child off at
arm's length, as far away from the oncoming ship as possible, while with
the other hand he sought to break the force of the blow.
The side of the ship hit Jarvis a tremendous blow. The lad's arm doubled
under him and his head drooped forward on the water.
``He's killed!'' cried the watchers.
Splash!
Another figure had dived from the rail. It was Steve. His dive took him
right under Bob and his burden. Rush came up the other side and struck
out for the couple with long, powerful strokes.
\gutchapter{CHAPTER XX}
\section*{\raggedright AN EXCITING RESCUE}
\textit{With} him Rush had carried a life ring attached to the end of a rope, the
other end of the rope having been, with rare presence of mind, made fast
to the rail by him before leaping.
He reached his companion just as Bob's head drooped over and he lost
consciousness. Still, Jarvis kept his grip on the arm of the child. Rush
had to tear the girl's dress in order to wrench Jarvis's grip free of
her. In so doing Steve lost the life ring. It was carried away from him
in a twinkling. Now he had two persons on his hands with the seas
rolling over him almost mountain high, though the ship, being on the
windward side, protected them somewhat.
``Haul in and cast the ring!'' Steve managed to shout, just before he was
jammed choking under a heavy wave.
Rush threw himself on his back with his head toward the ship, one arm
under Marie and the other arm supporting Bob, who was making desperate
efforts to help himself, though unable to do much in that direction.
Then Rush began kicking himself slowly toward the vessel, which had
been shifted about and was once more drifting down on them.
``Cast your lines before you get close enough to hit us!'' Steve cried
when he could do so without getting a mouthful of water.
Unfortunately those on deck were not very good shots at this sort of
target work and their life rings went far wide of the mark. The ropes on
all but one of them slipped through the hands of the casters and dropped
into the sea.
``Lubbers!'' roared the captain from the pilot-house window.
Steve caught the third ring. Twisting the rope about the body of Marie
just under her arms, he tore the ring loose.
``Haul up, quick!'' he shouted, swimming along with the child after having
thrust the life ring over the head of Bob Jarvis. Steve held to the girl
so that she should not be thrown against the ship head first, which
would have seriously injured her at least, and perhaps killed her then
and there. Possibly the little girl was dead already. Rush did not know,
but he thought he had detected life when he first grasped her.
``Hurry, hurry!'' he cried.
The girl was hauled free of the water, and, limp and lifeless, she was
tenderly lifted over the rail. Captain Simms, after hurling some brief
directions at the man at the wheel, dashed from the pilot-house, down
the steps and along the deck to the stern, where Marie lay on the deck.
The father lost no time in getting at work on her.
``Save those boys if it costs the ship to do it!'' he roared. ``Major, use
your wits! Get them out, I tell you. I'll hold you personally
responsible for their rescue!''
``Rush is hit!'' shouted a voice excitedly.
Looking over they saw Steve striking out blindly to where Bob was
floating away helplessly on the sea. It was plain that Rush had been
stunned by being thrown against the side of the ship. Still, by sheer
pluck, he was keeping himself up and swimming, but with evident effort,
toward his companion. Bob was in a helpless condition and every second
the life ring was slipping up and threatening to bob out from under his
head. Were that to happen there was little chance that he would be
saved.
Steve tried to shout to them, but his voice would not come. He swallowed
enough water in these attempts to drown the ordinary person. His eyes
were so full of water and he was so dazed from the bump he had
sustained, that he could not make out where Jarvis was.
``Port! Port!'' roared a voice from the deck.
Steve caught the direction and veered a little to port.
``More port. Can you keep it up?''
Rush did not answer, for he was beyond answering. Only his wonderful
pluck and endurance were keeping him from throwing up his hands and
sinking under the surface.
With a final burst of speed he reached his companion. Steve threw out
one hand and fastened on the other Iron Boy. As he did so the ring
slipped from Jarvis's head and floated away.
Rush realized at once what had happened, and began upbraiding himself
for his carelessness. The knowledge seemed to give him new strength. His
body fairly leaped from the water as he took several powerful strokes
toward the drowning Bob.
``Wake up!'' cried Steve, shaking his companion roughly.
Jarvis mumbled in reply, and tried feebly to help himself, but he was
too weak and too full of water to accomplish anything.
Steve, by a great effort, twisted his companion about and began swimming
toward the ship with him.
Shouts and suggestions were hurled at him from the ship, but he did not
hear them. The Iron Boy was making the fight of his life. At last, after
mighty struggles, he managed to get near enough to the ``Richmond'' to
catch a line that was tossed to him. This he quickly made fast about
Jarvis's waist and waved a hand to indicate that the men above were to
haul away.
Steve lay over on his back on the water with a great sigh of relief as
the men began hauling the other boy toward the deck.
``Get a line over there to Rush!'' thundered the captain. ``Don't you see
the boy is drowning?''
But Steve missed every line that was tossed to him. He was making
powerful efforts to pull himself together sufficiently to save himself,
but he could not do so.
``Take care of the child, Major. Keep pumping the water out of her.
She'll be all right in a moment,'' cried the captain. ``Give me a line,
quick!''
Before the brave skipper could carry out his purpose of climbing over
the rail preparatory to dropping into the lake, another man swiftly
leaped to the rail and let himself drop feet first. He carried two lines
with him.
``It's Smith, the stoker!'' cried a chorus of voices.
It was indeed the stoker, the enemy of the Iron Boys, who had determined
to avenge himself on them for the insults he believed they had heaped
upon him.
What sudden revulsion of feeling led the stoker to risk his life to save
that of Steve Rush none ever knew, nor would he ever afterwards discuss
it. Smith was a powerful fellow, a man who feared nothing and besides,
he was a strong swimmer.
He pounced upon Rush as if he were about to do him bodily injury. It was
the work of but a moment to make fast the line about the boy's body.
``Get him up, and be quick!'' yelled the stoker.
A cheer rose from the deck; two men at this time were working over Bob,
while the captain, having returned to his daughter, was ministering to
her.
Steve was hauled aboard, where he settled down in a heap. The sailors
turned him face downward, and then some one happened to think of the
stoker. Smith was keeping himself from being jammed against the side of
the ship by holding both hands against the side of it and hurling angry
imprecations at those on deck who had apparently forgotten his
existence.
``Smi---Smith---Get him!'' muttered Steve.
``Put a ladder over the side! Lash it to the rail and give the man a line
with which to steady himself!'' commanded the captain. ``Come, come! Have
you all lost your senses?''
His orders were carried out with a snap, and a moment later the dripping
figure of Smith appeared above the level of the deck.
``You're a fine lot of lubbers,'' growled the stoker. ``You let a man go
overboard and then forget he's there. I ought to throw the bunch of you
overboard.''
``Take those boys to their cabins as soon as you get the water out of
them,'' ordered Captain Simms.
``No, no; I'm all right,'' protested Steve, pulling himself together and
staggering away from the men who were thumping him with their closed
fists, hoping in that way to bring him back to himself.
The stoker had betaken himself to the fire room to dry off. His face had
once more regained its surly, hang-dog expression, and he made rough
answers to the few questions that were put to him by his fellow-workers
in the stoke-hole.
At last the workers succeeded in shaking most of the water out of Bob
Jarvis. He had swallowed a lot of it and was so weak that he could not
stand.
At Steve's suggestion they carried Bob around on the lee side of the
after deck-house. The steward came running out with a bottle of brandy,
some of which he sought to pour down between the boy's blue lips.
Jarvis thrust the bottle aside, half angrily.
``None---none of that horrible stuff for me! I---I'd rather be full of Lake
Superior water and---and \textit{that's} the limit------''
Steve stooped over, and placing his hands under the other boy's arms,
lifted him to his feet.
``Brace up! You're all right now,'' encouraged Rush.
``Yes. I'm all right, \textit{only}------''
The sailors laughed at this; then they shouted, more from relief from
the strain under which they had been laboring than because of the humor
of Jarvis's reply.
``Want to go in and lie down now?'' questioned Steve, barely able to keep
his feet.
``No!''
``Then we'll walk and see if we can get our sea legs,'' proposed Steve,
slipping an arm about his companion's waist and starting slowly toward
the stern. The boys could hardly keep their feet, they were still so
weak. They staggered from one side of the passage to the other, but
their iron grit kept them up.
``How is little Marie?'' demanded Jarvis, suddenly turning to Rush.
``Come; we will go and see. We were forgetting our duty,'' muttered Steve,
starting for the cabin, where the little girl had been taken.
\gutchapter{CHAPTER XXI}
\section*{\raggedright A NEW HAND AT THE WHEEL}
\textit{Marie} had entirely recovered consciousness when the lads entered the
steward's cabin. But the child's face was chalky white, her lips
colorless and her eyes dull.
Captain Simms had sent for his wife, who, ill in her stateroom, had not
known of the exciting events that were taking place at the other end of
the ship. Mrs. Simms forgot all about her seasickness when summoned and
told what had happened.
Marie's eyes lighted up when they rested on the dripping forms of the
Iron Boys.
``Hello, kiddie,'' greeted Jarvis. ``How'd you like your swim?''
``Come and kiss me,'' answered the child simply.
Jarvis blushed, but braced himself. Then, stooping over, he gently
kissed the little one on the cheek.
``You, too, Steve,'' she nodded with compelling eyes.
Then Steve Rush kissed her, patted her cheek and straightened up to meet
the arms of the captain's wife.
``You saved her life,'' she murmured.
``I beg your pardon, Mrs. Simms; it's Bob Jarvis whom you should thank.
He's the real hero this time. I'm only a sort of assistant hero,'' said
Steve with a laugh.
The captain tried to speak, but something seemed to stick in his throat.
He gulped, swallowed, then grasping both boys by the shoulders thrust
them from the cabin.
``Get out! Get out you young rascals before I give you a sound thumping!''
he exploded, as the Iron Boys, laughing heartily, were ejected to the
deck.
``That's a fine way to show a fellow's appreciation,'' snorted Bob. ``Do
you know where that kiddie was going when she was swept overboard? I
mean, before she was swept over?''
``Coming aft?''
``Yes; she was coming aft. She was coming aft to make a cake for you and
me, that's what she was doing. She told me she was going to bake one for
us to-day and she had the stuff in her hands that she was going to put
into the cake. It's a shame,'' added Jarvis, his voice pitched a little
higher than usual.
``Yes, but not half so bad as if we hadn't saved her, old man. I'm proud
of you, Bob Jarvis.''
``You needn't be. I was the easiest kind of a mark. I would have drowned
if it hadn't been for you.''
``And both of us would undoubtedly have gone down had it not been for the
stoker, Smith. What do you make of that, Bob?''
Jarvis halted reflectively.
``I think,'' announced the lad wisely, ``that he was---was---what do you say
a fellow is suffering from when he goes dippy up here?'' tapping the top
of his head.
``Temporary aberration?''
``That's it. I wish I could think of things ready-made, the way you do.
Well, I believe he must have been suffering from that. He'll be wanting
to lick us again the minute he sets eyes on us.''
``Here he comes now. He's just come up from his watch. Oh, Smith!''
The stoker halted, then started on again. Steve grasped his arm. The
fellow shook the lad loose.
``See here, we want to talk to you.''
Smith halted reluctantly.
``I want to take back every unpleasant thing I have ever said to you. At
the same time I want to apologize for what I have done. I've been in the
wrong all the time, I guess. Will you shake hands?''
The stoker hesitated, shifted uneasily, all the time avoiding looking
into the eyes of the Iron Boys. Finally he thrust out a reluctant hand.
Steve grabbed it and Bob caught up the other. The stoker, muttering half
sullenly, broke away and ran into the deck-house, leaving the boys
standing outside looking at each other.
``Well, that beats anything I ever saw,'' growled Bob.
``Do you know,'' said Steve reflectively, ``I believe that fellow has been
a criminal of some sort. The way his eyes avoid yours, his shifty,
hang-dog manner, reminds me of certain other gentlemen whom I have seen.
However, after what he has done for us, it is not for you and me to try
to get him into any further trouble. He saved our lives and that's all
there is about it so far as we are concerned. I don't believe he will
try any more tricks on us. He is the man who hit me on deck here the
other night. I'm just as sure of it as I am that we are standing here
now. Captain Simms gave him an awful walloping. Maybe that's what beat
some sense into the fellow's head.''
All the rest of the day Marie remained in bed. The captain, who had gone
back to the pilot-house after carrying the child to his own quarters,
made frequent trips below to see how she was getting on. She was doing
so well that she wanted to get up and play.
The rest of the day passed without incident, though the gale, if
anything, grew worse. The air was filled with flying spray that reached
high up on the masts. The wireless operator picked up messages from
other ships that had sought safe harbor on the lee side of the islands
along the lake, but thus far there had been no reports of disasters. The
captain had warned the operator to be on the sharp lookout for appeals
for help. To the satisfaction of all no cries for help came.
The boys went about their duties, Rush taking another trick at the wheel
late in the afternoon, leaving it along toward eight bells, midnight.
Bob, in this instance, relieved him.
The night was starless and intensely dark and the hurling spray made
necessary a sharp lookout ahead. Two men were stationed on the bridge
and another in the forepeak to watch for lights, though the captain did
not look for many that night. He knew that at least all the timid
skippers, had scudded for calm water at the first signs of a big blow.
Believing that all was safe he went to bed, and the ship went rolling
and plunging, lurching and tumbling on her way, creaking and groaning as
though the effort caused her great pain.
Shortly before daylight, Bob fancying that he heard some one entering
the pilot-house, glanced at the open door on the lee side. At first he
saw nothing. Then all of a sudden a huge, shadowy form seemed to rise
from the floor at that point.
Bob gazed in amazement.
``What's that, Mr. Major?'' he asked sharply.
``Where?'' demanded the mate, leaning out and looking forward.
``There, there, at the door?''
``I don't see anything.''
``Neither do I, now, but I did a moment ago. I------''
Bob received a blow from a huge paw that tipped him over sideways,
tumbling him over.
``Help!'' yelled the boy, bolting for the door.
About this time the first mate, who had run around to the rear of the
steering wheel, got a blow on the side of the head that laid him low.
He, too, scrambled to his feet and dashed for the door, slamming it shut
after him.
``What's the trouble in there?'' shouted one of the bridge watch, poking
his head in at the window. He had heard some sort of disturbance in the
pilot-house, he thought, but the wind being so strong he was unable to
decide what the disturbance was about.
There was no answer to his question.
``I say------'' he shouted; then something happened to him.
A huge paw was stretched out through the forward pilot-house window. It
came down on the head of the watch with a whack, laying him flat on the
deck.
The second watch ran to where his companion had fallen.
``Here, here, what's the mat------''
The watch did not finish the sentence. A cuff on the ear, and a mighty
cuff at that, sent him clear to the end of the bridge, and had the
weather cloths not been in place he would undoubtedly have been knocked
through between the rails and into the sea.
Both men set up a wild yell of fear.
``It's some kind of animal!'' shouted Bob. ``Send for the captain. I'm
going back to the wheel.''
Summoning all his courage the lad opened the pilot-house door, peering
cautiously in.
He got a blow that knocked him over backwards and Bob Jarvis tumbled all
the way down the stairs to the main deck.
Captain Simms came rushing out of his cabin in his pajamas.
He had heard the running on the deck above him and surmising that
something had gone wrong, rushed out to the deck.
``What's wrong? What's wrong?'' he bellowed, casting a quick glance ahead,
almost expecting to see another ship bearing down upon them. ``I say,
what's happened?''
``Help!'' howled the distant voice of Bob Jarvis from the lower deck.
``Help, help!'' yelled the two men on the bridge watch in chorus.
``Captain!'' roared First Mate Major, bounding down the stairs to where
the captain was standing.
The skipper grabbed the mate by the arm and shook him violently.
``Here, here! What's wrong? Have all of you lubbers gone mad?''
``It---it's in the pilot-house!'' gasped the now thoroughly frightened
mate.
``What's in the pilot-house?'' demanded Captain Simms angrily.
``Nobody---I mean I don't know. It's a------''
But the skipper waited to hear no more. He rushed up the stairs, two
steps at a jump. Reaching the bridge deck he sprang for the door of the
pilot-house and jerked it open. As he did so his keen eyes caught sight
of a huge, shadowy figure at the wheel. The strange, uncouth shape was
twirling the wheel merrily, while the ship was diving this way and that
in a most unusual and erratic manner.
The figure at the wheel suddenly bolted forward, making a grab for
Captain Simms. Quite a portion of the skipper's pajamas were left in
the grip of the strange object, causing the captain to retire hastily,
slamming the door as he did so.
``It's the bear! The bear has escaped!'' he shouted.
``The bear?'' yelled several voices.
``Yes, the bear in that crate in the lazaret. We were taking it down for
Mr. Carrhart, to be shipped to a friend of his in Pittsburgh.''
``Wow!'' cried Jarvis, who had been creeping up the stairs. He turned and
bolted down again with all speed.
\gutchapter{CHAPTER XXII}
\section*{\raggedright LEADING A LIVELY CHASE}
``\textit{The} bear has escaped!'' shouted a voice down on the main deck.
``What bear?''
``The one that was in the lazaret.''
``Didn't know there was any bear there. You're kidding,'' answered the
doubting sailor.
``Go up and take a peep into the wheel-house, if you don't believe it.
You'll get a bang on the side of the head that will make your ears ring
eight bells for the rest of the night.''
``I---I guess I'll take your word for it.'' The sailor turned and ran for
the deck-house.
Steve Rush, aroused by the shouting, got up and poked his head from the
cabin window.
``Hey, what's happening?'' he called.
Jarvis was on his way back to tell his chum the news.
``Old Bruin has escaped.''
``Who's he?''
``An old party we had cooped in a crate in the lazar------''
``A bear?''
``You bet he's a bear. He waved a paw at me that knocked me clean out of
the pilot-house.''
``Wait, I'll be out in a minute.''
Steve hurried into his clothes, and a few minutes later was out on the
rolling deck. He could barely make out the lights of the forward
deck-house through the mist of spray that hung over the ship like a
cloud.
``Where is he?'' cried the Iron Boy.
``Up there in the house.''
``But who is steering the ship?''
``I guess the bear is. Nobody else up there except the captain, jumping
around the bridge-deck in his pajamas, mad as a hatter.''
Steve, deciding that he would like a closer look, hurried to the bridge.
There he found Captain Simms in a plight if anything more ludicrous than
had been painted by Bob Jarvis. Rush saw that the ship was reeling about
like a crazy sailor.
``Do something, somebody!'' roared the skipper.
``What would you suggest?'' questioned Steve, taking a peep through an
open window and narrowly missing getting his eyes scratched out as a
hairy paw reached through the window with a downward, raking sweep.
Captain Simms forgot his anger long enough to laugh at the agility with
which Rush leaped backward, falling over a steel cleat, coming up
grinning but very red of face.
``That's what the beast did to me, only he got too much of my clothes for
comfort,'' remarked the skipper.
It was Steve's turn to laugh, which he did uproariously.
``Maybe you think it's funny, but you wouldn't if you were in my place.
The next question is how are we going to get that beast from the iron
range out of the pilot-house?''
``I'll tell you,'' said Bob, who had followed his companion up to the
bridge. ``We'll coax him out with a chunk of fresh meat.''
``Will you hold the meat?'' answered the master sharply.
``No, thank you,'' laughed Jarvis.
``Your idea isn't half bad. I believe I will get a piece of meat and try
it,'' replied Rush reflectively.
``See here, young man. Not quite so fast. What do you propose to do with
the beast when you get him out?''
``I---I---hadn't thought of that,'' stammered Rush.
``I suppose you'd let him dance about the decks and run us all overboard,
eh? No, sir. He stays where he is. You keep watch of him while I go down
stairs and get some clothing on. This summer costume is a little too
airy for this kind of a night.''
The two boys watched the pilot-house from a safe distance while the
captain went below. Day was beginning to dawn, and by the faint light
they could see Mr. Bruin spinning the pilot-wheel this way and that. He
seemed as pleased as a child with a new toy. The compass card, with its
dim white spot showing the position of the ship, attracted his
attention. Brain scratched on the glass over the compass card and
getting no satisfaction from so doing, returned to the wheel.
Such steering probably never had been seen on the Great Lakes before.
All at once five shrill blasts sounded dead ahead.
``There comes a steamer!'' yelled Bob.
``We'll run it down!'' shouted Steve. ``Hey, Captain!''
The up-coming steamer knew that something was wrong and her deck officer
was sounding a danger signal. It looked as if a collision could not be
avoided. Steve ran around to the front of the pilot-house, and rang in
the signal ``full speed astern'' on the bridge telegraph. Then the
``Richmond'' did cut up. Bruin was still steering as fancy dictated, the
bow of the ship wobbling this way and that.
Illustration: A Huge Form Stood at the Wheel.
In the meantime the captain of the other steamer was trying his best to
get his craft out of the way of the wobbling ``Richmond.''
``Sheer off! Sheer off!'' bellowed the skipper of the up-boat. ``You'll cut
us in two.''
The boys thought so as well, but there was nothing they could do save
wait for results and trust to luck.
Bang!
The nose of the ``Richmond'' caught the other boat a glancing blow and
bounced off. The sides of the two ships bumped together, then the stern
of the ``Richmond'' side-swiped the stranger with a smash that sent
everything jingling on the two ships, while the skipper of the up-craft
was dancing up and down the deck of his vessel, heaping abuse upon
Captain Simms and his ``fool crew.''
``We must get that beast out, at all costs,'' raged the master of the
``Richmond.''
Just then Bruin leaned back from the window and against the whistle
lever. Instantly a roar, accompanied by a cloud of steam, burst from the
whistle at the after end of the boat. The roaring of the siren did not
cease. It kept right up and Mr. Bear glanced about uneasily as if
suspecting that the noise was directed against him.
About this time the chief engineer rushed to the deck.
``Stop that blowing. You'll blow all the steam out of the boilers!'' he
commanded, shouting up to the bridge.
``Suppose you come up and stop it yourself,'' suggested Jarvis, grinning
over the rail.
``We shall have to try that meat plan, I guess, boys,'' decided the
master. ``How shall we do it without playing the part of the meat?''
``I have a plan,'' answered Steve. ``Bob, if you will get a piece of meat I
will see what I can do in the meantime.''
Bob hurried aft for the fresh meat while Steve busied himself by
preparing a rope which he placed at the foot of the stairs on the lower
deck. By this time, Jarvis had returned with the meat, the captain
having watched the arrangement with nods of approval.
``Please have some men stationed under cover of the deck-house below us
and have a tarpaulin, one of the canvas hatch covers, handy, will you?''
asked Rush.
``Certainly. Jarvis tell the mate to do as Steve suggests. I will open
the door of the pilot-house when you are ready.''
In the meantime Bruin had left the whistle lever and lumbered to the
starboard window where he stood observing the preparations for his
capture. His nose was upraised sniffing the air, for he smelled the
fresh meat.
``Look out that he doesn't jump out of the window,'' warned Bob.
``I hardly think he will. It is quite a drop,'' answered Rush. ``Now,
Captain, if you will open the door, I think we are ready,'' he added,
taking the meat from the hands of his companion.
``You don't need me now, do you, Steve?''
``Well not just this minute,'' laughed Rush.
Bob ran up the rope ladder of the foremast, and from this point of
safety he grinned his enjoyment of the scene. Captain Simms threw open
the pilot-house door; then he also shinned up the ladder. The bear was
ambling toward Steve at a rapid gait. But the Iron Boy did not appear to
be at all frightened. He slid down the stairs to the forward deck,
waited until the bear was almost upon him, then dropped to the main or
lower deck.
Bruin was after him without loss of time. Reaching the lower deck, Steve
dropped the fresh meat in the big loop of rope that he had spread out on
the deck, and quickly darted behind a hatch.
The bear seized the meat with an ugly growl. Steve gave the rope, one
end of which was in his hands, a violent jerk and the next second the
bear was floundering about the deck, fighting, pawing and uttering
fierce growls, with the noose of Steve's rope drawn down tight over one
of the animal's fore-legs.
Steve took a twist around a stanchion.
``The tarpaulin!'' he shouted.
Not a man made a move to do the lad's bidding.
``Bob! Come down here. I want you! Quick!''
``I'm coming.''
Jarvis was down the ladder in short order.
``What shall we do now?''
``Grab hold of this canvas and help me throw it over the beast.''
``But he'll bite,'' protested Bob.
``He will if we do not get him secured pretty soon. Hurry, there!''
Each taking hold of a corner of the big, heavy canvas the lads
approached the big beast with caution.
``Now, he-o!''
They swung the tarpaulin back and forth to give it momentum, Bruin
stretching out quick paws in an effort to grab the canvas, at the same
time showing his teeth and uttering fierce growls.
``Let go!'' shouted Rush.
The canvas fell completely over the beast, the centre of the covering
dropping directly on his head. Mr. Bear began to claw and roar, but the
more he clawed the more entangled did he become.
The crew uttered a cheer.
``Hurry up, men! Give me a hand or he'll get away from us yet!''
Steve threw himself upon the writhing heap, with Jarvis a close second.
But no sooner had the boys landed on the canvas than they were tossed
off. Back they sprang, making plucky efforts to twist the canvas into
position where the animal could not throw it off.
By this time Captain Simms was down the ladders and stairs, making for
the writhing heap on the jump.
``Get in there, you lubbers!'' he roared.
The men obeyed his command, though they did so with reluctance.
``Fall on the heap!''
After a lively battle, consuming some twenty minutes, the escaped bear
was hopelessly entangled in the tarpaulin, the corners of which were
tied securely, thus imprisoning him beyond the possibility of his
getting out.
``The next question is, what are we going to do with him, now that we
have him?'' inquired the captain.
``Is his crate broken so that it cannot be fixed?'' asked Rush.
``No; it can be fixed up,'' interjected the chief engineer.
``Hurry up and attend to it, Macrae.''
In a few minutes the crate was ready. Steve engineered the following
efforts, as he had those that had gone before. The bear was dragged back
to the stern. There the men waited while Steve put another large chunk
of meat in the cage.
``All ready, men. Throw him down the stairs. Be sure that you get him
down, or he'll be after us and then we shall have our hands full,''
shouted Steve.
``It strikes me we already have,'' muttered the captain, gazing admiringly
at the efforts of the Iron Boy.
``You ought to join a menagerie,'' suggested Jarvis.
``All ready now,'' warned Steve.
``All ready,'' answered the men.
Steve cast a final look about, taking careful note of the knots which
were ready to be unfastened at the word.
``Let go!'' he shouted.
With a roar Mr. Bruin went rolling, bumping and scratching down the
stairs into the lazaret.
Steve crept down the stairs.
``Everyone stay back,'' he warned.
None needed the advice. None of the ship's company felt the least
inclination to climb into that dark hole where the angry bear was
floundering about.
``Throw on a light,'' called Rush.
A solitary light gleamed in the darkness of the lazaret. About that time
the bear smelled the fresh meat in the cage. With a grunt and a growl he
went in search of it, nosing here and there. At last he found it.
Steve, crouching on the stairway was watching the beast with keen eyes.
The bear entered the cage. With a bound Rush dropped to the floor of the
lazaret.
Bang! The door of the cage swung to, the padlock securing it, quickly
slipped through the staple and locked.
Mr. Bear was a prisoner.
``There, you may all come down now, children,'' called the Iron Boy.
``Is he in?'' demanded a voice at the head of the stairs.
``He is. Bruin is having the rest of his breakfast now.''
``Three cheers for Steve Rush,'' cried the captain, pulling off his cap.
``Hip-hip-hurrah!'' yelled the sailors. ``Hip-hip-hurrah! Hip-hip-hurrah!
T-i-g-e-r!'' added Bob Jarvis.
Steve came up from the lower deck, his face flushed with triumph.
``Well, we got him, didn't we?'' he demanded.
``You mean \textit{you} got him,'' answered the captain.
``We all got him.''
``It is my opinion,'' added the skipper, ``that you ought to be the captain
of this boat. You've got more horse sense than all the rest of us
together.''
\gutchapter{CHAPTER XXIII}
\section*{\raggedright THE WIRELESS MESSAGE}
\textit{For} the rest of that day the ship had a measure of quiet, just for a
change. The storm kept on with its former severity and there was more or
less discomfort. Meals had to be eaten standing up, and life lines had
been run along the deck to support the one who ventured along the decks
forward or aft. Marie was not allowed to leave her father's cabin again
while the storm lasted. Considerable time had been lost, owing to the
trouble caused by the bear, so the ship was put to full speed.
Of late the boys had taken the keenest sort of interest in the wireless
outfit with which the ship was equipped. They spent much of their
leisure time with the wireless operator. Steve had learned part of the
Morse alphabet and occasionally he tried to operate the key.
Two days later, as they were sitting in the wireless room, where the
operator, with feet on his desk, was telling them a story of a wreck
that he had been in on the Atlantic when he was operator on a liner, a
flash from the switchboard told them that they had picked up a wireless
from another ship or station.
The operator quickly adjusted the receiver over his head, listened a
moment then threw his key open. A few quick sentences were crashed
forth, the aerials above the deck of the ship snapping out the message
in sundry vicious cracklings.
Steve tried to catch the drift of what was being said, but it was too
fast for him. He could not hear what the operator was receiving, but
after a while the operator picked up his pencil and began writing
industriously.
Glancing over the man's shoulder Steve's eyes caught a few words that
caused him to lean forward with renewed interest. Then he sat back,
possessing himself in patience until the message should have been
finished.
``That's strange,'' said the operator, laying down his head piece.
``What is it?'' questioned Bob.
``Nothing much. It is just a message I picked up about some fellow that
the police want.''
``Well, it isn't I, that's sure,'' said Jarvis with a confident laugh.
``It is---but here, read it for yourself.''
Steve read the message out loud.
``'Wanted: One, Gus Collins, for complicity in a post-office robbery at
Elgin on the night of June third. Collins has been a sailor and is said
to be on one of the ships on the lakes. About five feet ten in height,
gray eyes, blonde hair. Has a peculiar stoop to his shoulders, and a
habit of peering up suspiciously, but not meeting the eyes of the person
he is talking to. Five hundred dollars reward offered for his capture by
the post-office department.'''
``I'd like to make that five hundred,'' laughed Jarvis.
Steve did not reply at once. His face was serious. He was thinking.
``Well, there is one thing certain, Mr. Gus Collins isn't on this ship,''
announced the operator, hanging up his headstall. ``Funny message to send
out. Skippers of these boats have something else to do besides hunting
down criminals for the post-office department.''
Rush nodded thoughtfully.
Somehow, the description of the man seemed to strike a familiar chord in
him. He could not help feeling that he had seen some one who in a
measure answered that description.
``Ever seen him, Bob?'' questioned the lad.
Jarvis shook his head.
``Wouldn't have recognized him if I had seen him. Say!''
``Well?''
``Maybe the bear is Collins in disguise.''
There was a laugh at this. Rush read the message over again.
``Shall I take it up to the captain?''
``Yes, if you will.''
Steve did so. Captain Simms read the alarm message through twice.
``Pshaw!'' he grunted. ``Let the government find its own criminals. It
doesn't hire me to be a policeman. How's the bear?''
``I haven't heard him complain any since we put him back,'' answered Steve
with a grin. ``How did he get out, do you think?''
``The cage tipped over in a roll of the ship. No more wild animal shows
on this ship. Are you going to try to earn that five hundred dollars?''
demanded the skipper, changing the subject abruptly.
``I had not thought of doing so. You do not think he is on your ship, do
you?''
``If he was you'd catch him, even if you had to bait him with raw beef.
Say, are you going to stay with me?''
``Why, I am not thinking of leaving, Captain Simms.''
``I don't mean now. Of course, you wouldn't leave me in the middle of the
season. You're too square for that. I mean at the end of the season?''
``Of course, we shall have to work during the winter. We can't afford to
lie around in idleness.''
``Yes, of course. But what about next season?''
``That is a long way off,'' smiled Rush.
``Will you come back with me next year?''
``I could not promise. Frankly, Captain, I wish I might stay with you. I
like the life and I should be happy to spend the rest of my days on the
water, were it not for one fact.''
``What is that?''
``There isn't much of a future to the lake business.''
Captain Simms nodded.
``Nothing beyond being a captain. That's the stone wall we butt against
sooner or later, if we are lucky enough to get that far. I don't blame
you, but I am sorry. I was in hopes you would stay with us another
season.''
``This season is young yet. Perhaps you may be glad to get rid of me
before the end of it,'' laughed Rush.
``No danger of that. But I am going to make it worth your while to stay,
you see if I don't. Tell the operator to send back word, to the man that
sent out this message, that we haven't got any safe crackers on board
the `Richmond.'''
``Very well, sir.''
Steve picked up the message and left the cabin. He walked thoughtfully
aft to his own state room, where he found Jarvis getting ready to go on
duty. Rush sat down to study the description of the much-wanted
criminal.
``I can't get it out of my mind that I know that man.'' he muttered. ``I
know I have seen him somewhere. But where? Pshaw! Why should I trouble
myself about the matter? I'm no policeman, and I don't want to earn any
money at the price of another man's liberty.''
``What's the matter---gone crazy?'' demanded Jarvis, eyeing his companion
suspiciously. ``They say it's a sure sign, when a fellow gets the habit
of talking to himself.''
Rush laughed heartily.
``Then both of us must be in the same boat, for I heard you mumbling to
yourself this very day.''
``When?''
``At the time the bear was chasing you.''
``Huh!''
``Bob, listen.''
Steve read out the message, slowly, giving emphasis to that part
describing the man wanted by the government.
``Think hard, now. Isn't there some one whom you have seen that answers
that description, the stooping shoulders, the peculiar way of glancing
up from under the half-closed eyelids------''
``Nobody but Smith.''
``Smith!'' Rush gazed at the other boy blankly.
``That's so; he does rather answer the description.''
``Of course he isn't the man.''
``Perhaps not.''
All the rest of the day Steve thought over the contents of that message
and the suggestion made by Jarvis. He did not see the stoker, however,
until the following morning, just as Steve was coming off duty.
``Morning, Smith,'' greeted the lad, bending a scrutinizing gaze on the
surly fireman.
``Morning,'' mumbled the other.
``By the way, old chap; were you ever in Elgin?''
Smith gave the lad a quick, sharp look.
``What are you getting at?''
``Do you know a man named Collins---Gus Collins?'' persisted the Iron Boy.
``Co---Co---Collins?''
``Yes, a fellow who was interested in cracking a post-office safe out in
Elgin------''
``It's a lie!'' exploded the stoker, straightening up suddenly, his face
flushing and his features working convulsively.
``Ah! Then you do know something about this man, Collins, eh?''
``Ye---no, I don't know anything about him. I've heard of him, that's
all. Now you let me alone, or------''
``Smith, you saved my life. I'm not such a cur as to forget that. I think
you have something to say to------''
``I ain't got anything to say to you.''
``Oh, yes, you have. Come with me to my cabin, where we can talk without
interruption. It may be worth your while.''
``I won't go!''
Smith raised a hand as if he would strike the boy whose finger-tips were
resting on the stoker's shoulder.
``You come with me!'' commanded Steve, placing a firmer grip on the
shoulder of the stoker. In that way, and without further resistance,
Steve led him to his own stateroom.
``Sit down! Now tell me all about it.''
The fireman's face was sullen and rebellious.
``There---there ain't nothing to tell,'' answered the man in a low,
half-angry voice.
``You are Gus Collins! I know you, now. I was sure I had seen the man
whose description was sent out by the police and the government
officials.''
The stoker's face went ghastly.
``Yes, I am. Now what are you going to do about it?'' he demanded, rising
to his full height, standing over Rush in a threatening attitude.
``I am going to talk with you for the present. I think I have a right to
do that, and see if there isn't something I can do for you after all you
have done for me. Sit down, Gus.''
With a bewildered look on his face, the stoker sank into the chair.
``Tell me the whole story, Gus,'' urged Rush gently. ``You need not be
afraid of me. I am your friend, no matter what you have done.''
For a full five minutes Collins did not speak. It was plain to the
keen-eyed boy before him that the man was battling with himself and was
trying to decide what his course of action should be.
``Did you have any part in the robbery of that post-office?'' urged Steve.
``\textit{No!}'' fairly shouted the stoker.
``Then you have nothing to fear.''
``Yes, I have, too. I've got everything to fear. I'm a bad man, and------''
``Perhaps you were, but you have wiped that all out by your heroic act
in------''
``Boy, I've served time in Joliet. I'm an ex-convict. I stole something
once when I didn't know what I was doing. They put me away for five
years for that little job. While I was in prison my temper got the best
of me one day, and I hurt a man, and------''
``You don't mean you------''
``No, I didn't kill him, but I was used worse than a little yellow dog
after that. What little good there was in me was beaten out of me,
and---never let your temper get the best of you, boy. It's an awful thing
to have a temper like mine.''
Steve nodded.
``Well, I got out. My time was up.''
``When was that?''
``This spring. I was dogged from the time I left the prison until one day
I managed to give them the slip, and------''
``You mean the police were following you?''
``Yes; spotting me.''
``What for?''
``To see that I didn't get into any mischief. The last time they saw me I
was in Elgin. I left on the six o'clock train, after throwing the
spotters off. That night the post-office there was cracked. I read about
it in the papers next day, and I knew they'd put it on me. I got clear
of the place as soon as possible, shipped up the lakes from Chicago;
then got in with this crowd. Now I'll be sent back to Joliet again.''
``Perhaps not; not if you are innocent.''
``I am as innocent as you are, Steve Rush. Help me, boy! Help me to get
away. They'll nail me this time, sure. They've got the line drawn on me
fair and square. They sent out that alarm you've got in your hands
there. Help me to get away in the small boat to-night and I'll make
shore and disappear. I'll fool them. I did you a good turn. Do a great
one for me, now!''
``Yes, Gus; I will do you a turn, but I won't help you to escape. That
would be a foolish thing to do. The police would get you sooner or
later, and your flight would be the very worst thing possible for you
when they did get you.''
``You won't help me?''
``No, not in that way.''
``How then?''
``I shall have to think it over, but if you are innocent, have no fears,
for you shall be freed of the accusation. I must talk with the
captain------''
Collins started to protest.
``No one else on board shall know of it except my friend, Jarvis, and he
is true-blue. When we have you freed I will see to it that you get a
berth on this or some other boat, for life, if you want it.''
Collins shook his head.
``No; they'll fire me when they find out I've done time. Nobody wants an
ex-convict. They drive a man to the dogs after once he's fallen------''
``Here's one man who won't drive you, Gus Collins. Here's one man who's
going to stand right back of you and see that you get fair play. Then
you're going to hold your head up and be a man with other men. You leave
it all to me, will you? Will you promise to do so?''
Collins eyed the bronzed, manly face before him, for a full moment; then
he stretched out an impulsive hand.
``Put it there, little pard! I'll stand up, even if I do time for it, if
it'll please you any. You're the pluckiest, the squarest bunch of muscle
that I've ever come up with!''
\gutchapter{CHAPTER XXIV}
\gutchapter{CONCLUSION}
STEVE RUSH had told the whole story to Captain Simms, to all of which the captain listened in deep interest.
``Well, what do you propose to do about it?'' questioned the skipper, with a quizzical smile.
``If you will give me a leave of absence, I think I should like to go back to Elgin with Collins and help to get him free,'' announced Steve.
``Don't monkey with fire. A crook's a crook, and------''
``This one \textit{will} be, if he is sent up again. I propose to get him out, even if it takes all the rest of the summer to do it.''
``All right. Go ahead, lad, but for goodness' sake wait until we get the bear out of this ship,'' laughed the captain.
The result was that as soon as the ``Richmond'' reached its destination on Lake Erie, Steve and the stoker, both dressed in their best, slipped ashore and took a train for Chicago. Early the next forenoon they presented themselves at the police station in the town where the robbery had occurred, Steve acting as spokesman and stating that Collins had heard he was wanted and had come to give himself up, prepared to prove his innocence.
Of course the stoker was locked up. The man was sullen once more, and when the iron doors clanged behind him he gave up all hope.
``They've got me! I was a fool!'' he muttered.
Shortly after that Steve visited him, and when the boy left the man Collins was in a better frame of mind. Rush got to work at once. He must find some one who would remember to have seen Gus leaving town. Suddenly an idea occurred to the boy. He visited the railroad station. From one official to another he traveled, asking questions and getting scant courtesy. Everyone's hand appeared to be against him when the owner learned the object of Rush's mission.
It was not until the next day that he found the man for whom he was looking. That was the conductor of the train on which Collins had taken passage when he left the town the evening of the robbery, and several hours before it occurred. He had obtained from Collins a description of the clothes the latter wore on that night, and where he sat in the train, establishing the fact that the man's soft hat, tipped up behind, was pulled well down over his face, and that he wore a red necktie.
Armed with this description, Steve visited the conductor at the latter's home. At first the conductor did not seem to remember, but when Steve mentioned the felt hat, the red necktie and the stoop of the man's shoulders in connection with the furtive glancing up from beneath the eyelids, the railroad man, slapped his thigh violently.
``Of course I remember him. I'd know him if I saw him. He had a scar on his right cheek------''
``That's the man,'' cut in Rush triumphantly. ``Come over to the station with me and identify him. You will prevent a grave injustice being done if you will assist me in this matter.''
The conductor readily picked out Gus Collins as the man whom he had seen on his train proceeding the robbery. A few days later the conductor was summoned before the Grand Jury, at Steve's instigation, where he repeated his story in detail. Steve gave evidence also as to what he knew about the man, repeating the interview he had had with the stoker on board the ship.
The result was that Gus Collins stepped from his cell a free man that evening. He said little, but he seemed unable to keep his eyes from the face of the boy who had saved him from prison. Collins knew that nothing could have saved him had it not been for the Iron Boy, but somehow he could not find it possible to express his thankfulness.
``We will go back to Duluth,'' said the lad. ``We shall not be able to catch the ship down this way I guess. Anyhow, a few days' layoff will not hurt us in the least.''
``What are you going to do with me now?'' demanded the fireman, finding his voice at last.
``I shall take good care of you. Forget all that's past. You are a man now, and you are going to be a man henceforth. Quit brooding over your troubles. You haven't any. They were all washed out of you in the lake the day you went in after me. I have something in mind for you that I think will please you.''
Reaching Duluth, Steve sought Mr Carrhart at once and to the president the lad told the whole story.
``What do you want, my lad---what do you wish me to do for your friend?'' asked the president kindly.
Rush told him in a few words. The result was that Mr. Carrhart gave the boy a letter to the superintendent, telling Steve to return for an interview after he had finished with the Collins' business.
It was a proud and happy Steve who sought out Gus Collins an hour later, at the hotel where the man and the boy were stopping.
``Well, what about it?'' demanded the stoker, without the least trace of hopefulness in his tone.
``You are to report for duty on the `Richmond' as soon as she gets in.''
``Oh!'' Collins' face brightened.
``Here's your appointment,'' added Steve, handing over a document with the imprint of the steamship company at its head.
Collins read it through, changed color then stared at Steve.
``Is this some kind of a joke you're playing on me?''
``It is no joke, Gus. You are appointed foreman of the stoke-room of the ore carrier `Richmond,' and you'll save more coal for the company than any other stoker who ever bossed a fire-room.''
Collins sat down heavily. The tears were blinding his eyes. Steve did not try to stop them. He realized that they marked the turning point in what had been a hard life, a life that had bidden fair to be wholly wrecked in the name of justice. But what Steve Rush in his unselfishness did not realize, was that he had saved a human soul.
The interview with Mr. Carrhart took place that afternoon.
``Yes, sir; I think I have a few suggestions to make,'' answered Steve in reply to a question from the president. ``But first I should like to ask some questions of you.''
``Proceed.''
Steve asked the average cost of operating the ships of the fleet per month; what the ships earned by carrying coal for other concerns on the return trips, together with a number of other shrewd and pointed questions. All of these Mr. Carrhart answered freely, knowing that the boy's reasons for asking them were in the interest of his investigations.
Rush made some rapid calculations on a pad on the president's desk.
``You have some two hundred ships in the line, I believe, sir?''
``Yes; two hundred and ten.''
``Would it be any saving if you could save an hour in the unloading of these ships---two hundred and ten hours, in other words, every time the whole fleet made a trip down the lakes?''
``Well, I should say it would.''
``That is easy.''
``Explain.''
``Simply put on an extra unloader for each dock, so that both may work at the same time.''
Mr. Carrhart considered. He, too, made some calculations.
``Yes, that is an excellent suggestion. It will mark a very great saving in the transportation cost. Candidly, the idea never occurred to me. You have earned your salary for one year at least,'' added the president with an indulgent smile. ``I felt sure you would dig up something of value to us, to say nothing of the value the experience would be to you.''
``I'm not through yet,'' laughed the Iron Boy. ``I'm going to show you how you can save something like thirty thousand dollars a year more on the carrying proposition.''
``Why, Rush, you amaze me. It cannot be possible, after figuring down all transportations the way the experts of this company have done and been doing for years.''
``The old saying is to the effect that figures never lie. Perhaps mine do. If so, you will be able to discover the untruth at once.''
``May I ask how you propose to work this great saving?'' asked the president good-naturedly.
``Send your boats back light.''
``Send them back light?''
``Yes, sir; in water ballast.''
``But, my boy, don't you understand that it will mean the loss of a lot of money to do that? The ships earn a great many thousands of dollars a year by carrying freight for pay on the return trips.''
``Yes, sir; I understand that. Their cargo is mostly coal, is it not?''
``It is.''
``For ports all along the Great Lakes?''
``Certainly.''
``And through carrying this coal your ships lose from a week to ten days and some times two weeks' on every round trip.''
``How do you know this?'' interrupted Mr. Carrhart.
``I have asked questions,'' smiled Steve. ``Call it a week's loss of time on each trip. Do you know what that means?''
``I begin to see,'' answered the president reflectively.
``It means that every time your fleet makes a round trip, carrying coal back with them, the company loses their services to the enormous total of two hundred and ten weeks, more than four years, Mr. Carrhart. If you will glance over these figures of mine you will observe that, by this method, the company is losing about the figure stated by me a few minutes ago, over and above what you get in freights for carrying the coal.''
The president made a few brief calculations. He went over his figures and Steve's several times, his forehead corrugated with deep wrinkles as he did so. At last Mr. Carrhart glanced up, gazing steadily at the slightly flushed face of the Iron Boy.
``Rush you are a very remarkable young man,'' he said. ``Of course, I knew that before, but what I did not know was that you had a head for finance, such as you have just demonstrated. This is really a most remarkable showing. I shall bring it before the board at the next meeting. There is no doubt about your suggestions being adopted. I think it will come in the nature of a revelation to the board. My boy, I am proud of you. I can't tell you how proud I am, especially so because I picked you out, feeling from the first that you would prove a winner.''
``Thank you, sir.''
``And, in this connection, I received a long letter from Captain Simms from Cleveland yesterday. He made certain suggestions regarding yourself and your friend Jarvis, which it gives me great pleasure to act upon. You have been appointed second mate of the steamer `Richmond'; Jarvis, first wheelman. You will be called upon to pass a government examination for a license, which you will take to-morrow morning. You will have no difficulty about it, if you are as good a navigator as Captain Simms says you are, and I have no doubt you are. If you remain on the lakes we'll be making a captain of you some of these days. However, I have an idea you do not intend to be a sailor.''
``No, sir, not permanently.''
* * * * *
And so Steve Rush began as a watch officer on the Great Lakes. He proved that the confidence of his superiors was not misplaced, and for the rest of the season he remained on the ``Richmond,'' distinguishing himself in many ways. Gus Collins, with his fresh start in life, had dropped his hang-dog expression. When he talked to a man, now, he looked that man squarely in the eye, and from the moment of his return to the ship he was a daily worshipper at the shrine of Steve Rush.
At the close of the season Steve found the foreman a place with a manufacturing firm, with the help of a letter from Captain Simms. Then, bidding good-bye to their friends, the lads gathered up their dunnage and went home for a few weeks' rest before taking up the new life that they had about decided upon. What happened to them in their new calling will be related in detail in a following volume entitled, ``THE IRON BOYS IN THE STEEL MILLS; Or, Beginning Anew in the Cinder Pits.'' In the great steel mills the boys were to work among the roaring furnaces, the swiftly moving cranes and the moulding mills, where the metal that they had helped to mine ran in rivers that turned into gold. There the boys were to be called upon to face death many times, and in many forms, as they toiled among the rough men of the mills and laughed at the thousand and one perils of their new life.
THE END.
* * * * *
Transcriber's Note
Obvious spelling and punctuation errors have been corrected, missing
words have been added.
The Advertisement of The Boys of Steel Series contains the numbering
as presented in the book.
Differing spellings used throughtout the book for:
\begin{quotation}
life boat, lifeboat and life-boat light-house, lighthouse layoff, lay-off hatch cover, hatch-cover\end{quotation}
are retained as used by the author
* * * * *
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The Motor Boat Club Series
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Dot, Dash and Dare Cruise.
5 THE MOTOR BOAT CLUB IN FLORIDA; Or, Laying the
Ghost of Alligator Swamp.
6 THE MOTOR BOAT CLUB AT THE GOLDEN GATE; Or, A
Thrilling Capture in the Great Fog.
7 THE MOTOR BOAT CLUB ON THE GREAT LAKES; Or,
The Flying Dutchman of the Big Fresh Water.
Cloth, Illustrated Price, per Volume, 50c.
* * * * *
The Range and Grange Hustlers
By FRANK GEE PATCHIN
Have you any idea of the excitements, the glories of life on great
ranches in the West? Any bright boy will ``devour'' the books of this
series, once he has made a start with the first volume.
1 THE RANGE AND GRANGE HUSTLERS ON THE RANCH;
Or, The Boy Shepherds of the Great Divide.
2 THE RANGE AND GRANGE HUSTLERS' GREATEST
ROUND-UP; Or, Pitting Their Wits Against a Packers'
Combine.
3 THE RANGE AND GRANGE HUSTLERS ON THE PLAINS;
Or, Following the Steam Plows Across the Prairie.
4 THE RANGE AND GRANGE HUSTLERS AT CHICAGO;
Or, The Conspiracy of the Wheat Pit.
Cloth, Illustrated Price, per Volume, 50c.
Submarine Boys Series
By VICTOR G. DURHAM
These splendid books for boys and girls deal with life aboard submarine
torpedo boats, and with the adventures of the young crew, and possess,
in addition to the author's surpassing knack of storytelling, a great
educational value for all young readers.
1 THE SUBMARINE BOYS ON DUTY; Or, Life on a Diving
Torpedo Boat.
2 THE SUBMARINE BOYS' TRIAL TRIP; Or, ``Making Good''
as Young Experts.
3 THE SUBMARINE BOYS AND THE MIDDIES; Or, The
Prize Detail at Annapolis.
4 THE SUBMARINE BOYS AND THE SPIES; Or, Dodging
the Sharks of the Deep.
5 THE SUBMARINE BOYS' LIGHTNING CRUISE; Or, The
Young Kings of the Deep.
6 THE SUBMARINE BOYS FOR THE FLAG; Or, Deeding
Their Lives to Uncle Sam.
7 THE SUBMARINE BOYS AND THE SMUGGLERS; Or,
Breaking Up the New Jersey Customs Frauds.
Cloth, Illustrated Price, per Volume, 50c.
* * * * *
The Square Dollar Boys Series
By H. IRVING HANCOCK
The reading boy will be a voter within a few years; these books are
bound to make him think, and when he casts his vote he will do it more
intelligently for having read these volumes.
1 THE SQUARE DOLLAR BOYS WAKE UP; Or, Fighting the
Trolley Franchise Steal.
2 THE SQUARE DOLLAR BOYS SMASH THE RING; Or, In
the Lists Against the Crooked Land Deal.
Cloth, Illustrated Price, per Volume, 50c.
* * * * *
Ben Lightbody Series
By WALTER BENHAM
1 BEN LIGHTBODY, SPECIAL; Or, Seizing His First Chance
to Make Good.
2 BEN LIGHTBODY'S BIGGEST PUZZLE; Or, Running the
Double Ghost to Earth.
Cloth, Illustrated Price, per Volume, 50c.
Pony Rider Boys Series
By FRANK GEE PATCHIN
These tales may be aptly described as those of a new Cooper. In every
sense they belong to the best class of books for boys and girls.
1 THE PONY RIDER BOYS IN THE ROCKIES; Or, The Secret
of the Lost Claim.
2 THE PONY RIDER BOYS IN TEXAS; Or, The Veiled Riddle
of the Plains.
3 THE PONY RIDER BOYS IN MONTANA; Or, The Mystery
of the Old Custer Trail.
4 THE PONY RIDER BOYS IN THE OZARKS; Or, The Secret
of Ruby Mountain.
5 THE PONY RIDER BOYS IN THE ALKALI; Or, Finding a
Key to the Desert Maze.
6 THE PONY RIDER BOYS IN NEW MEXICO; Or, The End
of the Silver Trail.
7 THE PONY RIDER BOYS IN THE GRAND CANYON; Or,
The Mystery of Bright Angel Gulch.
Cloth, Illustrated Price, per Volume, 50c.
* * * * *
The Boys of Steel Series
By JAMES R. MEARS
The author has made of these volumes a series of romances with scenes
laid in the iron and steel world. Each book presents a vivid picture of
some phase of this great industry. The information given is exact and
truthful; above all, each story is full of adventure and fascination.
1 THE IRON BOYS IN THE MINES; Or, Starting at the Bottom
of the Shaft.
2 THE IRON BOYS AS FOREMEN; Or, Heading the Diamond
Drill Shift.
THE IRON BOYS ON THE ORE BOATS; Or, Roughing It on
the Great Lakes.
THE IRON BOYS IN THE STEEL MILLS; Or, Beginning
Anew in the Cinder Pits.
Cloth, Illustrated Price, per Volume, 50c.
West Point Series
By H. IRVING HANCOCK
The principal characters in these narratives are manly, young Americans
whose doings will inspire all boy readers.
1 DICK PRESCOTT'S FIRST YEAR AT WEST POINT; Or,
Two Chums in the Cadet Gray.
2 DICK PRESCOTT'S SECOND YEAR AT WEST POINT; Or,
Finding the Glory of the Soldier's Life.
3 DICK PRESCOTT'S THIRD YEAR AT WEST POINT; Or,
Standing Firm for Flag and Honor.
4 DICK PRESCOTT'S FOURTH YEAR AT WEST POINT; Or,
Ready to Drop the Gray for Shoulder Straps.
Cloth, Illustrated Price, per Volume, 50c.
* * * * *
Annapolis Series
By H. IRVING HANCOCK
The Spirit of the new Navy is delightfully and truthfully depicted in
these volumes.
1 DAVE DARRIN'S FIRST YEAR AT ANNAPOLIS; Or, Two
Plebe Midshipmen at the U. S. Naval Academy.
2 DAVE DARRIN'S SECOND YEAR AT ANNAPOLIS; Or,
Two Midshipmen as Naval Academy ``Youngsters.''
3 DAVE DARRIN'S THIRD YEAR AT ANNAPOLIS; Or, Leaders
of the Second Class Midshipmen.
4 DAVE DARRIN'S FOURTH YEAR AT ANNAPOLIS; Or,
Headed for Graduation and the Big Cruise.
Cloth, Illustrated Price, per Volume, 50c.
* * * * *
The Young Engineers Series
By H. IRVING HANCOCK
The heroes of these stories are known to readers of the High School Boys
Series. In this new series Tom Reade and Harry Hazelton prove worthy of
all the traditions of Dick \& Co.
1 THE YOUNG ENGINEERS IN COLORADO; Or, At Railroad
Building in Earnest.
2 THE YOUNG ENGINEERS IN ARIZONA; Or, Laying Tracks
on the ``Man-Killer'' Quicksand.
3 THE YOUNG ENGINEERS IN NEVADA; Or, Seeking Fortune
on the Turn of a Pick.
4 THE YOUNG ENGINEERS IN MEXICO; Or, Fighting the
Mine Swindlers.
Cloth, Illustrated Price, per Volume, 50c.
Boys of the Army Series
By H. IRVING HANCOCK
These books breathe the life and spirit of the United States Army of
to-day, and the life, just as it is, is described by a master pen.
1 UNCLE SAM'S BOYS IN THE RANKS; Or, Two Recruits in
the United States Army.
2 UNCLE SAM'S BOYS ON FIELD DUTY; Or, Winning Corporal's
Chevrons.
3 UNCLE SAM'S BOYS AS SERGEANTS; Or, Handling Their
First Real Commands.
4 UNCLE SAM'S BOYS IN THE PHILIPPINES; Or, Following
the Flag Against the Moros.
(\textit{Other volumes to follow rapidly.})
Cloth, Illustrated Price, per Volume, 50c.
* * * * *
Battleship Boys Series
By FRANK GEE PATCHIN
These stories throb with the life of young Americans on to-day's huge
drab Dreadnaughts.
1 THE BATTLESHIP BOYS AT SEA; Or, Two Apprentices in
Uncle Sam's Navy.
2 THE BATTLESHIP BOYS FIRST STEP UPWARD; Or,
Winning Their Grades as Petty Officers.
3 THE BATTLESHIP BOYS IN FOREIGN SERVICE; Or,
Earning New Ratings in European Seas.
4 THE BATTLESHIP BOYS IN THE TROPICS; Or, Upholding
the American Flag in a Honduras Revolution.
(\textit{Other volumes to follow rapidly.})
Cloth, Illustrated Price, per Volume, 50c.
* * * * *
The Meadow-Brook Girls Series
By JANET ALDRIDGE
Real live stories pulsing with the vibrant atmosphere of outdoor life.
1 THE MEADOW-BROOK GIRLS UNDER CANVAS; Or, Fun
and Frolic in the Summer Camp.
2 THE MEADOW-BROOK GIRLS ACROSS COUNTRY; Or,
The Young Pathfinders on a Summer Hike.
3 THE MEADOW-BROOK GIRLS AFLOAT; Or, The Stormy
Cruise of the Red Rover.
Cloth, Illustrated Price, per Volume, 50c.
* * * * *
High School Boys Series
By H. IRVING HANCOCK
In this series of bright, crisp books a new note has been struck.
Boys of every age under sixty will be interested in these fascinating
volumes.
1 THE HIGH SCHOOL FRESHMEN; Or, Dick \& Co.'s First
Year Pranks and Sports.
2 THE HIGH SCHOOL PITCHER; Or, Dick \& Co. on the
Gridley Diamond.
3 THE HIGH SCHOOL LEFT END; Or, Dick \& Co. Grilling on
the Football Gridiron.
4 THE HIGH SCHOOL CAPTAIN OF THE TEAM; Or, Dick \&
Co. Leading the Athletic Vanguard.
Cloth, Illustrated Price, per Volume, 50c.
* * * * *
Grammar School Boys Series
By H. IRVING HANCOCK
This series of stories, based on the actual doings of grammar school
boys, comes near to the heart of the average American boy.
1 THE GRAMMAR SCHOOL BOYS OF GRIDLEY; Or, Dick
\& Co. Start Things Moving.
2 THE GRAMMAR SCHOOL BOYS SNOWBOUND; Or, Dick
\& Co. at Winter Sports.
3 THE GRAMMAR SCHOOL BOYS IN THE WOODS; Or,
Dick \& Co. Trail Fun and Knowledge.
4 THE GRAMMAR SCHOOL BOYS IN SUMMER ATHLETICS;
Or, Dick \& Co. Make Their Fame Secure.
Cloth, Illustrated Price, per Volume, 50c.
* * * * *
High School Boys' Vacation Series
By H. IRVING HANCOCK
``Give us more Dick Prescott books!''
This has been the burden of the cry from young readers of the country
over. Almost numberless letters have been received by the publishers,
making this eager demand; for Dick Prescott, Dave Darrin, Tom Reade, and
the other members of Dick \& Co. are the most popular high school boys in
the land. Boys will alternately thrill and chuckle when reading these
splendid narratives.
1 THE HIGH SCHOOL BOYS' CANOE CLUB; Or, Dick \& Co.'s
Rivals on Lake Pleasant.
2 THE HIGH SCHOOL BOYS IN SUMMER CAMP; Or, The
Dick Prescott Six Training for the Gridley Eleven.
3 THE HIGH SCHOOL BOYS' FISHING TRIP; Or, Dick \& Co.
in the Wilderness.
4 THE HIGH SCHOOL BOYS' TRAINING HIKE; Or, Dick \&
Co. Making Themselves ``Hard as Nails.''
Cloth, Illustrated Price, per Volume, 50c.
* * * * *
The Circus Boys Series
By EDGAR B. P. DARLINGTON
Mr. Darlington's books breathe forth every phase of an intensely
interesting and exciting life.
1 THE CIRCUS BOYS ON THE FLYING RINGS; Or, Making
the Start in the Sawdust Life.
2 THE CIRCUS BOYS ACROSS THE CONTINENT; Or, Winning
New Laurels on the Tanbark.
3 THE CIRCUS BOYS IN DIXIE LAND; Or, Winning the
Plaudits of the Sunny South.
4 THE CIRCUS BOYS ON THE MISSISSIPPI; Or, Afloat with
the Big Show on the Big River.
Cloth, Illustrated Price, per Volume, 50c.
* * * * *
The High School Girls Series
By JESSIE GRAHAM FLOWER, A. M.
These breezy stories of the American High School Girl take the reader
fairly by storm.
1 GRACE HARLOWE'S PLEBE YEAR AT HIGH SCHOOL;
Or, The Merry Doings of the Oakdale Freshman Girls.
2 GRACE HARLOWE'S SOPHOMORE YEAR AT HIGH
SCHOOL; Or, The Record of the Girl Chums in Work and
Athletics.
3 GRACE HARLOWE'S JUNIOR YEAR AT HIGH SCHOOL;
Or, Fast Friends in the Sororities.
4 GRACE HARLOWE'S SENIOR YEAR AT HIGH SCHOOL;
Or, The Parting of the Ways.
Cloth, Illustrated Price, per Volume, 50c.
* * * * *
The Automobile Girls Series
By LAURA DENT CRANE
No girl's library---no family book-case can be considered at all complete
unless it contains these sparkling twentieth-century books.
1 THE AUTOMOBILE GIRLS AT NEWPORT; Or, Watching
the Summer Parade.
2 THE AUTOMOBILE GIRLS IN THE BERKSHIRES; Or,
The Ghost of Lost Man's Trail.
3 THE AUTOMOBILE GIRLS ALONG THE HUDSON; Or,
Fighting Fire in Sleepy Hollow.
4 THE AUTOMOBILE GIRLS AT CHICAGO; Or, Winning Out
Against Heavy Odds.
5 THE AUTOMOBILE GIRLS AT PALM BEACH; Or, Proving
Their Mettle Under Southern Skies.
Cloth, Illustrated Price, per Volume, 50c.
\gutchapter{End of Project Gutenberg's The Iron Boys on the Ore Boats, by James R. Mears}
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%\documentclass[12pt,shieldcrest]{ociamthesis} % use older shield crest logo
%load any additional packages
\usepackage{amssymb}
%input macros (i.e. write your own macros file called mymacros.tex
%and uncomment the next line)
%\include{mymacros}
\title{Codimension-Two\\[1ex] %your thesis title,
Free Boundary Problems} %note \\[1ex] is a line break in the title
\author{Keith Gillow} %your name
\college{St Catherine's College} %your college
%\renewcommand{\submittedtext}{change the default text here if needed}
\degree{Doctor of Philosophy} %the degree
\degreedate{Trinity 1998} %the degree date
%end the preamble and start the document
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\include{chapter2}
\include{conclusions}
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\include{appendix2}
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http://ctan.imsc.res.in/support/musixtex/doc/musixdoc/accidentals.tex | imsc.res.in | CC-MAIN-2022-49 | text/x-tex | application/x-tex | crawl-data/CC-MAIN-2022-49/segments/1669446710409.16/warc/CC-MAIN-20221127141808-20221127171808-00489.warc.gz | 11,844,982 | 1,984 | \chapter{Accidentals}
\vspace*{-3ex}
Accidentals can be introduced in two ways.
The first way, using explicit macros, consists for
example in coding \keyindex{fl}\pitchp~to put a \ital{flat} at the
pitch $p$, presumably right before a note at the same pitch. This is a
non-spacing command and will automatically place the accidental an
appropriate distance to the left of the anticipated note head.
Naturals, sharps, double flats and double sharps are coded \keyindex{na}\pitchp,
\keyindex{sh}\pitchp, \keyindex{dfl}\pitchp~and \keyindex{dsh}\pitchp~respectively.
The alternate macros \keyindex{lfl}, \keyindex{lna}, \keyindex{lsh},
\keyindex{ldfl} and \keyindex{ldsh}
place the same accidentals, but shifted one note head width
to the left. These can be used if a note head has been shifted to the left, or
to avoid collision with other accidentals
in a chord. If you want to shift an accidental by some other amount for
more precise positioning, you could use \keyindex{loffset} with the normal
accidental macro as the second parameter.
The second way of coding accidentals is to modify the parameter of a
note command. Just put the symbol
\verb|^| for a sharp, \verb|_| for a flat, \verb|=|~for a natural,
\verb|>| for a double sharp, or \verb|<| for a double
flat, right before the letter or number representing the pitch.
For example, \verb|\qb{^g}| yields a
$G\sharp$. This may be used effectively in collective coding, e.g.
\verb|\qu{ac^d}|.
There are two sizes of accidentals. By default they will be large unless there
is not enough space between notes, in which case they will be made small. Either
size can be forced locally by coding \keyindex{bigfl}, \keyindex{bigsh}, etc., or
\keyindex{smallfl}, \keyindex{smallsh}, etc. If you want all accidentals to
be large, then declare \keyindex{bigaccid} near the top of the input file. For
exclusively small ones use \keyindex{smallaccid}; \keyindex{varaccid} will restore
variable sizes.
For editorial purposes, small accidentals can be placed \ital{above} note
heads. This is done using \keyindex{uppersh}\pitchp, \keyindex{upperna}\pitchp, or
\keyindex{upperfl}\pitchp:
\begin{music}\nostartrule
\startextract
\NOtes\uppersh l\qa l\en
\NOtes\upperna m\qa m\en
\NOtes\upperfl l\qa l\en
\zendextract
\end{music}
\vspace*{-2ex}
It also possible to introduce \ital{\ixem{cautionary accidental}s},
i.e.,~small accidentals enclosed in parentheses. This is done by preceding
the name of the accidental keyword with ``\verb|c|''\label{cautionary}.
Available cautionary accidentals are \keyindex{csh}, \keyindex{cfl},
\keyindex{cna},
\keyindex{cdfl} and \keyindex{cdsh}, which give
\begin{music}\nostartrule
\startextract
\NOtes\csh g\qa g\en
\NOtes\cfl h\qa h\en
\NOtes\cna i\qa i\en
\NOtes\cdfl j\qa j\en
\NOtes\cdsh k\qa k\en
\zendextract
\end{music}
\vspace*{-2ex}
\noindent The distance between notes and accidentals is controlled by
\keyindex{accshift}\verb|=|\ital{any \TeX\ dimension}, where
positive values shift to the left and negative to right, with a
default of~\verb|0pt|.
For ``big'' cautionary accidentals, use, for example,
\verb|{|\keyindex{largenotesize}\verb|\csh|\pitchp\verb|}| or see Section~\ref{brapar}.
|
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https://mirror.anarhija.net/lib.anarhija.net/mirror/p/pc/prole-cat-anarchism-and-confederate-flag-culture.tex | anarhija.net | CC-MAIN-2021-25 | application/octet-stream | application/x-tex | crawl-data/CC-MAIN-2021-25/segments/1623487633444.37/warc/CC-MAIN-20210617192319-20210617222319-00501.warc.gz | 364,803,537 | 5,644 | \documentclass[DIV=12,%
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\title{Anarchism and Confederate-Flag Culture}
\date{}
\author{Prole Cat}
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% start a new right-handed page
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\section{One Man’s Journey from Southern Heritage to Libertarian Socialism}
If you are someone who displays a Confederate flag out of overt racism, this text is not for you. In fact, we will fight you in the streets.
If, however, you are someone who insists that he is not racist, but you have at some point in your life displayed a Confederate Flag out of a general sense of rebellion against the government, the boss, parents, pompous Yankee liberals, or just against modern society in general, then this text is addressed to you. Especially, if you are a working class southerner who flies the Cross of St. Andrew as an in-your-face act of protest against the mass production of national “culture,” a McDonaldized product that has the effect of smothering and burying authentic local cultures that (some feel) are symbolized by the Confederate flag\dots{} especially, then, this brief sketch of one man’s odyssey from the glorification of southern heritage to an appreciation of anarchist ideas and values, may have something to say to you.
As a child I was raised by the school, television, church, and my parents, in roughly that order of importance. All of these authorities told me what it was appropriate for me to think, do and feel at any given moment. I was supposed to love and obey a God who never bothered to show his face to me, and in a similar vein I was supposed to love and obey a familial father who didn’t have time for me, either. Parents and teachers were to be respected, and for children who failed in that endeavor the “policeman would come and get you” (which proved to be all too true.)
But at least I had the television\dots{} Mr. TV was my buddy, my fellow sufferer in the face of all this authority. Mr. TV was the coolest kid on the block, the guy who knew his way around the social pit-falls of school, the ultimate arbiter of what was cool and what was, gasp, “lame” (can you imagine a crueler, more horrible expression?)
The problem was, it was all a bunch of lies, and I knew it. (Or at least, once I got old enough to think for myself, I knew it.) The meaning-of-it-all that the church offered meant, in fact, nothing at all. It was illogical, but served the purpose of telling me to be a good servant, because I would get my reward after I was dead from an invisible person in the sky. (I don’t think the unlikelihood of THAT little scenario requires too much commentary.) The school, with its sports programs and detention halls, which claimed to be opening my mind to the mysteries of the universe and the joys of great art, was in fact training to me to become a cog in the great corporate machine. And my parents were too much in the thrall of this corporate religion themselves, to do anything but reinforce it.
Even my best friend, the TV, turned against me. He begin to say that if I was born a white southerner, then I was to blame for all the racial ills of mankind. That’s right, I, little ole southern white boy, had done it all, from the Grecian slave societies of antiquity to the Boston busing riots, from the rape of Nanking to the Holocaust, all the racial ills of mankind could be laid at my doorstep. By this point in time the church (and my parents) had stuffed me so full of irrational guilt that I was inclined to believe it\dots{} but somehow, it just didn’t add up.
So I took a big horn from a bottle of (Kentucky) bourbon, hung a Confederate flag in the window, and told the world to kiss my ass. I was through apologizing for being born\dots{}
Here is the summary version: the American corporate titans that control the TV, newspapers, and grammar school textbooks have declared all things southern to be racist, and all things racist to be southern, in order to confuse the issue and evade their own responsibilities. They portray slavery as having been a purely southern institution, instead of as a single component of a universally oppressive white\Slash{}Anglo economic system (that happened to find its worst excesses in the cotton fields of the southern United States in the 1800’s).
By painting slavery and racism as a uniquely southern phenomenon, the CEO’s manage to divert attention from the racist legacy that remains. When they falsely imply that racism is uniquely southern, and then correctly add that the racial situation in the south now mirrors that of the rest of the country, they declare the problem solved. Implicitly this has the effect of encouraging such reactionary nonsense as charges of “reverse discrimination.”
In fact, nothing could be further from the truth. The problem of white supremacy in America is anything but resolved. In fact, police officers all over America target people of color for searches and beatings, while the nation’s jails, prisons and housing projects are littered with the dark-skinned human refuse of the ultimate soulless commodity system, the great American labor market. In the 1850’s most blacks were subject to whips and chains, but a small portion were relatively “free”. In modern society, most people of color are impoverished or imprisoned, while a similarly small portion are middle-class, or relatively “well-off”. Very little has changed, other than the means of the enslavement.
These facts are what the “racism is a southern thing” myth is intended to obscure. Blacks, Latinos, and to a lesser extent, working-class southern whites are all harmed by this myth. It is time to place the responsibility for American racism and poverty squarely where it belongs, at the doorstep of the business class, and at the foot of the American flag (and all other Anglo-nationalist flags) which provide the business class with aid and comfort.
So, burn your Confederate flag — give it a respectful ceremony if you must, but really, get rid of it — and join the anarchist movement as we set out to combat, defeat and replace the racist, classist, patriarchal society that bores us with political speeches, numbs us with television, scares us with the superstitions of religion, hypnotizes us with the banalities of commercial advertising, and threatens us with the state-religion of patriotism. We are the “rebels” of the modern corporate-techno-nightmare age, and our ultimate goal is to replace the businesses, government and churches with a society of free equals, in which all live at peace with nature and each other.
Join us as we set out to build a new world, a world in which every man, woman and, yes, child is viewed and treated as a valuable part of the great whole of larger humanity, instead of as a competitor for money, sex, and power. Join us as we set out to build a world based on sharing and mutual respect, where local idiosyncrasies (that are supportive of human dignity) are respected, even celebrated. Join us, and be proud of the human being that you are, the community in which you live, and the planet on which you stand.
Down with McDonalds, Wal-Mart, ADM and the rest of the corporations! Up with your neighbors, and yourself!
Prole Cat
September, in the year of our store, 2003
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Library.Anarhija.Net
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Prole Cat
Anarchism and Confederate-Flag Culture
\bigskip
Retrieved on 29 January 2011 from \href{http://news.infoshop.org/article.php?story=03/09/22/5995007}{news.infoshop.org}
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\textbf{lib.anarhija.net}
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https://www.math.purdue.edu/~heinzer/preprints/qir39.tex | purdue.edu | CC-MAIN-2022-49 | text/x-tex | application/x-tex | crawl-data/CC-MAIN-2022-49/segments/1669446710972.37/warc/CC-MAIN-20221204104311-20221204134311-00028.warc.gz | 907,932,286 | 32,366 |
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% Address of record for the research reported here
\address{Department of Mathematics, Tulane University, New
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\email{fuchs@tulane.edu}
% Information for second author
\author{William Heinzer}
\address{Department of Mathematics, Purdue University, West
Lafayette, Indiana 47907}
\email{heinzer@math.purdue.edu}
\author{Bruce Olberding}
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module, Pr\"ufer domain, $m$-canonical ideal.}
\begin{abstract} Let $R$ be an integral domain
and let $Q$ denote the quotient field of $R$. We investigate the
structure of $R$-submodules of $Q$ that are $Q$-irreducible, or
completely $Q$-irreducible. One of our goals is to describe the
integral domains that admit a completely $Q$-irreducible ideal, or
a nonzero $Q$-irreducible ideal. If $R$ has a nonzero finitely
generated $Q$-irreducible ideal, then $R$ is quasilocal. If $R$ is
integrally closed and admits a nonzero principal $Q$-irreducible
ideal, then $R$ is a valuation domain. If $R$ has an $m$-canonical
ideal and admits a completely $Q$-irreducible ideal, then $R$ is
quasilocal and all the completely $Q$-irreducible ideals of $R$ are
isomorphic. We consider the condition that every nonzero ideal of
$R$ is an irredundant intersection of completely $Q$-irreducible
submodules of $Q$ and present eleven conditions that are equivalent
to this. We classify the domains for which every nonzero ideal can
be represented uniquely as an irredundant intersection of completely
$Q$-irreducible submodules of $Q$. The domains with this property
are the Pr\"ufer domains that are almost semi-artinian, that is,
every proper homomorphic image has a nonzero socle. We characterize
the Pr\"ufer or Noetherian domains that possess a completely
$Q$-irreducible ideal or a nonzero $Q$-irreducible ideal.
\end{abstract}
\maketitle
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\def\fg{finitely generated}
\def\fp{finitely presented}
\def\cp{cyclically presented}
\def\fr{finite rank}
\def\tf{torsion-free}\def\vd{valuation domain}
\def\vr{valuation ring}
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\def\Dds{Dedekind domains}
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\section{Introduction}
This article continues a study of commutative ideal theory in rings
without finiteness conditions begun in \cite{FHO}, \cite{FHO3},
\cite{FHO2} and \cite{HO}. In \cite{FHO} and \cite{FHO3} we examine
irreducible and completely irreducible ideals of commutative rings.
In the present article we investigate stronger versions of these two
notions of irreducibility for ideals of integral domains. In
particular, we consider irreducibility of an ideal of an integral
domain when it is viewed as a submodule of the quotient field of the
domain.
All rings in this paper are commutative and contain a multiplicative
identity. Our notation is as in \cite{FS}. Let $R$ be a ring and let
$C$ be an $R$-module. An $R$-submodule $A$ of $C$ is {\it
$C$-irreducible} if $A = B_1 \cap B_2$, where $B_1$ and $B_2$ are
$R$-submodules of $C$, implies that either $B_1 = A$ or $B_2 =A$. An
$R$-submodule $A$ of $C$ is {\it completely $C$-irreducible} (or
{\it completely irreducible} when the module $C$ is clear from
context) if $A = \bigcap_{i \in I}B_i$, where $\{B_i\}_{i \in I}$ is
a family of $R$-submodules of $C$, implies $A = B_i$ for some $i \in
I$.
In the case where the module $C$ is the ring $R$, an ideal $A$ of
$R$ is $R$-irreducible as a submodule of $R$ precisely if $A$ is
{\it irreducible} as an ideal in the conventional sense that $A$ is
not the intersection of two strictly larger ideals. It is
established by Fuchs in \cite[Theorem 1]{F} that a proper
irreducible ideal $A$ of the ring $R$ is a {\it primal ideal} in the
sense that the set of elements of $R$ that are non-prime to $A$ form
an ideal $P$ that is necessarily a prime ideal and is called the
{\it adjoint prime ideal} of $A$. One then says that $A$ is
$P$-primal. For such an ideal $A$, it is the case that $A =
A_{(P)}$, where $A_{(P)} = \bigcup_{x \in R \setminus P}(A:_Rx)$.
In Remark \ref{0.1} we record several general facts about completely
$C$-irreducible submodules. The straightforward proofs are omitted.
\begin{remark} \label{0.1}
For a proper submodule $A$ of $C$ the following are equivalent:
\begin{enumerate}
\item
$A$ is completely $C$-irreducible.
\item
There exists an element $x \in C \setminus A$ such that $x \in B$
for every submodule $B$ of $C$ that properly contains $A$.
\item
$C/A$ has a simple essential socle, that is, $C/A$ is a cocyclic
$R$-module.
\item
$C/A$ is subdirectly irreducible in the sense that in any
representation of $C/A$ as a subdirect product of $R$-modules, one
of the projections to a component is an isomorphism.
\end{enumerate}
\end{remark}
It is also straightforward to see that every submodule of a module
$C$ is an intersection of completely $C$-irreducible submodules of
$C$. Thus a nonzero module $C$ contains proper completely
$C$-irreducible submodules.
The main focus of our present study is the case where $R$ is an
integral domain and $C = Q$ is the quotient field of $R$.
(Throughout this paper $Q$ is understood to be the quotient field
of the integral domain $R$.) We are thus interested in
$Q$-irreducible and completely $Q$-irreducible submodules of $Q$. We
are particularly interested in determining conditions on an integral
domain $R$ in order that $R$ admit a completely $Q$-irreducible
ideal, or a nonzero $Q$-irreducible ideal. The zero ideal of $R$ is
always $Q$-irreducible, but if $R \ne Q$, the zero ideal of $R$ is
not completely $Q$-irreducible. In the case where $R$ admits
completely $Q$-irreducible ideals, or nonzero $Q$-irreducible
ideals, we are interested in describing the structure of such
ideals. Ideals with either of these properties are necessarily
primal ideals.
It is frequently the case that an integral domain $R$ may fail to
have any fractional ideals that are completely $Q$-irreducible, or
any nonzero ideals that are $Q$-irreducible. If $R = \mathbb Z$ is
the ring of integers, then every nonzero proper $Q$-irreducible
$R$-submodule of $Q$ is completely $Q$-irreducible and has the form
$p^n\mathbb Z_{p\mathbb Z}$, where $p$ is a prime integer and $n$ is
an integer. Thus for $R = \mathbb Z$ every nonzero proper
$Q$-irreducible $R$-submodule of $Q$ is a fractional ideal of a
valuation overring of $R$. Moreover, every nonzero fractional
$R$-ideal has a unique representation as an irredundant intersection
of infinitely many completely $Q$-irreducible $R$-submodules of $Q$.
It follows that $R$ has no nonzero fractional ideal that is
$Q$-irreducible.
In Section 2 we establish basic properties of irreducible submodules
of an $R$-module $C$ with special emphasis on the case where $C =
Q$. We prove in Theorem \ref{1.2} that if $R$ admits a nonzero
principal $Q$-irreducible fractional ideal, then $R$ is quasilocal,
and $R$ is integrally closed if and only if $R$ is a valuation
domain. In Theorem~\ref{qirreducible} we give several necessary
conditions for an integral domain to possess a nonzero
$Q$-irreducible ideal. If $A$ is a nonzero $Q$-irreducible ideal, we
prove that $\End(A)$ is quasilocal, and that $A$ is a primal ideal
of $\End(A)$ with adjoint prime the maximal ideal of $\End(A)$. If
the integral domain $R$ admits a nonzero finitely generated
$Q$-irreducible ideal, we prove that $R$ is quasilocal. Moreover,
every nonzero $Q$-irreducible ideal of a Noetherian domain is
completely $Q$-irreducible.
In Section 3 we review some relevant results and examples regarding
completely $Q$-irreducible fractional ideals. Over a quasilocal
domain, an $m$-canonical ideal (if it exists) is an example of a
completely $Q$-irreducible ideal. If $R$ has an $m$-canonical ideal
and admits a completely $Q$-irreducible ideal, we prove that $R$ is
quasilocal and all completely $Q$-irreducible ideals of $R$ are
isomorphic. We classify the Noetherian domains that admit a nonzero
$Q$-irreducible ideal.
In Proposition~\ref{3.3} of Section 4 we show that a proper
submodule $A$ of the quotient field $Q$ of a domain is an
irredundant intersection of $Q$-irreducible submodules if and only
if the injective hull of $Q/A$ is an interdirect sum of
indecomposable injectives.
In Section 5 we continue to examine irredundant intersections of
$Q$-irreducible submodules in $Q$. We draw on the literature to
give in Theorem~\ref{semi-artinian} eleven different module- and
ideal-theoretic conditions that are equivalent to the assertion that
every nonzero ideal of a domain is an irredundant intersection of
completely irreducible submodules of $Q$. We show in particular
that such a domain is locally almost perfect, and from this
observation we answer in the negative a question of Bazzoni and
Salce of whether every locally almost perfect domain $R$ has the
property that $Q/R$ is semi-artinian (Example~\ref{semi-artinian
example}). In Theorem~\ref{uniqueness} we classify the domains for
which every nonzero ideal can be represented {\it uniquely} as an
irredundant intersection of completely $Q$-irreducible submodules of
$Q$. The domains having this property have Krull dimension at most
one and are necessarily Pr\"ufer, that is, every nonzero finitely
generated ideal is invertible. They may be described precisely as
the Pr\"ufer domains $R$ that are almost semi-artinian, that is,
every proper homomorphic image of $R$ has a nonzero socle.
In light of Theorem~\ref{uniqueness} it is useful to describe the
completely irreducible submodules of the quotient field of a
Pr\"ufer domain. This is done in Theorem~\ref{Prufer case}. Also in
Section 6 we characterize the Pr\"ufer domains that possess a
completely $Q$-irreducible ideal, or a nonzero $Q$-irreducible
ideal. We prove that a Pr\"ufer domain $R$ that admits a nonzero
$Q$-irreducible ideal also admits a completely $Q$-irreducible
ideal, and this holds if and only if every proper $R$-submodule of
$Q$ is a fractional $R$-ideal.
In Section 7 we discuss several open questions, and in an appendix
we correct some errors in the article \cite{FHO2} that were pointed
out to us by Jung-Chen Liu and her student Zhi-Wei Ying. We are
grateful to them for showing us these mistakes.
\section{The structure of $Q$-irreducible ideals}
We begin with several general results.
\begin{proposition}\label{characterization}
Let $R$ be a ring and $C$ an $R$-module. The following statements are
equivalent for a proper $R$-submodule $A$ of $C$.
\begin{itemize}
\item[(i)]
$A$ is a completely $C$-irreducible $R$-submodule of $C$.
\item[(ii)] There
exists $x \in C \setminus A$ such that for all $y \in C \setminus A$
we have $x \in A+Ry$.
\item[(iii)] $A$ is $C$-irreducible and there exists a maximal ideal
$M$ of $R$ such that \newline $A \subset (A:_CM)$, where
$(A:_CM)=\{y \in C : yM \subseteq A\}$.
\end{itemize}
Furthermore, if $R$ is a domain, $A$ is torsionfree and $C$ is the
divisible hull of $A$, then statements (i)-(iii) are equivalent to:
\begin{itemize}
\item[(iv)] There is a maximal ideal $M$ of $R$ such that $A = AR_M$ and
$A$ is completely $C$-irreducible as an $R_M$-submodule of $C$.
\end{itemize}
\end{proposition}
\begin{proof}
(i) $\Rightarrow$ (ii) Let $A^*$ be the intersection of all
$R$-submodules of $C$ properly containing $A$. Then $A \subset
A^*$, and $A^*/A$ is a simple $R$-module. Hence $A^* = Rx + A$ for
some $x \in Q \setminus A$, and (ii) follows.
(ii) $\Rightarrow$ (iii) By (ii) there exists $x \in C \setminus
A$ such that $A^*:=A + Rx$ is contained in every $R$-submodule of
$C$ properly containing $A$. Hence $A^*/A$ is a simple $R$-module
and $A^*/A \cong R/M$ for some maximal ideal $M$ of $R$. Thus $A^*
\subseteq (A:_CM)$ so that $(A:_CM) \ne A$.
(iii) $\Rightarrow$ (i) Since $A$ is irreducible, $(A:_CM)/A \cong
R/M$ and every proper submodule containing $A$ contains $(A:_CM)$,
proving (i).
(i) $\Rightarrow$ (iv) Since $R$ is a domain and $A$ is
torsion-free, $A = \bigcap_{M \in \Max(R)}A_M$, where each $A_M$ is
identified with its image in $C = QA$. Because $A$ is completely
$C$-irreducible, $A = A_M$ for some maximal ideal $M$ of $R$. The
assumption that $A$ is completely $C$-irreducible as an $R$-module
clearly implies $A$ is completely $C$-irreducible as an
$R_M$-submodule of $C$.
(iv) $\Rightarrow$ (iii) Since we have established the equivalence
of (i)-(iii), and since by assumption $A$ is a completely
irreducible $R_M$-submodule of $C$, we have by (iii) (applied to
the $R_M$-module $A$) that there exists $x \in (A :_C MR_M)
\setminus A$. Now since $A = A_M$, we have $A \ne (A:_C MR_M) =
(A:_C M)$. Thus it remains to observe that $A$ is $C$-irreducible.
Suppose $A = B \cap D$ for some
$R$-submodules $B$ and $D$ of $C$. Then $A = A_M = B_M \cap D_M$,
so since by assumption $A$ is irreducible as an $R_M$-submodule of
$C$, it must be that $A = B_M$ or $A = D_M$. Thus $B \subseteq A$
or $D \subseteq A$, proving that $A$ is irreducible.
\end{proof}
\begin{remark} \label{1.1}
Let $R$ be an integral domain that is properly contained in its
quotient field $Q$.
{\rm (i)} By Remark \ref{0.1}, every $R$-submodule of $Q$ is an
intersection of completely irreducible submodules of $Q$. In
particular, every ideal of $R$ is an intersection of completely
irreducible submodules of $Q$.
{\rm (ii)} A fractional ideal $A$ of $R$ is completely
$Q$-irreducible if and only if $A$ is not the intersection of
fractional $R$-ideals that properly contain $A$. If $A$ is a
fractional $R$-ideal and $A \ne Q$, then $A$ is completely
$Q$-irreducible if and only if there exists $x \in Q \setminus A$
such that $x$ is in every fractional ideal that properly contains
$A$.
{\rm (iii)} A maximal ideal $P$ of $R$ is completely $Q$-irreducible
if it is $Q$-irreducible. This is immediate from Proposition
\ref{characterization}, since $P \subsetneq R \subseteq (P:_QP)$.
\end{remark}
In Lemma \ref{2.2}, we establish several general facts about
$Q$-irreducible and completely $Q$-irreducible ideals.
\begin{lemma} \label{2.2} Let $A$ be a proper
ideal of the integral domain $R$. Then
{\rm (i)} $A$ is $Q$-irreducible if and only if for each nonzero $r
\in R$ the ideal $rA$ is irreducible.
{\rm (ii)} For a nonzero $q \in Q$, the fractional ideal $qA$ is
$Q$-irreducible if and only if $A$ is $Q$-irreducible. Therefore the
property of being $Q$-irreducible is an invariant of isomorphism
classes of fractional $R$-ideals.
{\rm (iii)} $A$ is $Q$-irreducible if and only if there is a
prime ideal $P$ of $R$ such that $A = AR_{P}$ and $A$ is a
$Q$-irreducible ideal of $R_P$. It then follows that $P$ is uniquely
determined by $A$ and $A$ is $P$-primal.
{\rm (iv)} For a nonzero $q \in Q$, the fractional ideal $qA$ is
completely $Q$-irreducible if and only if $A$ is completely
$Q$-irreducible. Therefore the property of being completely
$Q$-irreducible is an invariant of isomorphism classes of fractional
$R$-ideals.
{\rm (v)} If $A$ is completely $R$-irreducible and if for each
nonzero $r \in R$ the ideal $rA$ is irreducible, then $A$ is
completely $Q$-irreducible.
\label{ideal characterization}
\end{lemma}
\begin{proof} {\rm (i)} Assume $A$ is $Q$-irreducible
and $r$ is a nonzero element of $R$. If $rA = B \cap C$ for ideals
$B$ and $C$ of $R$, then $A = r^{-1}B \cap r^{-1}C$. Since $A$ is
$Q$-irreducible, either $A = r^{-1}B$ or $A = r^{-1}C$. Hence
either $rA = B$ or $rA = C$ and $rA$ is irreducible. Conversely,
assume $A$ is not $Q$-irreducible. Then there exist $R$-submodules
$B$ and $C$ of $Q$ that properly contain $A$ such that $A = B \cap
C$. We may assume that $B$ and $C$ are fractional ideals of $R$.
Then there exists a nonzero $r \in R$ such that $rB$ and $rC$ are
integral ideals of $R$. Moreover, $A = B \cap C$ implies $rA = rB
\cap rC$ and $A \subset B$ implies $rA \subset rB$ and similarly $A
\subset C$ implies $rA \subset rC$. Therefore $rA$ is reducible.
This completes the proof of {\rm (i)}.
Statements {\rm (ii)} and {\rm(iv)} are clear since $A = \bigcap_{i
\in I}B_i$ if and only if $qA = \bigcap_{i \in I}qB_i$ and
multiplication by $q$ (or by $q^{-1}$) preserves strict inclusion.
{\rm (iii)} Assume $A$ is $Q$-irreducible. Then $A$ is $P$-primal
for some prime ideal $P$ of $R$, so that $A = A_{(P)} = AR_P \cap
R$. Since $A$ is $Q$-irreducible, this forces $A = AR_P$. Clearly
then $A$ is $Q$-irreducible as an $R_P$-module since it is
$Q$-irreducible as an $R$-module. Conversely, suppose that $A =
AR_P$ and $A$ is $Q$-irreducible as an ideal of $R_P$. If $A = B
\cap C$ for some $R$-submodules $B$ and $C$ of $Q$, then $A = AR_P =
BR_P \cap CR_P$, and since $A$ is a $Q$-irreducible $R_P$-submodule
of $Q$, $A = BR_P$ or $A = CR_P$. Thus $B \subseteq A$ or $C
\subseteq A$, which completes the proof.
{\rm(v)} Since $A$ is completely $R$-irreducible, there exists an
element $x \in R \setminus A$ such that $x$ is in every ideal of $R$
that properly contains $A$. Let $A^* = A + xR$. If $A$ is not
completely $Q$-irreducible, then there exists an $R$-submodule $B$
of $Q$ that properly contains $A$ but does not contain $x$. Since
there are no ideals properly between $A$ and $A^*$, $A = A^* \cap B$
and this intersection is irredundant. We may assume that $B$ is a
fractional ideal of $A$. Then there exists a nonzero $r \in R$ such
that $rB$ is an integral ideal of $R$. Therefore $rA = rA^* \cap rB$
is an irredundant intersection. It follows that $rA$ is not
irreducible.
\end{proof}
\begin{remark} \label{2.44}
With regard to Lemma \ref{2.2} we have:
\begin{enumerate}
\item
If $A$ is a nonzero $Q$-irreducible ideal of $R$ and $P$ is as in
Lemma \ref{2.2}(iii), then $R_P \subseteq \End(A)$ and $rA = A$ for
each $r \in R \setminus P$. It follows that $A$ is contained in
every ideal of $R$ not contained in $P$. Thus if $P$ is a maximal
ideal of $R$ and $A$ is $P$-primary with $A = AR_P$, then $R$ is
quasilocal.
\item
It is also true that if $A$ and $B$ are isomorphic $R$-submodules of
$Q$, then $A$ is (completely) $Q$-irreducible if and only if $B$ is
(completely) $Q$-irreducible. For $A$ and $B$ are $R$-isomorphic if
and only if there exists $q \in Q$ such that $A = qB$.
\end{enumerate}
\end{remark}
\begin{theorem}\label{1.2}
If the integral domain $R$ has a nonzero principal fractional ideal
that is $Q$-irreducible, then $R$ is quasilocal and every principal
ideal of $R$ is $Q$-irreducible. If $R$ is integrally closed, then
\begin{itemize}
\item[(i)]
$R$ is $Q$-irreducible if and only if $R$ is a valuation domain, and
\item[(ii)]
$R$ is completely $Q$-irreducible if and only if $R$ is a valuation
domain with principal maximal ideal. \end{itemize}
\end{theorem}
\begin{proof}{\rm(i)} Lemma \ref{ideal characterization} implies
that $R$ has a nonzero principal fractional ideal that is
(completely) $Q$-irreducible if and only if every nonzero principal
fractional ideal of $R$ is (completely) $Q$-irreducible. Suppose $R$
has distinct maximal ideals $M$ and $N$. Then there exist $x \in M$
and $y \in N$ such that $x + y = 1$. It follows that $xyR = xR \cap
yR$ is an irredundant intersection. By Lemma~\ref{ideal
characterization}(i), $R$ is not $Q$-irreducible.
{\rm(ii)} Suppose that $R$ is integrally closed and $Q$-irreducible
but is not a valuation domain. Then there exists $x \in Q$ such
that neither $x$ nor $1/x$ is in $R$. Let ${\mathcal{F}}$ be the
set of valuation overrings of $R$ that contain $x$ and let
${\mathcal{G}}$ be the set of valuation overrings of $R$ that
contain $1/x$. Let $A = \bigcap_{V \in {\mathcal{F}}}V$ and $B =
\bigcap_{W \in {\mathcal{G}}}W$. Then $x \in A$ implies $R
\subsetneq A$ and $1/x \in B$ implies $R \subsetneq B$. Observe that
every valuation overring of $R$ is a member of at least one of the
sets ${\mathcal{F}}$ or ${\mathcal{G}}$. Since $R$ is integrally
closed, we have $R = A \cap B$, a contradiction to the assumption
that $R$ is $Q$-irreducible. Conversely, it is clear that if $R$ is
a valuation domain, then $R$ is integrally closed and
$Q$-irreducible.
{\rm(iii)} By (ii) we need only observe the well-known fact that a
valuation domain $R$ is completely $Q$-irreducible if and only if
the maximal ideal of $R$ is principal. (See for example \cite{Baz}.)
\end{proof}
\begin{remark} \label{2.4} There exist integral domains $R$
that are completely $Q$-irreducible and are not integrally closed.
If $R$ is a one-dimensional Gorenstein local domain, then $R$, and
every nonzero principal fractional ideal of $R$, is completely
$Q$-irreducible. Thus, for example, if $k$ is a field and $a$ and
$b$ are relatively prime positive integers, then the subring $R :=
k[[t^a, t^b]]$ of the formal power series ring $k[[t]]$ is
completely $Q$-irreducible.
\end{remark}
Theorem~\ref{1.2}(ii) characterizes among integrally closed domains
$R$ the ones that are valuation domains as precisely those $R$ that
are $Q$-irreducible. As a corollary to
Proposition~\ref{characterization}, we have the following additional
characterizations of the valuation property in terms of
$Q$-irreducibility.
\begin{corollary} \label{valuation criterion} The following are equivalent
for a domain $R$ with quotient field $Q$.
\begin{itemize}
\item[(i)] $R$ is a
valuation domain.
\item[(ii)] Every irreducible ideal is $Q$-irreducible.
\item[(iii)]
Every completely irreducible ideal is completely $Q$-irreducible.
\item[(iv)]
There exists a maximal ideal of $R$ that is $Q$-irreducible.
\item[(v)]
There exists a maximal ideal of $R$ that is completely
$Q$-irreducible.
\end{itemize}
\end{corollary}
\begin{proof} (i) $\Rightarrow$ (ii)
If $R$ is a valuation domain, then it is
easy to see that irreducible ideals are $Q$-irreducible since the
$R$-submodules of $Q$ are linearly ordered.
(ii) $\Rightarrow$ (iii) If $A$ is a completely irreducible ideal of
$R$, then there is a maximal ideal $M$ of $R$ such that $(A:_R M)
\ne A$. Thus $(A:_QM) \ne A$, and since $A$ is by (ii)
$Q$-irreducible, we have from Proposition~\ref{characterization}
(iii) that $A$ is $Q$-irreducible.
(iii) $\Rightarrow$ (iv) This is clear from the fact that maximal
ideals are completely irreducible.
(iv) $\Rightarrow$ (v) This follows from Remark \ref{1.1}(iii).
(v) $\Rightarrow$ (i) Let $M$ be a completely $Q$-irreducible
maximal ideal of $R$. For every nonzero $r \in R$, $rM$ is
completely irreducible by Proposition~\ref{ideal characterization}.
It is shown in Lemma 5.1 of \cite{FHO3} that this property
characterizes valuation domains, so the proof is complete.
\end{proof}
\begin{corollary} \label{prime corollary} Let $P$ be a prime ideal of a
domain $R$. Then $P$ is $Q$-irreducible if and only if $P = PR_P$
and $R_P$ is a valuation domain. Thus if $P$ is $Q$-irreducible,
then $R_P/P$ is the quotient field of $R/P$, and $R$ is a pullback
of $R/P$ and the valuation domain $R_P$. Moreover $P$ is completely
$Q$-irreducible as an ideal of $R_P$.
\end{corollary}
\begin{proof} Suppose that $P$ is $Q$-irreducible. By
Lemma~\ref{2.2}, $P=PR_P$ and $PR_P$ is a $Q$-irreducible ideal of
$R_P$. Hence, by Corollary~\ref{valuation criterion}, $R_P$ is a
valuation domain.
Conversely, assume $P = PR_P$ and $R_P$ is a valuation domain. By
Corollary~\ref{valuation criterion}, $P$ is a $Q$-irreducible ideal
of $R_P$. Hence, by Lemma~\ref{2.2}, $P$ is $Q$-irreducible. It
follows from Remark \ref{1.1}(iii) that $P = PR_P$ is a completely
$Q$-irreducible ideal of $R_P$.
\end{proof}
\begin{remark} With $P = PR_P$ as in Corollary \ref{prime
corollary}, if $R \ne R_P$, then $P$ as an ideal of $R$ is not
completely $Q$-irreducible. For Proposition \ref{characterization}
(iii) implies that a completely $Q$-irreducible prime ideal is a
maximal ideal, and by Remark \ref{2.44}(i), if $P$ is maximal and
$Q$-irreducible, then $R = R_P$. It can happen however that $P$ is
$Q$-irreducible and nonmaximal. This is the case, for example, if
$P$ is a nonmaximal prime of a valuation domain $R$.
\end{remark}
\begin{remark} Pullbacks arising as in Corollary~\ref{prime corollary}
have been well-studied; for a recent survey see \cite{GaH}. For
example, a consequence of our Corollary~\ref{prime corollary} and
Theorem 4.8 in \cite{GaH2} is that if a domain $R$ has a
$Q$-irreducible prime ideal $P$, then $R$ is coherent if and only if
$R/P$ is coherent.
\end{remark}
\begin{theorem} Assume that $A$ is a
nonzero $\, Q$-irreducible ideal of the integral domain $R$. Then
\begin{itemize}
\item[(i)] If $A$ is not principal, then $AA^{-1}$ is
contained in the Jacobson radical of $R$.
\item[(ii)] $\End(A)$ is a quasilocal integral domain.
\end{itemize}
Let $M$ denote the maximal ideal of $\End(A)$.
\begin{itemize}
\item[(iii)] $A$ is an $M$-primal ideal of $\End(A)$.
\item[(iv)] If $\,M$ is finitely generated as an ideal of $\End(A)$, then
$A$ is completely $Q$-irreducible as an ideal both of $R$ and of
$\End(A)$.
\item[(v)] If $A$ is a finitely generated ideal of $R$,
then $R$ is quasilocal and the maximal ideal of $R$ is the adjoint
prime of $A$.
\item[(vi)] If both $A$ and its adjoint prime are finitely
generated ideals, then $A$ is completely $Q$-irreducible.
\end{itemize}\label{qirreducible}
\end{theorem}
\begin{proof}
(i) Let $x \in A^{-1}$ and suppose that there is a maximal ideal
$N$ of $R$ not containing $xA$. Then there exists $y \in N$ such
that $xA + yR = R$. It follows that $xyA = xA \cap yR$. By
Lemma~\ref{ideal characterization}(ii), $xyA$ is irreducible.
Therefore either $xyA = xA$ or $xyA = yR$. If $xA = xyA$, then $xA
\subseteq yR \subseteq N$, a contradiction, while if $xyA = yR$,
then $xA = R$ and $A$ is principal. We conclude that every maximal
ideal of $R$ contains $xA$. Therefore $AA^{-1}$ is contained in
the Jacobson radical of $R$.
(ii) and (iii) Since $A$ is $Q$-irreducible as an ideal of $R$, it
is also $Q$-irreducible as an ideal of $\End(A)$. By
Lemma~\ref{ideal characterization}(iii), there is a prime ideal $M$
of $\End(A)$ such that $A = A\End(A)_M$. Thus $\End(A)_M \subseteq
\End(A)$, which implies that $M$ is the unique maximal ideal of
$\End(A)$. Also by Lemma~\ref{ideal characterization}(iii), $A$ is
$M$-primal.
(iv) Let $x_1,\ldots,x_n$ generate $M$. By
Lemma~\ref{characterization}(iii), to show that $A$ is completely
$Q$-irreducible it suffices to prove that $(A:_QM) \ne A$. Now
$(A:_QM) = x_1^{-1}A \cap \cdots \cap x_{n}^{-1}A$, so if $(A:_QM) =
A$, then the $Q$-irreduciblity of $A$ implies $x_i^{-1}A = A$ for
some $i$. In this case, $x_i^{-1} \in \End(A)$, which is impossible
since $x_i \in M$, the maximal ideal of $\End(A)$.
(v) By Lemma~\ref{ideal characterization}(ii), $A = AR_P$ for some
prime ideal $P$ of $R$. Thus $R_P \subseteq \End(A)$. But $A$ is
a finitely generated ideal of $R$ implies that $\End(A)$ is an
integral extension of $R$. This forces $R = R_P$, so that $P$ is
the unique maximal ideal of $R$.
(vi) By (v), $R$ is quasilocal with maximal ideal $M$, and $M$ is
the adjoint prime of $A$. As in the proof of (iv), we have $A
\subset (A:_QM)$. Therefore Lemma~\ref{characterization}(ii) implies
that $A$ is completely $Q$-irreducible.
\end{proof}
\begin{corollary} \label{Noetherian case} Every nonzero $Q$-irreducible
ideal over a Noetherian domain is completely $Q$-irreducible. If the
Noetherian domain $R$ admits a completely $Q$-irreducible ideal,
then $R$ is local and $\dim R \le 1$.
\end{corollary}
\begin{proof}
Suppose that $A$ is a nonzero $Q$-irreducible ideal of $R$. By
Theorem~\ref{qirreducible}(vi) $A$ is a completely $Q$-irreducible
ideal of $R$, and hence also of $\End(A)$. By
Theorem~\ref{qirreducible}(ii), $\End(A)$ is quasilocal. Since $R$
is Noetherian, $\End(A)$ is a finitely generated integral extension
of $R$. Therefore $R$ is local.
If $\dim R > 1$, then there exists a nonzero nonmaximal prime ideal
$P$ of $R$. Let $x \in P$ with $x \ne 0$. Then $xM$ is completely
irreducible by Lemma~\ref{ideal characterization}(iv). However, by
Corollary 1.4 in \cite{FHO3} a completely irreducible ideal of a
Noetherian local domain is primary for the maximal ideal,
contradicting $xM \subseteq P$. Therefore $\dim R \le 1$.
\end{proof}
\begin{corollary}
If the integral domain $R$ admits an invertible $Q$-irreducible
ideal, then every invertible ideal of $R$ is principal and
completely $Q$-irreducible.
\end{corollary}
\begin{proof} Suppose that $A$ is an invertible $Q$-irreducible ideal of $R$.
By Theorem~\ref{qirreducible}(i) $A$ is principal. Let $B$ be
an invertible ideal of $R$. Since $A$
is invertible, $A = (B:_Q:(B:_QA))$. Moreover, $(B:_Q A)$ is an
invertible, hence finitely generated, fractional ideal of $R$. Hence
there are elements $q_1,\ldots,q_k \in Q$ such that $A = (B:_Q
(q_1,\ldots,q_k)R) = q_1^{-1}B \cap \cdots \cap q_k^{-1}B$. Since
$A$ is $Q$-irreducible, there exists $i \in \{1,\ldots,k\}$ such
that $B = q_iA$. Hence $B$ is principal and $R$-isomorphic to $A$.
By Lemma~\ref{2.2}, $B$ is $Q$-irreducible.
\end{proof}
\begin{remark} Statement (ii) of Theorem~\ref{qirreducible} is true
also when $A$ is a completely irreducible submodule of $Q$. For by
Lemma~\ref{characterization}(iv) (with $A$ viewed as a completely
irreducible $\End(A)$-submodule of $Q$) there is a maximal ideal $M$
of $\End(A)$ such that $A = A_M$ This forces $\End(A)_M \subseteq
\End(A)$, so $\End(A)$ is quasilocal. \end{remark}
\section{Completely $Q$-irreducible and $m$-canonical ideals}
As noted in Remark~\ref{1.1} every ideal of a domain is the
intersection of completely irreducible submodules of the quotient
field. Thus for a given domain there exists an abundance of
completely irreducible submodules of $Q$. However, as we observe in
Section 1, a domain need not possess a completely $Q$-irreducible
ideal (see also Example~\ref{no canonical}).
In this section we examine the existence and structure of completely
$Q$-irreducible ideals. We also consider the class of
``$m$-canonical'' ideals. A nonzero fractional ideal $A$ of a
domain $R$ is an {\it $m$-canonical} fractional ideal if for all
nonzero ideals $B$ of $R$, $B = (A:_Q(A:_Q B))$. This terminology is
from \cite{BHLP} and \cite{HHP}. Different terminology is used in
\cite{Baz} and \cite{FS} to express the same concept. An ideal $A$
is, in our terminology, $m$-canonical if and only if, in the
terminology of \cite{Baz} and \cite{FS}, $R$ is an
``$A$-divisorial'' domain and $\End(A) = R$. Notice that the
property of being an $m$-canonical ideal is invariant with respect
to $R$-isomorphism for fractional ideals of $R$.
It follows from \cite[Lemma 4.1]{HHP} that an $m$-canonical ideal of
a quasilocal domain is completely $Q$-irreducible. A deeper result
is due to S. Bazzoni \cite{Baz}: {\it A fractional ideal $A$ of a
quasilocal domain $R$ is $m$-canonical if and only if $A$ is
completely $Q$-irreducible, $\End(A) =R$ and for all nonzero $r \in
R$, $A/rA$ satisfies the dual AB-$5^*$ of Grothendieck's AB-5.} (An
$R$-module $B$ satisfies AB-$5^*$ if for any submodule $C$ of $B$
and inverse system of submodules $\{B_i\}_{i \in I}$ of $B$, it is
the case that $\bigcap_{i \in I}(C + B_i) = C+\bigcap_{i \in
I}(B_i)$.)
As examples later in this section show, a domain need not possess an
$m$-canonical ideal. However if $R$ admits an $m$-canonical ideal,
then all completely $Q$-irreducible ideals of $R$ are isomorphic:
\begin{proposition}\label{criterion} Let $R$ be a domain that is not a field.
If $R$ has an $m$-canonical ideal $A$, then every completely
$Q$-irreducible ideal of $R$ is isomorphic to $A$. Consider the
following statements.
\begin{itemize}
\item[(i)] $R$ has an $m$-canonical ideal.
\item[(ii)] Any two completely
$Q$-irreducible ideals of $R$ are isomorphic.
\end{itemize}
Then $(i) \Rightarrow (ii)$. If every completely irreducible
proper submodule of $Q$ is a fractional ideal of $R$, then $(ii)
\Rightarrow (i)$.
\end{proposition}
\begin{proof} Suppose that $R$ has an $m$-canonical ideal $A$.
If $B$ is a nonzero ideal of $R$, then $B = \bigcap_{q}q^{-1}A$,
where $q$ ranges over all nonzero elements of $(A:_Q B)$. Thus if
$B$ is completely $Q$-irreducible, then $B = q^{-1}A$ for some $0
\ne q \in (A:_QB)$. Thus every proper completely $Q$-irreducible
ideal is isomorphic to $A$, and (i) $\Rightarrow$ (ii).
Assume that any two completely $Q$-irreducible ideals are
isomorphic and every completely $Q$-irreducible proper submodule of
$Q$ is a fractional ideal of $R$. Let $A$ be a completely
irreducible $R$-ideal. By Remark~\ref{0.1} every ideal of $R$ is an
intersection of completely $Q$-irreducible submodules of $Q$ and
therefore of completely $Q$-irreducible fractional ideals of $R$.
Thus every ideal of $R$ is an intersection of ideals isomorphic to
$A$; that is, for any ideal $B$, there exists a set $X \subseteq Q$
such that $B = \bigcap_{q \in X}qA$. It follows that $B =
(A:_Q(A:_QB))$. Hence $A$ is an $m$-canonical ideal.
\end{proof}
\begin{remark} An integral domain may have an $m$-canonical ideal,
but not admit a completely $Q$-irreducible fractional ideal. For
example, if $R$ is a Dedekind domain having more than one maximal
ideal, then $R$ admits an $m$-canonical ideal, but does not have any
completely $Q$-irreducible fractional ideals. Indeed, as we observe
in Proposition \ref{quasilocal}, if $R$ has an $m$-canonical ideal
and admits a completely $Q$-irreducible ideal, then $R$ is
quasilocal.
\end{remark}
\begin{proposition} \label{quasilocal}
If $R$ has an $m$-canonical ideal and a completely $Q$-irreducible
ideal, then $R$ is quasilocal.
\end{proposition}
\begin{proof} Let $A$ be a completely $Q$-irreducible ideal of $R$.
By Proposition \ref{criterion}, $A$ is an $m$-canonical ideal.
Therefore $R = \End(A)$. By Theorem \ref{qirreducible}, $\End(A)$ is
quasilocal. Therefore $R$ is quasilocal.
\end{proof}
\begin{remark} If $A$ is a proper $R$-submodule of $Q$, then $A$ is
contained in a completely irreducible proper submodule of $R$. Thus
if every completely irreducible proper submodule of $Q$ is a
fractional ideal of $R$, then every proper submodule of $Q$ is a
fractional ideal of $R$. The latter property holds for $R$ if and
only if there exists a valuation overring of $R$ which is a
fractional ideal of $R$ \cite[Theorem 79]{M2}.
\end{remark}
Routine arguments show that a nonzero fractional ideal of a
valuation domain is $m$-canonical if and only if it is completely
$Q$-irreducible. Also in the Noetherian case, the condition
AB-$5^*$ is redundant, as we note next. The following proposition
is essentially due in the case of Krull dimension 1 to Matlis
\cite{Mat} and in the general case with the assumption that $\End(A)
= R$ to Bazzoni \cite{Baz}. Bazzoni's proof shows that you can omit
in our context the assumption that $\End(A) = R$. We outline how to
do this in the proof. We also include a different proof of the step
(iv) $\Rightarrow$ (iii).
\begin{proposition} \label{Bazzoni} \label{same}
{\em (Bazzoni \cite[Theorem 3.2]{Baz}, Matlis \cite[Theorem
15.5]{Mat})} The following statements are equivalent for a nonzero
fractional ideal $A$ of a Noetherian local domain $(R,M)$ that is
not a field.
\begin{itemize}
\item[(i)] $Q/A$ is
an injective $R$-module.
\item[(ii)] $R$ has Krull dimension 1 and $(A:M)/A$ is a simple $R$-module.
\item[(iii)] $A$ is an $m$-canonical ideal.
\item[(iv)] $A$ is $Q$-irreducible.
\end{itemize}
\end{proposition}
\begin{proof}
(i) $\Rightarrow$ (ii) By Proposition 4.4 in \cite{Mati} a
Noetherian domain that admits an ideal of injective dimension 1
necessarily has Krull dimension 1. Thus $\dim(R) =1$, so we may
apply Theorem 15.5 in \cite{Mat} to obtain (ii).
(ii) $\Rightarrow$ (iii) This is contained in Theorem 15.5 of
\cite{Mat}.
(iii) $\Rightarrow$ (i) If $A$ is an $m$-canonical ideal, then
necessarily $\End(A) =R$, so Theorem 3.2 of \cite{Baz} applies.
(iii) $\Rightarrow$ (iv) An $m$-canonical ideal of a quasilocal
domain is completely $Q$-irreducible \cite[Lemma 4.1]{HHP}.
(iv) $\Rightarrow$ (iii) Suppose that $A$ is $Q$-irreducible. By
Corollary~\ref{Noetherian case} $\dim R = 1$ and $A$ is completely
$Q$-irreducible. By Theorem~\ref{qirreducible} $\End(A)$ is a
quasilocal domain. Since $R$ is Noetherian, $\End(A)$ is Noetherian.
Thus by Theorem 3.2 in \cite{Baz} $A$ is an $m$-canonical ideal of
$\End(A)$.
By \cite[Theorem 15.7]{Mat} a Noetherian local domain of Krull
dimension 1 has an $m$-canonical ideal if and only if the total
quotient ring of the completion of the domain is Gorenstein.
Therefore the total quotient ring of the completion of $\End(A)$ is
Gorenstein. Now $\End(A)$ is an overring of $R$ that is finitely
generated as a module over $R$. Hence there exists a nonzero $x \in
R$ such that $x\End(A) \subseteq R$. It follows that the total
quotient ring $T$ of the completion of $R$ coincides with the
completion of $\End(A)$. Thus $T$ is a Gorenstein ring, and by the
result cited above, $R$ has an $m$-canonical ideal, say $B$. By
Proposition~\ref{criterion} $B$ is isomorphic to $A$, so $A$ is an
$m$-canonical ideal of $R$.
\end{proof}
\begin{remark}
Let $R$ be a Noetherian domain of positive dimension. If $R$ admits
a nonzero $Q$-irreducible ideal, then $R$ is local and $\dim R = 1$.
Every proper $R$-submodule of $Q$ is a fractional $R$-ideal if and
only if the integral closure $\overline{R}$ of $R$ is local (so a
DVR) and is a finitely generated $R$-module. In this case every
proper $R$-submodule of $Q$ that is completely $Q$-irreducible is a
fractional $R$-ideal. There exist, however, other one-dimensional
Noetherian local domains $R$ that admit completely $Q$-irreducible
ideals. By Proposition \ref{same}, $R$ admits a completely
$Q$-irreducible ideal if and only if the total quotient ring of the
completion of $R$ is Gorenstein. In particular, this is true if $R$
is Gorenstein. There exist examples where $R$ is Gorenstein and
$\overline{R}$ is not local, or not a finitely generated $R$-module,
or both. For such an $R$, nonzero principal fractional ideals of
$R$ are completely $Q$-irreducible, and there also exist completely
$Q$-irreducible proper $R$-submodules of $Q$ that are not
fractional $R$-ideals.
\end{remark}
\begin{example} \label{no canonical} {\it A one-dimensional Noetherian
local domain need not possess a nonzero $Q$-irreducible ideal.} As
noted in the proof of Proposition~\ref{same} it suffices to exhibit
a Noetherian local domain $R$ of Krull dimension 1 such that the
total quotient ring of $R$ is not Gorenstein. Such examples can be
found in Proposition 3.1 of \cite{FR} and Theorem 1.26 and Corollary
1.27 of \cite{HRS}. A specific example, based on \cite{HRS} is
obtained as follows. Let $x, y, z$ be algebraically independent over
the field $k$ and let $R = k[x, y, z]_{(x, y, z)}$. Let $f, g \in
xk[[x]]$ be such that $x, f, g$ are algebraically independent over
$k$. Let $u = y - f$ and $v = z - g$. Then $P := (u, v)k[[x, y, z]]$
is a prime ideal of height 2 of the completion $\widehat R = k[[x,
y, z]]$ of $R$ having the property that $P \cap R = (0)$. If $\q$ is
a $P$-primary ideal of $\widehat R$, it follows from \cite[Theorem
1.26]{HRS} that $(\widehat R/\q) \cap k(x,y,z)$ is a one-dimensional
Noetherian local domain having $\widehat R/\q$ as its completion. If
we take $\q = P^2 = (u^2, uv, v^2)\widehat R$, then the total
quotient ring of $\widehat R/\q$ is not Gorenstein.
\end{example}
\begin{remark}
(i) It is an open question whether a completely $Q$-irreducible
ideal of a quasilocal integrally closed domain $R$ is an
$m$-canonical ideal if $\End(A) = R$ \cite[Question 5.5]{Baz}. The
answer is affirmative when $A = R$: this is Theorem 2.3 of
\cite{Baz}.
(ii) In \cite{Baz} Bazzoni relates the question in (i) to a 1968
question of Heinzer \cite{H}: If $R$ is a domain for which every
nonzero ideal is divisorial, is the integral closure of $R$ a
Pr\"ufer domain? To obtain that $R$ has a Pr\"ufer integral closure
the weaker requirement that $R$ be completely $Q$-irreducible is
not sufficient, as we note below in Example~\ref{gilmerhoffmann}.
(iii) Bazzoni constructs in Example 2.11 of \cite{Baz} an example of
a quasilocal domain $R$ such that $R$ is completely $Q$-irreducible
but not $m$-canonical. By Lemma~\ref{Bazzoni} and (i) such a
domain is neither Noetherian nor integrally closed.
\end{remark}
The $D+M$ construction provides a source of interesting examples of
completely $Q$-irreducible ideals. The following example is from
\cite[Remark 5.3]{HHP}, as strengthened in \cite{BHLP}. We recall
it here, since it is relevant to Example~\ref{gilmerhoffmann}.
\begin{example} \label{HHP example} {\rm Let $k \subset F$ be a proper
extension of fields and $V$ be a valuation domain (that is not a
field) of the form $V = F +M$, where $M$ is the maximal ideal of
$V$. Define $R = k +M$. Then $R$ is a quasilocal domain with
maximal ideal $M$. If $U$ is any $k$-subspace of $F$ of codimension
$1$, then the fractional ideal $A = U + M$ is a completely
$Q$-irreducible fractional ideal of $R$ since every $R$-submodule of
the quotient field $Q$ of $R$ that properly contains $A$ contains
also $V$.
It is proved in Theorem 3.2 of \cite{BHLP} that if $F$ is an
algebraic extension of $k$ with $[F:k]$ infinite, then there exist
codimension $1$ subspaces $U$ and $W$ of $F$ such that $U +M$ and
$W+M$ are non-isomorphic completely $Q$-irreducible fractional
ideals of $R$. Thus by Proposition~\ref{criterion} $R$ does not
possess an $m$-canonical ideal. Indeed, it is shown in Theorem 3.1
of \cite{BHLP} that $R$ has an $m$-canonical ideal if and only if
$[F:k]$ is finite. }
\end{example}
We shall see in Theorem~\ref{existence} that it is possible for a
domain $R$ to possess a completely $Q$-irreducible ideal $A$ and not
be quasilocal. It follows from this result that $\End(A)$ need not
equal $R$. However, in this situation, $R$ is not quasilocal. The
next example shows that even when $R$ is quasilocal, it is possible
for a completely $Q$-irreducible ideal to have an endomorphism ring
not equal to $R$.
Gilmer and Hoffmann in \cite{GH} establish the existence of an
integral domain $R$ that admits a unique minimal overring, but has
the property that the integral closure of $R$ is not Pr\"ufer. In
Example~\ref{gilmerhoffmann} we modify this example to establish the
existence of an integral domain $R$ that has infinitely many
distinct fractional overrings $R_t$, $t \in \mathbb N$, such that
each $R_t$ is completely $Q$-irreducible as a fractional ideal of
$R$. Since $R_t$ is a fractional overring of $R$, $\End(R_t) = R_t$.
We remark that Bazzoni in \cite[Section 4]{Baz} has abstracted and
greatly generalized the example of \cite{GH}.
\begin{example} \label{gilmerhoffmann} Let $K$ be a field and let
$L = K((X))$ be the quotient field of the formal power series ring
$K[[X]]$. Every nonzero element of $L$ has a unique expression as a
Laurent series $\sum_{n \ge k}a_nX^n$, where $k$ is an integer, the
$a_n \in K$ and $a_k \ne 0$. Let $Y$ be an indeterminate over $L$
and let $V = L[[Y]]$ denote the formal power series ring in $Y$ over
the field $L$. Thus $V$ is a rank-one discrete valuation domain
(DVR) of the form $L + M$, where $M = YL[[Y]]$ is the maximal ideal
of $V$. Let $R = K + M^2$. It is well-known and readily established
that $R$ is a one-dimensional quasilocal domain with maximal ideal
$M^2$. For $t$ a positive integer, let $W_t$ be the set of all
elements $f \in K((X))$ such that $f = 0$ or the coefficient of
$X^{-t}$ in the Laurent expansion of $f$ is $0$. Notice that $W_t$
is a $K$-subspace of $L$ and $L = W_t \oplus KX^{-t}$ as $K$ vector
spaces. Let $R_t = K + W_tY + M^2$. Then $R_t$ is an overring of $R$
and $Y^2R_t \subseteq M^2$, so $R_t$ is a fractional ideal of $R$.
We show that $R_t$ is completely $Q$ irreducible as a fractional
$R$-ideal by proving that $X^{-t}Y$ is in every fractional ideal of
$R$ that properly contains $R_t$. Let $f \in Q \setminus R_t$. Since
$Q = L((Y))$, there exists an integer $j$ such that $f = \sum_{n \ge
j}b_nY^n$, where each $b_n \in L$ and $b_j \ne 0$. Notice that $f
\not\in R_t$ implies $j \le 1$. Since $L = K((X))$, there exists an
integer $k$ such that $b_j = \sum_{n \ge k}a_nX^n$, where each $a_n
\in K$ and $a_k \ne 0$. Since $a_k$ is a unit of $R$, the fractional
ideal $R_t + Rf = R_t + a_k^{-1}f$, so we may assume that $a_k = 1$.
If $j < 0$, then $X^{-k-t}Y^{1-j} \in M^2 \subset R$ and
$X^{-k-t}Y^{1-j}f = X^{-t}Y + \alpha Y + \beta Y^2$, where $\alpha
\in K[[X]]$ and $\beta \in V = L[[Y]]$. Since $\alpha \in W_t$,
$\alpha Y + \beta Y^2 \in R_t$. Hence $X^{-t}Y \in R_t + Rf$ if $j <
0$. If $j = 0$ and $k \ne 0$, then $X^{-k-t}Y^{1-j} \in W_tY \subset
R_t$ and $X^{-k-t}Yf = X^{-t}Y + \alpha Y + \beta Y^2$, where
$\alpha Y + \beta Y^2 \in R_t$, so $X^{-t}Y \in R_t + Rf$ in this
case. If $j = 0$ and $k = 0$, replace $f$ by $f-1$ to obtain a
situation where $k
>0$ and $j \ge 0$. If $j = 1$, then $f \not\in R_t$ implies $b_1 \not\in
W_t$. Hence $b_1 = c + dX^{-t}$, where $c \in W_t$ and $0 \ne d \in
K$. Hence $f - cY = dX^{-t}Y + \alpha Y^2$, where $\alpha \in
L[[Y]]$. Therefore also in this case $X^{-t}Y \in R_t + Rf$. We
conclude that $R_t$ is completely $Q$-irreducible.
\end{example}
In Example~\ref{gilmerhoffmann} the completely $Q$-irreducible
fractional ideals that are constructed have endomorphism rings
integral over the base ring. In Example \ref{valuation example} we
exhibit a Noetherian local domain $R$ and a completely
$Q$-irreducible $R$-submodule $A$ of $Q$ such that $\End(A)$ is not
integral over $R$. We first give a partial characterization of when
valuation overrings are (completely) $Q$-irreducible.
\begin{theorem} \label{divisible} Let $V$ be a valuation overring of the
domain $R$. Then the following two statements hold for $V$.
\begin{itemize}
\item[(i)] If $V/R$ is a
divisible $R$-module, then $V$ is a $Q$-irreducible $R$-submodule of
$Q$. Moreover, $V$ has a principal maximal ideal if and only if $V$
is a completely $Q$-irreducible $R$-submodule of $Q$.
\item[(ii)] Suppose that $V$ is a DVR. Then $V$
is a completely $Q$-irreducible $R$-submodule of $Q$ if and only if
$V/R$ is a divisible $R$-module.
\end{itemize}
\end{theorem}
\begin{proof} (i) The assumption that $V/R$ is divisible implies that every
$R$-submodule of $Q$ containing $V$ is also a $V$-submodule of $Q$.
For if $x \not \in V$, then $1/x \in V$. Since $V/R$ is divisible,
$V = (1/x)V + R$. Thus $V + xR =xV$. Hence $V + xR$ is a
$V$-submodule of $Q$. This implies that any $R$-submodule of $Q$
containing $V$ is a $V$-module. Since $V$ is $Q$-irreducible as a
$V$-submodule of $Q$, it follows that $V$ is $Q$-irreducible as an
$R$-submodule of $Q$.
If the valuation domain $V$ has principal maximal ideal, then, by
Theorem~\ref{1.2}, $V$ is a completely $Q$-irreducible
$V$-submodule of $Q$. Therefore $V$ is a completely $Q$-irreducible
$R$-submodule of $Q$.
Conversely, if $V$ is a completely $Q$-irreducible $R$-submodule of
$Q$, then necessarily $V$ is a completely $Q$-irreducible
$V$-submodule of $Q$. By Corollary~\ref{valuation criterion} every
principal ideal of $V$ is $Q$-irreducible. Hence by
Theorem~\ref{1.2} $V$ has a principal maximal ideal.
(ii) Suppose that $V$ is a completely $Q$-irreducible $R$-submodule
of $Q$. Let $0 \ne x \in R$. We claim that $V = R + xV$. Consider
the ideal $C = (R+xV :_Q V)$ of $V$. Since $V$ is a DVR, $C$ is
isomorphic to $V$. Also, $C = \cap_{y \in V} y^{-1}(R+xV)$, so
since $C$ is completely $Q$-irreducible, $C$ is isomorphic to
$R+xV$. Thus $V$ and $R+xV$ are isomorphic as $R$-modules, and since
these two modules are rings, this forces $R+xV = V$, proving that
$V/R$ is divisible. The converse follows from (i).
\end{proof}
\begin{remark}\label{dvr} Let $V$ be a DVR overring of the integral domain $R$
and let $P$ be the center of $V$ on $R$. Necessary and sufficient
conditions in order that $V/R$ be a divisible $R$-module are that
(i) $PV$ is the maximal ideal of $V$, and (ii) the canonical
inclusion map of $R/P \hookrightarrow V/PV$ is an isomorphism. By
Theorem \ref{divisible}(ii), these conditions are also necessary and
sufficient in order that $V$ be completely $Q$-irreducible as an
$R$-submodule of $Q$.
\end{remark}
\begin{example} \label{valuation example}
Let $K$ be a field, and let $X$ and $Y$ be indeterminates for $K$.
Define $R = K[X,Y]_{(X,Y)}$.
We construct a valuation overring $V$ of $R$ such that $V$ is a
completely $Q$-irreducible $R$-submodule of $Q$. Let $g(X) \in
XK[[X]]$ be such that $X$ and $g(X)$ are algebraically independent
over $K$. Define a mapping $v$ on $K[X,Y] \setminus \{0\}$ by $v(\:
f(X,Y) \:) = $ smallest exponent of $X$ appearing in the power
series $f(X, g(X))$. Then $v$ extends to a rank-one discrete
valuation on $K(X,Y)$ centered on $(X,Y)R$ and having residue field
$K$. (More details regarding this construction can be found in
Chapter VI, Section 15, of \cite{ZS}.) Since the valuation ring $V$
of $v$ has maximal ideal $(X,Y)V$ and residue field $V/(X,Y)V = K$,
it follows that $V = R + (X,Y)^kV$ for all $k>0$. Since $V$ is a
DVR, $V = R+fV$ for every nonzero $f \in R$. Hence $V/R$ is a
divisible $R$-module. By Theorem~\ref{divisible}, $V$ is a
completely $Q$-irreducible $R$-submodule of $Q$.
\end{example}
\section{$Q$-irreducibility and injective modules}
Let $N$ be a submodule of the \tf\ $R$-module $M$. $N$ is said
to be an {\it RD-submodule} (relatively divisible) if $rN = N \cap
rM$ for all $r \in R$. An $R$-module $X$ is called {\it
RD-injective} if every homomorphism from an RD-submodule $N$ of any
$R$-module $M$ can be extended to a homomorphism $M \to X$. Every
$R$-module $M$ can be embedded as an RD-submodule in an RD-injective
module, and among such RD-injectives there is a minimal one, unique
up to isomorphisms over $M$, called the {\it RD-injective hull}
$\widehat M$ of $M$. If $M$ is torsion-free, then so are both
$\widehat M$ and $\widehat M/M$.
The $R$-topology of an $R$-module $M$ is defined by declaring the
submodules $rM$ for all $0 \ne r \in R$ as a subbase of open
neighborhoods of $0$. If $M$ is torsion-free, then it is Hausdorff
in the $R$-topology if and only if it is reduced (i.e. it has no
divisible submodules $\ne 0$). $M$ is $R$-complete if it is complete
(Hausdorff) in the $R$-topology. If $M$ is reduced torsion-free,
then it is an RD-submodule of its $R$-completion $\widetilde M$.
Observe that for a prime ideal $P$ the $R$-completion and
$R_P$-completion of $R_P$ are identical. The $R$-completion
$\widetilde M$ of a torsion-free $R$-module $M$ is an RD-submodule
of the RD-injective hull $\widehat M$ such that $\widehat
M/\widetilde M$ is reduced torsion-free.
\begin{lemma} For a proper $R$-submodule $A$ of $Q$ the
following conditions are equivalent:
{\rm (i)} $A$ is $Q$-irreducible;
{\rm (ii)} the injective hull $E(Q/A)$ of the $R$-module $Q/A$ is
indecomposable;
{\rm (iii)} the RD-injective hull $\widehat A$ of $A$ is
indecomposable.
\end{lemma}
\begin{proof} (i) $\Leftrightarrow$ (ii) An injective module is
indecomposable exactly if it is uniform.
(ii) $\Leftrightarrow$ (iii) This equivalence is a consequence of
Matlis' category equivalence between the category of $h$-divisible
torsion $R$-modules $T$ and the category of reduced $R$-complete
torsion-free $R$-modules $M$, given by the correspondences
$$ T \mapsto \Hom_R(Q/R, T) \quad {\rm and} \quad M \mapsto Q/R
\otimes_R M$$ which are inverse to each other. Under the category
equivalence, $Q/A$ and the $R$-completion $\widetilde A$ of $A$
correspond to each other, and so do the injective hull of $Q/A$ and
the RD-injective hull $\widehat A$ of $A$. As equivalence preserves
direct decompositions, the claim is evident.
\end {proof}
Let $I$ be an ideal of the ring $R$. It is well known that if
$E(R/I)$ is indecomposable, then $I$ is irreducible. Note that
$E(R/I)$ can also be written as $E(Q/A)$ for a $Q$-irreducible
$R$-submodule $A$ of $Q$. In fact, $E(R/I)$ is a summand of
$E(Q/I)$, so we can write: $E(Q/I) = E(R/I) \oplus E$ for an
injective $R$-module $E$. The kernel of the projection of $Q/I$ into
the first summand is of the form $A/I$ for a $Q$-irreducible
submodule $A$ of $Q$, and then $E(R/I) = E(Q/A)$.
Conversely, if $A$ is a $Q$-irreducible proper submodule of $Q$,
and $x \in Q \setminus A$, then the set $I = \{r \in R \ | \ rx \in
A\}$ is a primal ideal of $R$ such that $E(Q/A) = E(R/I)$. The
adjoint prime $P$ of the primal ideal $I$ may be called the {\it
prime associated to} $A$: this is uniquely determined by $A$, though
$I$ depends on the choice of $x$.
\begin{lemma} Every indecomposable injective $R$-module $E$
can be written as $E(Q/A)$ for a $Q$-irreducible $R$-submodule of
$A$ of $Q$. Moreover, there is a unique prime ideal $P$ of $R$ such
that $E(Q/A) \cong E(R/I)$ for a $P$-primal ideal $I$ of $R$, and
$P$ is a maximal ideal whenever $A$ is completely $Q$-irreducible.
\qed
\end{lemma}
We can add that $I$ can be replaced by $P$ if and only if $P$ is a
strong Bourbaki associated prime for $I$. Indeed, $E(R/I) = E(R/P)$
if and only if there are elements $r \in R \setminus I$ and $s \in R
\setminus P$ such that $(I:_Rr) = (P:_Rs)$. Since $(P:_Rs) = P$,
this is equivalent to $P = (I:_Rr)$, that is, $P$ is a strong
Bourbaki associated prime of $I$.
It is clear that every proper submodule of $Q$ is the intersection
of $Q$-irreducible submodules. This intersection is in general
redundant. A criterion for irredundancy is as follows.
\begin{proposition} \label{3.3} A proper submodule $A$ of $Q$ admits an
irredundant representation as an intersection of $Q$-irreducible
submodules if and only if $E(Q/A)$ is an interdirect sum of
indecomposable injectives.
\end{proposition}
\begin{proof} Suppose $A= \bigcap_{i \in I} A_i$ is an
irredundant intersection with $Q$-irreducible submodules $A_i$ of
$Q$. Setting $B_i = \bigcap_{j \in I, j \ne i} A_j$, it is clear
that the submodule generated by $B_i/A \ (i \in I)$ in $Q/A$ is
their direct sum. Hence $E(Q/A)$ contains the direct sum of the
injective hulls $E(Q/A_i) \cong E(B_i/A)$. As $Q/A$ embeds in the
direct product of the $Q/A_i$, $E(Q/A)$ embeds in the direct product
of the $E(Q/A_i)$. Thus $E(Q/A)$ is an interdirect sum of the
$E(Q/A_i)$ (these are evidently indecomposable).
Conversely, suppose $E(Q/A)$ is an interdirect sum of indecomposable
injectives $E_i \ (i \in I)$. Since $E_i$ is a uniform module, we
have $(Q/A) \cap E_i \ne 0$ for each $i \in I$. Clearly, $A_i$
(defined by $A_i/A = (Q/A) \cap \prod_{j \in I, j \ne i} E_j$) is a
submodule of $Q$, which is maximal disjoint from $E_i$, so
$Q$-irreducible. The intersection $A = \bigcap_{i \in I} A_i$ is
evidently irredundant.
\end{proof}
\section{Irredundant decompositions and semi-artinian modules}
In this section we examine domains for which every nonzero submodule
of $Q$ is an irredundant intersection of completely irreducible
submodules of $Q$. Such domains are closely related to the class of
almost perfect rings.
A ring $R$ is {\it perfect} if every $R$-module has a projective
cover; equivalently, (since our rings are assumed to be commutative)
$R$ satisfies the descending chain condition on principal ideals
\cite{Ba}. In their study \cite{BS1} of strongly flat covers of
modules, Bazzoni and Salce introduced the class of {\it almost
perfect domains}, consisting of those domains $R$ for which every
proper homomorphic image of $R$ is perfect. Every Noetherian domain
of Krull dimension 1 is almost perfect, but the class of almost
perfect domains includes also non-Noetherian non-integrally closed
domains-- see for example Section 3 of \cite{BS}.
There are a number of applications of perfect and almost perfect
domains in the literature, most of which are motivated by the rich
module theory for these classes of rings \cite{BS,BS1,EJ}. In this
section we emphasize different features of the module and ideal
theory of almost perfect domains, namely, the close connection with
irredundant decompositions into completely irreducible submodules.
If $R$ is a ring, then an $R$-module $A$ is (almost) {\it
semi-artinian} if every (proper) homomorphic image of $A$ has a
nonzero socle. In a semi-artinian module every irreducible
submodule is completely irreducible (see for example \cite[Lemma
2.4]{DC}), but this property does not characterize semi-artinian
modules \cite[Example 1.7]{FHO3}.
As indicated by Lemma~\ref{DC} below, the semi-artinian property is
both necessary and sufficient for irredundant decompositions into
completely irreducible submodules. Bazzoni and Salce note in
\cite{BS} that:
\begin{center}
$R$ almost perfect $\Rightarrow Q/R$ semi-artinian $\Rightarrow$ $R$
locally almost perfect.
\end{center}
They show also that $R$ is almost perfect if and only if $R$ is
$h$-local and every localization of $R$ at a maximal ideal is almost
perfect. In general, the first implication cannot be reversed
\cite[Example 2.1]{BS}. Smith asserts in \cite{Sm} that the
converse of the second implication is always true, but as noted in
\cite[p. 288]{BS} the proof is incorrect. Thus Bazzoni and Salce
raise the question in \cite[p. 288]{BS} of whether the converse is
always true; namely, if $R$ is locally almost perfect, is $Q/R$
necessarily semi-artinian?
We give an example in this section to show that the answer is
negative, and we characterize in Theorem~\ref{semi-artinian}(vi) and
(vii) precisely when a locally almost perfect domain $R$ has $Q/R$
semi-artinian. We collect also in this theorem a number of
different characterizations of domains $R$ for which $Q/R$ is
semi-artinian.
The following lemma is a special case of a lattice theoretic result
\cite[Theorem 4.1]{DC}. A number of other properties of irredundant
intersections of completely irreducible submodules of semi-artinian
modules can be deduced from this same article.
\begin{lemma} \label{DC} {\em (Dilworth-Crawley \cite{DC})} Let $R$ be a
ring and $A$ be an $R$-module. Then $A$ is (almost) semi-artinian
if and only if every (nonzero) submodule of $A$ is an irredundant
intersection of completely irreducible submodules of $A$.\qed
%
%\item[(ii)]
% $A$ is a distributive (almost) semi-artinian module if
%and only if every (nonzero) submodule of $A$ is a unique
%irredundant intersection of completely irreducible
%submodules of $A$.
%%
%
%\end{itemize}
\end{lemma}
% and
%statement (ii) follows from Theorem 6.1 and its second corollary in
%\cite{DC}.
In order to formulate (vii) of the next theorem, we recall that a
topological space $X$ is {\it scattered} if every nonempty subspace
of $X$ contains an isolated point.
\begin{theorem} \label{semi-artinian} The following
statements are equivalent for a domain $R$ with quotient field $Q$.
\begin{itemize}
\item[(i)] $Q/R$ is semi-artinian.
\item[(ii)] Every nonzero torsion module is semi-artinian.
\item[(iii)] $R$ is almost semi-artinian.
\item[(iv)] $Q$ is almost semi-artinian.
\item[(v)] For each nonzero proper ideal $A$ of $R$, there is
a maximal ideal that is a strong Bourbaki associated prime of $A$.
\item[(vi)] $R$ is locally almost perfect and for each nonzero
radical ideal $J$ of $R$, there is a maximal ideal of $R/J$ that is
principal.
\item[(vii)] $R$ is locally almost perfect and for each
nonzero radical ideal $J$ of $R$, $\Spec(R/J)$ is scattered.
\item[(viii)] For each torsion $R$-module $T$, every submodule
of $T$ is an irredundant intersection of completely irreducible
submodules of $T$.
\item[(ix)] For each torsion-free module $A$, every nonzero
submodule of $A$ is an irredundant intersection of completely
irreducible submodules of $QA$.
\item[(x)] Each nonzero submodule of $Q$ is an
irredundant intersection of completely irreducible submodules of
$Q$.
\item[(xi)] Each nonzero ideal of $R$ is an irredundant
intersection of completely irreducible submodules of $Q$.
\item[(xii)] Each nonzero ideal of $R$ is an irredundant
intersection of completely irreducible ideals.
\end{itemize}
\end{theorem}
\begin{proof} The equivalence of (i)-(iv) can be found in {\em
\cite[Theorem 4.4.1]{EJ}}. It follows then from Lemma~\ref{DC} that
(i) - (iv) are equivalent to (viii), (ix), (x) and (xii). The
equivalence of (vi) and (vii) is a consequence of Corollary 2.10 in
\cite{HO}. To complete the proof it is enough to show that (v) and
(vi) are equivalent to (i) and that (xi) is equivalent to (iii).
(i) $\Rightarrow$ (vi) Since $Q/R$ is semi-artinian, $R$ is locally
almost perfect. We have already established that (i) is equivalent
to (xii). That (xii) implies (vi) is a consequence of Corollary
2.10 of \cite{HO}.
(vi) $\Rightarrow$ (v) Suppose that $A$ is a proper nonzero ideal
of $R$. Since for every nonzero radical ideal $J$ of $R$, $R/J$ has
a maximal ideal of $R$ that is principal, every nonzero ideal of
$R$ has a Zariski-Samuel associated prime $M$ \cite[Theorem
2.8]{HO}; that is, $M = \sqrt{A:_Rx}$ for some $x \in R \setminus
A$. Since $R$ has Krull dimension $1$, $M$ is a maximal ideal of
$R$. By (vi) $R_M/(A_M:_{R_M} x)$ contains a simple $R_M$-module.
Thus there exists $y \in R \setminus (A_M:_{R_M}x)$ such that $MR_M
= (A_M:_{R_M}x):_{R_M}y = A_M:_{R_M}xy$. Since $A:_Rx \subseteq
A:_Rxy \subseteq M$ and $ \sqrt{A:_Rx} = M$, it follows that $M$ is
the only maximal ideal of $R$ containing $A:_Rxy$. Thus since
$A_M:_{R_M}xy = MR_M$, it is the case that $A:_Rxy = M$.
(v) $\Rightarrow$ (iii) If $A$ is a proper nonzero ideal of $R$ and
$M$ is a strong Bourbaki associated prime of $A$, then $A:_RM \ne
A$, so $R/A$ contains a simple $R$-module.
(iii) $\Rightarrow$ (xi) Since (iii) is equivalent to (x), it is
sufficient to note that (x) implies (xi).
(xi) $\Rightarrow$ (iii) Let $A$ be a proper nonzero ideal of $R$.
Then there exists a completely irreducible submodule $C$ of $Q$ such
that $A = C \cap D$ is an irredundant intersection for some
submodule $D$ of $Q$. Let $x \in D \setminus C$. Now $(C:_Q M)/C$
is the essential socle of $Q/C$, so if $y \in (C:_QM) \setminus C$,
then $y \in xR +C$. Thus $rx \in yR + C$ for some $r\in R$ such
that $rx \not \in C$. Consequently, $rxM \subseteq C$, and since $x
\in D$, it is the case that $rxM \subseteq A$ with $rx \not \in A$.
Thus $rx + A$ is a nonzero member of the socle of $R/A$. Statement
(iii) now follows.
\end{proof}
An integral domain $R$ is {\it almost Dedekind} if for each maximal
ideal $M$ of $R$, $R_M$ is a DVR. In \cite[Theorem 3.2]{O2} it is
shown that if $X$ is a Boolean (i.e. compact Hausdorff totally
disconnected) topological space, then there exists an almost
Dedekind domain $R$ with nonzero Jacobson radical such that
$\Max(R)$ is homeomorphic to $X$. Thus we obtain the following
corollary to Theorem~\ref{semi-artinian}(vii).
\begin{corollary} The following statements are equivalent for a
Boolean topological space $X$.
\begin{itemize}
\item[(i)] $X$ is a scattered space.
\item[(ii)] There exists a domain $R$ with nonzero Jacobson
radical such that $Q/R$ is semi-artinian and $\Max(R)$ is
homeomorphic to $X$. \qed
\end{itemize}
\end{corollary}
\begin{remark} In Example 2.1 of \cite{BS} an example is given of
a domain $R$ for which $Q/R$ is semi-artinian but $R$ is not almost
perfect. Using the corollary, we may obtain many such examples.
Indeed, let $X$ be an infinite Boolean scattered space. Then there
exists an almost Dedekind domain $R$ such that $\Max(R)$ is
homeomorphic to $X$ and $R$ is not a Dedekind domain. In
particular, $R$ is not $h$-local, since an $h$-local almost Dedekind
domain is Dedekind. Thus $Q/R$ is semi-artinian but $R$ is not
almost perfect.
\end{remark}
It is not difficult to exhibit infinite Boolean scattered spaces.
For example, let $X$ be a well-ordered set such that not every
element has an immediate successor. Then $X$ is a scattered space
with respect to the order topology on $X$, and the isolated points
of $X$ are precisely the smallest element of $X$ and the immediate
successors of elements in $X$ (see \cite[Example 17.3, p. 272]{Ko}).
In \cite{BS} Bazzoni and Salce raise the question of whether every
locally almost perfect domain $R$ has the property that $Q/R$ is
semi-artinian. Using Theorem~\ref{semi-artinian} we give an example
to show that this is not the case.
\begin{example} \label{semi-artinian example} Let $X$ be a Boolean space
that is not scattered (e.g. let $X$ be the Stone-\^Cech
compactification of the set of natural numbers with the discrete
topology). As noted above, there exists an almost Dedekind domain
$R$ such that $\Max(R)$ is homeomorphic to $X$ and $R$ has nonzero
Jacobson radical. Then $R$ is locally almost perfect but by
Theorem~\ref{semi-artinian}(vii) $Q/R$ is not semi-artinian.
\end{example}
In \cite{FHO} it is shown that every irreducible ideal of an almost
perfect domain is primary. A similar argument yields:
\begin{lemma}
\label{primary} If $R$ is a locally almost perfect domain, then
every proper irreducible ideal is primary. \end{lemma}
\begin{proof} Let $A$ be a nonzero
irreducible ideal. Then $A$ is primary if and only if any strictly
ascending chain of the form $A \subset A:_Rb_1 \subset A:_Rb_1b_2
\subset \cdots \subset A:_Rb_1b_2 \cdots b_n \subseteq \cdots$ for
$b_1,b_2,\ldots,b_n,\ldots \in R$ terminates \cite{F}. Suppose
there is an infinite such strictly ascending chain, and let $M$ be
a maximal ideal containing every residual $A:_Rb_1b_2 \cdots b_n$.
Since $R_M$ is an almost perfect domain, $R_M/A_M$ has the
descending chain condition for principal ideals. Thus there exists
$n>0$ such that $A_M:_Rb_1b_2 \cdots b_n = A_M:_Rb_1b_2 \cdots
b_{n+1}$. If $r \in A:_Rb_1b_2 \cdots b_{n+1}$, then there exists $x
\in R \setminus M$ such that $xr \in A:_Rb_1b_2 \ldots b_{n}$. An
irreducible ideal of a domain of Krull dimension 1 is contained in a
unique maximal ideal (see for example \cite[Lemma 2.7]{HO}), so
necessarily $A$ is $M$-primal. Thus $x$ is prime to $A$ and it
follows that $r \in A:_Rb_1b_2 \cdots b_n$. However, this forces
$A:_Rb_1b_2 \cdots b_n = A:_Rb_1b_2 \cdots b_{n+1}$, contrary to
assumption. Thus $A$ is primary.
\end{proof}
\begin{theorem} If $R$ is
an almost semi-artinian domain, then every ideal of $R$ is an
irredundant intersection of primary completely irreducible ideals.
\end{theorem}
\begin{proof} The theorem follows from Lemma~\ref{primary} and
Theorem~\ref{semi-artinian}(xii).
\end{proof}
We characterize next the domains $R$ for which every nonzero
submodule of $Q$ can be represented uniquely as an irredundant
intersection of completely $Q$-irreducible $R$-submodules.
An $R$-module $B$ is {\it distributive} if for all submodules
$A_1,A_2$ and $A_3$ of $B$, $(A_1 \cap A_2) + A_3 = (A_1 + A_3) \cap
(A_2 \cap A_3)$. The module $B$ is {\it uniserial} if its
submodules are linearly ordered by inclusion. An $R$-module is
distributive if and only if for all maximal ideals $M$ of $R$, $B_M$
is a uniserial $R_M$-module \cite{LS}.
\begin{lemma} Let $R$ be a ring and $B$ be an $R$-module. Let $\AA$ be
the set of all $R$-submodules of $B$ that are finite intersections
of completely irreducible submodules of $B$. Then the module $B$ is
distributive if and only if for each $A \in \AA$, the representation
of $A$ as an irredundant intersection of completely irreducible
submodules of $B$ is unique.
Furthermore, if a submodule $B$ of a distributive $R$-module can be
represented as a (possibly infinite) irredundant intersection of
irreducible submodules, then this representation is unique.
\label{distributive}\end{lemma}
\begin{proof} Suppose that each representation of $A \in \AA$ as an
irredundant intersection of completely $Q$-irreducible submodules of
$B$ is unique. Then this property holds also for the
$R_M$-submodules of $B_M$ for each maximal ideal $M$ of $R$. Thus
by the remark preceding the theorem, to prove that $B$ is
distributive it suffices to show that $B_M$ is a uniserial
$R_M$-module. Thus we may reduce to the case where $R$ is a
quasilocal domain with maximal ideal $M$ and show that $B$ is a
uniserial $R$-module. If $B$ is not uniserial, there exist
incomparable completely $B$-irreducible submodules $C_1$ and $C_2$
of $B$. Define $A = C_1 \cap C_2$, $C_1^*= C_1:_B M$ and $C_2^* =
C_2:_B M$. By Lemma~\ref{characterization}, $C_1 \subset C_1^*$ and
$C_2 \subset C_2^*$. Now there exist $x \in (C_1^* \cap C_2)
\setminus A$ and $y \in (C_1 \cap C_2^*) \setminus A$. (This
follows from the irreduciblity of the $C_i$ and the modularity of
the lattice of submodules of $Q$; see for example Noether
\cite[Hilfssatz II]{No}.) We have Soc $B/A = (A + xR + yR)/A$ is a
2-dimensional vector space over $R/M$ and $x+y \not \in C_1 \cup
C_3$. Let $C_3$ be an $R$-submodule of $B$ containing $A + (x+y)R$
that is maximal with respect to $x \not \in C_3$. Then $C_3$ is
completely $B$-irreducible, distinct from $C_1$ and $C_2$ and $A =
C_1 \cap C_3$. Yet $A \in \AA$, so this contradiction means that
the submodules of $B$ are comparable. The converse and the last
assertion follow from the fact that in a complete distributive
lattice, an irredundant meet decomposition into meet-irreducible
elements is unique \cite[pp. 5-6]{D} .
\end{proof}
\begin{theorem} \label{uniqueness}
The following are equivalent for a domain $R$ with quotient field
$Q$.
\begin{itemize}
% \item[(ii)]
%Every nonzero ideal of $R$ is an irredundant intersection $A = \bigcap_i
%M_i^{e_i}$ of powers of maximal ideals $M_i$ of $R$.
\item[(i)] Every
nonzero submodule of $Q$ can be represented uniquely as an
irredundant intersection of completely irreducible submodules of
$Q$.
\item[(ii)] Every nonzero ideal of $R$ can be represented uniquely as an
irredundant intersection of completely irreducible submodules of
$Q$.
\item[(iii)] Every nonzero
proper ideal of $R$ can be represented uniquely as an irredundant
intersection of completely irreducible ideals of $R$.
\item[(iv)]
$R$ is an almost Dedekind domain such that for each radical ideal $J$ of
$R$, $R/J$ has a finitely generated maximal ideal.
\item[(v)] $R$ is an almost semi-artinian Pr\"ufer domain.
\end{itemize} \end{theorem}
\begin{proof}
(i) $\Rightarrow$ (ii) This is clear.
(ii) $\Rightarrow$ (iii) This follows from
Theorem~\ref{semi-artinian} and Lemma~\ref{distributive}.
(iii) $\Leftrightarrow$ (iv) This is proved in \cite[Corollaries
2.10 and 3.9]{HO}.
(iv) $\Rightarrow$ (v) This follows from
Theorem~\ref{semi-artinian}.
(v) $\Rightarrow$ (i) Since $R$ is a Pr\"ufer domain, $Q$ is a
distributive $R$-module. Thus (i) is a consequence of
Theorem~\ref{semi-artinian} and Lemma~\ref{distributive}.
\end{proof}
\section{Pr\"ufer domains}
In light of Theorem~\ref{uniqueness} it is of interest to describe
the completely irreducible submodules of the quotient field of a
Pr\"ufer domain. We do this in Theorem~\ref{Prufer case}. We need
for the proof of this theorem a description of the completely
irreducible ideals of a Pr\"ufer domain. This is a special case of
Theorem 5.3 in \cite{FHO3}: {\it A proper ideal $A$ of a Pr\"ufer
domain is completely irreducible if and only if $A = MB_{(M)}$ for
some maximal ideal $M$ and nonzero principal ideal $B$ of $R$.}
\begin{lemma}\label{flat} Let $R$ be an integral domain and
let $A$ be a flat $R$-submodule of $Q$. If $A$ is $Q$-irreducible,
then $\End(A)$ is quasilocal and is $Q$-irreducible as an
$R$-submodule of $Q$. \end{lemma}
\begin{proof} Since $A$ is a flat $R$-submodule of $Q$, it is the case that
$A(B \cap C) = AB \cap AC$ for all $R$-submodules $B$ and $C$ of $Q$
\cite[I.2, Proposition 6]{B}.
Suppose now that $\End(A) = B \cap C$ for $R$-submodules
$B$ and $C$ of $Q$. Then $A = A\End(A) = A(B \cap C) = AB \cap AC$,
and since $A$ is $Q$-irreducible, $A = AB$ or $A = AC$. Thus $B
\subseteq \End(A)$ or $C \subseteq \End(A)$, so that $\End(A)$ is
$Q$-irreducible. Finally, if $\End(A)$ is not quasilocal, then
there exist two nonzero non-units $x,y \in \End(A)$ such that
$x\End(A) + y\End(A) = \End(A)$. Thus $xy\End(A) = x\End(A) \cap y
\End(A)$, so $\End(A) = y^{-1}\End(A) \cap x^{-1}\End(A)$. Since
$\End(A)$ is $Q$-irreducible, this forces $x$ or $y$ to be a unit, a
contradiction.
\end{proof}
\begin{theorem} \label{Prufer case} Let $R$ be a Pr\"ufer domain. Then
\begin{itemize}
\item[(i)] the $Q$-irreducible $R$-submodules of $Q$ are precisely the
$R$-submodules of $Q$ that are also $R_P$-submodules for some prime
ideal $P$, and
\item[(ii)] the completely
$Q$-irreducible proper $R$-submodules of $Q$ are precisely the
$R$-submodules of $Q$ that are isomorphic to $MR_M$ for some maximal
ideal $M$ of $R$.
\end{itemize}
Conversely, either of statements (i) and (ii) characterizes among
the class of domains those that are Pr\"ufer. \end{theorem}
\begin{proof}
(i) If $A$ is $Q$-irreducible submodule of $Q$, then by
Lemma~\ref{flat} $\End(A)$ is quasilocal. Since $R$ is a Pr\"ufer
domain, there is a prime ideal $P$ of $R$ such that $R_P = \End(A)$
and $A$ is an $R_P$-submodule of $Q$.
Conversely, if $P$ is a prime
ideal of $R$, $A$ is an $R_P$-submodule of $Q$ and $A = B \cap C$
for some $R$-submodules $B$ and $C$ of $Q$, then $A = BR_{P} \cap
CR_P$. Since $R_P$ is a valuation domain $A = BR_P$ or $A = CR_P$.
Thus $A = B$ or $A = C$ and $A$ is $Q$-irreducible.
(ii) Suppose that $R$ is a Pr\"ufer domain and let $A$ be a
completely $Q$-irreducible proper $R$-submodule of $Q$. Then by
Proposition~\ref{characterization}, $A = AR_M$ for some maximal
ideal $M$ of $R$ and $A$ is a completely $Q$-irreducible submodule
of $R_M$. Since $R_M$ is a valuation domain, there exists $q \in Q$
such that $qA \subseteq R_M$. Moreover, $qA$ is a completely
irreducible ideal of $R_M$, so by Lemma 5.1 of \cite{FHO3}, $qA =
xMR_M$ for some $x \in R_M$. Hence $A$ is isomorphic to $MR_M$.
On the other hand, if $A$ is an $R$-submodule of the form $xMR_M$
for some $x \in Q$, then $A$ is a completely irreducible fractional
ideal of the valuation domain $R_M$ \cite[Lemma 5.1]{FHO3}. Since
$R_M$ is a valuation domain, $A$ is a completely $Q$-irreducible of
$R_M$. Thus by Proposition~\ref{characterization}, $A$ is a
completely $Q$-irreducible $R$-submodule of $Q$.
It is easy to see that statement (i) characterizes Pr\"ufer domains.
For let $M$ is a maximal ideal of $R$, and observe that since by (i)
the ideals of $R_M$ are irreducible, they are linearly ordered.
Finally, suppose that each completely $Q$-irreducible proper
$R$-submodule of $Q$ is isomorphic for some maximal ideal $M$ to the
maximal ideal of $R_M$. Let $M$ be a maximal ideal of $R$. Then by
assumption $rMR_M$ is an irreducible ideal of $R_M$ for all $r \in
R$. By Lemma 5.1 of \cite{FHO3}, $R_M$ must be a valuation domain.
Thus $R$ is a Pr\"ufer domain since every localization of $R$ at a
maximal ideal is a valuation domain.
\end{proof}
In Theorem \ref{existence}, we describe the Pr\"ufer domains that
have a completely $Q$-irreducible ideal.
\begin{theorem} \label{existence}The following statements are
equivalent for a Pr\"ufer domain $R$.
\begin{itemize}
\item[(i)] There exists a completely $Q$-irreducible ideal of $R$.
\item[(ii)] There exists a nonzero $Q$-irreducible ideal of $R$.
\item[(iii)] There is a nonzero prime ideal contained in the
Jacobson radical of $R$.
\item[(iv)] Every proper $R$-submodule of $Q$ is a fractional ideal of $R$.
\end{itemize}
\end{theorem}
\begin{proof} (i) $\Rightarrow$ (ii) This is clear.
(ii) $\Rightarrow$ (iii) Suppose that $A$ is a $Q$-irreducible ideal
of $R$.
By Lemma~\ref{ideal
characterization}, $A = AR_P$ for some prime ideal of $R$. If $A$
is an invertible ideal of $R$, then by Theorem~\ref{qirreducible}
$P$ is the unique maximal ideal of $R$, so that statement (iii) is
clearly true. It remains to consider the case where $A$ is not
invertible. By Theorem~\ref{qirreducible}, if $x$ is a nonzero
element in $A^{-1}$, then $xA$ is contained in the Jacobson radical
of $R$. Since by Lemma~\ref{ideal characterization}(ii), $xA$ is
$Q$-irreducible we may assume without loss of generality that $A$
itself is contained in the Jacobson radical of $R$.
Now let $\{N_i\}$ be the set of maximal ideals of $R$. Since $AR_P$
is an ideal of $R$ and $A$ is contained in each $N_i$, it follows
that for each $i$, $AR_PR_{N_i} = AR_{N_i} \subset R_{N_i}$. Thus
there is prime ideal $P_i$ contained in $P$ and $N_i$ that contains
$A$ (the ideal $P_i$ can be chosen to be the contraction of the
maximal ideal of the ring $R_PR_{N_i}$ that contains $A$). Because
$R$ is a Pr\"ufer domain, the prime ideals contained in $P$ are
linearly ordered by inclusion. Thus if $Q = \bigcap_{i} P_i$, then
$Q$ is a nonzero prime ideal of $R$ (for it contains $A$) and $Q$ is
contained in every maximal ideal of $R$.
(iii) $\Rightarrow$ (i)
Let $P$ be a nonzero prime ideal of $R$ contained in the Jacobson
radical of $R$. Since $R$ is a Pr\"ufer domain, $P = PR_P$, so if
$0 \ne x$ is in $P$ it follows that $xR_M$ is contained in $P$. Thus
$xMR_M$ is contained in $P = PR_M$. Moreover by
Proposition~\ref{Prufer case} $xMR_M$ is a completely
$Q$-irreducible $R$-submodule of $Q$.
(iii) $\Rightarrow$ (iv) Statement (iv) is equivalent to the
assertion that there exists a valuation overring $V \subset Q$ of
$R$ such that $(R:_QV) \ne 0$ \cite[Theorem 79]{M2}. If $R$
satisfies (iii), then a nonzero prime ideal $P$ contained in the
Jacobson radical of $R$ has the property that $PR_P = P$. Thus
$V$ can be chosen to be $R_P$.
(iv) $\Rightarrow$ (ii) By the theorem of Matlis cited in (iii)
$\Rightarrow$ (iv), there exists a valuation ring $V$ with $(R:_QV)
\ne 0$. Thus since $R$ is a Pr\"ufer domain there is a prime ideal
$P$ with $V = R_P$ and $rR_P \subseteq R$ for some nonzero $r \in
R$. By Proposition~\ref{Prufer case}, $rR_P$ is a $Q$-irreducible
ideal of $R$.
\end{proof}
\begin{remark}
If $R$ is a Pr\"ufer domain with nonzero Jacobson radical ideal $J$,
then there exists a unique largest prime ideal $P$ contained in $J$.
If $M$ is a maximal ideal of $R$, then $PR_M = PR_P$ since $R_M$ is
a valuation domain. Thus $P = \bigcap_{M \in \Max(R)}PR_M = PR_P$.
It follows that $R_P/P$ is the quotient field of $R/P$. Using this
observation it is not hard to see that a Pr\"ufer domain $R$
satisfies the equivalent conditions of Theorem~\ref{existence} if
and only if $R$ occurs in a pullback diagram of the form
\begin{center} $\begin{CD} R @>>> D \\ @VVV \: @V{\alpha}VV \\ V
@>{\beta}>> K \end{CD}$
\end{center}
where
\begin{itemize}
\item[$\bullet$]
$\alpha$ is injective and $D$ is a Pr\"ufer domain such that the Jacobson
radical of $D$ does not contain a nonzero prime ideal,
\item[$\bullet$] $K$ is isomorphic to the quotient field of $D$,
and
\item[$\bullet$] $\beta$ is surjective with $V$ a valuation
domain.
\end{itemize}
Thus if $D$ is any Pr\"ufer domain with quotient field $Q$ and $X$
is an indeterminate for $Q$, then $D+XQ[[X]]$ is a Pr\"ufer domain
satisfying the equivalent conditions of Theorem~\ref{existence}.
\end{remark}
%\begin{proposition}
%Let $R$ be a Pr\"ufer domain. The following statements are equivalent for
%a
%completely $Q$-irreducible $R$-submodule $A$ of $Q$ with adjoint maximal
%ideal
%$M$.
%\begin{itemize}
%\item[(i)] $Q/A$ is an injective $R$-module.
%\item[(ii)] $R_M$ is an almost maximal valuation domain.
%\item[(iii)] $R$ is $A$-reflexive.
%\end{itemize}
%\end{proposition}
%\begin{proof} (i) $\Rightarrow$ (ii) Since $Q/A$ is injective, $Q/\End(A)$
%is
%also an injective $R$-module [reference needs to be inserted]. By
%Proposition~\ref{Prufer case}, $\End(A) = R_M$. Thus $Q/R_M$ is injective
%and
%since $R_M$ is a valuation domain, $R_M$ is almost maximal \cite{FS}.%
%(ii) $\Rightarrow$ (i) Since $R_M$ is an almost maximal valuation domain
%and
%$A$ is an $R_M$-module, $A$ has injective dimension one as a module over
%$R_M$-,
%hence over $R$.
%(i) $\Leftrightarrow$ (iii) (This follows from something in one of may
%papers--
%I need to look up the reference.)
%\end{proof}
\section{Questions}
We conclude with several questions that we have not been able to
resolve. Other questions touching on similar issues can be found in
\cite{BHLP}, \cite{Baz} and \cite{HHP}.
\begin{question}\label{2} What conditions on a domain $R$ guarantee
that any two completely $Q$-irreducible fractional ideals are
necessarily isomorphic?
\end{question}
Proposition~\ref{criterion} gives an answer to this question in the
case where every proper submodule of $Q$ is a fractional $R$-ideal.
By Theorem~\ref{Prufer case} if $R$ is a valuation domain, then all
completely $Q$-irreducible ideals of $R$ are isomorphic. If $R$ is a
Noetherian local domain, then by Propositions~\ref{criterion}
and~\ref{same} any two $Q$-irreducible ideals are isomorphic.
\begin{question} \label{3} What integral domains $R$ admit a completely
$Q$-irreducible ideal? a nonzero $Q$-irreducible ideal?
\end{question}
The Noetherian and Pr\"ufer cases of Question~\ref{3} are settled in
Proposition~\ref{same} and Theorem~\ref{existence}, respectively.
\begin{question} \label{33} If $R$ admits a nonzero $Q$-irreducible
ideal, does $R$ also admit a completely $Q$-irreducible ideal?
\end{question}
The answer to Question \ref{33} is yes if $R$ is Pr\"ufer or
Noetherian.
\begin{question} \label{4} If $A$ is a (completely)
irreducible submodule of the quotient field of a quasilocal domain
$R$, what can be said about $\End(A)$? For a completely
$Q$-irreducible ideal $A$ of a quasilocal domain $R$ does it follow
that $\End(A)$ is integral over $R$?
\end{question}
Theorem \ref{existence} along with the fact that if $A$ is
completely irreducible, then $\End(A)$ is quasilocal, shows that if
$R$ is not quasilocal, then $\End(A)$ need not be integral over $R$
even if $R$ is a Pr\"ufer domain.
Theorem~\ref{qirreducible}, Example~\ref{gilmerhoffmann} and
Example~\ref{valuation example} are relevant to Question~\ref{4}.
\begin{question}\label{5} If $R$ is a (Noetherian) domain, what are the
completely irreducible submodules of $Q$?
\end{question}
Theorem~\ref{Prufer case} answers Question~\ref{5} in the case where
$R$ is Pr\"ufer.
\begin{question} \label{6} If $A$ is a completely $Q$-irreducible
$R$-submodule of $Q$, when is $A$ a fractional ideal of $R$? of
$\End(A)$?
\end{question}
If $R$ is a valuation domain, then every proper submodule of $Q$ is
a fractional ideal of $R$. The case where $R$ is a one-dimensional
Noetherian domain is deeper, but has been resolved independently by
Bazzoni and Goeters. A consequence of Theorem 3.4 of \cite{Baz} is
that if $A$ is a completely $Q$-irreducible submodule of $Q$ such
that $\End(A)$ is Noetherian and has Krull dimension 1, then (by
Theorem~\ref{qirreducible}) $\End(A)$ is local and (by the cited
result of Bazzoni) $A$ is a fractional ideal of $\End(A)$. Indeed, a
more general result due to H. P. Goeters is true: If $A$ is a
submodule of the quotient field of a local Noetherian domain of
Krull dimension 1, then $A$ is a fractional ideal of $\End(A)$
\cite[Lemma 1]{Goe}. Recently, Goeters has extended this to all
quasilocal Matlis domains \cite{Goe2}.
\section{Appendix: Corrections to \cite{FHO2}}
In this appendix we correct several mistakes from our earlier paper
\cite{FHO2}. We include also a stronger version of Lemma 3.2 of
this paper. The main corrections concern Lemmas 2.1(iv) and 3.2 of
\cite{FHO2}. The notation and terminology of this appendix is that
of \cite{FHO2}.
The proof of statement (iv) of Lemma 2.1 of \cite{FHO2} is
incorrect. Statement (iv) should be modified in the following way:
\begin{itemize}
\item[(iv)] {\it For each nonzero nonmaximal prime ideal $P$ of $R$,
if $\{M_i\}$ is the collection of maximal ideals of $R$ not
containing $P$, then $R_P \subseteq (\bigcap_{i}R_{M_i})R_M$ for
each maximal ideal $M$ of $R$ containing $P$.}
\end{itemize}
{\noindent}Having changed statement (iv), we modify now the original
proofs of (iii) $\Rightarrow$ (iv) and (iv) $\Rightarrow$ (v) in
the following way. For (iii) $\Rightarrow$ (iv) we note that by
Theorem 3.2.6 of \cite{FHP} $\End(P) = R_P \cap (\bigcap_i R_{M_i})$
and $\End(P_M) = R_P$. Thus by (iii) $R_P = \End(P_M) = \End(P)_M =
R_P \cap (\bigcap_{i}R_{M_i})R_M$, and (iv) follows.
For the proof of (iv) $\Rightarrow$ (v), we have as in the original
proof that
$$
R_P = \End(A)_M =(\bigcap_{Q \in \XX_A} R_{Q})R_M \cap
(\bigcap_{N}R_N)R_M.
$$
We claim that $\bigcap_{Q \in \XX_A} R_{Q} \subseteq R_P$. If this
is not the case then since $R_M$ is a valuation domain it must be
that $R_P \subset (\bigcap_{Q \in \XX_A} R_{Q})R_M$ (proper
containment). Hence from the above representation of $\End(A)_M$ we
deduce that since $R_P$ is a valuation domain, $R_P =
(\bigcap_{N}R_N)R_M$. Thus $(\bigcap_{N}R_N)R_M \subset (\bigcap_{Q
\in \XX_A} R_{Q})R_M$. By (iv), $R_{Q'} \subseteq
(\bigcap_{N}R_N)R_M$ since no $N$ contains $Q'$. However $Q' \in
\XX_A$, so this implies $R_{Q'} \subset R_{Q'}R_M$, but since $M$
contains $Q'$, $R_{Q'}R_M = R_{Q'}$. This contradiction implies
that $\bigcap_{Q \in \XX_A}R_Q \subseteq R_P$, so every element $r
\in P$ is contained in some $Q \in \XX_A$. Consequently, no element
of $P$ is prime to $A$.
\medskip
Reference is made in the first paragraph of the proof of Lemma 3.3
of \cite{FHO3} to the original version of statement (iv). In
particular it is claimed that since $R$ has the separation property,
$P_iS $ is a maximal ideal of $S$. This can be justified now using
the following more general fact, which does not appear explicitly in
\cite{FHO2}:
\begin{lemma} A Pr\"ufer domain $R$ has the separation property if and
only if for each collection $\{P_i:i \in I\}$ of incomparable prime
ideals, the ideals $P_i$ extend to maximal ideals of
$S:=\bigcap_{i\in I} R_{P_i}$.
\end{lemma}
\begin{proof} If $R$ has the separation property, then for each $j \in I$,
$\End(P_j) = R_{P_j} \cap (\bigcap_{N}R_N)$ by Theorem 3.2.6 of
\cite{FHP}, where $N$ ranges over the maximal ideals of $R$ that do
not contain $P_j$. Thus $\End(P_j) \subseteq S$ since the $P_i$'s
are comaximal. By Lemma 2.1(ii) of \cite{FHO2} $P_j$ is a maximal
ideal of $\End(P_j)$, and since $R$ is a Pr\"ufer domain, either
$P_j$ extends to a maximal ideal $SP_j$ of $S$ or $SP_j = S$. The
latter case is impossible since $S \subseteq R_{P_j}$. Thus $SP_j$
is a maximal ideal of $S$. The converse follows from Theorem 3.2.6
of \cite{FHO} and Lemma 2.1(ii) of \cite{FHO2}.
\end{proof}
A second reference to the original version of Lemma 2.1(iv) is made
in the first paragraph of the proof of (i) $\Rightarrow$ (ii) of
Theorem 3.7. In this paragraph it is claimed that since $\End(A)_M
= R_P$, the elements of $P$ are not prime to $A$. Since (by Theorem
2.3 of \cite{FHO2}) $R$ has the separation property, this claim is
immediate from Lemma 2.1(v) and the original argument that appealed
to Lemma 2.1(iv) is unnecessary. \medskip
The argument in the third paragraph of the proof of Lemma 3.2 of
\cite{FHO2} is incorrect, but rather than patch this argument we
give below a stronger version of this lemma. It requires a slight
strengthening of Lemma 3.1 of \cite{FHO2}.
\begin{lemma}
\label{lemma 6.6} (cf. Lemma 3.1 of \cite{FHO2}) Let $A$ be an
ideal of a Pr\"ufer domain $R$. Suppose $Q$ is a prime ideal of $R$
that contains $A$, and $P$ is a prime ideal such that $\End(A)_Q =
R_P$. If $P \in \Ass(A)$, then $\End(A)_Q = \End(A_Q)$. \end{lemma}
\begin{proof} Since $P \in \Ass(A)$, $A_{(P)}$ is a primal ideal with
adjoint prime $P$, and it follows that $A_P$ is a $P_P$-primal
ideal. By \cite[Lemma 1.4]{FHO2}, $\End(A_P) = R_P$. Thus
$\End(A_P) = \End(A)_Q$, so $A\End(A_P) = A\End(A)_Q$ implies $A_P =
A_Q$. Consequently, $ \End(A_Q) = \End(A_P) = R_P =
\End(A)_Q$.\end{proof}
\begin{lemma}
\label{lemma 6.7} (cf. Lemma 3.2 of \cite{FHO2})
Let $R$ be a Pr\"ufer domain with field of
fractions $F$, let $X$ be an $R$-submodule of $F$, and let $M$ be a
maximal ideal of $R$. Then $\End(X)_M = R_P$ for some $P \in \Spec
R$ with $P \subseteq M$. Assume that $P$ is the union of prime
ideals $P_i$, where each $P_i$ is the radical of a finitely
generated ideal. Then $\End(X)_Q = \End(X_Q)$ for all prime ideals
$Q$ such that $P \subseteq Q \subseteq M$. \end{lemma}
\begin{proof} Since $R_M \subseteq \End(X)_M$ and $R_M$ is a
valuation domain, $\End(X)_M = R_P$ for some prime ideal $P
\subseteq M$. If $\End(X)_M = F$, then clearly $\End(X)_M =
\End(X_M)$, so we assume $\End(X)_M \ne F$ and thus $P \ne (0)$. Let
$Q$ be a prime ideal of $R$ such that $P \subseteq Q \subseteq M$.
Since $\End(X)_M = R_P$, we have $\End(X)_Q = R_P$. Now
$R_P = \End(X)_Q \subseteq \End(X_Q) \subseteq
\End(X_P)$, so to prove Lemma \ref{lemma 6.7}, it suffices to show
that $\End(X_P) \subseteq R_P$.
Let $S = \End(X)$. Now $PS \subseteq PR_P$, so $PS \ne S$. Since $S$ is
an overring of the Pr\"ufer domain $R$, $S$ is a flat extension of
$R$, so $PS$ is a prime ideal of $S$ and $S_{PS} = R_P$. Also,
$PS$ is the union of the prime ideals $P_iS$, and each $P_iS$ is
the radical of a finitely generated ideal of $S$.
Let $L$ be a prime ideal of $S$ such that $L \subseteq PS$ and such
that $L = \sqrt{I}$, where $I$ is a finitely generated ideal of $S$.
We prove there exists a nonzero $q \in F$ such that $qX_L$ is an
ideal of $S_L$ that is primary for $L_L$. The invertible ideal $I^2$
of $S$ is an intersection of principal fractional ideals of $S$.
Since $\End(X) = S$, each principal fractional ideal of $S$ is an
intersection of $S$-submodules of $F$ of the form $qX$, $q \in F$.
Since $I^2 \subseteq L$, $I^2$ is an intersection of ideals of $S$
of the form $L \cap qX$, where $q \in F$. Since $I^2 \subset I
\subseteq L$ (where $\subset$ denotes proper containment), there
exists $q \in F$ such that $I^2 \subseteq L \cap qX \subset L$.
Hence there exists a maximal ideal $N$ of $S$ with $L \subseteq N$
such that $I^2_N \subseteq L_N \cap qX_N \subset L_N$. Since $S_N$
is a valuation domain, the $S_N$-modules $qX_N$ and $L_N$ are
comparable and $I^2_N \subseteq L_N \cap qX_N \subset L_N$ implies
$I^2_N \subseteq qX_N \subset L_N$. Now $\sqrt{I^2} =\sqrt{I} = L$
and $I^2 \subseteq N$ implies $L \subseteq N$. Thus $I^2_L \subseteq
qX_L \subseteq L_L$, and we conclude that $\sqrt{qX_L} = L_L$.
We observe next that $X_P \ne F$. Since $P \ne 0$, there exists $i$
such that $P_i \ne 0$ and $L := P_iS \subseteq PS$, where $L =
\sqrt{I}$ for some finitely generated ideal $I$ of $S$. As we have
established in the paragraph above, there exists a nonzero $q \in F$
such that $qX_L$ is an ideal of $S_L$. Thus $qX_P \subseteq qX_L
\subseteq S_L$, so it is not possible that $X_P =F$.
Fix some member $L$ of the chain $\{P_iS\}$. Since $X_P \ne F$, $L
\subseteq PS$ and $R_P$ is a valuation domain, there exists a
nonzero element $s$ of $S$ such that $sX \subseteq L_L$. Since
$\End(X_P) = \End(sX_P)$ and we wish to show that $\End(X_P)
\subseteq R_P$ we may assume without loss of generality that $s =
1$; that is, we assume for the rest of the proof that $X \subseteq
L_{L}$. Define $A = X \cap S$. Then $A$ is an ideal of $S$.
Moreover $A$ is contained in $L$ since $A_{L} \subseteq X_L
\subseteq L_L$.
With the aim of applying Lemma~\ref{lemma 6.6}, we show that $PS \in
\Ass(A)$. For each $i$ define $L_i = P_iS$. It suffices to show
each $L_i$ with $L \subseteq L_i \subseteq PS$ is in $\Ass(A)$,
since this implies that $PS = \bigcup_{L_i \supseteq L}L_i$ is a
union of members of $\Ass(A)$. Let $i$ be such that $L \subseteq
L_i$. Since $L_i$ is the radical of a finitely generated ideal of
$S$, there exists (as we have established above) a nonzero $q \in
F$ such that $qX_{L_i}$ is an ideal of $S_{L_i}$ that is primary for
$(L_i)_{L_i}$. Now $A_{L_i} = X_{L_i} \cap S_{L_i}$. Since $S_{L_i}$
is a valuation domain, $A_{L_i} = X_{L_i}$ or $S_{L_i} \subseteq
X_{L_i}$. By assumption, $X \subseteq L_L$. Since $L \subseteq
L_i$, it follows that $X_{L_i} \subseteq L_{L}$, so it is impossible
that $S_{L_i} \subseteq X_{L_i}$. Thus $A_{L_i} = X_{L_i}$.
Consequently, $qX_{L_i} = qA_{L_i}$ and $qA_{L_i}$ is an ideal of
$S_{L_i}$ that is primary for $(L_i)_{L_i}$. Since $S_{L_i}$ is a
valuation domain, it follows that $qA_{L_i}= A_{L_i}:s$ for some $s
\in S$. Thus $(L_i)_{L_i} \in \Ass(A_{L_i})$, so $L_i \in
\Ass(A)$. This proves $PS \in \Ass(A)$.
Since $A =X \cap S$ is an ideal of $S$, $S \subseteq \End(A)$. For
each maximal ideal $N$ of $S$, either $A_N = X_N$ or $A_N = S_N$ It
follows that $\End(A) \subseteq \End(X) = S$, so $\End(A) = S$.
Thus $\End(A)_P = S_P = R_P$, and by Lemma~\ref{lemma 6.6},
$\End(A_P) = R_P$. (We have used here that $S_{SP} = R_P$.) Now
$A_P = X_P \cap S_P = X_P \cap R_P$. Since $R_P$ is a valuation
domain, $A_P = X_P$ or $R_P \subseteq X_P$. The latter case is
impossible since $X_P \subseteq X_L \subseteq L_L$. Thus
$A_P = X_P$. We conclude that End($X_{P}) =$ End($A_{P}) = R_P$.
\end{proof}
Finally we make two corrections to the proof of Lemma 3.3. The
third paragraph should read: {\it Define $A = JR_Q \cap R$. Then $AS
= JR_Q \cap S$ is $QS$-primary. In particular, $QS$ is the unique
minimal prime of $AS$ and $A \not\subseteq P_iS \cap R = P_i$ for
each $i \ge 1$.}
Also, in the fifth paragraph an exponent is incorrect: $x_i$ needs
to be chosen in $A_i \setminus (P_1 \cup \cdots \cup P_i \cup
A^{i+1})$. Then in the eighth paragraph, we have $x_{i+1}S_N
\subset x_{i}S_N$ since $x_i \in A^i \setminus A^{i+1}$ and
$A^{i+1}S_N \cap R = A^{i+1}R_Q \cap R = A^{i+1}$.
%\bibliographystyle{amsplain}
\begin{thebibliography}{FHP3}
\bibitem{BHLP} V. Barucci, E. Houston, T. Lucas and I. Papick,
$m$-canonical ideals in integral domains II, in {\it Ideal theoretic
methods in commutative algebra (Columbia, MO, 1999)}, 89-108,
Lecture Notes in Pure and Appl. Math., { 220}, Dekker, New York,
2001.
\bibitem{Ba} H. Bass, Finitistic dimension and a homological
generalizaton of semiprimary rings, Trans. Amer. Math. Soc. { 95}
(1960), 466-488.
\bibitem{Baz} S. Bazzoni, Divisorial domains, Forum Math. { 12} (2000),
397-419.
\bibitem{BS2} S. Bazzoni and L. Salce, Warfield domains, J. Algebra
185 (1996), 836-868.
\bibitem{BS} S. Bazzoni and L. Salce, Almost perfect domains,
Coll. Math. 95 (2003), 285-301.
\bibitem{BS1} S. Bazzoni and L. Salce, Strongly flat covers, J.
London Math. Soc. 66 (2002), 276-294.
\bibitem{B} N. Bourbaki, {\it Commutative Algebra},
Chapters 1 - 7, Springer-Verlag, 1989.
\bibitem{D} R. Dilworth, Aspects of distributivity, Algebra Universalis 18
(1984), 4-17.
\bibitem{DC} R. Dilworth and P. Crawley, Decomposition
theory for lattices without chain conditions, Trans. Amer. Math.
Soc. 96 (1960), 1-22.
\bibitem{EJ} E. Enochs and O. Jenda, {\it Relative homological
algebra}, de Gruyter Exp. Math. 30, de Gruyter, 2000.
\bibitem{FHP} M. Fontana, J. Huckaba and I.
Papick, {\it Pr\"ufer domains}, Marcel Dekker, 1998.
\bibitem{FR} D. Ferrand and M. Raynaud, Fibres formelles d'un anneau
local noeth\'{e}rian, Ann. Scient. \'{E}c. Norm. Sup. ${4^e}$
s\'{e}rie { 3} (1970), 295-311.
\bibitem {F1} L. Fuchs, A condition under which an irreducible ideal
is primary, Quart. J. Math. Oxford 19 (1948), 235-237.
\bibitem {F} L. Fuchs,
On primal ideals, Proc. Amer. Math. Soc. 1 (1950), 1-6.
\bibitem{FHO} L. Fuchs, W. Heinzer and B. Olberding,
Commutative ideal theory without finiteness conditions: primal
ideals, Trans. Amer. Math Soc., to appear.
\bibitem{FHO3} L. Fuchs, W. Heinzer and B. Olberding, Commutative ideal
theory with finiteness conditions: completely irreducible ideals,
Trans. Amer. Math. Soc., to appear.
\bibitem{FHO2} L. Fuchs, W. Heinzer and B. Olberding, Maximal prime divisors
in arithmetical rings, in {\it Rings, modules, algebras, and abelian
groups}, 189--203, Lecture Notes in Pure and Appl. Math., 236,
Dekker, New York, 2004..
%\bibitem{FM} L. Fuchs and E. Mosteig, Ideal theory in \Pds\
%| an unconventional approach, J. Algebra 252 (2002), 411-430.
\bibitem{FS} L. Fuchs and L. Salce, {\it Modules over non-Noetherian
Domains}, Math. Surveys 84 (2001).
\bibitem{GaH2} Coherentlike conditions in pullbacks, Michigan Math. J. 44
(1997), no. 1, 99-123.
\bibitem{GaH} S. Gabelli and E. Houston, Ideal theory in pullbacks,
in {\it Non-Noetherian commutative ring theory}, 199-227, Math.
Appl., 520, Kluwer Acad. Publ., Dordrecht, 2000.
\bibitem{GH} R. Gilmer and J. Hoffmann, The integral closure need
not be a Pr\"ufer domain, Mathematika { 21} (1974), 233-238.
\bibitem{Goe} H. P. Goeters, Noetherian stable domains,
J. Algebra { 202} (1998), no. 1, 343-356.
\bibitem{Goe2} H. P. Goeters, $A$-divisorial Matlis domains, to
appear.
\bibitem{H} W. Heinzer, Integral domains in which each nonzero ideal
is divisorial, Mathematika { 15} (1968), 164--170.
\bibitem{HHP} W. Heinzer, J. Huckaba and I. Papick, $m$-canonical
ideals in integral domains, Comm. in Algebra { 26} (1998),
3021-3043.
%\bibitem{HO} W. Heinzer and J. Ohm, Locally noetherian commutative
% rings, Trans. Amer. Math. Soc. {\bf 158} (1971), 273-284.
\bibitem{HO} W. Heinzer and B. Olberding, Unique irredundant intersections
of completely irreducible ideals, J. Algebra, to appear.
\bibitem{HRS} W. Heinzer, C. Rotthaus and J. Sally, Formal Fibers and
Birational Extensions, Nagoya Math. J. { 131} (1993), 1-38.
%\bibitem{Hu} I. C. Huang, A residue map and some applications to
%some one-dimensional rings, Proc. Amer. Math Soc. 123 (1995),
%2369-2375.
\bibitem{Ko} S. Koppelberg, {\it Handbook of Boolean algebras}, vol.
1., North Holland, 1989.
%\bibitem{LM} M. Larsen and P. McCarthy, Multiplicative Theory of Ideals,
%Academic Press, 1971.
\bibitem{LS} W. J. Lewis and T. S. Shores, Serial modules and endomorphism
rings, Duke Math J. 41 (1974), 889-909.
\bibitem{M} E. Matlis, Cotorsion modules, Memoires Amer. Math.
Soc. 49 (1964).
\bibitem{M2} E. Matlis, {\it Torsion-free modules}, The University of Chicago
Press, 1972.
\bibitem{Mat} E. Matlis, {\it 1-dimensional Cohen-Macaulay rings}, Lecture
Notes in Math. { 327}, Springer-Verlag, 1973.
\bibitem{Mati} E. Matlis, Ideals of injective dimension $1$,
Michigan Math. J. { 29} (1982), no. 3, 335-356.
%\bibitem{Ma} H. Matsumura, Commutative Ring Theory, Cambridge
%University Press, 1986.
\bibitem{No} {E. Noether,} Idealtheorie in Ringbereichen, Math. Ann. { 83}
(1921), 24-66.
%\bibitem{N} M. Nishi, On the ring of endomorphisms of an
%indecomposable injective module over a Pr\"ufer ring, Hiroshima
%Math. J. 2 (1972), 271-283.
%\bibitem{O} B. Olberding, Globalizing local properties of
%Pr\"ufer domains, J. Algebra (1998).
\bibitem{O2} B. Olberding, Factorization into radical ideals, Marcel
Dekker, to appear.
%\bibitem{OS} B. Olberding and S. Saydam, {\it Ultraproducts of
%commutative rings}, in {\it Commutative ring theory and applications
%(Fez, 2001)}, 369-386, Lecture Notes in Pure and Appl. Math., 231,
%Dekker, New York, 2003.
%\bibitem{OSh} B. Olberding and J. Shapiro, {\it Prime ideals in
%ultraproducts of commutative rings,} J. Algebra, to appear.
%\bibitem{OSS} B. Olberding, J. Shapiro and S. Saydam, {\it Completions,
%valuation and ultrapowers of
%Noetherian domains}, J. Pure and Appl. Algebra, to appear.
\bibitem{Sm} J. R. Smith, Localy domains with topologically
$T$-nilpotent radical, Pacific J. Math 30 (1969), 233-245.
\bibitem{ZS} O. Zariski and P. Samuel, {\it Commutative Algebra}, Vol. II,
Van Nostrand, Princeton, 1958.
\end{thebibliography}
\bigskip
\end{document}
\section*{Questions}
{\noindent}This section will eventually be deleted.
\begin{itemize}
\item[(1)]
Is a completely $Q$-irreducible ideal of a quasilocal integrally
closed domain an m-canonical ideal?
\item[(2)] Find conditions on $R$
in order that any two completely $Q$-irreducible fractional
$R$-ideals are necessarily isomorphic.
\item[(3)] What integral domains $R$ admit a completely $Q$-irreducible
fractional ideal?
\item[(4)] If $R$ is a quasilocal domain with completely $Q$-irreducible
ideal $A$, is $\End(A) = R$?
\item[(5)] If $R$ is a Noetherian domain, then is it possible to describe
all completely $Q$-irreducible submodules of the quotient field $Q$?
(Proposition~\ref{Prufer case} takes care of the Pr\"ufer case.)
\item[(6)] If $A$ is a completely $Q$-irreducible submodule of the quotient
field of a domain, is $A$ a fractional ideal over $\End(A)$? It is
easy to see that this is true for Pr\"ufer domains. I believe
Bazzoni shows that it is also true when $\End(A)$ is a Noetherian
domain.
\item[(7)] If $A$ is a completely $Q$-irreducible $R$-submodule of the
quotient field of a quasilocal domain $R$, what can be said about
$\End(A)$? I think at the very least it is true that $\End(A)M$ is
not equal to $\End(A)$, where $M$ is the maximal ideal of R. (This
is because $\Hom(M,A)$ can be viewed as a cover of $A$.) Must
$\End(A)$ be integral over $R$?
\item[(8)] Is it possible that an ideal of a non-Dedekind (local?)
Noetherian domain $R$ is an infinite irredundant intersection of
completely $Q$-irreducible submodules of the quotient field of $R$?
\item[(9)] Can it happen that every ideal of a Noetherian domain is an
irredundant intersection of completely $Q$-irreducible submodules of
the quotient field of R? (Is it intended here to be every nonzero
ideal? For a domain that is not a field, I believe $(0)$ is never an
irredundant intersection of completely $Q$-irreducible ideals. On
the other hand we are asserting that for $R = \mathbb Z$ this is
true. I bet it is true for all Dedekind domains.)
\item[(10)] If $R$ is a quasilocal domain and $A$ is an $R$-submodule of
$Q$, is it true that: $\End(A)$ is $A$-reflexive iff $Q/A$ is
injective and $A$ is completely $Q$-irreducible. (The terminology
is from Bazzoni and Salce and is also in \cite{FS}.)
\item[(11)] Are valuation overrings useful in constructing examples of
completely $Q$-irreducible submodules of $Q$ when the base ring $R$
is Noetherian? If $V$ is a DVR overring of a quasilocal domain $R$
(with maximal ideal $M$) that is completely $Q$-irreducible as an
$R$-submodule of $Q$, then I believe $V$ is centered on a maximal
ideal of $R$. Furthermore I believe $V/VM = R/M$ so that $V$ is
zero-dimensional. For $VM = Vm$ for some $m$ in $M$. Thus $[V:M] =
[V:VM] = V(1/m)$, so $[V:M] / V = V(1/m) / V = V / Vm.$ (By
$[V:M]$ I mean the submodule of $Q$ that is identified with
$Hom(M,V)$.) If $V$ is completely $Q$-irreducible, then $[V:M] / V$,
hence $V / Vm$, must be $R/M$. \end{itemize}
\end{document}
%End Document
\end{document}
Let $A$ be a fractional ideal of a domain $R$. Then $R$ is an {\it
$A$-reflexive domain} if and only if the canonical homomorphism $$G
\rightarrow \Hom_R(\Hom_R(G,A),A)$$ is an isomorphism for all
$\End(A)$-submodules $G$ of finite rank free $\End(A)$-modules. It
is a consequence of Theorem 5.3 in \cite{FS} that if $\End(A) = R$,
then $R$ is an $A$-reflexive domain if and only if $A$ is an
$m$-canonical ideal of $R$ and $Q/A$ is an injective $R$-module.
This raises the question of whether ``$m$-canonical'' can be
weakened to ``completely $Q$-irreducible'':
\begin{question} \label{7} If $R$ is a quasilocal domain and $A$ is an
$R$-submodule of $Q$, is it true that: $\End(A)$ is $A$-reflexive if
and only if $Q/A$ is injective and $A$ is completely
$Q$-irreducible.
\end{question}
By Lemma~\ref{Bazzoni} the answer to Question~\ref{7} is affirmative
if $R$ is Noetherian. Similarly, the answer is affirmative for
valuation domains since completely $Q$-irreducible ideals of these
domains are $m$-canonical.
\begin{proposition} If $R$ is a domain and $A$ is a fractional ideal of $R$,
then $A$ is a completely $Q$-irreducible fractional ideal of $R$ iff
$A$ is an completely $Q$-irreducible fractional ideal of $R_M$ for
some maximal ideal of $M$ of $R$. \end{proposition}
\begin{proof} It suffices to prove the claim when $A$ is an ideal of $R$.
This is because a fractional ideal $B$ of a ring $S$ is completely
$Q$-irreducible if and only if every fractional ideal isomorphic to
$B$ is completely $Q$-irreducible.
Suppose that $A$ is a completely $Q$-irreducible ideal of $R$. Then $A =
\cap AR_M$, where $M$ ranges over the maximal ideals of $R$, so
since $A$ is completely $Q$-irreducible, $A = AR_M$ for some maximal
ideal $M$ of $R$. Clearly $A$ is a completely $Q$-irreducible ideal
of $R_M$.
Conversely, suppose that $A$ is a completely $Q$-irreducible ideal of$R_M$
for some maximal ideal $M$. Since $A$ is a completely
$Q$-irreducible ideal of $R_M$, there exists $x \in (A : MR_M)
\setminus A$. Write $x = \frac{c}{b}$, where $c \in R$ and $b \in R
\setminus M$. Then if $c \in A$, since $A = AR_M$ it follows that
$x \in A$, contrary to the choice of the $x$. Thus $x \in (A:M)
\setminus A$, and to prove that $A$ is a completely $Q$-irreducible
ideal of $R$, it suffices to show that $x$ is in every fractional
ideal $J$ properly containing $A$. We show in fact that $x$ is in
$JR_N$ for all maximal ideals $N$ of $R$. By the choice of $x$, we
have that $x \in (A: MR_M)$, so since $A$ is a completely
$Q$-irreducible ideal of $R_M$, $(A : MR_M)$ is contained in $JR_M$.
(Note that $A$ is properly contained in $JR_M$, since otherwise $A =
AR_M = JR_M$, and $J \subseteq A$, contrary to assumption.) Finally
if $N$ is a maximal ideal of $R$ distinct from $M$, then since $x$
is in $(A:M)$, we have $xM \subseteq AR_N$, so $x \in AR_N \subseteq
JR_N$. This shows $x \in JR_N$ for every maximal ideal $N$ of $R$,
proving the claim.
\end{proof}
\begin{corollary} There exists a completely $Q$-irreducible ideal
of $R$ if and only if there is a maximal ideal $M$ of $R$ such that
$R_M$ has an absolutely irreducible ideal and $R_M$ is a fractional
ideal of $R$. \end{corollary}
(i) $\Rightarrow$ (iii) Suppose that $A$ is a completely
$Q$-irreducible ideal of $R$. Then $A = \bigcap_{M \in \Max(R)}
AR_M$, where $M$ ranges over the maximal ideals of $R$, so since $A$
is completely $Q$-irreducible, $A = AR_M$ for some maximal ideal $M$
of $R$. Clearly $A$ is a completely $Q$-irreducible ideal of $R_M$.
(iii) $\Rightarrow$ (i) Suppose that $A$ is a completely
$Q$-irreducible ideal of $R_M$ for some maximal ideal $M$. Since
$A$ is a completely $Q$-irreducible ideal of $R_M$, there exists $x
\in (A : MR_M) \setminus A$. Write $x = \frac{c}{b}$, where $c \in
R$ and $b \in R \setminus M$. Then if $c \in A$, since $A = AR_M$
it follows that $x \in A$, contrary to the choice of the $x$.
Thus $x \in (A:M) \setminus A$, and to prove that $A$ is an absolutely
irreducible ideal of $R$, it suffices to show that $x$ is in every
fractional ideal $J$ properly containing $A$. We show in fact that
$x$ is in $JR_N$ for all maximal ideals $N$ of $R$. By the choice
of $x$, we have that $x \in (A: MR_M)$, so since $A$ is a completely
$Q$-irreducible ideal of $R_M$, $(A : MR_M)$ is contained in $JR_M$.
(Note that $A$ is properly contained in $JR_M$, since otherwise $A =
AR_M = JR_M$, and $J \subseteq A$, contrary to assumption.) Finally
if $N$ is a maximal ideal of $R$ distinct from $M$, then since $x$
is in $(A:M)$, we have $xM \subseteq AR_N$, so $x \in AR_N \subseteq
JR_N$. This shows $x \in JR_N$ for every maximal ideal $N$ of $R$,
proving the claim. No virus found in this outgoing message. Checked
by AVG Anti-Virus. Version: 7.0.300 / Virus Database: 265.8.6 -
Release Date: 2/7/2005
|
https://www.utoledo.edu/nsm/mathstats/docs/exams/masters/S06msanal.tex | utoledo.edu | CC-MAIN-2022-33 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2022-33/segments/1659882572163.61/warc/CC-MAIN-20220815085006-20220815115006-00124.warc.gz | 911,899,453 | 3,601 | \documentclass[11pt]{amsart}
\usepackage{amssymb}
\newcommand{\R}{\mbox{$\Bbb R$}}
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\voffset -1in \hoffset -.7in \textwidth 6in \textheight 10in
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\begin{document}
\begin{center}
Master of Science Comprehensive Analysis Exam Spring 2006
\end{center}
\bigskip
\begin{center}
Real and Complex Analysis
\end{center}
\bigskip
\begin{center}
{\bf To obtain full credit you must show all your work}\\
\end{center}
\vspace{.2in}
\begin{center}
Part 1. Real Analysis. 100\% will be obtained for \emph{complete} answers to four questions. Indicate clearly
which four questions you wish to be graded.
\end{center}
\vspace{.6in}
\noindent 1. (i) State the definition of convergence of a sequence of real numbers.\\
\noindent (ii) Prove that if $\lim_ {n \rightarrow \infty} a_n=a$
and $\lim_ {n \rightarrow \infty} b_n=b$, then
$\lim_ {n \rightarrow \infty} (a_n+b_n)=a+b$.\\
\noindent(iii) Prove that if $-1 < x < 1$, then $\lim_ {n
\rightarrow \infty} x^n=0.$
\vspace{.5in}
\noindent 2. (i) A sequence of real numbers $x_n$ is said to be
non-decreasing if $p > n$ implies that $x_p \geq x_n$.
Prove that a bounded non-decreasing sequence of real numbers is convergent.\\
\noindent (ii) Define a sequence $\{x_n\}$ by $x_1=\sqrt 2$ and
$x_{n+1}=\sqrt{(2 +\sqrt x_{n})}$ for $n=1,2,3,\cdots$. Prove that
$\{x_n\}$ is convergent and find the limit.
\vspace{.5in}
\noindent 3. (i) State the definition of continuity for a real-valued function whose domain is a subset of $\R$.\\
\noindent (ii) Prove that a real-valued function $f(x)$ whose domain is a subset of $\R$ is continuous at $x \in
X$ if for all sequences $\{x_n\}$ such
that $\lim_ {n \rightarrow \infty} x_n=x$ we have that $\lim_ {n \rightarrow \infty} f(x_n)=f(x)$.\\
\noindent (iii) Consider the function
\begin{equation}
f(x)= \begin{cases} x^2, &x \geq 0, \\
-x^2, &x < 0.\notag \end{cases}
\end{equation}
\noindent Discuss the existence and continuity of $f$ and its
first two derivatives at all points of $x \in \R$. Justify your
answers but you do not need to prove standard theorems.
%Prove from the definition in (i) that the function $f(x)=x^2$ is continuous at $x=2$.\\
\vspace{.5in}
\noindent 4. (i) State Rolle's Theorem.\\
\noindent (ii) Suppose that an $\R$-valued function $f(x)$ is differentiable at $x=a$ and $f(x) \leq f(a)$
for all $x$ in some open interval containing $a$. Prove that $f^{\prime}(a)=0.$\\
\noindent [Hint: It is sufficient to consider left hand and right hand limits].\\
\noindent (iii) Deduce Rolle's Theorem from (ii).\\
\newpage
\noindent 5. (i) Let $X$ be a non-empty subset and define a map
$d:X \times X \mapsto \R $ such that for all $x,y \in X$,
$d(x,y)=2$ if $x \neq y$ and for all $x \in X $, $d(x,x)=0$. Prove
in detail that $(X,d)$ is a metric space.
\bigskip
\noindent (ii) Prove that the sequence of points $x_n=\frac{n}{n+1}$, $n\in\N$ is a Cauchy sequence.\\
\noindent (iii) Let $(X,d)$ be a metric space and let $Y \subset X$ . Show that a subset $A \subset Y$ is open in
$Y$ if and only if there exists a subset $B$ open in $X$ such that $A=B \cap Y$.\\
\vspace{.5in}
\noindent 6. (i) Prove from the definition that the Riemann integral $\int^1_0 (2x+1)dx$ exists.\\
\noindent (ii) Decide whether the following series converge and justify your answers briefly:\\
$\sum^{\infty}_{n=0} (-1)^n \frac{1}{2n+1}$, $\sum^{\infty}_{n=1} \frac{2^n n!}{n^n}$,$\sum^{\infty}_{n=1} \frac{\ln n^2}{n}$. \\
\vspace{.5in}
\noindent 7. Suppose that $(X,d)$ is a complete metric space and
$T$ is a map from $X$ to itself such that for all $x,y \in X$
$d(T(x),T(y)) \leq k d(x,y)$ where $0 < k < 1$. Prove that there
is a unique $x_0 \in X$ such that $T(x_0)=x_0$.
\newpage
\begin{center}
\noindent Part 2. Complex Analysis. 100\% will be obtained for \emph{complete} answers to four questions. Indicate
clearly which four questions you wish to be graded.
\end{center}
\vspace{.3in}
\noindent 1. (i) Evaluate completely $(1+i)^{(1-i)}$.\\
\noindent (ii) Determine either from the definition or by means of the Cauchy-Riemann equations the points in
$\C$ where the function $f(z)=z\bar{z}$ is differentiable as a complex function.
\vspace{.4in}
\noindent 2. (i) Define $f(z)=e^{(\frac{1}{z})} \quad (z \neq
0), f(0)=0$. At what points is $f(z)$
differentiable as a complex function? Justify your answer.\\
\noindent (ii) The complex numbers $z_1,z_2$ and $z_3$ are the vertices of an isosceles right-angled triangle
with the right angle at $z_3$. Prove that $(z_1-z_3)^2=2(z_1-z_3)(z_2-z_3)$.
\vspace{.4in}
%\noindent 2 (i) Let $w=f(z)=u(x,y)+iv(x,y)$ be complex-analytic in some region $D$ of $\C$. Show that the pair
%$(u(x,y),v(x,y))$ satisfies the Cauchy-Riemann equations in $D$.
%\noindent (ii) Find a complex analytic function whose real part is\\
%\noindent (a) $x^3-3xy^2$.\\
%\noindent (b) $\exp(x)\cos(y)$.
\noindent 3. (i) Find a complex analytic function whose real part is $e^x(x\cos(y)-y\sin(y))$.\\
(ii) Show that the M\"obius transformation $T$ preserves the cross ratio: that is if $w_i=T(z_i) \quad (1 \leq i
\leq 4)$ then $\frac{(z_1-z_4)(z_2-z_3)}{(z_1-z_2)(z_3-z_4)}=\frac{(w_1-w_4)(w_2-w_3)}{(w_1-w_2)(w_3-w_4)}$.
\vspace{.4in}
%\noindent 3
%Complete the following statement: Suppose that $f(z)$ is complex-differentiable on the open disk of
%radius $R$ and center $z_0$ and that $0 < \ r < R$. Then $f(z)=\frac{1}{2\pi i} \int ...$. Hence or otherwise
%Evaluate by any valid method $\int_C \frac{dz}{(z-a)(z-b)}$ where $C$ denotes the unit circle centered the origin
%in the complex plane discussing the cases:\\
%depending on the values of $a$ and $b$
%\noindent (i) $|a|,|b| < 1$.\\
%\noindent (ii) $|a| < 1,|b| > 1$.\\
%\noindent (iii) $|a| ,|b| > 1$.\\
\noindent 4. Evaluate by any valid method:\\
(i) $\int^{2\pi}_0 \frac{dx}{a+\cos(x)}$.\\
(ii) By integrating $\frac{e^{iz}}{z}$ over a suitable contour evaluate $\int^{\infty}_0 \frac{\sin(x) dx}{x}$.\\
\vspace{.4in}
\noindent 5. (i) Let $f(z)=\frac{z^3+2z^2+4}{(z-1)^3}$. Find the
Laurent expansion for $f(z)$ about the singular
point $z=1$. For what values of $z$ is this expansion valid?\\
\noindent (ii) Let $C$ be a piecewise smooth closed contour in $\C$. Suppose that $f(z)$ is a analytic inside and
on $C$ and that $a$ and $b$ are distinct points inside $C$. Show that $\int_C \frac{f(z) dz}{(z-a)(z-b)}=
\frac{2\pi i}{a-b}(f(a)-f(b))$.\\
%Deduce Liouville's theorem: a bounded entire function is constant.\\
%\noindent [Hint: Use the assumption that $f(z)$ is bounded to estimate the left hand side and use the fact that a
%function is constant if its values at two arbitrary points are equal.]
\vspace{.4in}
\noindent 6. (i) Evaluate $\int_C
(2z^2+3z+5+\frac{(z^4+2z+1)}{(z-2)}+\frac{1}{(2z-1)})dz$ where $C$
is the unit
circle center at the origin in $\C$.\\
\noindent (ii) Compute the residues of the following functions at the points indicated:\\
$\frac{1}{z^2+1}$ at $z=i$, $\frac{1}{(z-\sin(z)}$ at $z=0$.
\vspace{.4in}
%\noindent 7 (i) $\int^{\infty}_{-\infty} \frac{ dx}{(1+x^2)^2}$.\\
\noindent 7. (i) Find a Mobius transformation that maps $1$, $2$ and $i$ to $i$,$\infty$ and $1$, respectively.\\
%\noindent 7 (i) State Rouche's Theorem relating the location of the roots of two polynomials with complex
%coefficients. Show that the roots of the equation $z^4+z+1=0$ lie between the circles $z=\frac{5}{4}$ and
%$z=\frac{2}{3}$.
\noindent (ii) Evaluate $\int_C \frac{(z^4+2z+1) dz}{(z-2)^4}$ where $C$ in any piecewise smooth closed contour
containing the point $z=2$.
\bigskip
\end{document}
|
https://is.jabok.cz/cv/cv?lang=en;uco=4048;zjazyk=cze;varianta=9;tiskproh=latex | jabok.cz | CC-MAIN-2023-14 | application/x-text | application/x-tex | crawl-data/CC-MAIN-2023-14/segments/1679296949642.35/warc/CC-MAIN-20230331113819-20230331143819-00160.warc.gz | 378,132,370 | 2,546 | \documentclass[12pt]{article}
\usepackage[latin2]{inputenc}
\usepackage[czech]{babel}
\newenvironment{ul}{\begin{itemize}}{\end{itemize}}
\newenvironment{ol}{\begin{enumerate}}{\end{enumerate}}
\begin{document}\noindent
\vspace{1.2cm}{\LARGE {\bfseries Jana Zajícová}}
\vspace{0.8cm} \noindent {\bfseries Současné pracoviště}
\begin{ul}
\item Vyšší odborná škola sociálně pedagogická a teologická Jabok\\
\noindent Salmovská 8\\
\noindent 120 00 Praha 2\\
\noindent
\end{ul} \noindent
{\bfseries Funkce}
\begin{ul}
\item učitelka
\end{ul} \noindent
{\bfseries Dřívější zaměstnání}
\begin{ul}
\item 2000 - 2003 vedoucí redaktorka Magazínu AD - Křesťanství a svět, Portál s.r.o.\\
\noindent
\item 1991 - 2000 redaktorka Magazínu AD - Křesťanství a svět, Portál s.r.o.\\
\noindent
\item 1982 - 1984 učitelka hudby v Lidové škole umění Praha 9 - Vysočany\\
\noindent
\item 1980 - 1982 učitelka hudby v Lidové škole umění Praha 6 - Břevnov\\
\noindent
\item 1977 - 1978 učitelka hudby v Lidové škole umění Praha 6 - Bubeneč\\
\noindent
\end{ul} \noindent
{\bfseries Vzdělání}
\begin{ul}
\item Vyšší odborné: Konzervatoř v Praze, obor hudební
\end{ul} \noindent
{\bfseries Kurzy a výcviky}
\begin{ul}
\item 2014 Výcvik pro práci s metodou Instrumentálního obohacování R. Feuersteina, Cogito - Centrum kognitivní edukace\\
\noindent
\item 2014 Práce s dětskou kresbou, poradenský psycholog Zdeněk Altman\\
\noindent
\item 2009 - 2014 Sebezkušenostní psychoterapeutický výcvik REMEDIUM II, Remedium Praha\\
\noindent
\item 2009 Muzikoterapeutický kurz Matěje Lipského: Muzikoterapie a životní cesta, Praha\\
\noindent
\item 2006 Kurz anglického jazyka, Lilian Bishop school, Londýn\\
\noindent
\item 2005 Muzikoterapeutický kurz Alfréda Moréna, Fokus Praha\\
\noindent
\item 1999 - 2000 Výcvik krizové intervence, SOS Centrum Diakonie Praha\\
\noindent
\item 1994 Kurz pro píšící novináře, Svobodná Evropa\\
\noindent
\item 1986 - 1990 Teologický kurz, bytové semináře Praha\\
\noindent
\end{ul} \noindent
{\bfseries Výuka na VOŠ Jabok}
\begin{ul}
\item Metody muzikoterapie pro výchovu a rozvoj\\
\noindent
\item Cílená muzikoterapie\\
\noindent
\item Diplomní seminář\\
\noindent
\item
\end{ul} \noindent
{\bfseries Výuka v kurzech dalšího vzdělávání}
\begin{ul}
\item Muzikoterapie pro celostní rozvoj osobnosti\\
\noindent
\item Komunikace ve skupině prostřednictvím hudby, pohybu a výtvarné činnosti\\
\noindent
\item
\end{ul} \noindent
{\bfseries Členství v orgánech a dobrovolnická činnost}
\begin{ul}
\item 2004 - 2006 členkou Školské rady Vyšší odborné školy publicistiky\\
\noindent
\item 1999 - 2000 telefonická krizová intervence na Lince důvěry SOS Diakonie\\
\noindent
\item 1990 - dosud: pastorační činnost, vedení katechezí a vyučování náboženství v Římskokatolické farnosti Praha 4 - Michle\\
\noindent
\item 1990 - 1996 vedení katechezí a vyučování náboženství v~ Římskokatolické farnosti Praha 4 - Spořilov\\
\noindent
\end{ul} \noindent
{\bfseries Publikační a přednášková činnost}
\begin{ul}
\item Zajícová, Jana. Bůh je tady. Vydání první. Praha: Portál, 2018. 72 stran. ISBN: 978-80-262-1405-2\\
\noindent
\item Zajícová Jana: Muzikoterapie v historii a současnosti. Přednáška pro Českou křesťanskou akademii Tachov 6. 10. 2010\\
\noindent
\item Zajícová, Jana. Recenze knihy V bezpečí a svoboden. Univerzum 1/2010\\
\noindent
\item Zajícová, Jana. Recenze sborníku Pastorální a etické výzvy v oblasti manželství, rodiny a sexuality. Univerzum 6/2009\\
\noindent
\item Zajícová, Jana. Medvědí náruč s ženskou duší. Teologie \& Společnost, Speciál 2005\\
\noindent
\item Zajícová, Jana. Jabok má pět P. Salesiánská rodina 1/2005\\
\noindent
\item Zajícová, Jana. Ádéčko v hodině pravdy. Katolický týdeník 7/2001\\
\noindent
\item Zajícová, Jana. Budou věřit naše děti? Katolický týdeník 11/2000\\
\noindent
\item Zajícová, Jana. Autorské články v Magazínu AD - Křesťanství a svět, Portál 1993 - 2003\\
\noindent
\end{ul} \noindent
{\bfseries Účast na konferencích a umělecká činnost}
\begin{ul}
\item 2016 - Mezinárodní konference kreativních terapií Space for art therapies\\
\noindent
\item 1987 - 1991 členkou a sólistkou komorního smyčcového orchestru Quatro Corde\\
\noindent
\item 1989 koncertní cesta Bulharsko\\
\noindent
\item 1988 koncertní cesta Velká Británie, Holandsko, Belgie\\
\noindent
\item 1987 koncertní cesta Švýcarsko, NSR\\
\noindent
\item 1986 Večer autorské poezie Jany Zajícové a Michala Vondráčka v~ přednesu Radovana Lukavského a Veroniky Žilkové, Vyšehradské probošství v Praze\\
\noindent
\end{ul} \noindent
\vspace{0.5cm} \noindent 15. 8. 2019
\vspace{0.5cm} \noindent \end{document}
|
https://www.andrew.cmu.edu/course/15-251/Assignments/assignment03/hw03.tex | cmu.edu | CC-MAIN-2022-40 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2022-40/segments/1664030335004.95/warc/CC-MAIN-20220927100008-20220927130008-00309.warc.gz | 678,807,942 | 4,116 | \documentclass[12pt]{exam}
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\begin{center}
\textbf{\large{15-251 : Great Theoretical Ideas In Computer Science
\\ \vspace{0.2in} Fall 2014
\\ \vspace{0.2in} Assignment 3
}}
\vspace{0.2in}
\large{Due: Thursday, Sep. 18, 2014 11:59 PM}
\end{center}
\vspace{0.5in}
\hbox to \textwidth{Name:\enspace\hrulefill}
\vspace{0.2in}
\hbox to \textwidth{Andrew ID:\enspace\hrulefill}
\vspace{0.2in}
% End title box
\vspace{0.5in}
\vspace*{1in}
\begin{center}
\gradetable[h][questions]
\end{center}
\begin{questions}
\setcounter{question}{-1}
\setcounter{numquestions}{-1}
\newpage\Q{Warmup}
\begin{parts}
\part{Suppose there are 170 CS majors, 80 ECE majors and 50 math majors in a class. Of these, 30 are
double majors in CS and ECE, 10 are double majors in ECE and math. If five students are triple
majors and there are 250 total students, how many of the students are double majors in CS and
math?}
\vspace{0.5in}
\part{How many ways can 6 pirates split 50 gold pieces if the first pirate needs at least 10 pieces, the
second needs at least 8, the third needs at least 6, the fourth needs at least 4, and the fifth needs
at least 2, and the sixth didn't really help with the plundering, so he can get any amount?
}
\vspace{0.5in}
\part{We have $n$ sandwiches to give out to some kittens. Each kitten is going to be assigned 2 sandwiches, and every sandwich can be assigned to multiple kittens. How many kittens do we need to in order to guarantee that there will be two kittens which are assigned the same 2 sandwiches?}
\vspace{0.5in}
\part{How many distinguishable ways are there to rearrange the letters in \\``OHMYGODIMONFIRE'' ?
}
\vspace{0.5in}
\part{Explain why \[\binom{3n}{3} = 3 \binom{n}{3} + 6 \binom{n}{2} n + n^3\] by counting in two ways. Come up with a set that both of these expressions count. (Hint: Start with the simpler side)}
\end{parts}
\newpage\Q{More Problems Than You Can Count}
\begin{parts}
\part[10] Klaas loves painting, and he wanted to include Peter in his hobby, so he challenged him to a painting game. Klaas will paint 29 points in the plane such that for any 3 points, at least two of them are at a distance less than one unit from each other. Then, if Peter could draw a unit circle around at least 15 of the points, he would win. If not, then Klaas wins. \\
Assuming that Klaas and Peter both play optimally, who will win this game? Prove your answer.
\begin{solution}
\end{solution}
\vspace{0.5 in}
\part[10] When you place an order at Razzy Fresh, you must choose either vanilla or chocolate frozen yogurt. Also, you must choose EXACTLY 2 toppings. There are 10 to choose from, 4 of which contain nuts, and 6 of which do not. An order consists of both a flavor and a choice of toppings.\\
Patrick decides to send his students on a field trip. There are 15,251 students, 7,625 or whom are female and 7,626 of whom are male. Every student will choose one of 250 Razzy locations in Pittsburgh to visit, with the restriction that the number of boys and girls in each Razzy store must differ by at most 1. In each restaurant, the students group into as many male/female couples as possible. Each couple will then place one order for the two of them to share. Since they want to feel special, every couple must choose a different order than all the other couples in their own restaurant. (If there is a single person left over, they can order whatever they want). \\
However, you are worried because every male student is allergic to nuts, and will die if they eat any. Patrick believes that there is a way for everyone to follow these rules and eat their frozen yogurt without anyone dying. Is he correct? Prove your answer.
\begin{solution}
\end{solution}
\end{parts}
\newpage\Q{Why Can't I Count All These Arrangements?}
\bigskip
\begin{parts}
\part[10] In lecture, we showed that the number of ways to divide 20 pieces of gold amongst 5 pirates is $\binom{24}{4}$ by counting all strings with $20$ G's and $4$ /'s. \\ \\
The following alternate method was suggested to count such strings: \\
Write down 20 G's. Each of the $4$ /'s can go to $21$ places, for a total of $21^4$ possibilities. The /'s are ``indistinguishable'', so their odering does not matter. Thus, we divide by $4!$ since we could have placed the $4$ /'s in any order. So the answer must be \[ \frac{21^4}{4!} \]
However, this is certainly not correct as it is not equivalent to our answer $\binom{24}{4}$, and in fact it is not even an integer! \\
Explain carefully and concisely what is wrong with this approach. In particular, does it overcount or undercount? Why?
\begin{solution}
\end{solution}
\vspace{0.5 in}
\part[15] David and Taehoon are making shishkebabs. Together, they have $b$ pieces of beef and $o$ pieces of onion, and
they will each get one shishkebab. A shishkebab is some non-empty sequence of pieces of onion and pieces of
beef, but neither person wants two pieces of beef next to each other. Also, they want to use up all of the pieces of beef and onion that they have. In how many ways can they create and choose their two shishkebabs? \\
For example, with $b=3, o=2$, there are 10 possible ways.
$(B, BOBO), (B, OBOB), (B, BOOB), (BO, BOB), (OB, BOB), \\
(BOB, BO), (BOB, OB), (BOBO, B), (OBOB, B), (BOOB, B)$
\begin{solution}
\end{solution}
\end{parts}
\newpage\Q{Counting Identities} \\
\begin{parts}
\part[15] Show that \\
\[\sum_{i=0}^{m}{ \binom{n-i}{m-i} \binom{k+i}{i}} = \binom{n+k+1}{m} \] \\
by making a combinatorial argument, i.e. counting in two ways. You should assume that $n \ge m$.
\begin{solution}
\end{solution}
\vspace{0.5 in}
\part[15] The binomial theorem \[(x+y)^n = \sum_{k=0}^{n} \binom{n}{k} x^ky^{n-k} \] can be related to many problems in combinatorics. Use the binomial theorem to prove the following identity. \\
\[ \sum_{i=k}^{n}{\binom{i}{k}\binom{n}{i}} = \binom{n}{k}2^{n-k} \]
\begin{solution}
\end{solution}
\end{parts}
\newpage\Q{Counting to 251}
\begin{parts}
\part[3] Andy has tennis balls labeled $1 \dots 251$ in a pile that he wants to break apart. At each step, he chooses a pile with at least $2$ balls in it and splits it into two non-empty piles, not necessarily of equal size. He repeats this process until all the piles are of size $1$. \\
How many steps will this process take? \\
\begin{solution}
\end{solution}
\part[12]
Prove that the number of ways for Andy to carry out the process from part (a) is
\[\binom{251}{2}\binom{250}{2}\binom{249}{2} \cdots \binom{2}{2} \]
For two ways to be considered identical, they must split the same set and create the same two subsets at every single step in the process.
\begin{solution}
\end{solution}
\vspace{0.5 in}
\part[10] Victor and Venkat are helping their students to form homework groups, so they have every student fill out a form listing all of the other students who they would be willing to work with. \\
There are 251 students in the class, and every student lists exactly 168 other students who they would be willing to work with. For any two students in the class, if student A puts student B on their list, then student B will also have student A on their list. \\
Show that there must be some group of 4 students who are all willing to work with one another.
\begin{solution}
\end{solution}
\end{parts}
\end{questions}
\end{document}
|
http://www.aips.nrao.edu/TEXT/PUBL/AIPSMEMO68.TEX | nrao.edu | CC-MAIN-2022-33 | application/x-tex | text/x-matlab | crawl-data/CC-MAIN-2022-33/segments/1659882572063.65/warc/CC-MAIN-20220814173832-20220814203832-00344.warc.gz | 49,975,380 | 6,118 | %-----------------------------------------------------------------------
%; Copyright (C) 1995
%; Associated Universities, Inc. Washington DC, USA.
%;
%; This program is free software; you can redistribute it and/or
%; modify it under the terms of the GNU General Public License as
%; published by the Free Software Foundation; either version 2 of
%; the License, or (at your option) any later version.
%;
%; This program is distributed in the hope that it will be useful,
%; but WITHOUT ANY WARRANTY; without even the implied warranty of
%; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%; GNU General Public License for more details.
%;
%; You should have received a copy of the GNU General Public
%; License along with this program; if not, write to the Free
%; Software Foundation, Inc., 675 Massachusetts Ave, Cambridge,
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%; Internet email: aipsmail@nrao.edu.
%; Postal address: AIPS Project Office
%; National Radio Astronomy Observatory
%; 520 Edgemont Road
%; Charlottesville, VA 22903-2475 USA
%-----------------------------------------------------------------------
% Summary of standard aips calibration process.
% last edited by glen langston
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\newcommand{\eeddes}{\end{description}} % description list
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\newcommand{\APEIN}[1]{{\normalsize \sc {#1}}}
\newcommand{\IF}{{\normalsize \sc IF}~}
\newcommand{\SN}{{\normalsize \sc SN}~}
\newcommand{\SU}{{\normalsize \sc SU}~}
\newcommand{\CL}{{\normalsize \sc CL}~}
\newcommand{\TCTES}{{\normalsize \sc 3C286}~}
\newcommand{\TCOTE}{{\normalsize \sc 3C138}~}
\newcommand{\normalstyle}{\baselineskip 7mm \parskip 1mm \large}
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\begin{document}
\pagestyle{myheadings}
\newcommand{\HEADING}{{\it \AIPS Calibration Summary} \hfill
\AIPS Memo Number 68 \hfill Page~~}
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\centerline{\huge{\it Summary of \AIPS UV-data Calibration}}
\centerline{{\it From VLA Archive Tape to a UV FITS Tape}}
%\centerline{Glen Langston and Dean Schlemmer}
\centerline{\lastedit}
The Gentle User enters the Computer room with their VLA archive
tape containing a scientific breakthrough.
For the sake of demonstration, let's call the user's sources
\APEIN{source1} and \APEIN{source2}.
The interferometer phase is calibrated by observations of the
calibration sources \APEIN{cal1} and \APEIN{cal2}.
The flux density scale is calibrated by observing \TCTES.
Mount your tape on drive number {\it n}, log in and start \AIPS.
Example user input: \APEIN{AIPS NEW}. Mount the tape:
\APEIN{INTAP {\it n}; DENS=6250; MOUNT}.
\beddes
\myitem{PRTTP} Find out what is on the tape, get project number and
bands: \APEIN{TASK='PRTTP'; PRTLEV=-2; NFILES=0; INP;GO; WAIT; REWIND}.
\myitem{FILLM} Load your data from tape.
\APEIN{TASK='FILLM'; VLAOBS='?'; BAND=''; DOALL=1; NFILES={\it m}; INP;GO}.
FILLM will load your visibilities (UV data) into a large file
and create 6 \AIPS tables.
The tables have two letter names:
\tablestyle
\beddes
\mybitem{HI} Human readable history of things done to your data.
Use PRTHI to read it.
\mybitem{AN} Antenna location and polarization tables. Antenna
polarization calibration is placed here.
\mybitem{NX} Index into visibility file based source name and
observation time. Not modified by calibration.
\mybitem{SU} Source table contains the list of sources observed
and indexes into the frequency table. The flux densities of the
calibration sources are entered into this table.
\mybitem{FQ} Frequencies of observation and bandwidth with index
into visibility data. Not modified.
\mybitem{CL} Calibration table describing the antenna based gains.
Version 1 should never be modified. Ultimate goal of calibration
is to create a good version 2. Use PRTAB to read tables.
\eeddes
\normalstyle
\myitem{PRTAN} Print out the antenna locations (\APEIN{PRTLEV=0; TASK
'PRTAN'; INP; GO}) and choose a good Reference antenna
near the center of the array (\APEIN{REFANT=?}). Check the VLA
operater log to make sure the antenna was OK during the entire observation.
\myitem{LISTR} Lists your UV data in a variety of ways. Make a list
of your observations:
\APEIN{TASK='LISTR'; OPTYP='SCAN'; DOCRT=-1; CALCODE=''; SOUR=''; TIMER 0;
INP;GO}. NOTE: If you have observed in a such a way as to create more than one
\APEIN{FREQID}, you must run through the entire calibration procedure which
follows {\it ONCE FOR EACH} \APEIN{FREQID}. For new users, it is better at this
point to use \APEIN{UVCOP} to copy each \APEIN{FREQID} into separate files
and then calibrate each file separately.
\myitem{UVCOP} Skip this step if your data consists of only one
\APEIN{FREQID}. Copies different \APEIN{FREQID}s into separate files.
\APEIN{TAST='UVCOP'; FREQID=?; OUTNAME='?'; OUTDI=INDI
; INP; GO}. The
result will be a .\APEIN{UVCOP} file.
\myitem{SETJY} Sets the flux of your flux calibration source in the \SU
table:
\APEIN{TASK='SETJY'; SOUR='3C286',''; OPTYP='CALC'; INP;GO}.
\myitem{TASAV} As insurance, make a copy of all your tables:
\APEIN{TASK='TASAV'; CLRON; OUTDI=INDI; INP;GO}.
\myitem{CALIB} \APEIN{CALIB} is the heart of the \AIPS
calibration package.
Execute \APEIN{VLAPROCS}, an \AIPS ``runfile'', to create
procedures \APEIN{VLACALIB, VLACLCAL} and \APEIN{VLARESET} (\APEIN{RUN
VLAPROCS}). The procedure \APEIN{VLACALIB} runs \APEIN{CALIB}.
Set the UV and Antenna limits for \APEIN{3C286}.
For L, C and X band, 10\% and 10 degree errors are OK;
for other bands the limits are higher.
\tablestyle
\beddes
\mybitem{SN} Solution table contain antenna based gains corrections.
These \SN table results are latter placed in a \CL table by task
\APEIN{CLCAL}.
\eeddes
\normalstyle
\APEIN{TASK='VLACAL'; CALS='3C286',''; CALCODE='*';~REFANT=?;
UVRA=0; MINAMP=10; MINPH=10; INP; VLACAL}.
The task \APEIN{CALIB} lists antenna pairs which deviate
significantly from the solution.
\myitem{TVFLG} If you have lots of errors, then
carefully examine your data using \APEIN{TVFLG}. (See \AIPS Cookbook)~
If only a few antenna pairs are bad over a limited time range, use
\APEIN{UVFLG} to flag that antenna for the time from just after the previous
good \APEIN{cal} observation to before the next good \APEIN{cal} observation
and then run \APEIN{VLACAL} again.
\myitem{UVFLG} Flags bad UV-data. Skip this step if you have no bad data.
\APEIN{TASK='UVFLG'; ANTEN=?,0; BASELI=0; TIMER=?; FLAGV=1;
SOUR=''; OPCOD=''; INP;GO}.
If in doubt about any \uvdata, \APEIN{FLAG THEM!}
This will create a Flag Table (\APEIN{FG}). You want to use
\APEIN{FG} table version 1 for all tasks.
\tablestyle
\beddes
\mybitem{FG} A flag table marks bad data. FG tables contain
an index into the UV data based
on time range, antenna number, frequency and \IF number.
\eeddes
\normalstyle
\myitem{CALIB} Now calibrate the antenna gain based on the
rest of the cal sources.
Look in the Calibrator manual for UV limits; If there are limits,
\APEIN{VLACAL} must be run separately for these sources (i.e. enter \APEIN{
TGET VLACAL; CALS='?',''; ANTEN=?; BASELI=0; INP; VLACAL} for \APEIN{cal1}
and then again for \APEIN{cal2}). Otherwise:
\APEIN{TGET VLACAL; CALS='cal1','cal2',''; ANTENN=0; BASELI=0; INP; VLACAL}.
Flag bad baselines listed. Continue if only a few are listed, otherwise
run VLACAL again.
\myitem{GETJY} Sets the flux of phase calibration sources in the \SU table.
\APEIN{TASK 'GETJY'; SOUR='cal1','cal2',''; CALS='3C286','';
BIF=0; EIF=0; INP;GO}.
\myitem{TASAV} Good time to save your tables:
\APEIN{TGET='TASAV'; OUTDI=INDI; CLRON; INP;GO}.
\myitem{CLCAL} Calibrate the antenna gain and interpolates it into
a new \CL table.
Each execution of \APEIN{CLCAL} adds to
output \CL table version 2.
\APEIN{CLCAL} is run using the procedure \APEIN{VLACLCAL}.~
\APEIN{TASK='VLACLC'; SOUR='source1','cal1',''; CALS='cal1','';
OPCODE='CALI'; TIMER=0; INTERP='2PT'; INP; VLACLC}.
Run \APEIN{CLCAL} for the second source using the second calibrator:
\APEIN{TGET VLACLC; SOUR='source2','cal2',''; CALS='cal2',''; INP;
VLACLC}. Next, self-calibrate the flux calibrator: \APEIN{TGET VLACLC;
SOUR='3C286',''; CALS='3C286',''; INP; VLACLC}.~
\myitem{LISTR} Make a matrix listing of the Amplitude and RMS of
calibration sources with calibration applied:
\APEIN{TASK='LISTR'; OPTYP='MATX'; SOUR='cal1','cal2',''; DOCAL=1;
DOCRT=-1; DPARM=3,1,0; UVRA=0; ANTEN=0; BASELI=0; BIF=1; INP;GO}.~
Look for antenna pairs with wild RMSs and flag them with \APEIN{UVFLG}.
If only a few are bad, continue, else delete \CL table 2 and the \SN table
using \APEIN{VLARESET}. Then return to the first \APEIN{CALIB} step.
If the data look good, run \APEIN{LISTR} again for the remaining
\IF(s). \APEIN{TGET LISTR; BIF=2; INP;GO}
\myitem{UVPLT} Plots the \uvdata in a variety of ways. Make at Flux
versus Time plot first. Choose \APEIN{XINC} so the plot will have
approximately 1000 points (divide the number of visibilities by 1000 and
choose the closest prime number to that).
Set \APEIN{ANTEN=0; BASELI=0; TIMER=0}. Then:
\APEIN{TASK='UVPLT'; SOUR='source1','',''; XINC=13; BPARM(1)=11;
DOCAL=1; BIF=1; INP;GO}.~
Repeat \APEIN{UVPLT} with your calibrators also.
Look at the plots with \APEIN{QMSPL, TVPL} or \APEIN{TXPL} (for plotting
on the QMS, the TV, or the terminal, respectively).
Plot other \IF(s). Flag wild points using \APEIN{UVFND} and either
\APEIN{UVFLG} or \APEIN{CLIP}. Plot Flux versus baseline:
\APEIN{TGET UVPLT; BPARM=0; INP;GO}.
If the calibration failed because of a bad reference antenna or too much
noisy data, you may reset the parameters with: \APEIN{INP VLARESET; VLARESET}
This will bring you back to the first \APEIN{CALIB} step above.
\eeddes
Calibration is now complete for continuum, un-polarized observations.
Skip down to FITTP.
For polarization observations, the following steps are required.
For 21cm or longer wavelength observations, ionospheric Faraday
rotation corrections may be needed. See FARAD in the \AIPS cookbook.
\begin{figure}[h]
\vskip 4in
{\it \hskip 1.5in a) \hfill b) \hskip 1.5in}
{\bf Figure:}
{\it a)} Uncalibrated \uvdata and {\it b)}
calibrated \uvdata from an X-band snapshot of 3C286.
Default VLA gains are a tenth of the actual gains and
show significant scatter.
Only wild \uvdata points $\sim$50 \% greater than the average
can be detected before calibration.
\end{figure}
\clearpage
\centerline{\bf{POLARIZATION CALIBRATION}}
\beddes
\myitem{TASAV} As added insurance, save your tables again:
\APEIN{TGET TASAV; INP;GO}.
\myitem{LISTR} Examine the parallactic angles of your calibrator observations:
\APEIN{TASK='LISTR'; ANTEN=0; SOUR=''; CALCOD='*'; OPTYPE='GAIN'; DPARM=9,0;
INP; GO.}
\myitem{PCAL} Intrinsic antenna polarization calculation. This step
is only possible if you have observed calibration sources at many
parallactic angles. PCAL will only modify the \APEIN{AN} table.
\APEIN{TASK='PCAL'; CALS='cal1','cal2',''; BIF=1; EIF=2;
REFANT=?; INP;GO}
\myitem{TACOP} Make a copy of the last \APEIN{CL} table;
In case the \APEIN{CLOCR} fails, the original \APEIN{CL} table will be
preserved. \APEIN{TASK='TACOP'; OUTDI=INDI ; INEXT='CL'; INVER=2; NCOUNT=1;
OUTVER=3; INP; GO}. Use \APEIN{CL} table version 3 for all following steps.
\myitem{LISTR} Now determine the absolute linear
polarization angle. Make a matrix listing of the angle of \TCTES.
The observed angles
are different for each frequency and \IF.
\APEIN{TASK='LISTR'; SOUR='3C286',''; DOCAL=1; GAINUSE=3; BIF=1; DOPOL=1;
OPTYP='MATX';
INP; GO}.
Record the matrix average angle, $\phi_1$, for \IF 1.
Run LISTR again for \IF 2.
\APEIN{TASK='LISTR'; BIF=2; INP; GO}.
Record the matrix average angle, $\phi_2$, for \IF 2.
\myitem{CLCOR} Now apply the angle correction to CL table 3.
\APEIN{CLCOR} needs only to be run once, unless you make a mistake.
The phase correction is applied to the Left circularly polarized
signal. (The relative phase of L and R produces the
linear polarization angle)
The angle of linear polarization for \TCTES is $66^o$.
(For \TCOTE, $\phi=-24^o$.)
\APEIN{TASK='CLCOR'; STOKES='L'; SOUR=''; OPCOD='POLR'; BIF=1; EIF=2;
\mbox{GAINVER=3; CLCORPA=66-$\phi_1$,66-$\phi_2$,0;} INP; GO}.~
Run \APEIN{LISTR} again to check the phases.~
\APEIN{TGET LISTR; DOPOL=1; INP; GO}.~
Check the phases, if they are wrong run \APEIN{CLCOR} again.
\APEIN{TGET CLCOR; OPCOD='PHAS';
\mbox{CLCORPA=66-$\phi'_1$,66-$\phi'_2$,0;} INP;GO}~
\myitem{FITTP} Writes the output \uvdata to tape.
\APEIN{DISMOUNT} your archive; \APEIN{MOUNT} your output tape.
\APEIN{TASK='FITTP'; DOEOT=-1;BLOCK=10; OUTTAP=INTAP; INP;GO}.
\myitem{Mapping} See \AIPS cookbook for instructions on
using \APEIN{TASK='SPLIT'} to create a single source data set.
Next use your favorite Fourier Transform task
(i.e. \APEIN{MX} or \APEIN{HORUS}).
Automatic imaging and self-calibration is now possible using the \AIPS
procedure \APEIN {MAPIT}. See the \AIPS \APEIN {MAPIT} memo for more details.
\eeddes
Please send comments to Glen Langston or Dean Schlemmer, NRAO-Charlottesville.
E-mail addresses: glangsto@nrao.edu, dschlemm@nrao.edu
\end{document}
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https://browse.dgit.debian.org/yosys.git/plain/manual/PRESENTATION_ExSyn.tex?id=816fe6bbe0ad90f7a696dd208dae6db8139dfd00 | debian.org | CC-MAIN-2021-49 | text/plain | application/x-tex | crawl-data/CC-MAIN-2021-49/segments/1637964358842.4/warc/CC-MAIN-20211129194957-20211129224957-00579.warc.gz | 229,707,958 | 5,508 |
\section{Yosys by example -- Synthesis}
\begin{frame}
\sectionpage
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Typical Phases of a Synthesis Flow}
\begin{frame}{\subsecname}
\begin{itemize}
\item Reading and elaborating the design
\item Higher-level synthesis and optimization
\begin{itemize}
\item Converting {\tt always}-blocks to logic and registers
\item Perform coarse-grain optimizations (resource sharing, const folding, ...)
\item Handling of memories and other coarse-grain blocks
\item Extracting and optimizing finite state machines
\end{itemize}
\item Convert remaining logic to bit-level logic functions
\item Perform optimizations on bit-level logic functions
\item Map bit-level logic gates and registers to cell library
\item Write results to output file
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Reading the design}
\begin{frame}[fragile]{\subsecname}
\begin{lstlisting}[xleftmargin=0.5cm, basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=ys]
read_verilog file1.v
read_verilog -I include_dir -D enable_foo -D WIDTH=12 file2.v
read_verilog -lib cell_library.v
verilog_defaults -add -I include_dir
read_verilog file3.v
read_verilog file4.v
verilog_defaults -clear
verilog_defaults -push
verilog_defaults -add -I include_dir
read_verilog file5.v
read_verilog file6.v
verilog_defaults -pop
\end{lstlisting}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Design elaboration}
\begin{frame}[fragile]{\subsecname}
During design elaboration Yosys figures out how the modules are hierarchically
connected. It also re-runs the AST parts of the Verilog frontend to create
all needed variations of parametric modules.
\bigskip
\begin{lstlisting}[xleftmargin=0.5cm, basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=ys]
# simplest form. at least this version should be used after reading all input files
#
hierarchy
# recommended form. fails if parts of the design hierarchy are missing, removes
# everything that is unreachable from the top module, and marks the top module.
#
hierarchy -check -top top_module
\end{lstlisting}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{The {\tt proc} command}
\begin{frame}[fragile]{\subsecname}
The Verilog frontend converts {\tt always}-blocks to RTL netlists for the
expressions and ``processes'' for the control- and memory elements.
\medskip
The {\tt proc} command transforms this ``processes'' to netlists of RTL
multiplexer and register cells.
\medskip
The {\tt proc} command is actually a macro-command that calls the following
other commands:
\begin{lstlisting}[xleftmargin=0.5cm, basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=ys]
proc_clean # remove empty branches and processes
proc_rmdead # remove unreachable branches
proc_init # special handling of "initial" blocks
proc_arst # identify modeling of async resets
proc_mux # convert decision trees to multiplexer networks
proc_dff # extract registers from processes
proc_clean # if all went fine, this should remove all the processes
\end{lstlisting}
\medskip
Many commands can not operate on modules with ``processes'' in them. Usually
a call to {\tt proc} is the first command in the actual synthesis procedure
after design elaboration.
\end{frame}
\begin{frame}[fragile]{\subsecname{} -- Example 1/3}
\begin{columns}
\column[t]{5cm}
\lstinputlisting[basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=verilog]{PRESENTATION_ExSyn/proc_01.v}
\column[t]{5cm}
\lstinputlisting[basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=ys, frame=single]{PRESENTATION_ExSyn/proc_01.ys}
\end{columns}
\hfil\includegraphics[width=8cm,trim=0 0cm 0 0cm]{PRESENTATION_ExSyn/proc_01.pdf}
\end{frame}
\begin{frame}[t, fragile]{\subsecname{} -- Example 2/3}
\vbox to 0cm{\includegraphics[width=\linewidth,trim=0cm 0cm 0cm -2.5cm]{PRESENTATION_ExSyn/proc_02.pdf}\vss}
\vskip-1cm
\begin{columns}
\column[t]{5cm}
\lstinputlisting[basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=verilog]{PRESENTATION_ExSyn/proc_02.v}
\column[t]{5cm}
\lstinputlisting[basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=ys, frame=single]{PRESENTATION_ExSyn/proc_02.ys}
\end{columns}
\end{frame}
\begin{frame}[t, fragile]{\subsecname{} -- Example 3/3}
\vbox to 0cm{\includegraphics[width=\linewidth,trim=0cm 0cm 0cm -1.5cm]{PRESENTATION_ExSyn/proc_03.pdf}\vss}
\vskip-1cm
\begin{columns}
\column[t]{5cm}
\lstinputlisting[basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=ys, frame=single]{PRESENTATION_ExSyn/proc_03.ys}
\column[t]{5cm}
\lstinputlisting[basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=verilog]{PRESENTATION_ExSyn/proc_03.v}
\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{The {\tt opt} command}
\begin{frame}[fragile]{\subsecname}
The {\tt opt} command implements a series of simple optimizations. It also
is a macro command that calls other commands:
\begin{lstlisting}[xleftmargin=0.5cm, basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=ys]
opt_const # const folding
opt_share -nomux # merging identical cells
do
opt_muxtree # remove never-active branches from multiplexer tree
opt_reduce # consolidate trees of boolean ops to reduce functions
opt_share # merging identical cells
opt_rmdff # remove/simplify registers with constant inputs
opt_clean # remove unused objects (cells, wires) from design
opt_const # const folding
while [changed design]
\end{lstlisting}
The command {\tt clean} can be used as alias for {\tt opt\_clean}. And {\tt ;;}
can be used as shortcut for {\tt clean}. For example:
\begin{lstlisting}[xleftmargin=0.5cm, basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=ys]
proc; opt; memory; opt_const;; fsm;;
\end{lstlisting}
\end{frame}
\begin{frame}[t, fragile]{\subsecname{} -- Example 1/4}
\vbox to 0cm{\includegraphics[width=\linewidth,trim=0cm 0cm 0cm -0.5cm]{PRESENTATION_ExSyn/opt_01.pdf}\vss}
\vskip-1cm
\begin{columns}
\column[t]{5cm}
\lstinputlisting[basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=ys, frame=single]{PRESENTATION_ExSyn/opt_01.ys}
\column[t]{5cm}
\lstinputlisting[basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=verilog]{PRESENTATION_ExSyn/opt_01.v}
\end{columns}
\end{frame}
\begin{frame}[t, fragile]{\subsecname{} -- Example 2/4}
\vbox to 0cm{\includegraphics[width=\linewidth,trim=0cm 0cm 0cm 0cm]{PRESENTATION_ExSyn/opt_02.pdf}\vss}
\vskip-1cm
\begin{columns}
\column[t]{5cm}
\lstinputlisting[basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=ys, frame=single]{PRESENTATION_ExSyn/opt_02.ys}
\column[t]{5cm}
\lstinputlisting[basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=verilog]{PRESENTATION_ExSyn/opt_02.v}
\end{columns}
\end{frame}
\begin{frame}[t, fragile]{\subsecname{} -- Example 3/4}
\vbox to 0cm{\includegraphics[width=\linewidth,trim=0cm 0cm 0cm -2cm]{PRESENTATION_ExSyn/opt_03.pdf}\vss}
\vskip-1cm
\begin{columns}
\column[t]{5cm}
\lstinputlisting[basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=ys, frame=single]{PRESENTATION_ExSyn/opt_03.ys}
\column[t]{5cm}
\lstinputlisting[basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=verilog]{PRESENTATION_ExSyn/opt_03.v}
\end{columns}
\end{frame}
\begin{frame}[t, fragile]{\subsecname{} -- Example 4/4}
\vbox to 0cm{\hskip6cm\includegraphics[width=6cm,trim=0cm 0cm 0cm -3cm]{PRESENTATION_ExSyn/opt_04.pdf}\vss}
\vskip-1cm
\begin{columns}
\column[t]{5cm}
\lstinputlisting[basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=verilog]{PRESENTATION_ExSyn/opt_04.v}
\column[t]{5cm}
\lstinputlisting[basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=ys, frame=single]{PRESENTATION_ExSyn/opt_04.ys}
\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{When to use {\tt opt} or {\tt clean}}
\begin{frame}{\subsecname}
Usually it does not hurt to call {\tt opt} after each regular command in the
synthesis script. But it increases the synthesis time, so it is favourable
to only call {\tt opt} when an improvement can be archieved.
\bigskip
The designs in {\tt yosys-bigsim} are a good playground for experimenting with
the effects of calling {\tt opt} in various places of the flow.
\bigskip
It generally is a good idea to call {\tt opt} before inherently expensive
commands such as {\tt sat} or {\tt freduce}, as the possible gain is much
higher in this cases as the possible loss.
\bigskip
The {\tt clean} command on the other hand is very fast and many commands leave
a mess (dangling signal wires, etc). For example, most commands do not remove
any wires or cells. They just change the connections and depend on a later
call to clean to get rid of the now unused objects. So the occasional {\tt ;;}
is a good idea in every synthesis script.
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{The {\tt memory} command}
\begin{frame}[fragile]{\subsecname}
In the RTL netlist, memory reads and writes are individual cells. This makes
consolidating the number of ports for a memory easier. The {\tt memory}
transforms memories to an implementation. Per default that is logic for address
decoders and registers. It also is a macro command that calls other commands:
\begin{lstlisting}[xleftmargin=0.5cm, basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=ys]
# this merges registers into the memory read- and write cells.
memory_dff
# this collects all read and write cells for a memory and transforms them
# into one multi-port memory cell.
memory_collect
# this takes the multi-port memory cell and transforms it to address decoder
# logic and registers. This step is skipped if "memory" is called with -nomap.
memory_map
\end{lstlisting}
\bigskip
Usually it is preferred to use architecture-specific RAM resources for memory.
For example:
\begin{lstlisting}[xleftmargin=0.5cm, basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=ys]
memory -nomap; techmap -map my_memory_map.v; memory_map
\end{lstlisting}
\end{frame}
\begin{frame}[t, fragile]{\subsecname{} -- Example 1/2}
\vbox to 0cm{\includegraphics[width=\linewidth,trim=0cm 0cm 0cm -6cm]{PRESENTATION_ExSyn/memory_01.pdf}\vss}
\vskip-1cm
\begin{columns}
\column[t]{5cm}
\lstinputlisting[basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=ys, frame=single]{PRESENTATION_ExSyn/memory_01.ys}
\column[t]{5cm}
\lstinputlisting[basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=verilog]{PRESENTATION_ExSyn/memory_01.v}
\end{columns}
\end{frame}
\begin{frame}[t, fragile]{\subsecname{} -- Example 2/2}
\vbox to 0cm{\hfill\includegraphics[width=7.5cm,trim=0cm 0cm 0cm -5cm]{PRESENTATION_ExSyn/memory_02.pdf}\vss}
\vskip-1cm
\begin{columns}
\column[t]{5cm}
\lstinputlisting[basicstyle=\ttfamily\fontsize{6pt}{8pt}\selectfont, language=verilog]{PRESENTATION_ExSyn/memory_02.v}
\column[t]{5cm}
\lstinputlisting[basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=ys, frame=single]{PRESENTATION_ExSyn/memory_02.ys}
\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{The {\tt fsm} command}
\begin{frame}[fragile]{\subsecname{}}
The {\tt fsm} command identifies, extracts, optimizes (re-encodes), and
re-synthesizes finite state machines. It again is a macro that calls
a series of other commands:
\begin{lstlisting}[xleftmargin=0.5cm, basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=ys]
fsm_detect # unless got option -nodetect
fsm_extract
fsm_opt
clean
fsm_opt
fsm_expand # if got option -expand
clean # if got option -expand
fsm_opt # if got option -expand
fsm_recode # unless got option -norecode
fsm_info
fsm_export # if got option -export
fsm_map # unless got option -nomap
\end{lstlisting}
\end{frame}
\begin{frame}{\subsecname{} -- details}
Some details on the most importand commands from the {\tt fsm\_*} group:
\bigskip
The {\tt fsm\_detect} command identifies FSM state registers and marks them
with the {\tt (* fsm\_encoding = "auto" *)} attribute, if they do not have the
{\tt fsm\_encoding} set already. Mark registers with {\tt (* fsm\_encoding =
"none" *)} to disable FSM optimization for a register.
\bigskip
The {\tt fsm\_extract} command replaces the entire FSM (logic and state
registers) with a {\tt \$fsm} cell.
\bigskip
The commands {\tt fsm\_opt} and {\tt fsm\_recode} can be used to optimize the
FSM.
\bigskip
Finally the {\tt fsm\_map} command can be used to convert the (optimized) {\tt
\$fsm} cell back to logic and registers.
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{The {\tt techmap} command}
\begin{frame}[t]{\subsecname}
\vbox to 0cm{\includegraphics[width=12cm,trim=-15cm 0cm 0cm -20cm]{PRESENTATION_ExSyn/techmap_01.pdf}\vss}
\vskip-0.8cm
The {\tt techmap} command replaces cells with implementations given as
verilog source. For example implementing a 32 bit adder using 16 bit adders:
\vbox to 0cm{
\vskip-0.3cm
\lstinputlisting[basicstyle=\ttfamily\fontsize{6pt}{7pt}\selectfont, language=verilog]{PRESENTATION_ExSyn/techmap_01_map.v}
}\vbox to 0cm{
\vskip-0.5cm
\lstinputlisting[xleftmargin=5cm, basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, frame=single, language=verilog]{PRESENTATION_ExSyn/techmap_01.v}
\lstinputlisting[xleftmargin=5cm, basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=ys, frame=single]{PRESENTATION_ExSyn/techmap_01.ys}
}
\end{frame}
\begin{frame}[t]{\subsecname{} -- stdcell mapping}
When {\tt techmap} is used without a map file, it uses a built-in map file
to map all RTL cell types to a generic library of built-in logic gates and registers.
\bigskip
\begin{block}{The built-in logic gate types are:}
{\tt \$\_NOT\_ \$\_AND\_ \$\_OR\_ \$\_XOR\_ \$\_MUX\_}
\end{block}
\bigskip
\begin{block}{The register types are:}
{\tt \$\_SR\_NN\_ \$\_SR\_NP\_ \$\_SR\_PN\_ \$\_SR\_PP\_ \\
\$\_DFF\_N\_ \$\_DFF\_P\_ \\
\$\_DFF\_NN0\_ \$\_DFF\_NN1\_ \$\_DFF\_NP0\_ \$\_DFF\_NP1\_ \\
\$\_DFF\_PN0\_ \$\_DFF\_PN1\_ \$\_DFF\_PP0\_ \$\_DFF\_PP1\_ \\
\$\_DFFSR\_NNN\_ \$\_DFFSR\_NNP\_ \$\_DFFSR\_NPN\_ \$\_DFFSR\_NPP\_ \\
\$\_DFFSR\_PNN\_ \$\_DFFSR\_PNP\_ \$\_DFFSR\_PPN\_ \$\_DFFSR\_PPP\_ \\
\$\_DLATCH\_N\_ \$\_DLATCH\_P\_}
\end{block}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{The {\tt abc} command}
\begin{frame}{\subsecname}
The {\tt abc} command provides an interface to ABC\footnote[frame]{\url{http://www.eecs.berkeley.edu/~alanmi/abc/}},
an open source tool for low-level logic synthesis.
\medskip
The {\tt abc} command processes a netlist of internal gate types and can perform:
\begin{itemize}
\item logic minimization (optimization)
\item mapping of logic to standard cell library (liberty format)
\item mapping of logic to k-LUTs (for FPGA synthesis)
\end{itemize}
\medskip
Optionally {\tt abc} can process registers from one clock domain and perform
sequential optimization (such as register balancing).
\medskip
ABC is also controlled using scripts. An ABC script can be specified to use
more advanced ABC features. It is also possible to write the design with
{\tt write\_blif} and load the output file into ABC outside of Yosys.
\end{frame}
\begin{frame}[fragile]{\subsecname{} -- Example}
\begin{columns}
\column[t]{5cm}
\lstinputlisting[basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=verilog]{PRESENTATION_ExSyn/abc_01.v}
\column[t]{5cm}
\lstinputlisting[basicstyle=\ttfamily\fontsize{8pt}{10pt}\selectfont, language=ys, frame=single]{PRESENTATION_ExSyn/abc_01.ys}
\end{columns}
\includegraphics[width=\linewidth,trim=0 0cm 0 0cm]{PRESENTATION_ExSyn/abc_01.pdf}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Other special-purpose mapping commands}
\begin{frame}{\subsecname}
\begin{block}{\tt dfflibmap}
This command maps the internal register cell types to the register types
described in a liberty file.
\end{block}
\bigskip
\begin{block}{\tt hilomap}
Some architectures require special driver cells for driving a constant hi or lo
value. This command replaces simple constants with instances of such driver cells.
\end{block}
\bigskip
\begin{block}{\tt iopadmap}
Top-level input/outputs must usually be implemented using special I/O-pad cells.
This command inserts this cells to the design.
\end{block}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Example Synthesis Script}
\begin{frame}[fragile]{\subsecname}
\begin{columns}
\column[t]{4cm}
\begin{lstlisting}[basicstyle=\ttfamily\fontsize{6pt}{7pt}\selectfont, language=ys]
# read and elaborate design
read_verilog cpu_top.v cpu_ctrl.v cpu_regs.v
read_verilog -D WITH_MULT cpu_alu.v
hierarchy -check -top cpu_top
# high-level synthesis
proc; opt; fsm;; memory -nomap; opt
# substitute block rams
techmap -map map_rams.v
# map remaining memories
memory_map
# low-level synthesis
techmap; opt; flatten;; abc -lut6
techmap -map map_xl_cells.v
# add clock buffers
select -set xl_clocks t:FDRE %x:+FDRE[C] t:FDRE %d
iopadmap -inpad BUFGP O:I @xl_clocks
# add io buffers
select -set xl_nonclocks w:* t:BUFGP %x:+BUFGP[I] %d
iopadmap -outpad OBUF I:O -inpad IBUF O:I @xl_nonclocks
# write synthesis results
write_edif synth.edif
\end{lstlisting}
\column[t]{6cm}
\vskip1cm
\begin{block}{Teaser / Outlook}
\small\parbox{6cm}{
The weird {\tt select} expressions at the end of this script are discussed in
the next part (Section 3, ``Advanced Synthesis'') of this presentation.}
\end{block}
\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Summary}
\begin{frame}{\subsecname}
\begin{itemize}
\item Yosys provides commands for each phase of the synthesis.
\item Each command solves a (more or less) simple problem.
\item Complex commands are often only front-ends to simple commands.
\item {\tt proc; opt; fsm; opt; memory; opt; techmap; opt; abc;;}
\end{itemize}
\bigskip
\bigskip
\begin{center}
Questions?
\end{center}
\bigskip
\bigskip
\begin{center}
\url{http://www.clifford.at/yosys/}
\end{center}
\end{frame}
|
http://labtrop.ib.usp.br/doku.php?id=equipe:antigos:diogo_kawaguchi&do=export_latexit | usp.br | CC-MAIN-2022-05 | application/x-latex | application/x-latex | crawl-data/CC-MAIN-2022-05/segments/1642320304959.80/warc/CC-MAIN-20220126162115-20220126192115-00676.warc.gz | 40,121,910 | 1,512 | \documentclass[a4paper, oneside, 10pt]{article}
\usepackage[unicode]{hyperref}
\usepackage[utf8x]{inputenc}
\usepackage[english]{babel}
\date{\today}
\title{}
\author{}
\begin{document}
\subsection{\texorpdfstring{DIOGO KAWAGUCHI}{DIOGO KAWAGUCHI}}
\label{sec:diogo_kawaguchi}
Olá a todos!
Sou aluno do 6º (e último) ano do Instituto de Biociências da USP e atualmente estou fazendo um projeto de Conservação em Pesquisa em Biologia, baseado em dois estudos sobre \emph{Euterpe edulis} e utilizando-se para isto \textbf{matrizes de transição}.
Além disso, já trabalhei em empresa, na Natura Cosméticos, onde fiz parte de uma equipe de Tecnologia de Produção Vegetal, cujo trabalho principal era elaborar modelos de produção vegetal sustentáveis para suprir a demanda de fornecimento de Matéria prima para esta empresa.
Gostaria de deixar aqui uma frase de autoria própria:
,,A Vida torna-se mais fácil quando olhamos menos para fora e mais para dentro de nós mesmos. Tornamo-nos vencedores quando depois de tudo isto conseguimos voltar nossos olhos para o mundo."
\subsection{\texorpdfstring{Orientador}{Orientador}}
\label{sec:orientador}
Prof. Dr. Alexandre Adalardo de Oliveira
\end{document}
|
http://refbase.cidis.espol.edu.ec/search.php?sqlQuery=SELECT%20author%2C%20title%2C%20type%2C%20year%2C%20publication%2C%20abbrev_journal%2C%20volume%2C%20issue%2C%20pages%2C%20keywords%2C%20abstract%2C%20thesis%2C%20editor%2C%20publisher%2C%20place%2C%20abbrev_series_title%2C%20series_title%2C%20series_editor%2C%20series_volume%2C%20series_issue%2C%20edition%2C%20language%2C%20author_count%2C%20online_publication%2C%20online_citation%2C%20doi%2C%20serial%2C%20area%20FROM%20refs%20WHERE%20serial%20%3D%20158%20ORDER%20BY%20year%20DESC%2C%20first_author%2C%20author_count%2C%20author%2C%20title&client=&formType=sqlSearch&submit=Cite&viewType=&showQuery=0&showLinks=1&showRows=10&rowOffset=&wrapResults=1&citeOrder=year&citeStyle=APA&exportFormat=RIS&exportType=html&exportStylesheet=&citeType=LaTeX&headerMsg= | espol.edu.ec | CC-MAIN-2022-40 | application/x-latex | application/x-latex | crawl-data/CC-MAIN-2022-40/segments/1664030336921.76/warc/CC-MAIN-20221001195125-20221001225125-00639.warc.gz | 47,752,963 | 1,326 | %&LaTeX
\documentclass{article}
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\usepackage{textcomp}
\begin{document}
\section*{2021}
Santos, V., Sappa, A.D., Oliveira, M. \& de la Escalera, A. (2021). Editorial: Special Issue on Autonomous Driving and Driver Assistance Systems -- Some Main Trends. \textit{In Journal: Robotics and Autonomous Systems. (Vol. 144, Article number 103832)}, .
\end{document}
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https://sea.theanarchistlibrary.org/library/325.tex | theanarchistlibrary.org | CC-MAIN-2021-31 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2021-31/segments/1627046156141.29/warc/CC-MAIN-20210805161906-20210805191906-00504.warc.gz | 511,768,667 | 5,555 | \documentclass[DIV=12,%
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\title{Komunike dari Kolektif 325 Terhadap Serangan Represif Kontra-Informasi Internasional}
\date{29\Slash{}03\Slash{}2021}
\author{325 Collective}
\subtitle{}
% https://groups.google.com/d/topic/comp.text.tex/6fYmcVMbSbQ/discussion
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pdfencoding=auto,
pdftitle={Komunike dari Kolektif 325 Terhadap Serangan Represif Kontra-Informasi Internasional},%
pdfauthor={325 Collective},%
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pdfkeywords={komunike; information; release; 325; repression}%
}
\begin{document}
\begin{titlepage}
\strut\vskip 2em
\begin{center}
{\usekomafont{title}{\huge Komunike dari Kolektif 325 Terhadap Serangan Represif Kontra-Informasi Internasional\par}}%
\vskip 1em
\vskip 2em
{\usekomafont{author}{325 Collective\par}}%
\vskip 1.5em
\vskip 3em
\includegraphics[keepaspectratio=true,height=0.5\textheight,width=1\textwidth]{3-5-325-1.jpg}
\vfill
{\usekomafont{date}{29\Slash{}03\Slash{}2021\par}}%
\end{center}
\end{titlepage}
\cleardoublepage
Pada 29 Maret 2021 pihak kepolisian Belanda menggerebek pusat penyimpanan data server nostate.net, menyita data server sebagai bagian investigasi atas tindakan kriminal ‘terorisme’. Nostate.net adalah kolektif yang menyediakan \emph{platform} situs gerakan internasional bagi kelompok untuk solidaritas tahanan, berbagai kampanye kolektif, situs anti-KTT, dan media tanding kontra-informasi internasional. Situs yang menggunakan nostate.net sebagai \emph{platform}, yang secara signifikan menjadi target serangan represifitas dari kepolisian Belanda diantaranya Anarchist Black Cross Berlin, Montreal Counter-Info, Northshore Counter-Info, Act For Freedom Now! (saat ini coba diaktifkan kembali noblogs.org \href{https://actforfree.noblogs.org}{\texttt{https://actforfree.noblogs.org}}) dan 325.
Kami sebagai kolektif sadar bahwasanya ini bukan hanya sekedar penyerangan oleh polisi Belanda, tetapi merupakan tindakan terkoordinasi dengan Unit Penanggulangan Terorisme Inggris karena sehubungan dengan serangan represif mereka yang baru-baru ini terhadap lingkaran anarkis di kawasan Inggris. Tidak hanya mereka mengancam diri kita sebgai individu, namun baru-baru ini mereka pun mengancam nostate.net, untuk munutup server. Bersamaan dengan tindakan ini, mereka menuntut informasi diberikannya identitas siapa pun yang terlibat dalam jaringan 325. Namun sejauh mana pihak kepolisian menyerang kami dan siapa pun yang mereka curigai membantu kami bukanlah hal yang baru dan mengejutkan bagi kami, kami telah melihat melalui sejarah, kekuatan negara secara massif akan merepresi siapa pun yang berani berdiri dan melawan mereka.
Serangan represif ini mestinya dilihat sebagai serangan terhadap semua orang dan tiap kontra-informasi di kalangan anarkis internasional. Dalam kondisi Covid-19 yang sedang berlangsung saat ini dibarengi dengan tindakan represif berbagai negara di seluruh dunia, tidak mengherankan bagi kami bahwa mereka bekerja sama di tingkat internasional, tindakan represif baru-baru ini terhadap kamerad anarkis Gabriel Pomba da Silva, melalui kerja sama Negara Spanyol, Italia, dan Portugis, ini merupakan contoh yang jelas. Ingatan kita kembali pada tindakan represi Indymedia di Jerman dan Yunani, serta belum lama ini terjadi penangkapan kawan-kawan yang terlibat di Culmine, Parole Armata dan Croce Nera Anarchica di Italia. Seiring berjalannya waktu, gerakan anarkis internasional telah memiliki mode komunikasi untuk orang-orang yang mengalami penyerangan melalui publikasi anarkis yang tak terhitung jumlahnya, kawan-kawan ditangkap dan publikasinya disensor, bahkan dihancurkan, seperti yang terjadi di masa lalu kepada Alfredo M.Bonnano’s ‘Armed Joy’ di Italia, serta Conspiracy of Cells of Fire’s ‘The Sun Still Rises’ di Yunani.
Tentunya bukan kebetulan bahwa serangan represif ini terjadi setelah publikasi ‘325 \#12 – \emph{Against the Fourth and Fifth Industrial Revolutions}’ baru-baru ini. Publikasi yang kami rasa menyerang inti dari apa yang distimulasi oleh negara dan kapitalisme, di masa lalu dan terlebih lagi sekarang, di balik kedok pandemi Covid-19, yang merupakan rencana pembungkaman, penyerangan serta perampasan segala hal yang dianggap menggangu. Serangan kepolisian untuk sementara mempengaruhi distribusi publikasi kami, baik secara online maupun fisik, namun itu tak akan bertahan lama dan gagal. Para teknokrat yang ingin membentuk dunia kita menjadi masyarakat penjara yang termiliterisasi dengan teknologi sedang diekspos, tidak hanya dari tiap individu tetapi juga serangan yang sudah berkembang secara internasional terhadap infrastruktur mereka. Inilah yang mereka takuti, bahwa ini bisa tumbuh dan inilah mengapa mereka mengejar dan menyerang kita. Dari apa yang kami ketahui, polisi yang mencoba memburu kami, mereka mengandalkan taktik penindasan lama mereka, mencoba membuat orang lain mengadu dan menutup informasi tandingan. Sejak ‘Operasi Rhone’ mereka bertujuan menyerang lingkaran anarkis di Bristol, mereka hanya menangkap satu orang yang terlibat dalam serangan, tetapi tidak ada yang bersangkutan dengan Federasi Anarkis Informal atau serangan anarkis lain yang tak terhitung jumlahnya.
Sudah terlalu lama senyap di pulau konformitas ini, sementara dunia di luar mulai terbakar lagi, bara api itu masih bercahaya dan kami merasakan kehangatannya. Lebih dari sebelumnya ada kebutuhan mutlak untuk koordinasi internasional antara tiap jaringan, untuk menyerang secara langsung mayat busuk ini, yang mencoba untuk membangkitkan dirinya sendiri, memenjarakan kita lebih jauh. Kontra-informasi adalah bagian integral dari koordinasi internasional, agar memungkinkan mereka yang ingin bertindak demi kebebasan di dunia ini untuk melihat sinyal keterlibatan dalam setiap bahasa dan cara yang memungkinkan, untuk berbicara dalam satu bahasa pemberontakan dan anarki. Harus ada re-energi dari jaringan kontra informasi internasional, agar sekali lagi menjadi ancaman internasional, setelah serangan represif yang berusaha mengisolasi anarkis dari satu sama lain, tidak hanya di seluruh dunia tetapi bahkan secara lokal. 325 Kolektif terus bergerak di jalur yang sudah kami lalui, bahkan sekarang kami melanjutkan proyek publikasi kami termasuk cetak ulang ‘325 \# 12’, edisi baru yang yang memperluas isu ‘Dark Nights’. Mereka tidak akan membungkam atau menghentikan kita dan kita akan mendapatkan milik kita
Tentang situs web, kami belum tahu apakah akan kembali, sangat jelas bagi kami bahwa jika kembali sebagai ‘325’, maka pihak berwenang akan segera menjadikannya target kembali. Ini juga berarti bahwa kami dapat membahayakan \emph{platform} mana pun di masa mendatang, serta menempatkan proyek kontra-informasi dan pergerakan lainnya dengan risiko ditutup seperti yang terjadi pada serangan represif baru-baru ini. Siapa yang tahu kemana semua ini akan terjadi? Apa yang kita tahu adalah bahwa kita jauh dari kata mundur, tidak ada satu langkah pun untuk mundur, dalam menghadapi musuh. Mungkin yang terbaik adalah kembali ke cara tradisional, bertatap muka langsung, berbicara secara nyata, serta berkonspirasi. Kami tidak mengatakan tidak akan kembali ke media situs, juga tidak memanifestasikan kembalinya sebagai proyek baru, hanya waktu yang akan memberi tahu.
\forcelinebreak
Untuk saat ini, solidaritas mutlak kami kepada nostate.net \& Bertindak untuk Kebebasan Sekarang! Bersama dengan semua proyek kontra-info lainnya.
TAK ADA YANG SELESAI, PERJUANGAN BERLANJUT!
325 Kolektif
% begin final page
\clearpage
% new page for the colophon
\thispagestyle{empty}
\begin{center}
\smallskip
Anti-Copyright
\bigskip
\includegraphics[width=0.25\textwidth]{/var/lib/amusewiki/repo/sea/site_files/sea_pdf_image.png}
\bigskip
\end{center}
\strut
\vfill
\begin{center}
325 Collective
Komunike dari Kolektif 325 Terhadap Serangan Represif Kontra-Informasi Internasional
29\Slash{}03\Slash{}2021
\bigskip
\href{https://palanghitamanarkis.noblogs.org/post/2021/04/15/komunike-dari-kolektif-325-terhadap-serangan-represif-kontra-informasi-internasional/}{\texttt{https://palanghitamanarkis.noblogs.org/post/2021/04/15/komunike-dari-kolektif-325-terhadap-serangan-represif-kontra-informasi-internasional/}}
Teks aslinya berjudul \href{https://325.nostate.net/\#Communique20210409-english}{\emph{Communique from 325 Collective on the Repressive Attack upon International Counter-Information}} dan diterjemahkan oleh Palang Hitam Indonesia (wa)
\bigskip
\textbf{sea.theanarchistlibrary.org}
\end{center}
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http://ftp.ipv4.heanet.ie/pub/ctan.org/tex/graphics/mgltex/sample.tex | heanet.ie | CC-MAIN-2023-06 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2023-06/segments/1674764500215.91/warc/CC-MAIN-20230205032040-20230205062040-00752.warc.gz | 15,254,104 | 4,706 | \documentclass{article}
\usepackage[comments,3x,jpg]{mgltex}
\usepackage{hyperref}
\title{\mglTeX*{} usage sample}
\author{Diego Sejas Viscarra \and Alexey Balakin}
\date{\today}
\begin{mglsetupscript}
define gravity 9.81 # [m/s^2]
\end{mglsetupscript}
\begin{document}
\maketitle
\begin{abstract}
\noindent \mglTeX{} is a \LaTeX{} package that allows the creation of graphics directly from MGL scripts of the MathGL library (by Alexey Balakin) inside documents. The MGL code is extracted, executed (if shell escape is activated), and the resulting graphics are automatically included.
This document is intended as a sample of the capabilities of \mglTeX{}, as well as a brief introduction to the package, for those who want to start right away to use it, without diving into the a little bit more technical documentation.
\end{abstract}
\section{Basics on environments}
\begin{description}
\item[mgl] The easiest way to embed MGL code is the \verb|mgl| environment. It extracts its contents to a main script associated to the document.\footnote{Generally, the main script has the same name as the document being compiled. In order to rename it or create a new one, the \texttt{\textbackslash mglname} command can be used.} If shell escape is activated, \LaTeX{} will take care of calling \verb|mglconv| (the MathGL compiler) with the appropriate settings, and the resulting image will be automatically included.
For example, you could write:
\begin{verbatim}
\begin{figure}[!ht]
\centering
\begin{mgl}[width=0.95\textwidth,height=6cm]
call 'prepare1d'
subplot 2 1 0 '<_' : title 'Standard data plot'
box : axis : grid 'xy' ';k'
plot y ’rGb’
subplot 2 1 1 '<_' : title 'Region plot'
ranges -1 1 -1 1 : origin 0 0
new y1 200 'x^3-x' : new y2 200 'x'
axis : grid 'xy' 'W'
region y1 y2 'ry'
plot y1 '2k' : plot y2 '2k'
text -0.75 -0.35 '\i{A}_1' 'k' : text 0.75 0.25 '\i{A}_2' 'k'
\end{mgl}
caption{A simple plot created by \mglTeX's \texttt{mgl} environment}
\end{figure}
\end{verbatim}
This will produce the following image:
\begin{figure}[!ht]
\centering
\begin{mgl}[width=0.95\textwidth,height=5.5cm]
call 'prepare1d'
subplot 2 1 0 '<_' : title 'Standard data plot'
box : axis : grid 'xy' ';k'
plot y '2'
subplot 2 1 1 '<_' : title 'Region plot'
ranges -1 1 -1 1 : origin 0 0
new y1 200 'x^3-x' : new y2 200 'x'
axis 'AKDTVISO' : grid 'xy' ';W'
region y1 y2 'ry'
plot y1 '2k' : plot y2 '2k'
text -0.75 -0.35 '\i{A}_1' 'k' -2 : text 0.75 0.25 '\i{A}_2' 'k' -2
\end{mgl}
\caption{A simple plot create by \mglTeX's \texttt{mgl} environment}
\end{figure}
Two important aspects of \mglTeX{} can be noted from this example: First, the \verb|mgl| environment accepts the same optional argument as the \verb|\includegraphics| command from the \verb|graphicx| package. Actually, it also accepts other optional arguments, called \verb|gray| (to activate/deactivate gray-scale mode), \verb|mglscale| (to set the factor for scaling the image file), \verb|quality| (to set the quality of the image), \verb|variant| (to chose the variant of the arguments of MGL commands in the script), \verb|imgext| (to specify the extension of the resulting graphic file), and \verb|label| (to specify a name to save the image). Most of these options are available to every \mglTeX{} environment or command to create graphics.
The second aspect to be noted about the example is that this script calls a MGL function, \verb|prepare1d|, which hasn't been defined yet. \mglTeX{} provides the \verb|mglfunc| environment for this purpose (see below).
\item[mglfunc] This environment can be used in any part of the \LaTeX{} document; \mglTeX{} takes care of placing the corresponding code at the end of the main script, as has to be done in the MGL language.
For example, the function \verb|prepare1d| that is called in the script above is defined like this
\begin{verbatim}
\begin{mglfunc}{prepare1d}
new y 50 3
modify y '0.7*sin(2*pi*x)+0.5*cos(3*pi*x)+0.2*sin(pi*x)'
modify y 'sin(2*pi*x)' 1
modify y 'cos(2*pi*x)' 2
\end{mglfunc}
\end{verbatim}
\begin{mglfunc}{prepare1d}
new y 50 3
modify y '0.7*sin(2*pi*x)+0.5*cos(3*pi*x)+0.2*sin(pi*x)'
modify y 'sin(2*pi*x)' 1
modify y 'cos(2*pi*x)' 2
\end{mglfunc}
As you can see, only the body of the function has to be written. The number of arguments of the function can be passed to \verb|mglfunc| as optional argument, like in the code \verb|\begin{mglfunc}[3]{func_with_three_args}|.
\item[mgladdon] This environment just adds its contents to the main script, without producing any image. It is useful to load dynamic libraries, define constants, etc.
\item[mglcode] The \verb|mglcode| environment is similar to \verb|mgl|, but it creates its own script, whose name is passed as mandatory argument. The same optional arguments are accepted, except \verb|label| (for obvious reasons).
\begin{verbatim}
\begin{figure}[!ht]
\begin{mglcode}[height=5cm,width=8cm]{vectorial_flow}
new a 20 30 'sin(pi*x)*sin(pi*y)+cos(2*pi*x*y)'
new b 20 30 'cos(pi*x)*cos(pi*y)+cos(2*pi*x*y)'
subplot 1 1 0 '' : title 'Flow of vector field' : box
flow a b 'v'; value 20
\end{mglcode}
\end{figure}
\end{verbatim}
\begin{figure}[!ht]
\centering
\begin{mglcode}[height=5cm,width=8cm]{vectorial_flow}
new a 20 30 'sin(pi*x)*sin(pi*y)+cos(2*pi*x*y)'
new b 20 30 'cos(pi*x)*cos(pi*y)+cos(2*pi*x*y)'
subplot 1 1 0 '' : title 'Flow of a vector field' : box
flow a b '2v'; value 10
\end{mglcode}
\end{figure}
\item[mglscript] This environment just creates a script, whose name is specified as mandatory argument. It is useful, for example, to create MGL scripts which can later be post-processed by another package, like \verb|listings| or \verb|pygments|.
For example, the following won't produce any image, just a script:
\begin{verbatim}
\begin{mglscript}{Gaston_Neiza}
clf 'k'
attachlight on
subplot 1 1 0 '' : title 'Gaston\utf0x0027{}s Surface'
ranges -13 13 -40 40
new a 200 200 '-x+(2*0.84*cosh(0.4*x)*sinh(0.4*x))/(0.4*((sqrt(0.84)*cosh(0.4*x))^2+(0.4*sin(sqrt(0.84)*y))))+0.5*sin(pi/2*x)'
new b 200 200 '(2*sqrt(0.84)*cosh(0.45*x)*(-(sqrt(0.84)*sin(y)*cos(sqrt(0.84)*y))+cos(y)*sin(sqrt(0.84)*y)))/(0.4*((sqrt(0.84)*cosh(0.4*x))^2+2*(0.4*sin(sqrt(0.84)*x))^2))'
new c 200 200 '(2*sqrt(0.84)*cosh(0.45*x)*(-(sqrt(0.84)*cos(y)*cos(sqrt(0.84)*y))-sin(y)*sin(sqrt(0.84)*y)))/(0.4*((sqrt(0.84)*cosh(0.4*x))^2+2*(0.4*sin(sqrt(0.84)*x))^2))'
rotate 60 60
light on : light 0 1 1 0
xrange c : yrange b : zrange a : crange c
surf c b a '#'; meshnum 100
subplot 2 1 1 ''
title 'Neiza\utf0x0027{}s Rose'
ranges -13 13 -40 40
new a 700 700 '-x+(1.5*cos(x^2))/(0.4*((sqrt(0.84)*cosh(0.4*x))^2+(0.4*sin(sqrt(0.84)*y))))+0.5*cos(pi/2*x)'
new b 700 700 '(sqrt(0.5)*cos(0.25*x)*((sqrt(0.84)*sin(y)*cos(0.75*y))+cos(y)*sin(sqrt(0.84)*y)))/(0.4*((sqrt(0.84)*cosh(0.4*x))^2+2*(0.4*sin(sqrt(0.84)*x))^2))'
new c 700 700 '(sqrt(0.5)*cos(0.25*x)*((sqrt(0.84)*cos(y)*sin(0.75*y))-sin(y)*sin(sqrt(0.84)*y)))/(0.4*((sqrt(0.84)*cosh(0.4*x))^2+2*(0.4*sin(sqrt(0.84)*x))^2))'
rotate 75 130
light on : light 0 0 0 1 'w' 0.5 : light 1 -1 0 0 'r' 0.85 : light 2 -1 0 0 'w' 0.75
xrange c : yrange b : zrange a : crange c
surf c b a 'r'
\end{mglscript}
\end{verbatim}
\begin{mglscript}{Gaston_Neiza}
clf 'k'
attachlight on
subplot 2 1 0 ''
ranges -13 13 -40 40
new a 200 200 '-x+(2*0.84*cosh(0.4*x)*sinh(0.4*x))/(0.4*((sqrt(0.84)*cosh(0.4*x))^2+(0.4*sin(sqrt(0.84)*y))))+0.5*sin(pi/2*x)'
new b 200 200 '(2*sqrt(0.84)*cosh(0.45*x)*(-(sqrt(0.84)*sin(y)*cos(sqrt(0.84)*y))+cos(y)*sin(sqrt(0.84)*y)))/(0.4*((sqrt(0.84)*cosh(0.4*x))^2+2*(0.4*sin(sqrt(0.84)*x))^2))'
new c 200 200 '(2*sqrt(0.84)*cosh(0.45*x)*(-(sqrt(0.84)*cos(y)*cos(sqrt(0.84)*y))-sin(y)*sin(sqrt(0.84)*y)))/(0.4*((sqrt(0.84)*cosh(0.4*x))^2+2*(0.4*sin(sqrt(0.84)*x))^2))'
rotate 60 60
light on : light 0 1 1 0
xrange c : yrange b : zrange a : crange c
surf c b a '#'; meshnum 100
title 'Gaston\utf0x0027{}s Surface'
subplot 2 1 1 ''
title 'Neiza\utf0x0027{}s Rose'
ranges -13 13 -40 40
new a 700 700 '-x+(1.5*cos(x^2))/(0.4*((sqrt(0.84)*cosh(0.4*x))^2+(0.4*sin(sqrt(0.84)*y))))+0.5*cos(pi/2*x)'
new b 700 700 '(sqrt(0.5)*cos(0.25*x)*((sqrt(0.84)*sin(y)*cos(0.75*y))+cos(y)*sin(sqrt(0.84)*y)))/(0.4*((sqrt(0.84)*cosh(0.4*x))^2+2*(0.4*sin(sqrt(0.84)*x))^2))'
new c 700 700 '(sqrt(0.5)*cos(0.25*x)*((sqrt(0.84)*cos(y)*sin(0.75*y))-sin(y)*sin(sqrt(0.84)*y)))/(0.4*((sqrt(0.84)*cosh(0.4*x))^2+2*(0.4*sin(sqrt(0.84)*x))^2))'
rotate 75 130
light on : light 0 0 0 1 'w' 0.5 : light 1 -1 0 0 'r' 0.85 : light 2 -1 0 0 'w' 0.75
xrange c : yrange b : zrange a : crange c
surf c b a 'r'
\end{mglscript}
\item[mglblock] It writes its contents verbatim to a file, specified as mandatory argument, and to the \LaTeX{} document.
For example:
\begin{verbatim}
\begin{mglblock}{fractal}
list A [0,0,0,.16,0,0,.01] [.85,.04,-.04,.85,0,1.6,.85] [.2,-.26,.23,.22,0,1.6,.07] [-.15,.28,.26,.24,0,.44,.07]
ifs2d f A 100000
subplot 2 1 0 '<_' : title 'A fractal fern'
ranges f(0) f(1) : axis
plot f(0) f(1) 'G#o '; size 0.05
subplot 2 1 1 '<_' : title 'Bifurcation plot'
ranges 0 4 0 1 : axis
bifurcation 0.005 'x*y*(1-y)' 'R'
\end{mglblock}
\end{verbatim}
\begin{mglblock}{fractal}
list A [0,0,0,.16,0,0,.01] [.85,.04,-.04,.85,0,1.6,.85] [.2,-.26,.23,.22,0,1.6,.07] [-.15,.28,.26,.24,0,.44,.07]
ifs2d f A 100000
subplot 2 1 0 '<_' : title 'A fractal fern'
ranges f(0) f(1) : axis
plot f(0) f(1) 'G#o '; size 0.05
subplot 2 1 1 '<_' : title 'Bifurcation plot'
ranges 0 4 0 1 : axis
bifurcation 0.005 'x*y*(1-y)' 'R'
\end{mglblock}
As you can see, although this is a verbatim-like environment, very long lines of code are split to fit the paragraph. Each line of code is numbered, this can be disabled with the \verb|lineno| option, like \verb|\begin{mglblock}[lineno=false]{fractal}|.
\item[mglverbatim] This is like \verb|mglblock| environment, but it doesn't produce any script, just typesets the code to the \LaTeX{} document. It accepts the \verb|lineno| option, plus the \verb|label| option, in case you want to associate a name to the code.
\item[mglcomment] This environment is used to embed comments in the document. You can control whether the contents of this environment are displayed or not, using the \verb|comments| and \verb|nocomments| package options, or the \verb|\mglcomments{on}| and \verb|mglcomments{off}| commands.
An example of this would be:
\begin{verbatim}
\begin{mglcomments}
This comment will be shown because we used the "comments" package option for mglTeX
\end{mglcomments}
\end{verbatim}
\begin{mglcomment}
This comment will be shown because we used the "comments" package option for mglTeX
\end{mglcomment}
Once again, long lines are broke down to fit the paragraph.
\end{description}
\section{Basics on commands}
\begin{description}
\item[\textbackslash mglgraphics] This command takes the name of an external MGL script, compiles it, and includes the resulting image. It accespt the same optional arguments as the \verb|mgl| environment, except for \verb|label|, plus a \verb|path| option, which can be used to specify the location of the script. This is useful when you have a script outside of the \LaTeX{} document (sent by a colleague for example), but you don't want to transcript it to your document.
For example, in order to display the image of the script we created with \verb|mglscript| environment, we write:
\begin{verbatim}
\begin{figure}[!ht]
\centering
\mglgraphics[height=9cm,width=18cm]{Gaston_Neiza}
\caption{``Gaston's Surface'' and ``Neiza's Rose'' are named after Diego Sejas' parents}
\end{figure}
\end{verbatim}
\begin{figure}[!ht]
\centering
\mglgraphics[height=8cm,width=14cm]{Gaston_Neiza}
\caption{``Gaston's Surface'' and ``Neiza's Rose'' are named after Diego Sejas' parents}
\end{figure}
We could also could compile the script we created with the \verb|mglblock| environment:
\begin{verbatim}
\begin{figure}[!ht]
\centering
\mglgraphics[height=7cm,width=10cm]{fractal}
\caption{Examples of fractal behavior}
\end{figure}
\end{verbatim}
\begin{figure}[!ht]
\centering
\mglgraphics[height=7cm,width=10cm]{fractal}
\caption{Examples of fractal behavior}
\end{figure}
\item[\textbackslash mglinclude] This is equivalent to the \verb|mglblock| environment, but works for external scripts.
\item[\textbackslash mglplot] This command allows the fast creation of plots. It takes one mandatory argument, which is a block of MGL code to produce the plot. Accepts the same optional arguments as the \verb|mgl| environment, plus an additional one, \verb|setup|, that can be used to specify a block of code to append, defined inside a \verb|mglsetup| environment (see the example below).
The \verb|mglsetup| environment can be used if many plots will have the same settings (background color, etc.). Instead of writing the same code over and over again, it can be introduced in that environment, and used with the \verb|\mglplot| command.
An example of use of the \verb|mglsetup| environment and the \verb|\mglplot| command would be:
\begin{verbatim}
\begin{mglsetup}{3d}
clf 'W'
rotate 50 60
light on
box : axis : grid 'xyz' ';k'
\end{mglsetup}
\begin{figure}[!ht]
\centering
\mglplot[setup=3d,height=5cm,width=8cm]{fsurf 'cos(4*pi*hypot(x,y))*exp(-abs(x+y))'}
\end{figure}
\begin{figure}[!ht]
\centering
\mglplot[setup=3d,height=5cm,width=8cm]{fsurf 'sin(pi*(x+y))'}
\end{figure}
\end{verbatim}
\begin{mglsetup}{3d}
clf 'W'
rotate 50 60
light on : light 0 0 1 0 'w' 0.25
box : axis : grid 'xyz' ';k'
\end{mglsetup}
\begin{figure}[!ht]
\centering
\mglplot[setup=3d,height=5cm,width=8cm]{fsurf 'cos(4*pi*hypot(x,y))*exp(-abs(x+y))'}
\end{figure}
\begin{figure}[!ht]
\centering
\mglplot[setup=3d,height=5cm,width=8cm]{fsurf 'sin(pi*(x+y))'}
\end{figure}
\end{description}
There are more environments and commands defined by \mglTeX{}. The ones presented here are the most basic. More on this topic can be found in the documentation.
\end{document} |
https://authorea.com/users/389148/articles/503775/download_latex | authorea.com | CC-MAIN-2021-10 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2021-10/segments/1614178370752.61/warc/CC-MAIN-20210305091526-20210305121526-00253.warc.gz | 217,410,293 | 2,886 | \documentclass[10pt]{article}
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\title{Omega-3 polyunsaturated fatty acids supplementation improve clinical
symptoms in patients with covid-19: A randomized clinical trial}
\author[1]{Mohsen Sedighiyan}%
\author[1]{Hamed Abdollahi}%
\author[2]{Elmira Karimi}%
\author[1]{Mostafa Badeli}%
\author[1]{Reza Erfanian}%
\author[1]{Shima Raeesi}%
\author[1]{Rezvan Hashemi}%
\author[1]{Zahra Vahabi}%
\author[1]{Behzad Asanjarani}%
\author[1]{Mina ABDOLAHI}%
\affil[1]{Affiliation not available}%
\affil[2]{Tehran University of Medical Sciences}%
\vspace{-1em}
\date{\today}
\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup
\selectlanguage{english}
\begin{abstract}
Objective: We hypothesized that omega-3 fatty acids would be an
appropriate adjunct therapy for alleviating the inflammatory response
and clinical manifestation in hospitalized patients with covid-19
disease. Methods: This was a single-blind randomized controlled trial in
Amir-Alam hospital in Tehran. Thirty adult men and women diagnosed with
covid-19 were allocated to either control group (receiving
Hydroxychloroquine) or intervention group (receiving Hydroxychloroquine
plus 2 grams of DHA+EPA) for 2 weeks. Primary outcome of the
intervention including CRP, ESR as well as clinical symptoms including
body pain, fatigue, appetite and olfactory and secondary outcomes
including liver enzymes were determined at the baseline and after
omega-3 supplementation. Clinical signs were measured using
self-reported questionnaires. There were commercial kits for
determination of CRP and liver enzymes concentrations in the serum of
patients. For determination of ESR automated hematology analyzer was
applied. Results: In comparison to control group, patients receiving
omega-3 indicated favorable changes in all clinical symptoms except for
olfactory ((p\textless{}0.001 for body pain and fatigue, p= 0.03 for
appetite and p=0.21 for olfactory). Reducing effects of omega-3
supplementation compared to control group were also observed in the
levels of ESR and CRP after treatment (p\textless{}0.001 for CRP and
p=0.02 for ESR). However, no between group differences in the liver
enzymes serum concentrations were observed after supplementation
(p\textgreater{}0.05). Conclusion: Current observations are very
promising and indicate that supplementation with moderate dosages of
omega-3 fatty acids may be beneficial in the management of
inflammation-mediated clinical symptoms in covid-19 patients. Key words:
Covid-19, omega-3, inflammation, clinical symptoms%
\end{abstract}%
\sloppy
\textbf{Hosted file}
\verb`Manuscript.omega-3(1)-final.pdf` available at \url{https://authorea.com/users/389148/articles/503775-omega-3-polyunsaturated-fatty-acids-supplementation-improve-clinical-symptoms-in-patients-with-covid-19-a-randomized-clinical-trial}
\selectlanguage{english}
\FloatBarrier
\end{document}
|
https://theanarchistlibrary.org/library/willful-disobedience-wolfi-landstreicher-willful-disobedience-volume-5-number-3.tex | theanarchistlibrary.org | CC-MAIN-2021-17 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2021-17/segments/1618038879374.66/warc/CC-MAIN-20210419111510-20210419141510-00226.warc.gz | 663,044,181 | 22,710 | \documentclass[DIV=12,%
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\title{Willful Disobedience Volume 5, Number 3}
\date{Spring 2006}
\author{Willful Disobedience, Wolfi Landstreicher}
\subtitle{}
% https://groups.google.com/d/topic/comp.text.tex/6fYmcVMbSbQ/discussion
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pdftitle={Willful Disobedience Volume 5, Number 3},%
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{\usekomafont{title}{\huge Willful Disobedience Volume 5, Number 3\par}}%
\vskip 1em
\vskip 2em
{\usekomafont{author}{Willful Disobedience, Wolfi Landstreicher\par}}%
\vskip 1.5em
\vfill
{\usekomafont{date}{Spring 2006\par}}%
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\cleardoublepage
\tableofcontents
% start a new right-handed page
\cleardoublepage
\emph{\textbf{What is the point of asking questions if we are not free to answer?}}
\emph{\textbf{What is the point of answering if the questions are always false?}}
\section{Editor's Note}
After this issue, I will stop publishing \emph{Willful Disobedience} in order to work on a number of other projects. I have several translations in the works, as well as a few major writing projects. I am also working on compiling a selection of my writings from about 1995 to 2005 to put together as a book in order to better clarify the development of my ideas as well as the common threads that run through them. So for now I want to put my time and energy into these projects without having to think about publishing a semi-regular publication.
I originally intended to make this last issue a single long essay, an attempt to reflect on a number of problems and questions that I continually wrestle with, but that project has proven to be greater than I thought and is becoming a small book. So instead this last issue brings together a few essays, journal entries and translations that I feel are of some interest for sparking discussion and maybe provoking action.
\emph{Wolfi Landstreicher}
\section{The City: A Few Random Thoughts}
\emph{(The thoughts below are rather random meanderings provoked by reading a few books of urban analysis. Within the present world I have tended to find wild areas on the one hand and cities on the other as the environments that most stimulate my thoughts and imagination. At the same time I recognize that every city that we know of has been a monument to domination, commerce and alienation. In these meanderings, I consider what it is about cities that I find stimulating and raise questions about how these things might exist in a world without cities. This is} not \emph{a defense of cities)}
Ultimately I want to do away with the city. It represents the values of civilization which boil down to alienated and centralized power and wealth. Yet there are aspects of the city that I enjoy, particularly the opportunity for chance encounters with stimulating strangers. Where human beings do not congregate in large numbers, the opportunities for such encounters are much reduced or even disappear. But nowadays cities are built to serve the needs of capitalism and the state. And they have always served the interests of the ruling powers who had them built: priesthoods, military elites, those who stole the wealth and creative energy of others in order to set themselves up as rulers.
In her otherwise interesting book \emph{The Death and Life of Great American Cities}, Jane Jacobs forgets this aspect of the city, its role as symbol and tool of the ruling class. This is not so surprising since at a certain point cities become too large and chaotic for the rulers to keep them in hand. So Jane Jacobs tries to look at cities in terms of how they actually function as relationships among human beings and between the human being and this particular artificial environment. What I find most interesting in Jacobs’ book is her assessment that the city functions best as an environment for human life when it is diverse and vibrant with a wide variety of people and activities interweaving with each other. This parallels what comprises a healthy wild environment — it needs a wide variety of different life forms carrying out a variety of different activities that weave themselves together. The destruction of such diversity indicates a moribund situation.
Going back to the city as Jacobs conceives it, we see the need for an active street life. This is where the interweaving diversity manifests itself most clearly. According to Jacobs, for this to function most effectively, wide sidewalks where various activities could take place would have to combine with a mixture of different sorts of uses of space in the neighborhood. Consider, for example, how a café with outdoor tables on the sidewalk in a neighborhood that also included people’s homes and public spaces for other purposes could encourage regular interaction and discussion of experiences among those who live in the neighborhood. All in all, Jacobs considers a wide variety of different levels of relationship as necessary for making cities livable human environments.
Jacobs is wrong in considering the various suggestions of city planners that undermine this diversity and empty the streets to be well-intentioned mistakes. She is giving these well-paid servants of power too much credit. As I pointed out above, cities emerged with centralized power and wealth and have always been meant to serve the purposes of the rulers who hold these. As industrialism congregated greater and greater numbers of those in the exploited classes into cities, they began to turn the environment to their own purposes, and the ruling class had to take action to counter this. City planning as a recognized specialization can be traced back to Hausmann whose changes in Paris were intended to limit the possibility of insurrection by making it easier for the state’s troops to maneuver through the streets. This should make it clear that the aim of city planning has always been control in the ruling class’s interest. If, in times of “social peace”, vibrant and varying activity on the streets prevents the petty unpleasantness that might otherwise mar people’s daily lives, it also provides a network of relationships that can form the basis for self-organization among the poor and exploited in times of social unrest, with the potential of pushing that unrest in the direction of insurrection. In such situations, these networks of communication can be turned to such interesting purposes as keeping an eye out for the cops. It is in the interest of the ruling class to do all that it can to hinder the formation of such networks of communication. And the forms of city planning Jacobs describes and attacks in her book do precisely that.
The division of cities into zones for different purposes is a prime example. Downtown shopping areas, more specialized shopping areas for “bohemian” tastes, arts districts, residential areas, industrial areas, may not always have strict boundaries, but they still indicate the specialization of space in cities. This specialization affects the nature of foot traffic, allowing for greater social control and reducing the opportunities for stimulating chance encounters. When I live in New Orleans in 1991, many neighborhoods had not yet succumbed to this sort of specialization. If I occasionally encountered some less than pleasant realities, I also encountered a vibrant, active street life that offered a wide variety of interesting encounters and led to the discovery of some wonderful secrets about the city. Of course, New Orleans has changed drastically since then. And the devastation that Katrina caused has opened the door to building the city completely in the service of capital.
Portland, on the other hand, already has its divisions. It is not as bad as some places, but increasingly the only public spaces that exist are those dedicated to commerce in some form, and these are being more and more concentrated into malls, strips and other areas devoted almost exclusively to commercial interaction. So these become the areas of activity while residential sidewalks are mostly deserted. Thus, for the most part, public gathering is specifically attached to commodity consumption. Nonetheless, in some of the poorer neighborhoods, the streets are more active with playing children, adults hanging out on their porches, at bus stops, etc. But it is not the vital street life Jacobs describes from fifty years ago.
So the question arises, where will we find the networks of communication we will need in times of social unrest? This is particularly important now in the US where class reality is often hidden under racial tension. In a riot provoked by another cop killing another black person, how are black people on the street to know who their “white” accomplices are when day-to-day interaction is so minimal? This is not a minor problem.
In the context of industrial civilization, the desire for chance encounters with strangers is more readily fulfilled in cities than in any other human environment. But this comes about purely by accident due to the concentration of large numbers of people in these artificial environments for much less desirable reasons. (Cities have generally been formed for purposes of control and commerce — having military, religious and\Slash{}or economic origins.) Over the last several decades, city planners, obviously working in the interest of the ruling order, have been doing all they can to reduce the possibilities for such encounters, keeping them confined to locales where they are easily controlled and generally connected to commodity consumption — bars, cafes, malls, etc. These environments are becoming less and less conducive to such encounters due to imposed noise, surveillance and the unpleasantness of most modern urban architecture. This combines with the reification and commodification of social identities and relationships that has made it harder for people to reach out beyond their own cliques and subcultures and the underlying everyday fear of the other that has insinuated its way into our minds from a variety of media scare stories to transform modern cities into wastelands of overcrowded desolation.
There are people who are content to stick with their cliques or retreat to small town or rural provincialism with only the expected and known relationships. But this is often a recipe for stagnation. The desire for chance encounters is a reflection of a desire to be stimulated and challenged in new ways, to be provoked to explore the unknown, to act and think outside one’s usual habits. The people that we know too well, that we see and interact with regularly, rarely provide such stimulation. These known relationships are necessary for providing intimacy, comfort, trust, complicity, affinity and the support necessary for exploring the unknown. But it is the encounter with the unknown, the stranger, the encounter with \emph{difference}, that keeps life vibrant and lush.
But this brings up another way in which this society has been undermining the joy of chance encounters. The reification of social identities into defined categories, particularly in this age when mass media guarantees an increasing standardization of these identities, undermines the capacity for individuals to express their uniqueness. It is increasingly difficult for many people to break out of a character that is simply a collage of social identities to express anything deeper. So most “chance” encounters now have a ritualized style similar to the sorts of encounters this society imposes. This raises an immediately practical question: what can we do to break through these standardized rituals? Here the ideas of creating situations, \emph{detournement} and subversion take on a significant personal meaning in the context of daily life.
As cities are increasingly designed to enforce the suppression of these encounters, to be stagnant swamps of enslaved humanity capable only of serving the needs of the state and capital, it becomes urgent for everyone who loves these encounters, and particularly those of us who see the need to destroy civilization and, thus, cities to reflect on how we could maintain the possibility for such encounters, both now within (and outside of) increasingly sterilized, prison-like cities, and in the future in a world without cities. The purpose of such reflection is not to come up with the solution, the blueprint, the guarantee of an ideal future. Rather it is an area for exploration and experimentation.
In \emph{Letters of Insurgents}, Jan describes his dream of possibilities in a world without the economy or the state: “We’ll leave the clearing and walk through the forest to the neighboring village and we’ll think we’re dreaming, because the village won’t be there anymore; we’ll find thousands of people building a city like no city that’s ever been built and they’ll welcome us and ask us to help because they’ll all be our friends; there won’t be any policemen or prying old women because they’ll all be too busy building or making love. We’ll stay in our friends’ beautiful city as long as we want and not a minute longer; we’ll be as free as birds; we’ll roam across the entire country; we’ll visit streams and caverns and other cities, and in each city we’ll find only friends; they’ll all beg us to join them in what they’re doing and we won’t know where to turn first because every activity to which we’re invited will seem more gratifying than the rest.” Certainly, the capacity to freely roam will play a significant factor in the opening possibilities for chance encounters, as will experiments in creating different ways that human beings can be together, based upon the active creation of our desires.
1 also think of large festivals and gatherings that may last for weeks, based upon the sheer enjoyment of other people rather than on shared ideas — or shared subcultural style. It seems that in certain areas of the world, before permanent trading centers arose, temporary bazaars would be set up in recognized places for trade and other forms of human encounter. Although these bazaars originated in economic exchange, many other sorts of interactions could and did happen there. In addition, Native American powwows are an example of people coming together for larger scale interaction.
A writer who was once interesting (but who has sadly since become disgusting) suggested an area for exploration along these lines: “the importance of the time\Slash{}space of non-work, which, until the stage of the real domination of society was reached (i.e., before World War II), was one of encounters between individuals as opposed to simply one of recreation. The city represented the space in which the activities of reproducing the labor force were détourned into the streets, cafes, festivals (especially traveling carnivals), dances and music, expressing the existence of individuals who were both unique \emph{and} separated from their social relationships\dots{}”
Because I don’t have or desire a blueprint for what a decivilized, anarchic society might be like, I would not rule out the possibility of a different sort of large-scale, more permanent gathering of human beings. — something for which we have no words since such gatherings certainly wouldn’t be like any city that has ever existed, being free of all the economic, political, religious and military aims or constraints that have been the purpose behind every city since the beginning of civilization. The question of how any of this might manifest is an area for creative exploration and the practical application of imagination. There are numerous sources of inspiration: William Blake, the surrealists, the Diggers, various radical millenarian movements, Native American powwows and villages, the wide variety of festivals that have existed throughout human history. This is a realm for creative dreaming, for considering the broad spectrum of human possibilities and what we could create from it to realize our various and conflicting desires.
\section{On Wildness}
\emph{The question of human “wildness” demands serious reflection. If it is something that each of us must create, it is also something that can never be created once and for all, definitively. Like uniqueness, it is a concept that has no content in itself. We give it content by the ways we choose to create it, to live it in each moment, and this content changes with each moment. This is why wildness must always remain an unknown, why it cannot be a reduced to a set of skills or an adherence to instinct nor raised to an ideal to which we surrender ourselves. As soon as it becomes something definable, it has been domesticated and is obviously no longer wildness. Sanctified “wildness” (“Wild Nature” or the “Primal Being”), like all gods, is a domesticated beast. This domestication becomes obvious when this beast is used to judge, to determine right and wrong. Those whose “instincts” tell them what ideas are right or wrong, those whose “gut feelings” allow them to judge the choices and behaviors of others on a moral level, are domesticated creatures with domesticated “instincts” and feelings.}
\emph{Of course, when I bring out what is in the depths of my being, what has been repressed by this civilized society, I do not lose the capacity to make distinctions. But these distinctions are not based on any absolutes, on universal concepts of “right” and “wrong”. So I do not make these distinctions by casting absolute judgments, declaring, for example, that “I know in my heart this is wrong”. Rather I use my capacity to make distinctions for determining whether something is likely to enhance my existence, increasing my self-enjoyment or not. In this process, I don't merely rely on “instincts” or “gut-level feelings”. Rather I use all the tools I have at hand including my capacities to decide, to reason, to plan, to organize my activities, to consciously develop relationships with others with whom I can develop projects.}
\emph{But I have veered from my main intention which was to speak about “wildness”. As I said above, it is an unknown that has to be perpetually created and re-created. Since we have already been civilized and domesticated, it can only be of use to us as that which perpetually negates domestication and this capacity to negate resides precisely in its remaining an unknown, an empty concept which we perpetually fill with our desire to create our lives as our own as it confronts the world that has stolen our lives. Once reified into an ideal to which we must conform and from which we can cast judgments, it becomes a domesticator itself. Thus, its real use is as an iconoclasts hammer for smashing all reified concepts including that of “wildness” itself if that becomes necessary.}
\emph{Conceived as this indefinable, unknown concept whose content we create in every moment, wildness is nothing more nor less than a poetic way of describing the uniqueness of each of us. For like wildness, uniqueness is destroyed the moment it is defined. It too is an empty concept that we endlessly fill through our perpetual creative activity. And since “wildness” has begun to have more and more ideological constructions attached to it, perhaps it is better to simply speak of uniqueness as the tool through which each of us can negate the processes of domestication civilization has imposed upon us.}
\begin{center}
* * *
\end{center}
\textbf{Subversion is a game of wild, barbarous forces.}
\section{Play Fiercely! Our Lives Are at Stake: Anarchist Practice as a Game of Subversion}
When I first encountered anarchist ideas in the late 1970s and early 1980s, it was quite common to talk about play and the subversive game, thanks to the influence of the Situationist International and better aspects of the counterculture. There is a lot to be drawn from thinking of our practice on these terms. In particular, I think that looking at anarchist revolutionary practice as a subversive game is a fruitful way of understanding anarchist aims, principles and methodologies as a basis for developing our strategies and tactics.
The thing that has distinguished anarchism from other conceptions of radical transformation is that anarchists have generally considered their ideas to be something to live here and now as much as possible as well as goals to be realized on a global scale. While there have certainly been anarchists who have chosen to turn their perspective into mere politics, the idea of living anarchy immediately gives anarchism a scope that goes far beyond such meager visions, opening it to the whole of life.
This aspect of anarchism is what makes anarchist practice resemble a game. Let me explain. A game could be describes as an attempt to achieve a specific aim using only those means that fit certain conditions accepted by those involved for the enjoyment they find in following these conditions, even though they may lower efficiency. The aim of anarchist practice would be to achieve a world free of all domination, without state, economy or the myriad of institutions through which our current existence is defined. I cannot claim to know what the most efficient way to get there would be. From an anarchist point of view, there has not yet been a successful revolution, so we have no models for efficiency. But those who desire this end, not out of a sense of duty as a moral cause, but rather as a reflection on a grand scale of what they want immediately, for their own lives, petty calculations of efficiency in achieving this end are hardly a priority. I know that I would rather attempt to achieve this end in a way that gives me the immediate joy of beginning to take back my life here and now in defiance of the social order I aim to destroy.
Here is where anarchist “principles” - the “rules” of the game — come in. The refusal to choose masters, promote laws, go to the negotiating table with the enemy, etc. are based on the desire to make our lives our own here and now, to play this game in a way that gives us joy immediately. So we choose these “rules” not out of a sense of moral duty nor because they are the most efficient way for achieving our goals, but rather for the joy we get from living on these terms.
In this light, we can also understand why in the area in which compromise is most forcefully imposed on us — the realm of survival in a world based upon economic relationships, which always opposes the fullness of life — we will choose whatever methods are necessary to keep us alive (how else could we play this game). But we will do what necessity imposes on us in these situations (work, theft, scamming, etc.) as temporary measures for sustaining our capacity to steal back our lives and fight for the world we desire, maintaining our defiance in the face of this imposition. This is, in fact, one aspect of the subversive game in practice, twisting the impositions of this world against it.
Here, I feel it would be good to draw a distinction between the outlaw and the anarchist who is playing the game of subversion. Of course, every anarchist is to some extent an outlaw, since we all reject the idea that we should determine our activity on the basis of laws. But most outlaws are not playing the subversive game. Rather they are centered on the much more immediate game of outwitting the forces of order without seeking to destroy them. For the anarchist revolutionary outlaw, this immediate game is simply a small part of a much greater game. She is making a much bigger wager than that of the immediate “crime”. He is grasping his life now in order to use it to grasp the world.
So this game combines the goal of destroying the ruling order so that we can create a world free of all domination with the desire to grasp our lives here and now, creating them as far as possible on our own terms. This points to a methodology of practice, a series of means that reflect our immediate desire to live our lives on our own terms. This methodology can be summarized as follows: 1) direct action (acting on our own toward what we desire rather than delegating action to a representative); 2)autonomy (refusal to delegate decision-making to any organizational body; organization only as coordination of activities in specific projects and conflicts); 3) permanent conflict (ongoing battle toward our end without any compromise); 4) attack (no mediation, pacification or sacrifice; not limiting ourselves to mere defense or resistance, but aiming for the destruction of the enemy). This methodology reflects both the ultimate aim and the immediate desire of anarchist revolutionary practice.
But if we are to consider this practice as a game, it is necessary to understand what type of game this is. We are not dealing with a game in which two (or more) opponents are competing against each other in an effort to achieve the same goal. In such a game, there could be room for compromise and negotiation. On the contrary, the subversive game is a conflict between two absolutely opposed aims, the aim of dominating everything and the aim of putting an end to all domination. Ultimately, the only way this game could be won is through one side completely destroying the other. Thus, there is no place for compromise or negotiation, especially not for the anarchists who are clearly in a position of weakness where to “compromise” would, in fact, be to give up ground.
The aims, principles, methodology and understanding of the nature of the battle at hand describe the anarchist revolutionary game. As with any game, it is from this basis that we develop strategy and tactics. Without such a basis, talk of strategy and tactics is just so much babble. While tactics are something we can only talk about in the specific contexts of deciding what moves to make at specific points, it is possible to speak in a more general way about strategy.
Strategy is the question of how to go about reaching one’s goals. This requires an awareness of a certain factors. First of all what is the context in which one is trying to achieve these goals? What relationship do the goals have with the context? What means are available for achieving these goals? Who might act as accomplices in this endeavor? These questions take on an interesting twist for anarchists, because our goal (the eradication of all domination) is not just something we want for a distant future. Not being good christians, we aren't interested in sacrificing ourselves for future generations. Rather, we want to experience this goal immediately in our lives and in our battle against the ruling order. So we need to examine these questions in terms of this dual aspect of our goal. The question of context involves analyzing the broader global context, the nature of the ruling institutions, the broader tendencies that are developing and the potential points of weakness in the ruling order and the areas for potential rupture. It also involves examining the immediate context of our lives, our voluntary and involuntary relationships and encounters, the immediate terrains that we traverse, our immediate projects and so on. The relationship between what we are striving for and the general context of this social order is one of total conflict. Because we are striving not only to destroy domination, but also to live immediately against it, we are enemies of this order. This conflict is deeply ingrained in our daily lives, in the variety of activities that are imposed on us by the rule of survival over life. So this conflict is central to determining our strategy. Since part of our goal is to grasp our lives back here and now, our means need to embody this. In other words, any means that involves surrendering our grasp on our lives (such as voting) is already a failure. But this is where it becomes necessary to distinguish what activities constitute such a surrender (voting, litigation, petitioning, bargaining with the enemy) and which can be incorporated into the reappropriation of one’s life and the attack against institutions of domination (for example, a temporary job, certain sorts of scams, etc., that give one access to certain resources, information and skills that are of use in one’s subversive activity). And our accomplices could be anyone, regardless of whether they have a conscious anarchist critique or not, who uses means in their specific battles against what immediately dominates and oppresses them that correspond to our own — means through which they are actively grasping their lives and struggles as their own immediately. And our complicity would last only as long as they used such means, ending the moment that they give up their autonomy or begin to bargain with their rulers.
Having established this basis, here are a few areas for discussing strategy:
Survival vs. the fullness of life - Strategies for continually overturning the dominance of survival over our lives, for making our projects and desires determine how we deal with survival to the greatest extent possible - for example, when one needs to take a job, using it against the institution of work and the economy through theft, giving things away, sabotage, using it as a free school to pick up skills for one’s own projects, always seeing it as a temporary means to ends of one’s own and being prepared to quit as soon as one's desire requires it.
Solidarity - There are two distinct aspects to this. 1) There are many flare-ups of social conflict that partially reflect the desire to take back life and destroy domination and that use a methodology like that described above, but without a full conscious critique on the part of the participants. How do we connect our conscious, ongoing conflict with the ruling order to these flare-ups of conflict in a way that fits with our aims, “principles” and methodology? Since evangelism and “moral leadership” conflict with these “principles” by turning us into pawns of a cause that we are trying to promote, we need to think in terms of complicity and straightforwardness. 2) Then there are the times when the enemy grabs some of our comrades and accomplices and locks them up. There is a habit in these situations of falling into a framework of support\Slash{}social work\Slash{}charity. In terms of our aims and desires, I think this is a huge mistake. Without denying the necessity in building defense funds and keeping communication open, our primary question is how to turn this situation into a way for attacking the ruling order. The anti-prison activities of the French group \emph{Os Cangaceiros} give some food for thought here.
Small-scale, everyday ruptures - There are events that happen every day on a small scale that cause temporary breaks in the social routine. How can we use these subversively against this order, to expose the reality of this society and to open other possibilities? How can we create such ruptures in a way that undermines resignation and acceptance of normality?
Large scale ruptures — Disasters, riots, local and regional uprisings all cause ruptures that can reveal a great deal about the ruling order and that move people to self-activity, generosity and a temporary rejection of the moral order of this society. How can we take advantage of such situations in a timely manner? What can we do to help extend the awareness and the rejection of the moral order beyond the moment? How can we expose the various politicians and bureaucrats of rupture — political parties, union leaders, militants and activists - without coming across as another one of that parasitical bunch?
So there is a vast and challenging game before us, one that I believe could make our lives into something marvelous. It is a game we have to play fiercely, because in this game our lives are the stake. There are no guarantees, no sure-fire methods for winning. But for each of us, as individuals, there is one sure-fire way to lose. That is to give in, to resign oneself to what the ruling order imposes. Who's ready to play?
\section{Beyond Survival: Some Thoughts on Giving our Projects and the Enjoyment of our Lives Priority}
\begin{quote}
\emph{The search for joy is therefore an act of will, a firm refusal of the fixed conditions of capital and its values.—Alfredo M. Bonanno}
\end{quote}
Over the past few years, I have noticed that it has been becoming trickier to live my life and carry out my projects in the way that I desire while also managing to take care of my basic needs. And among my friends, I am one of the luckier ones. When I am strapped, I know that it will only last till the first of the next month. In fact, most of the people I know are struggling to get by, to pay the rent and bills, to take care of basic needs and have a bit of fun in the process.
This is no surprise. We all know that we live in a capitalist society, and in our daily lives the essence of that society manifests in the opposition between survival and the fullness of life. The process of alienation by which capitalism is maintained transforms the methods by which we meet our needs into tedious tasks stealing our lives away from us (or at best, as in my case, isolated scams that skim the excess off the state without in any way threatening it). In recent times, transformations in the functioning of capitalist social relationships along with a real deterioration in the economy have made precariousness the common experience of most of the exploited, Including ourselves. This has led to a situation in which a number of creative, intelligent people are being forced to eat away their time in search of the means to survive.
My own experience and the often even more nerve-racking experience of a number of close friends and comrades has been causing me to think a great deal about the need to develop ways of giving our lives in their potential fullness and our projects of revolt and enjoyment priority over survival. In other words, I’ve been asking myself, how do I and those with whom I share ideas, desires, life and enjoyment turn survival into a mere tool for creating our lives on our terms — obviously against the very logic of capitalism.
In confronting this question, for the most part, anarchists have continued to operate on a fragmented, atomized level. Scams, school, temporary jobs and so on are the ways we deal with survival. To some extent this is inevitable. We do live in this world, even if we also try to live against it. And the specific aspects of what we do to survive are less important than whether questions of survival continue to dominate our existence at the expense of enjoyment, revolt and the fullness of our lives and projects. And this is where I feel we need to make a serious effort to get beyond atomization and the fragmented ways of encountering life that this society imposes. I think it is worthwhile to look at experiences of people who have confronted this, whether from a specific revolutionary understanding or simply from a lust for life.
\subsection{North Beach, 1960}
In the introduction to Dancing in the Streets, Franklin Rosemont describes his experience in the bohemian culture of North Beach, San Francisco in 1960:
\begin{quote}
“Life in North Beach was the closest thing to marvelous anarchy it has ever been my pleasure to enjoy. Despite battles with landlords, harassment by tourists, and mounting police terror, the Beats and their allies — old time hoboes, jazz musicians, oyster pirates, prostitutes, drug addicts, winos, homosexuals, bums and other outcasts — maintained a vital community based on mutual aid, and in which \textbf{being different} was an asset rather than a liability. In this community made up of people of many different races and nationalities, the practice of equality and solidarity was second nature. Almost everyone was poor, but no one went hungry, and newcomers had no trouble finding places to stay. In North Beach, 1960, what mattered most was poetry, freedom, creativity and having a good time.”
\end{quote}
This brief description expresses more the general \emph{feeling} Franklin Rosemont had of his experience living North Beach at that time than how this reality worked itself out practically. But those of us who have experienced similar situations can imagine such details, and I feel that Rosemont’s evocative description brings out some significant points. In particular, the last sentence stands out: \emph{“}\emph{I}\emph{n North Beach, 1960, what mattered most was poetry, freedom, creativity and having a good time.”} In other words, among the people Rosemont hung out with in North Beach, their creative projects and the enjoyment of their lives were their active priorities, and so they simply did what was necessary to live these priorities, acting together to guarantee that the ground on which to build their creative projects would be there. In this case, most of the people involved were not revolutionaries or anarchists, but simply individuals who had no interest in fitting into the normal grind of existence in this society.
\subsection{Os Cangaceiros}
We are all familiar with the uprising that happened in France in 1968. One of the slogans that reflected the most radical elements of this revolt was “Never work, ever!”, and there were many who took this slogan to heart in the creation of their lives after the uprising was suppressed. One group is particularly outstanding in that their choices reflect a clear awareness that work wasn’t simply productive activity or the “job”, but rather was an entire system of social relationships. Thus, the refusal of work couldn’t simply mean work avoidance or the reduction of work to the bare minimum. It meant creating life in a different manner and attacking the system of social relationships that is work. This group, which came together in Nice in 1968, was made up of “delinquents” already familiar with the world of crime who discovered a revolutionary perspective in the days of insurgence in France. When they first came together to share their capacities and resources for creating life on their own terms, they called themselves the Gravediggers of the Old World. This informal group of comrades traveled first around southern France, making connections taking part in struggles and doing what was necessary to provide the basis for their lives. Throughout the 1970s and 1980s they traveled throughout Europe, participating in revolts, including those in Italy in the mid to late 1970s, in Poland in 1980, in England, France and Belgium in the early 1980s. A statement they made in 1980 indicates the spirit they brought to their revolt:
\begin{quote}
“If we loot banks, it is because we have recognized money as the central cause of all our unhappiness. If we smash windows, it’s not because life is dear, but because commodities prevent us from living at all costs. If we break machines, it is not because of a wish to protect work, but to attack wage slavery. If we attack the police bastards, it’s not to get them out of our faculties, but to get them out of our lives. The Spectacle wanted to make us appear dreadful. We intend to be much worse.”
\end{quote}
In pursuit of their ongoing project of revolt and the full enjoyment and experience of life, they used whatever means gave them greatest control over their own lives, means that were often illegal. They refused any sort of meagerness or pseudo-revolutionary asceticism, squatting, for example, in luxury buildings which they armored well against the police. Being of the underclass, they were able to easily develop networks of support that went beyond the limits of any radical connections they had. Their way of living inevitably brought them into conflict with the law and in time started to focus a greater amount of their energy into attacks against the judicial and prison systems. This was about the mid-1980s. At this point they began to call themselves \emph{Os Cangaceiros} (after a group of mystical outlaw insurgents who were active in Brazil at the beginning of the 20th century). They were active at this time in prison revolts, sabotage of prison construction, disruption of judicial activity, escapes and so on. Around 1990, they stole plans for the construction of new, advanced technology prisons, made thousands and thousands of copies of these plans and mailed them with analyses of the prison society to thousands of people. Unlike the previous example, these are people with a conscious revolutionary perspective, developed in the course of an uprising, who decided to go on living that perspective. This decision, rigorously embraced, moved them to discover the means for living their revolt, their projects and their pleasures on their own terms, defying the alienation imposed by capital.
\subsection{My Experience in the Early 1990s}
From the time I first encountered anarchist and revolutionary ideas, it was clear to me that they couldn’t simply be words tossed from one’s mouth into the air. They had to affect how one lived. Thus, my decision to embrace such ideas was a decision to wrestle with how I would live. At this point, I have been wrestling with this for more than twenty-seven years. At various times, I have found others with whom to share this ongoing battle to create my life on my terms. What we created, how consciously we created it and how far it went in expressing our desires and dreams varied, but at no time did I simply give up my pursuit of a life of revolt and joy. Perhaps the most outstanding period of my life happened in the early 1990s here in Portland. In certain ways, what I experienced with specific friends and the networks we developed is reminiscent of Rosemont’s description of North Beach in 1960. I moved to Portland at the end of 1991, where I met several people who were to be my closest companions and accomplices for the next few years, and a few of whom remain among my best friends to this day. While each of us had various ways of bringing in the money that we needed to get by, this aspect of our lives was always kept subordinate to our enjoyment, our revolt and our projects. Not everyone among our little group of friends was an anarchist, but everyone, at least for the time, had an irrepressible lust for life that couldn’t help but express itself in rebellious way in this society. Our life together involved endless adventures: theft, travels, small attacks against various manifestations of the world we hated, public playful disruptions of daily life. I remember one May Day in which we wandered around downtown Portland through the business district playing improvised noise on various instruments, handing out flyers inviting people to come join us for an afternoon picnic rather than going back to work. We had stolen a fairly good supply of food and beer — quite a bit more than we ourselves needed. We had a delightful time and received quite a positive response (from smiles to “thumbs-up” gestures to encouraging comments), but I don’t recall anyone else quite having the courage to take the afternoon off and join our picnic. Still we had a delightful time, and this event is reflective of the sort of life we chose to live together. Also these activities, a short-lived anarchist coffeehouse that we did in our house and our constant posting of poetic messages of revolt on telephone poles and other places helped us develop a network of connections that kept a fairly decent flow of all the material pleasures of life available. This network, which extended far outside specifically anarchist milieus, provided a good bit of the material basis for how we chose to live. If in North Beach, “what mattered most was poetry, freedom, creativity and having a good time”, for us it was rebellion, poetic living, creativity and having a good time. If some of us had a revolutionary perspective that was lacking in the North Beach scene Rosemont describes, at the same time we certainly did not have the clarity about our life projects that \emph{Os Cangaceiros} had. We had amazing utopian dreams, but did not really conceive of our lives as totalities for us to create against the totality of this society. Our visions lacked projectuality except in the broadest sense (and that only among the few of us who were anarchist), and this limited the extent of our projects. Nonetheless, at this time in my life I experienced in Portland something similar to what Rosemont experienced in North Beach, a kind of semi-conscious utopian practice against this world which made life a delight and created some of my closest friendships.
\subsection{And Us? Here? Now?}
What do these examples have to say to us? Certainly, there is no use in trying to imitate any of these examples. Our times, our circumstances, our needs and our capacities are our own. But there are specific lessons that can be drawn from these examples. First and foremost, in each of these instances, those involved chose to put their projects and the enjoyment of their lives before survival, rejecting the blackmail that capitalism imposes. This transforms the means used for acquiring basic necessities into nothing more than tools for constructing our lives and projects. This is the practical meaning of a reversal of perspective with regards to this world. In order to achieve the capacity to do this, in each instance people acted together developing networks of mutual aid and complicity. Of course, the North Beach scene, based mostly on a fairly loose bohemian affinity, faded as the Beat scene disintegrated and many of those involved moved into the mainstream in different ways. The situation that I lived in Portland also eventually disintegrated as some friends chose to drop into a more mainstream existence and the rest of us started exploring different ways toward our shared dreams of anarchy and the fullness of life. Although the last I heard of \emph{Os Cangaceiros} was in the early 1990s, it is possible that they are still living on these same terms — after all, they had been living this way, on their own terms, for over twenty years. Certainly there are other individuals in Europe who have come together for much the same purpose, continuing to develop their ways of living against the ruling order. I think that what distinguishes \emph{Os Cangaceiros} from the other situations is that they clearly recognized what they opposed as a totality of intertwining social relationships that had to be practically fought in its completeness and also clearly perceived their own lives as total projects to create in conscious rebellion against this world for the sheer joy and adventure of doing so.
And I think it is this perception of life not as a series of random, disconnected moments, but as a totality to be created on our own terms that provides the basis for turning the blackmail of this society on its head and subjugating survival to the fullness of life and revolt. Of course, we will be doing this in a context that on the global and the everyday life scale absolutely opposes this. But this only means we need to have that much more resoluteness in our decision to carry on this project. Here is where a conscious choice to act with specific others can be of great significance. With others whose aspirations, dreams and desires correspond with ours, possibilities expand exponentially. But only if we actually talk with each other about our dreams, our desires, our needs, the tools and skills we have to share, the projects we are trying to create. We are all aware that when we have a small project to do — say cooking a meal or building a cabin — it is necessary to consider the details of what we want to accomplish, figure out the tools and methods necessary to accomplish it, figure out the various hindrances that stand in our way and how to go about eradicating them. The same idea applies to the project of creating our lives as an unfragmented, total project against this society. And so, if we have some affinity in terms of our broader conceptions of a life free from the state and capital, in terms of our dreams and desires for self-created existence and in terms of the necessity for destroying the social reality that stands in the way of this, we need to talk about these dreams and desires, about the specific ideas for projects of revolt and enjoyment we have, about the tools and capabilities we have to share and teach other, about ways to develop informal networks of mutual aid so that no one among us is ever really forced to place survival above their projects or lives.
I know that these are particularly tough times for such defiance, that a number of us are just scraping by. But we are smart, strong, defiant individuals capable of great dreams and great enmity toward that which tries to steal our dreams. This is something we all have to remember. A habit has developed in anarchist circles of thinking of ourselves as weak, as damaged, as hurt. I think this stems from bringing too much of the language of disease, therapy and healing into our social analysis — but that is a question that would need to be gone into more thoroughly elsewhere. The point I want to make here is that we need to start from the assumption that we can accomplish the things we desire, from the smallest projects to the ultimate destruction of the social order we hate and the creation of our lives on our own terms. Starting from this assumption, we need to begin to assess the specific problems we face with the aim of overcoming them — recognizing that as long as this society continues to exist this will be an ongoing project.
So let’s discuss our dreams and our rebellious aspirations not on a purely abstract level, but in terms of how we can develop relationships of practical affinity, complicity and concrete solidarity in the project of creating total lives of revolt here and now. Those of us who are feeling the crunch of survival in particularly hard ways can share their dreams and their needs, and among us, we should be able to figure out ways to open possibilities for getting beyond this without falling into the usual limited atomized solutions.
If we remember that work is not simply the job but precisely the system of social relationships that forces us to give survival priority over life, joy, revolt and creativity, then it becomes clear that this reversal of perspective is a necessary basis for our revolt. The effort put into avoiding work without having an ongoing project of creating one’s life as a whole itself stinks of work \textasciitilde{} here too survival still has priority. But if we have a clear life project and the specific means we use to get money and other necessities imposed by this society are only temporary tools for moving that life project forward. This already breaks down the logic of survival and work even if sometimes these specific means are jobs. But such a project is built precisely out of our relationships with the world and with each other. The individuals in the situations described above were able to place their enjoyment, their lives and their projects above survival, because they made the decision to create their lives together on their own terms, and rejecting the fragmentation imposed by capitalism, this included figuring out how to meet basic needs together without being dominated by survival. We have a lot to offer each other. Let’s figure it out and find the ways to defy this blackmail together.
\subsection{A Few Questions to Consider}
How does each of us conceive of our lives? How do we want to live both on grand social terms and in our immediate lives? Where do our various visions coincide? Where do they differ? Where can they enhance each other? Where do they actually conflict?
How do we perceive revolution? Insurrection? Subversion? Destruction of the ruling order? Where do these ideas coincide and differ? Where can they enhance each other and where do they conflict?
What great and small projects do we imagine? What ones are we actually doing now? How can these intertwine? What tools, knowledge and capacities do we have to share to enhance these projects and better interweave them in mutuality?
What stands in the way, on an immediately daily life level, of creating our lives on our own terms, of accomplishing our projects? In other words, where does the blackmail of survival have us by the throats? What ideas do we have for overcoming this? What knowledge, skills or means might some of us have to share for overcoming this?
We need to consider that creating life on one’s own terms requires having the space and time for doing so, and capital does tend to dominate all space and time. So we need to ask as well, how do we take the space and time we need to carry out these projects of creating our lives on our terms and destroying the social order that stands in our way? How do we give priority to grasping whatever space and time we can for this purpose? What spaces and moments do we currently have access to and how can we expand them? How can we steal those spaces and times that survival in this society imposes on us and use for our own purposes, against this society?
\textbf{I don’t pretend to have answers, but this is a project I want to pursue, a game I want to play, because in any case my life is at stake, so I might as well try to wager it on my own terms. My hope is that others feel the same and that we can begin to explore what this means together.}
\begin{quote}
\emph{We, however, start from the beginning. We are poor, we have unlearned how to play. We have forgotten it, our hands have unlearned how to dabble.}
—Ernst Bloch
\end{quote}
\section{A Few Last Words About Words}
\emph{We have a tendency to overvalue words. We put so much time into producing them, as if they were the source of life itself}\emph{.} \emph{We believe that there are words and ways of using words that are inherent sources of oppression and spend vast amounts of time trying to suppress these words, impoverishing our language in the process. In the meantime, the real practices of oppression go on, often carefully using the correct words to hide the practical reality, At the same time, we think that if we find the right combination of words, this will spark rebellion. So we make flyer after flyer,} \emph{z}\emph{ine after zine, with an evangelistic zeal, forgetting our own lives, our own desire for freedom, joy and the intensity of existence. By giving words such great value, we forget our own purpose in using them. They become our masters. This becomes evident in the attempt to evangelize, where our words become means for winning others over to a position, assuming that when enough people believe the right thing, they will rise up. But have those who rise up for words, and not for their lives, really risen up at all or are they just embracing a new master? If my aim is to take back my life, to create my desire, my joy, my passion, then how can I tum my words into tools for a position? They would cease to be my own words. For me, words can only be} \emph{a tool (or toy) for expressing and communicating my desire, my project, my life; one of the many tools I use to find accomplices, to create m}\emph{y} \emph{enjoyment and express the intensity of my passions, the wildness of my dreams. But disconnected from life, from practice, they are empty. And any word in the service of a cause, any evangelistic word, any word intended to draw followers to a position, has been disconnected from life, separated from the immediate practice of freedom, and so is empty. Thus, in overvaluing words, we drain them of meaning, because their meaning comes precisely from our lives and our choices.}
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The Anarchist Library
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Anti-Copyright
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Willful Disobedience, Wolfi Landstreicher
Willful Disobedience Volume 5, Number 3
Spring 2006
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Retrieved on 15 October 2018 from \href{https://archive.org/download/willful\_disobedience\_5.3/willful\_disobedience\_5.3.pdf}{archive.org}
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\textbf{theanarchistlibrary.org}
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Se proviamo a leggere la realtà che ci circonda ci accorgiamo che stiamo assistendo allo sviluppo di profonde trasformazioni dal punto di vista della gestione del potere politico ed economico. Tali cambiamenti si riflettono anche a livello sociale. È necessario confrontarsi con le trasformazioni in atto e tenerne conto in quelle che sono le nostre analisi e prospettive di attacco.
Il capitale non è in crisi, ma più ‘semplicemente’ le scelte finanziarie degli Stati hanno creato delle difficoltà nella tradizionale gestione del mercato e hanno prodotto, in generale, un peggioramento delle condizioni di vita dei consumatori cittadini. Le contraddizioni che il capitale ha sviluppato hanno contribuito a determinare in alcune zone delle occasioni di scontro, più o meno cruente e di lunga durata, fra i guardiani del potere e le sue strutture e quelle sacche di popolazione stanche di essere escluse dagli agi che il fasullo benessere delle società del consumo promettono.
Di fronte a ciò è naturale chiedersi che fare. Essere “qui ed ora” è infatti alla base del nostro desiderio di rottura violenta con ogni sistema di valori, con il capitale e le sue sfumature.
Nell’ambito di tali riflessioni e nella definizione di prospettive che possano orientarci nelle strade incerte ed inesplorate della rivolta crediamo sia necessario evitare di confrontarsi con la realtà con gli occhi insabbiati da quei facili entusiasmi che rischiano di far vedere insurrezioni ad ogni angolo, complici in ogni indignato, soggetti rivoluzionari in ogni sfruttato. Al tempo stesso crediamo sia altrettanto pericoloso rimanere ancorati ad una sorta di pessimismo realista che rischia di renderci immobili di fronte allo scorrere del tempo, di trasformarci in attendisti imprigionati in una logica di tipo determinista.
Ciò che riteniamo fondamentale è porsi in un’ottica di lucida osservazione che può consentirci di cogliere le trasformazioni in atto, individuare gli aspetti vulnerabili del nemico, per poter meglio valutare cosa e come attaccare.
In una condizione mentale e materiale in cui domina l’urgenza di esserci (e non di essere), cioè di definizione di un proprio ruolo all’interno di una possibile conflittualità diffusa, si rischia di perdere di vista la centralità della questione: la necessità di partire da sé, dalle proprie idee e prospettive anarchiche. Ecco dunque che in occasione di una rivolta spontanea il problema degli anarchici non è quello di cercare un ruolo tra altri ruoli, di trovare il modo per farsi accettare dagli altri, di risultare gradevoli o nascondere i propri veri desideri per catturare alleanze. Sarebbe semmai utile scegliere delle condizioni di attacco che impediscano un ritorno alla normalità, sperimentare l'agire che ci appartiene, trovare degli obiettivi che la spontaneità da sola può non essere in grado di trovare. Qualsiasi ipotesi insurrezionale è imprevedibile e indipendente da noi, ma come anarchici, in un’ottica di conflittualità permanente e di definizione di progetti insurrezionali possiamo certo dare un contributo fondamentale a quando accade. .
Il problema che bisognerebbe porsi, secondo noi, non è tanto come relazionarsi alle possibilità di rivolta per strada, di lotte territoriali e\Slash{}o specifiche che potrebbero radicalizzarsi e diffondersi, quanto come continuare ad agire e ad attaccare, in una dimensione pratica e teorica, alla luce delle trasformazioni in atto all’interno della società e dei meccanismi di dominio.
Analizzare le pratiche e i percorsi di lotta in relazione agli obiettivi è tappa fondamentale di un discorso volto ad individuare i limiti e le prospettive nella teoria e nella pratica della sovversione sociale. Per poter meglio toccare i diversi quesiti e proposte che intendiamo portare avanti in questa sede individuiamo in alcuni punti alcune delle argomentazioni che vorremmo portare all’attenzione dei compagni.
Crediamo sia urgente affrontare la questione delle modalità di comunicazione fra compagni. Il problema può essere affrontato distinguendo due aspetti, quello delle modalità con cui decidiamo di comunicare e quello del valore che riconosciamo agli strumenti che di volta in volta scegliamo di utilizzare. Nello specifico ci riferiamo all'uso della rete telematica e il modo con cui ci relazioniamo alla stessa. L'utilizzo da parte nostra degli strumenti, seppur in piccola parte, è un dato di fatto, ma questo non è di certo un elemento per il quale possiamo considerarli utili in caso di insurrezioni o strumento fondamentale nella definizione delle nostre prospettive o, addirittura, qualcosa di cui possiamo liberamente disporre.
I sistemi di comunicazione di tipo virtuale hanno avuto uno sviluppo incredibile all'interno delle società in cui viviamo negli ultimi vent'anni e permeano ogni giorno di più la realtà e il sistema di relazioni fra le persone. Non possiamo ignorare che tali sistemi siano lentamente entrati nelle nostre vite, condizionando inevitabilmente anche il nostro modo di rapportarci con gli altri, con ciò che ci circonda e con gli strumenti telematici stessi. Tutto ciò è accaduto nonostante ognuno di noi sia consapevole che l'irrealtà virtuale è funzionale al potere e ne è la forza.
Nell'ultimo decennio i metodi tradizionali con cui facevamo circolare le idee, come ad esempio giornali, volantini, manifesti, libri, si sono ridotti sensibilmente e la diffusione delle idee stesse è stata quasi totalmente delegata all'universo virtuale. È più che mai indispensabile tornare a rispolverare le vecchie forme di incontro e comunicazione fra compagni e sperimentarne di nuove, ma che siano soltanto nostre e non del nemico. Tornare ad incontrarsi e prendersi il tempo per farlo, cosa resa sempre più difficile dai ritmi imposti dalla vita moderna, ritmi che più o meno consapevolmente abbiamo fatto nostri.
Capita spesso di sentire qualcuno fare considerazioni sulla possibilità di sfruttare gli strumenti telematici in situazioni specifiche, ma trovarsi faccia a faccia con un uso pressoché quotidiano di internet, in particolare per lo scambio di informazioni e idee, ci ha mostrato quanto la realtà virtuale giunge a condizionare in modo negativo il modo di relazionarsi stesso. L'idea di un \emph{buon uso} della realtà virtuale in una prospettiva rivoluzionaria non ci convince, crediamo infatti che prendere in considerazione una tale possibilità comporterebbe scegliere delle vie che non danno alcuna garanzia perché funzionali al capitale e gestite dal potere. La telematica e lo sviluppo tecnologico devono semmai essere potenziali obiettivi d'attacco.
\section{Sabotare la produzione}
La macchina del capitale si alimenta grazie alle strutture di potere (burocrazie e istituzioni), meccanismi di repressione e di controllo (carceri, tribunali, forze militari e di polizia, sistemi di sorveglianza), al lavoro, al consenso, alla produzione. La critica radicale e le prospettive di attacco devono quindi svilupparsi su più livelli, da un punto di vista sia teorico che pratico. Nello specifico il sistema di produzione e consumo è ciò che lega ed incatena direttamente gli individui al capitale e alle sue sfumature. La creazione di falsi bisogni determina la sottomissione, più o meno consapevole, allo sfruttamento nel lavoro, alle logiche di colonialismo economico. La produzione di energia, i complessi industriali e di fabbrica più o meno delocalizzati, la diffusione della merce sono alla base del funzionamento di questo mondo.
Ed è proprio in questa direzione che bisogna agire, senza aspettare che quel muro di mercificazione, che si sta infiltrando in ogni aspetto dell'esistenza, ci crolli inesorabilmente addosso, mentre proviamo a scalfirlo mirando alla superficie e non alle fondamenta, seppellendo ogni possibilità di tentativo futuro di attacco. Acquisire, scambiare e diffondere informazioni, pratiche e teoriche, in merito al reperimento e all'utilizzo di strumenti e conoscenze è uno degli aspetti che crediamo sia indispensabile discutere e sviluppare.
Possiamo porci degli interrogativi su come agire e come attaccare, ma è altrettanto importante chiedersi contro cosa agire e quali gli obiettivi da individuare, puntando sull'iniziativa piuttosto che rinchiudersi in una logica di risposta. Ciò che ci circonda pullula di luoghi attraverso i quali il capitale prolifera. Luoghi che sono nati o mutati radicalmente negli ultimi decenni. Facciamo, brevemente, un esempio, col quale mettere facilmente in evidenza alcuni dei cambiamenti ai quali facciamo riferimento. Si pensi alla differenza che c'è fra degli archivi cartacei e i database. In passato il rogo di documentazione all'interno di un ufficio anagrafe, del lavoro, di un grosso complesso industriale poteva essere un'azione distruttiva concreta. Oggi no, le informazioni, i dati d'archivio vengono conservate nei database, in piccoli strumenti elettronici, scorrono lungo chilometri di cavi. Non è forse necessario tenerne conto? E non è forse palese che i cambiamenti che il nemico sono stati radicali e non si posso ignorare, ma è necessario approfondirli e conoscerli?
Non vogliamo in questa sede fare un elenco di quelli che possono essere possibili obiettivi di attacco, preferiamo lasciare ad ognuno la fantasia nella ricerca e la creatività nel definire le proprie prospettive di rivolta.
Un altro punto sul quale ci interessa puntare brevemente l'attenzione è la dimensione internazionale che credo debba assumere o tornare ad avere la prospettiva insurrezionale. Occasioni come questa consentono di vedersi, di discutere, di confrontarsi fra compagni provenienti da diversi posti, e devono costituire un punto di partenza per l'approfondimento di relazioni future, laddove nascano e si desideri approfondirle. Ma la possibilità di stringere rapporti individuali o fra diverse realtà non è l'obiettivo finale, ma un presupposto e un aspetto della dimensione internazionalista alla quale aspiriamo. Avere dei rapporti con i compagni che vivono all'estero o scambiarsi materiale e conoscenze da solo non basta, occorre anche che ognuno di noi sappia proiettarsi in un ottica di osservazione ed azione che superi i confini territoriali.
Per spiegarci meglio. Pensiamo a ciò che è accaduto in Grecia negli ultimi anni, l'insurrezione di dicembre, mille attacchi disseminati su tutto il territorio, conflittualità ripetuta con le forze dell'ordine e vari simboli e luoghi di potere, saccheggi nei supermercati e tante altre azioni che ci hanno scaldato il cuore e infuocato gli animi. Fuochi che però raramente sono traboccati dai nostri animi e hanno assunto una dimensione di concretezza.
Le ragioni sono diverse e differenti l'una dall'altra. Mancanza di contatti? Una realtà troppo lontana dalla nostra? Condizioni interne difficilmente decifrabili? Notizie sporadiche e spesso esclusivamente legate alle fonti di regime? Di certo sì, sono ragioni che probabilmente hanno pesato. Ma prima fra tutte, ad essere determinante, è stato il fatto che non eravamo, e non siamo, preparati e quindi incapaci di cogliere delle occasioni. Riuscire a portare fuori dai confini greci una conflittualità permanente e degli attacchi mirati, essere capaci di comprendere le contraddizioni che il capitale sta sviluppando un po' ovunque, essere in grado di contrattaccare avendo a disposizione informazioni e strumenti sviluppati in precedenza, avrebbe potuto fare la differenza. È anche riflettendo su questa occasione mancata, ma se ne potrebbero citare molte altre, che si può comprendere quanto sia necessario avere la capacità di volgere lo sguardo al di là delle cose che stanno nel breve raggio attorno ad ognuno di noi ed essere pronti, essere preparati.
Nell'urgenza di voler esserci, nella smania di partecipare alla possibilità del dilagare dell'indignazione si rischia di smarrirsi fra le provocazioni del capitale e le traiettorie di strade che non ci appartengono. Non abbiamo un mondo da salvare, né coscienze da conquistare, né verbi da diffondere. Seppur sia fondamentale una creatività che determini anche l'imprevedibilità, le prospettive e gli obiettivi non devono essere tirate fuori da un qualche magico cilindro, non ci si può svilire in una ossessiva ricerca di ruoli, numeri e presenze. È tuttavia importante l'esplorazione di nuovi sentieri di attacco, l'esplorazione di nuovi mezzi, strumenti e tecniche in relazione non solo agli obiettivi, ma ai contesti e alle forze disponibili.
Esistono infinite possibilità di intervento in senso critico e distruttivo rispetto alla realtà che ci circonda, e in tal senso riteniamo importante estendere e diversificare le pratiche di conflitto tentando di renderle, di volta in volta, riproducibili.
Palermo, 31 ottobre
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Contributo barbaro
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\textbf{tabularasa.anarhija.net}
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https://cr.yp.to/bib/1979/swanson-type.tex | yp.to | CC-MAIN-2020-16 | text/plain | application/x-tex | crawl-data/CC-MAIN-2020-16/segments/1585370494349.3/warc/CC-MAIN-20200329140021-20200329170021-00244.warc.gz | 421,980,246 | 635 | \bib{1979/swanson-type}
\yr 1979
\isbn 0--8218--0053--1
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\by Ellen Swanson
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%
% TEMPLATE.TEX -- APN3 (2003) ASP Conference Proceedings template.
%
% Derived from ADASS VIII (98) ASP Conference Proceedings template
% Updated by N. Manset for ADASS IX (99), F. Primini for ADASS 2000,
% D.Bohlender for ADASS 2001, and H. Payne for ADASS XII and LaTeX2e.
%
% Use this template to create your proceedings paper in LaTeX format
% by following the instructions given below. Much of the input will
% be enclosed by braces (i.e., { }). The percent sign, "%", denotes
% the start of a comment; text after it will be ignored by LaTeX.
% You might also notice in some of the examples below the use of "\ "
% after a period; this prevents LaTeX from interpreting the period as
% the end of a sentence and putting extra space after it.
%
% You should check your paper by processing it with LaTeX. For
% details about how to run LaTeX as well as how to print out the User
% Guide, consult the README file. You should also consult the sample
% LaTeX papers, sample1.tex and sample2.tex, for examples of including
% figures, html links, special symbols, and other advanced features.
%
% If you do not have access to the LaTeX software or a laser printer
% at your site, you can still prepare your paper following the
% instructions in the User Guide. In such cases, the editors will
% process the file and make any necessary editorial adjustments.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\documentclass[11pt,twoside]{article} % Leave intact
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% If you have the old LaTeX 2.09, and not the current LaTeX2e, comment
% out the \documentclass and \usepackage lines above and uncomment
% the following:
%\documentstyle[11pt,twoside,adassconf]{article}
\begin{document} % Leave intact
%-----------------------------------------------------------------------
% Paper ID Code
%-----------------------------------------------------------------------
% Enter the proper paper identification code. The ID code for your
% paper is the session number associated with your presentation as
% published in the official conference proceedings. You can
% find this number locating your abstract in the printed proceedings
% that you received at the meeting or on-line at the conference web
% site; the ID code is the letter/number sequence proceeding the title
% of your presentation.
%
% This will not appear in your paper; however, it allows different
% papers in the proceedings to cross-reference each other. Note that
% you should only have one \paperID, and it should not include a
% trailing period.
%
% EXAMPLE: \paperID{O4-1}
% EXAMPLE: \paperID{P7-7}
%
\paperID{O10-1}
%%%% ID=O10-1
%-----------------------------------------------------------------------
% Paper Title
%-----------------------------------------------------------------------
% Enter the title of the paper.
%
% EXAMPLE: \title{A Breakthrough in Astronomical Software Development}
%
% If your title is so long as to fill the page header when you print it,
% then please supply a short form as a \titlemark.
%
% EXAMPLE:
% \title{Rapid Development for Distributed Computing, with Implications
% for the Virtual Observatory}
% \titlemark{Rapid Development for Distributed Computing}
%
\title{Observer versus software engineer: The dawn of the armchair astronomers}
\titlemark{Observer versus software engineer}
%-----------------------------------------------------------------------
% Authors of Paper
%-----------------------------------------------------------------------
% Enter the authors followed by their affiliations. The \author and
% \affil commands may appear multiple times as necessary (see example
% below). List each author by giving the first name or initials first
% followed by the last name. Authors with the same affiliations
% should grouped together.
%
% EXAMPLE: \author{Raymond Plante, Doug Roberts,
% R.\ M.\ Crutcher\altaffilmark{1}}
% \affil{National Center for Supercomputing Applications,
% University of Illinois Urbana-Champaign, Urbana, IL
% 61801}
% \author{Tom Troland}
% \affil{University of Kentucky}
%
% \altaffiltext{1}{Astronomy Department, UIUC}
%
% In this example, the first three authors, "Plante", "Roberts", and
% "Crutcher" are affiliated with "NCSA". "Crutcher" has an alternate
% affiliation with the "Astronomy Department". The fourth author,
% "Troland", is affiliated with "University of Kentucky"
\author{Frossie Economou, Tim Jenness, Kynan Delorey, Brad Cavanagh, Shaun de Witt}
\affil{Joint Astronomy Centre, 660 N. A`oh\={o}k\={u} Place, University Park,
Hilo, Hawaii, 96720}
\author{Alasdair Allan}
\affil{School of Physics, University of Exeter, Exeter, EX4 5EN, UK}
%-----------------------------------------------------------------------
% Contact Information
%-----------------------------------------------------------------------
% This information will not appear in the paper but will be used by
% the editors in case you need to be contacted concerning your
% submission. Enter your name as the contact along with your email
% address.
%
% EXAMPLE: \contact{Dennis Crabtree}
% \email{crabtree@cfht.hawaii.edu}
%
\contact{Frossie Economou}
\email{f.economou@jach.hawaii.edu}
%-----------------------------------------------------------------------
% Author Index Specification
%-----------------------------------------------------------------------
% Specify how each author name should appear in the author index. The
% \paindex{ } should be used to indicate the primary author, and the
% \aindex for all other co-authors. You MUST use the following
% syntax:
%
% SYNTAX: \aindex{Lastname, F. M.}
%
% where F is the first initial and M is the second initial (if
% used). This guarantees that authors that appear in multiple papers
% will appear only once in the author index.
%
% EXAMPLE: \paindex{Crabtree, D.}
% \aindex{Manset, N.}
% \aindex{Veillet, C.}
%
% NOTE: this information is also used to build the author list that
% appears in the table of contents. Authors will be listed in the order
% of the \paindex and \aindex commmands.
%
\paindex{Economou, F.}
\aindex{Jenness, T.}
\aindex{Delorey, K. K.}
\aindex{Cavanagh, B.}
\aindex{de Witt, S.} % Remove this line if there is only one author
\aindex{Allan, A.}
%-----------------------------------------------------------------------
% Author list for page header
%-----------------------------------------------------------------------
% Please supply a list of author last names for the page header. in
% one of these formats:
%
% EXAMPLES:
% \authormark{Lastname}
% \authormark{Lastname1 \& Lastname2}
% \authormark{Lastname1, Lastname2, ... \& LastnameN}
% \authormark{Lastname et al.}
%
% Use the "et al." form in the case of seven or more authors, or if
% the preferred form is too long to fit in the header.
\authormark{Economou, Jenness, Delorey, Cavanagh, de Witt \& Allan}
%-----------------------------------------------------------------------
% Subject Index keywords
%-----------------------------------------------------------------------
% Enter a comma separated list of up to 6 keywords describing your
% paper. These will NOT be printed as part of your paper; however,
% they will be used to generate the subject index for the proceedings.
% There is no standard list; however, you can consult the indices
% for past proceedings (http://adass.org/adass/proceedings/).
%
% EXAMPLE: \keywords{visualization, astronomy: radio, parallel
% computing, AIPS++, Galactic Center}
%
% In this example, the author noticed that "radio astronomy" appeared
% in the ADASS VII Index as "astronomy" being the major keyword and
% "radio" as the minor keyword. The colon is used to introduce another
% level into the index.
\keywords{flexible scheduling, pipelines, intelligent agents, Virtual Observatory, JCMT, UKIRT}
%-----------------------------------------------------------------------
% Abstract
%-----------------------------------------------------------------------
% Type abstract in the space below. Consult the User Guide and Latex
% Information file for a list of supported macros (e.g. for typesetting
% special symbols). Do not leave a blank line between \begin{abstract}
% and the start of your text.
\begin{abstract} % Leave intact
% Place the text of your abstract here - NO BLANK LINES
Traditional ground-based observatories have moved into a new era where the
dominant consumers for their data products are astronomers who no longer come
out to use the facility themselves. Using the JCMT and UKIRT as an example, we
discuss the wide variety of software systems that are necessary for
maintaining a high level of scientific involvement for the absentee
observer. These include cradle-to-grave flexible scheduling support, advanced
data reduction pipelines, VO integration and intelligent agent networks. Is
the observational astronomer becoming an endangered species, and does this
really matter?
\end{abstract}
%-----------------------------------------------------------------------
% Main Body
%-----------------------------------------------------------------------
% Place the text for the main body of the paper here. You should use
% the \section command to label the various sections; use of
% \subsection is optional. Significant words in section titles should
% be capitalized. Sections and subsections will be numbered
% automatically.
%
% EXAMPLE: \section{Introduction}
% ...
% \subsection{Our View of the World}
% ...
% \section{A New Approach}
%
% It is recommended that you look at the sample papers, sample1.tex
% and sample2.tex, for examples for formatting references, footnotes,
% figures, equations, html links, lists, and other special features.
\section{Software and the Observatory}
The Joint Astronomy Centre (JAC) operates two facilities, the
sub-millimetre James Clerk Maxwell Telescope (JCMT) and the United
Kingdom Infrared Telescope (UKIRT), both of which are now fully
flexibly scheduled to maximize prevalent weather conditions. In order
to operate efficiently and effectively in the absence of the PI on
behalf of which data is being taken, we have put in place a large
number of integrated software systems providing a ``cradle-to-grave''
approach the operation of the observatory (Economou et al.\ 2002;
Economou, Jenness \& Rees 2002).
The JAC flexible scheduling model (see e.g.\ Robson 2002) has two
major points of departure from that commonly practiced in other
facilities. First, we do not impose a deadline for submitting
observations; PIs are free to modify their programmes throughout the
semester in the light of incoming data. This model requires a seamless
flow of observation definitions data and information from the
observatory to the PI.
The second difference to other queue-scheduled operational models is
that we do not have the resources to have staff doing the
observations, as our funding was not increased after the switch from
classical scheduling to flexed observing. We therefore run a hybrid
model in which some PIs do come out to observe, but are required to do
projects ``off the queue'' as soon as weather departs from the
parameters allocated to their project. This means that we may have
observers that are quite inexperienced with the instrument in use, and
therefore need a system which allows observations to be done correctly
in such cases.
\begin{description}
\item[Observation Preparation]
Necessary for any kind of queue-scheduled system is an Observation
Preparation tool (also known as a ``Phase II'' tool) (Wright et al.\
2001; Folger et al.\ 2002). This allows the PI to fully specify their
observation completely, as to avoid any subsequent interpretation
error that would affect the quality of the data, since as mentioned
above the actual observer may not be too experienced. It is also
important for this information to be provided in a way that focuses
on scientific descriptions of the observation (e.g.\ use wavelength
ranges rather than filter names), as to allow a PI that may not be
intimately familiar with the facility to specify their observations in
an effective way.
\item[Dynamic Scheduling]
In order to make a timely response to the rapid changes seen in
mid-infrared and sub-millimetre conditions, we practice dynamic
scheduling; that is, we do not pre-generate night plans, but ask at
the end of each observing block what the best thing to do next is,
given the known weather and project parameters. The success of this
approach is, of course, also based on the ability of our facilities to
seamlessly transition from one instrument to another with little or no
overhead. In software terms, when the PI submits a project with the
Phase II tool our server splits it into individual observation blocks
that are stored in a database; a tool is provided to the observer to
enable them to query the database for what to do next.
\item[Automated Data Reduction]
Critical to the success of flexible scheduling are robust, automated
data reduction pipelines that produce high-quality reduced data at the
telescope to provide instant feedback to the observer and for
immediate dissemination to the absent PI. At the JAC facilities we use
ORAC-DR (Cavanagh et al.\ 2003; Currie 2004), which in its various
instances for each of our instruments provides advanced data products,
such as source catalogues (imaging) and fully extracted
flux-calibrated spectra (spectroscopy).
\item[Observation Management]
A whole suite of software systems is in use to manage information flow
about a project, allow data eavesdropping and access and automatically
generate highly detailed project status reports for both PIs and
staff. These are described in greater detail in Delorey et al.\
(2004), where a
simple diagram of the general software architecture can also be
found. Such systems are critical to keeping the large number of people
involved in the execution of projects informed, and also generate
valuable meta-data for any archive.
\item[Transients and Rapid Follow-up]
The presence of all the systems described above makes possible the use
of a number of automated time critical operational modes, such as the
publication of any discoveries of transient events (e.g.\ flares of variable
sources, minor planetary bodies) as well as rapid follow-up of
transient events discovered elsewhere (e.g.\ supernovae, $\gamma$-ray
bursters). Because our architecture is based entirely upon
machine-readable information and well-defined interfaces, we can
integrate into alert systems initially developed for robotic
telescopes, such as e-Star (Allan et al.\ 2004). An intelligent agent that
is monitoring a detection channel of say, a $\gamma$-ray burster, can
submit an observing block to our system for sub-millimetre follow-up
using an override priority code; next time the observer at the
telescope queries the system for an appropriate block they will find
this observation and execute it; ORAC-DR then reduces the data
and provide the information to another intelligent agent which takes
appropriate action (such as informing the PI or submitting additional
follow-up observations, such as spectroscopy, as appropriate).
\end{description}
\section{The Benefits}
There are many benefits to such complex integrated software systems
such as described above. Astronomers that have been awarded telescope
time benefit from the maximization of their chances of getting their
project completed that comes with flexible scheduling. They have to
give up very little for this advantage, since our operational mode
retains many of the advantages of classical scheduling, such as the
ability to constantly modify one's observing strategy, as well as
eavesdropping access to data as it is being taken. Staff members make
use of software systems that manage the bureaucracy of flexible
scheduling (such as time accounting and removal of exhausted
projects), thus freeing them to provide science-level support to
projects. Observers at the telescope can carry out observations for
others confident that the PIs are getting what they actually asked
for. Astronomers interested in transient events can obtain data
without the need of being in constant communication with various
facilities. Archive users end up being the beneficiaries of
significant quantities of meta-data that provide an audit trail for
the provenance and quality of their data. And last, but not least, the
facility gets to maximize its scientific output without increasing its
operational cost.
\section{Concerns}
While the wide variety of automated and autonomous software systems
are geared toward maximizing observing efficiency in present
facilities, there is a concern as to their long-term effects in the
community. These are largely speculative at this point; however we
believe we have seen signs of both recently. The problem is that with
the move toward automated and staffed observing, not to mention data
mining, there are fewer opportunities for the younger astronomers to
cut their teeth on the many challenges of observational astronomy by
coming out for practical experience at a data-taking facility.
The first reason for concern relates to the pool of astronomers from
which we draw our instrument builders. These are in every case highly
experienced users of our facilities who then moved on to
instrumentation labs. Their innovative designs are often based on
detailed understandings of current instrumentation and their
experience with first-hand data analysis in the wavelength of their
choice.
The second reason for concern addresses software development at
modestly funded facilities such as our own. Our ability to provide
comprehensive software suites to our users hinges on our ability to
hire staff experienced in both scientific data analysis and software
engineering. These individuals have a top-to-bottom understanding of
the products they develop, often fulfilling the often critical ``hero
programmer'' role (Lupton et al.\ 2001). In the absence of such people, much
larger teams containing both astronomers and industry programmers
under formal project management need to be formed. This is a model
that is out of reach for many world-class facilities that are subject
to stringent funding constraints.
We suspect that the trend of serving the astronomical community a
highly-processed data product from centralized archive facilities
will only grow in the future. In order to retain a pool of technical
expertise in the astronomical community, both in instrumentation and
software, we would like to see placement of post-graduate students at
observatories working in the more practical areas of observational
astronomy.
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\reference Allan, A., Naylor, T., Steele, I., Carter, D., Jenness, T.,
Economou, F.\ \& Adamson, A.\ J.\ 2004, \adassxiii, \paperref{O7-4}
\reference Cavanagh, B., Hirst, P., Jenness, T., Economou, F., Currie,
M.\ J., Todd, S.\ \& Ryder, S.\ D.\ 2003, \adassxii, 237
\reference Currie, M.\ J.\ 2004, \adassxiii, \paperref{P4-25}
\reference Delorey, K., Jenness, T., Cavanagh, B.\ \& Economou, F.\
2004, \adassxiii, \paperref{P9-10}
\reference Economou, F., Jenness, T.\ \& Rees, N.\ P.\ 2002, Proc.\
SPIE, 4844, 321
\reference Economou, F., Jenness, T., Tilanus, R.\ P.\ J., Hirst, P.,
Adamson, A.\ J., Rippa, M., Delorey, K.\ K.\ \& Isaak, K.\ G.\
2002, \adassxi, 488
\reference Folger, M., Bridger, A., Dent, B., Kelly, D.,
Adamson, A., Economou, F., Hirst, P.\ \& Jenness, T.\
2002, \adassxi, 453
\reference Lupton, R.\ H., Gunn, J.\ E., Ivezic, Z., Knapp, G.\ R.,
Kent, S.\ \& Yasuda, N.\ 2001, \adassx, 269
%\reference Rippa, M., Economou, F., Jenness, T., Hirst, P., Tilanus,
% R., Delorey, K.\ \& Adamson, A.\ 2002, \adassxi, 144
\reference Robson, I.\ 2002, Proc.\ SPIE, 4844, 86
\reference Wright, G.\ S.\ et al.\ 2001, \adassx, 137
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\title{The Next Eclipse}
\date{2018}
\author{anonymous}
\subtitle{A Vision for Regional Autonomy}
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\chapter{An invitation and a challenge}
\emph{The Next Eclipse} is an invitation to shift our perspective on southern Illinois. Rather than seeing it as a dying region waiting for outside interests to save it, we propose that what makes it special is rooted in its status of being economically overlooked. A better future for this region will be built not by the wealthy or their politicians, and certainly not by more polluting industries, but by everyday people organizing ourselves to build a unique way of living and sustaining the life, history, and struggle of this region.
\emph{The Next Eclipse} is a challenge to build the capacity for regional autonomy in this time between the eclipses. By “autonomy,” we mean the possibility of a life outside the existing economic and political relations, the possibility of a dignified, free, and equal life here in southern Illinois.
\emph{The Next Eclipse}, finally, is a short book that has been passed hand to hand in southern Illinois, its intended audience, and shared over a far broader range. It has inspired others to think about their own regions in new ways, and there are rumors of similar projects in different places.
We are currently collecting stories from people who have lived and struggled in Little Egypt. We are interested in stories about a wide variety of topics: subsistence farming, labor struggles, struggles against racism; about fights for the forest; about what you cherish most about life in southern Illiniois. If you would like to share your stories with us, please visit our contact page by clicking here. ( https:\Slash{}\Slash{}thenexteclipse.wordpress.com\Slash{}contact\Slash{} )
\chapter{vol. 1: The Next Eclipse}
\section{Preface}
The following text was written in the weeks before a solar eclipse, the totality of which passed over southern Illinois on August 21th, 2017. In seven years, a second total solar eclipse will be visible from the same place. The two paths of these eclipses make an X across the so-called United States, intersecting in Makanda, IL.
\emph{The Next Eclipse} is the beginning of a vision for regional autonomy, and a challenge to southern Illinois to build the infrastructure for such autonomy in the time between the eclipses. It is an attempt to allow these astronomical events, reduced by local governments and businesses to nothing more than opportunities for tourism, to have some deeper significance for the inhabitants of the region.
It has been a pleasant surprise to find that the text has resonated with people in other places as well. Reading groups have formed in a handful of places around the country. We hope that the text inspires the reflections of others in their own regions, as we have been inspired by movements for autonomy around the world.
The night before the 2017 eclipse, a march led by musicians took the main strip in Carbondale, IL. A hundred or so people clapped in time and sang “Negra luna [Black moon],” a song from a musical tradition rooted in resistance to colonization. A banner at the front of the march declared “THIS EMPIRE, TOO, WILL BE ECLIPSED.”
Since that eclipse, it has become more and more clear that certainties are scarce regarding even the near future. None of us know what seven years’ time will bring. On the short list of certainties, things around which a life can be build, three things stand out:
First, it is certain that at 1:59 pm on April 8th, 2024, for 4 minutes and 9 seconds, southern Illinois will fall into darkness in a shadow cast by the moon.
Second, it is certain that we owe nothing to the institutions that prolong this empire, and that we owe everything to each other, to those working to retrieve the world from the ecocidal and biocidal clutches of the economy and its government.
Finally, it is certain that in the course of time, this empire, like all the others before it, will be eclipsed.
Nothing can prepare you for a total solar eclipse. It is worth stopping whatever else you are doing. It is worth traveling great distances for. And it is worth allowing it to take on significance in your life – not merely the dumb movements of rocks and gases, but a moment that reveals, that inspires, that ignites.
For life and joy; for freedom, equality, and dignity; for a patient, deep, and sensitive rebellion.
Carbondale, IL, February 2018
\section{1. What is an eclipse?}
In ancient Greek, éklipses meant “the abandonment,” “the downfall,” “a failing or forsaking,” or “the darkening of a heavenly body.”
Two of the most pronounced differences of the natural world – day and night – find themselves momentarily confused, reshuffled, paradoxically intertwined.
In those moments, all the ranks, badges, and hierarchies that bind the powers of the earth, are revealed for what they are: the stupid games of humans, who have forgotten their place in the mortal order of things. The eclipse reminds us, contrary to the meticulously structured optical illusion of this social system, that it is the sun and not money that breaths life into the inhabitants of earth.
The fact that the eclipse has been viewed by the ruling class of the area as a momentary economic manna from heaven only underlines their idiocy, their disconnection from the world.
The fact that we tie our fate to them, that we allow them to decide the fate of this beautiful region, only underlines ours.
What is an eclipse?
an abandonment of those dependencies which prevent our lives from flourishing;
a downfall of those powers that destroy us;
an honest recognition of what has failed and forsaken us;
a darkening of those entities who seek to decide our fate as if from the heavens;
What is an eclipse?
Let’s allow the eclipse to be an invitation to be present, together, before the challenges we face.
Perhaps \emph{to eclipse} is something we do. Perhaps an eclipse is something we become.
\Slash{}\Slash{}\Slash{}
This is a call. It is meant for those who hear it.
We’re not trying to argue. We are writing for those who have all the arguments and reasons they need. Consider this a flare shot into the momentary night of the totality:
for those who are looking,
for those who are sending out flares of their own,
for those who may have caught sight, through an accidental glance, and recognize a part of themselves in what they see.
For those who understand that we are living through the end of a civilization, and who want to build a new world within its empty shells, its ruins, its ashes, its wake.
For those who see that such a world will not come from the politicians or divine economic forces, but only from our own prolonged and committed efforts.
For those who have given up faith in all the mechanisms of “change,” and are ready to assume responsibility for their own future.
For those who understand that there is no hope on the horizon, unless we create it.
We offer no argument. We only want to state the obvious and point the direction that follows.
\section{2. What is obvious?}
We all know it is ending.
Trump is not an aberration. There will be no “return to normal.” The damage has been done. America is over.
For some of us, America – while flawed and incompletely realized – was inseparable from an inspiring vision of human progress. It is therefore not without some pain that we watch it become a parody of itself, its hallowed institutions transformed into reality television, its ideals turn into propaganda for the naïve, its most evil traditions of white supremacy, exploitation, and sexism once again resurgent.
For others of us, we say “good riddance” to a country whose founding values were inscribed in blood-red hypocrisy, and whose world-historical legacy is to have accelerated the genocidal and eco-cidal forces of capitalism.
But whether it is a moment of solemn acceptance or celebratory joy, the truth is obvious: America is over. The question now is whether we have the courage to go beyond it, or whether we will accept its zombie-like afterlife, marked by a blatant effort at total control over its population.
\Slash{}\Slash{}\Slash{}
At a more local level, we can see the writing on the wall: the economic fate of Carbondale is tied to the University, which is tied to state funding. State funding has revealed itself to be fundamentally unreliable. With Rauner, a process that has been underway for decades was merely accelerated to the point where it has become undeniably clear. The state cannot be depended on to care for the fate of this region.
To some, this has been clear for a long time. The university has been ravaged for decades by a rotating managerial class that has shown itself unable to chart a path that works for the university, let alone the region in which it is embedded.
A new Chancellor arrives, carefully projecting a gruffy masculinity designed to assure us that daddy is here, that someone is going to save the day, that he’s done it before. How many times will we fall for this? We know how these people operate: cut some things, build some things, send out applications to the next University. Progress on your C.V. is all that counts. The chaos of southern Illinois has been a ladder for too many administrative entrepreneurs.
The only plan that will ever count as “realistic” to that managerial class is to “streamline” the university. Liberal arts will be increasingly consolidated into fewer departments, and corporate money will be attracted to build the robots and drones that will displace workers, surveil everyday life, and wage war against anyone who challenges the power of corporations to turn the world into a giant open air prison. This is the only real growth industry of our time, hidden behind the innocuous banner of ‘tech.’ The university will be brought into the twenty-first century, a bit late, as a research\&development extension of the powerful.
In this context, many are looking for a way to jump-ship, to leave town and find some stable employment elsewhere. But there’s not enough room in the world’s gated communities for everyone. Instability and precarity are the present and future of this world. You can desperately try to save your own hide, but the odds are stacked against you. Another path must be created for those of us who understand that stability at the expense of others is an illusion, always threatened by the fear of those excluded others. Another path must be made for those who want to create the conditions for a good life – abundance, comradery, virtue, compassion – here where we call home.
Such a path cannot be found on the existing political or economic map. It is off the boring charts of liberal and conservative and libertarian and socialist. It is a road that must be made by walking.
There are some, in their own places, who have taken steps in this direction. Small experiments in resurrecting a sense of collective life, a concern for the fate of a whole community. A town of 3000 people in the hills of Spain, Marinaleda, has created an agricultural co-operative that is owned by and employs the whole town. They deliberately chose labor-intensive crops to make sure they could give everyone work. If you help build your house, its yours for 15 euro a month. There are no police, because there is no crime, because there is no poverty. The city is cleaned every few Sundays by its own people, who make a party of it. While the unemployment rate in Spain is approaching 50\%, and while the foreclosure crisis displaced hundreds of thousands, Marinaleda remains insulated from these market forces because it has built material and political autonomy at the local level.
There are other examples, each a unique attempt to forge a different world. The ZAD, or Zone to Defend: an autonomous zone the size of Carbondale and Makanda, composed of occupied farms and blocking the construction of an airport in the north of France. Two dozen small, interlinked communes inhabit the zone, building on it a world that is inconsistent with the airport and the world that demands it. A few times a year, tens of thousands of people flock there to express their support and show their commitment to defend the zone from eviction.
Rojava: in northern Syria, the Kurds took the civil war as an opportunity to launch a revolutionary project in democratic autonomy against capitalism, patriarchy, and the state. They created a form of government that is answerable to neighborhood assemblies and have shown themselves the most effective combatants against ISIS.
On every inhabited continent there are tiny worlds breaking off from global capitalism, sometimes quietly, sometimes accompanied by a fight. People building the possibility of a world beyond this imploding civilization.
Meanwhile, in Southern Illinois, people are placing their bets on an eclipse to provide a windfall of cash\dots{} for what? So they can continue the same course for a few more years, against all the winds of history that are desperately trying to blow us in another direction. Why couldn’t a dozen towns in Little Egypt go the direction of Marinaleda?
\Slash{}\Slash{}\Slash{}
There are some of us who feel ourselves to be inseparable from this region. Some others are scrambling to get out. In the latter group, many came for work, at the hospital, at the university. Some were raised here with the idea that their future is obviously elsewhere. No matter how many years we stay, many of us still think we are merely passing through. This is a local symptom of a wider phenomenon.
In the last few decades, the economy’s imperative to go where the money is has uprooted people from their places on a scale that is historically only paralleled by wars and colonization efforts. With that uprooting, we are sucked out of our networks of family and childhood friends, transformed into isolated individuals or nuclear family units, whose sole responsibility is to care for our small bubble. Nothing is worth struggling for in any particular place; if things get too hard, just move.
Of course, not everyone can. And not everyone will, even if they can. Two types of people are emerging: those who feel so connected to a place that they refuse to uproot themselves without a fight, and those who refuse themselves that contact with reality. The latter surf on the waves of a turbulent economy, thinking their work is more important than the ground they stand on to do it. Life is a highway and places are pit-stops.
The relation to every place as somewhere one is merely passing through is what prevents the kinds of struggles that are needed from emerging. It is what makes every particular place expendable.
Creating a future requires allowing ourselves to develop and take seriously our connection to a place. To recognize its fate as our own.
\Slash{}\Slash{}\Slash{}
On April 8th, 2024, a second eclipse will pass through Little Egypt. We can let these two eclipses be nothing more than an astronomical coincidence. We can let the movements of planetary bodies remain separate from the movements of our hearts, let their migration have no effect on our social life apart from being two opportunities to scam the tourists. We can do that.
But why? Aren’t we looking for something? Aren’t we waiting for something to reorient us, to trigger the transformation of life that is necessary to survive, let alone to thrive?
Let the next eclipse be ours. Let the first eclipse be a period, a hard stop that brings relief to the long winded speech of those who have told us this is the only life on offer, there is no alternative, you’d tear yourselves apart without us, and on and on. Period. Thank you for your thoughts, but now its time for some of our own. What can be accomplished in seven serious years, here in Little Egypt?
\textbf{Economic autonomy}. The ability to meet the needs of Little Egypt through growing and producing in Little Egypt. With it, the confidence that, were the global economy to collapse, we’d be alright – better maybe?
\textbf{A social safety-net from below.} The ability to provide care for those whose health and well-being the state has abandoned, or is always a law or two away from abandoning.
\textbf{Ecological restoration and defense}. The ability to not merely beg those who call themselves our leaders to stop fracking, but to physically prevent such a disastrous industry from poisoning our region.
\textbf{A sense of collective fate}. Forms of celebrating the forgotten history of resistance, of feeling ourselves as we really are: fragile links in a human story of struggle.
How far can seven years take us? Seven years from now, will we have squandered our lives working to pay off debts and rents to those who we feel, deep down, that we owe nothing?
There are no maps for where we must go. There is a direction, and a path to make by walking.
\section{3. Fragments of a Future}
Every block has a garden and a tool library. Houses are fixed up and owned through use and care. Contracts are for people who hate each other, and they still get written up from time to time, but shelter is not something you deprive even someone you hate. In the garden, the neighborhood watch meets twice a week to practice de-escalation techniques and nonviolent communication, and trains for situations when those don’t work. The strip is dotted with every variety of eatery, collectively run with locally grown food and some specialty items acquired through autonomous trade routes. We always have enough, but we don’t have everything all the time. The excitement around sharing something special returns to us.
\Slash{}\Slash{}\Slash{}
Its a shitty morning. Its the day of your twice-monthly shift for trash collection, because we still make trash for the time being. Your crew gets up early, because you all want it to be over by lunch time. As you roll up in the bio-diesel powered truck, someone gets the idea that turns the mood: death metal. You will blast death metal as you all toss cans of trash into the truck. Its perfect, as if the genre, invented decades ago, existed in a sort of limbo until it discovered its sole purpose as the soundtrack to a communal trash collection team. Those sleeping in along your route yell for you to turn it down, but whatever. When its their shift on trash duty, you promise yourself, you’ll let them get through it however they need to.
\Slash{}\Slash{}\Slash{}
There’s a bonfire again on the strip, this time for the Tomato Fertility Festival, which has moved out of clandestinity and into the open air of the town. The chant of TO-MA-TO echos throughout the neighborhoods, as marches start from various gardens led by children carrying baskets of the first tomato harvest. Gallons of the red fruit are poured into a cauldron over the fire and a sauce is cooked slowly amidst dancing, which is still more fun because its in the streets.
\Slash{}\Slash{}\Slash{}
You can’t get out of bed. You can’t stand the light. Nothing happened to you; there isn’t any reason. You just can’t see other people, hear their voices, feel their touch. All that you can do today is feel. And even though it feels like pain, you don’t mind it. It has messages for you, which you can hear if you have the time to listen. And you do now. You’re allowed to feel. No one judges you or shames you and you won’t get fired since there are no jobs. There’s always work to do, but work and life and fun and play are integrated, and none of those things are jobs. The work you are responsible for can wait, or someone else can pick up your slack for the time being. You are allowed to feel. You are encouraged to feel. You are free to feel. And there will be no penalties, no consequences for staying in bed all day, all night, and for however many days it takes for you to feel all the parts and moments of that feeling. When you emerge from the fog, you remember you were cared for, and your responsibilities were cared for, and you are refreshed.
\Slash{}\Slash{}\Slash{}
Hospitals are run as cooperatives. Specialist doctors and surgeons commit blocks of time toward patient care and participate in skill share, which trains other health care workers to the extent they can. Through the collective nurses have become household physicians, the family doctor. Cooperative Hospitals provide access to tests, medicine, and are hubs for emergency treatment when a nurse cannot be accessed. They serve the severely sick, those with ongoing, intense treatment plans, and are sterile environments for surgeries, but most ailments are treated in the home. Babies are born where mothers want them to be – at home, at a house run by midwives, in the hospitals. Notably, with a large-scale diet shift from processed foods to regionally grown and raised, organic meat and produce, in combination with the shift from jobs to collective work forces which have reduced anxiety and depression, the health of the general public has increased dramatically. When people are terminally ill, they are placed with their families and loved ones, provided end of life care with a nurse (there’s usually one in every communal unit), and are allowed to die in peace, however they desire. While we once required the need for death doulas — emotionally mature individuals who could guide the unfeeling through trauma— we now are able to take the time we need to mourn, to feel, and to celebrate the life of those who leave.
\Slash{}\Slash{}\Slash{}
A group of kids and adults are repairing a broken node on the solar powered mesh network that keeps the internet running, free from the infrastructure of the big telecom companies who still dominate in some places. A few trucks are moving the day’s harvest to neighborhood food hubs, where young kids load bags of produce onto bicycle trailers. You’ve had the longest day, you think, as you sip peach brandy on your porch. What did it start with? Death metal, right. And then there was the Yemeni festival for lunch, then someone asked if you would help mediate a conflict they were having over in the Arbor district – a fight about someone sucking up all the block’s electricity, which admittedly tested your patience. Then there was that walk with that someone to that persimmon tree, the one with the candy-tasting fruit the size of tomatoes that you had kept secret til today. Then the hour of canning while the old woman read aloud from One Hundred Years of Solitude. Then the cleaning out of the rainwater filter, a quick but messy job. Then the dinner you shared with the sunset. And now the brandy, and the sound of music growing down the block. But your friend is on their way over, and you plan to continue tonight the friendly debate you’ve been having for a decade, since even before life became the pleasant chaos that it is: what is happiness? Its a question that doesn’t get old.
\Slash{}\Slash{}\Slash{}
Across fires and under stars, we share stories of how silly we were. We have to look at it as silly, so as not to fall into a rage at the ideas and practices that our ancestors allowed to decimate so much beauty in the world.
“It turns out people like to create things, and like it even more when what they create is useful to others. This obvious fact about our being, so evident all around us, was obscured by the foggy lens of ‘the economy.’ They had actually convinced some of us that it was money and selfishness that made people work! Having never actually allowed people to live without scrambling for their basic necessities, the economists never actually got to observe free people undertaking free activity. As if humans before the economy were isolated misers, as if they weren’t born from and dependent on one another. As if our greatest joy wasn’t to be found in being the cause of joy to others!”
A child speaks up: “But what was ‘the economy’ you’re all always talking about?”
Old timers laugh: “We didn’t know either! That’s what was so crazy about it!”
A more serious voice rises: “When you were in it, it was hard to see it for what it was. When you were in it, it just looked like ‘the way the world worked’: you had to sell your time in exchange for some paper or numbers, in order to buy the ability to live and sell your time more. You got a weekend, a few holidays, some vacations if you were lucky, but otherwise your life was owned by the companies you sold it to. At the end there, it seemed like people turned themselves into little corporations, and forgot entirely what it meant to be free. Now, outside of it, we can see it more clearly: it was a way of controlling us, of governing us. Of keeping us ignorant of the fact that we didn’t need the companies and the governments who said we needed them.”
“But how did such a thing ever take hold of everyone in the first place?”
“That’s a very good question.” The fire crackles. “Let me tell you about our ancestor, Tecumseh.”
\Slash{}\Slash{}\Slash{}
Tecumseh was a Shawnee Indian chief, who led a rebellion against the colonizing forces of early America. In 1811, a year before the rebellion he fomented broke out, Tecumseh passed through southern Illinois during his ceaseless efforts to unite the tribes. He carried with him a bundle of sticks, demonstrating that while a single stick can be broken, a united bundle holds under pressure. This image was so powerful it was eventually taken up by his – and our – enemies, to signify their commitment to a united force of colonization and genocidal conquest.
After Tecumseh’s visit through southern Illinois, the New Madrid fault line let loose an earthquake that reportedly rang church bells as far as Boston. The most powerful active fault line in the North American continent, it slumbers, for now, in the southernmost parts of Little Egypt. The 1811 quake was taken as a sign of the justness of Tecumseh’s cause.
“But what was his cause?”
Well, as he put it:
* ‘No tribe has the right to sell land, even to each other, much less to strangers \dots{} Sell a country!? Why not sell the air, the great sea, as well as the earth? Didn’t the Great Spirit make them all for the use of his children?’
You see, the game the economists and the others who controlled us played was to tell us that people like Tecumseh were not our ancestors. That they were backward or savage or that their way of doing things would never work again. And so they gave new names to the genocide and the destruction of all the possibilities in the world. They called them ‘progress,’ and they taught us that we were better than all those folks who’d lived for so many thousands of years.
\Slash{}\Slash{}\Slash{}
\emph{We construct tiny utopian glimpses because they are potent exercises in unfreezing the imagination.} \textbf{For too long its been easier to imagine the end of the world than to imagine the end of capitalism}\emph{. Maybe the image of chaos that we are told lies beyond this tightly controlled society is just the ruling class’s view of what autonomy would mean: a world that could not be controlled from above. A world of free communities, unsubmissive to the rule of money.}
\section{4. Autonomy}
Autonomy. It’s a word that today has more of a direction and a practice than a meaning, per se. Around the globe, from the Zapatistas of southern Mexico, to the Kurds of northern Syria, to networks of communes throughout Europe and North America, autonomy is the dream taking shape.
We could define it as collective self-determination, the ability for the people of a place to chart their own future. To eclipse the power of financial, industrial, and political elites.
The obstacles to autonomy are twofold: on the one hand, a global economy that wraps people’s everyday lives in an international network of money exchanges, and on the other hand, the governments and their police whose job, at bottom, is to keep it that way.
Struggles for autonomy, then, involve both building and fighting. Building the means for regional production outside the existing economic order. Fighting for the right to organize our lives in ways are inevitably contrary to the laws of the state. Those laws, whatever their stated intention, have the fundamental purpose of keeping us dependent on the institutions that are destroying the earth and its various worlds. Reducing us to isolated individuals, whose sole course for freedom involves submission to the gambling ring called the economy.
Autonomy is about creating different freedoms. Creating different worlds. Creating the conditions to create ourselves, with all the potential dangers and joys that such a project entails.
\section{5. How?}
How would we do it? How would we eclipse their power?
a. Many of us are already doing it. Around the continent and around the region, networks of organic farms are self-organizing. Spaces are being taken over and filled with people and projects for the struggle. What is necessary is not some party or political organization that sucks us into the dying gasps of a system that, with Trump, has shown its true colors. We are already a party, partisans, of a world that is inconsistent with this one. Acknowledging this fact, deepening our cooperation, and extending our ambitions are our first tasks.
b. Start with desires, and build what is needed to fulfill them. None of us want a life reduced to blandness and scarcity. We want a luxurious life that can be shared with others, and we’re willing to work for it. A craft brewery or ice cream company that builds its own local production network can be a partisan project, building within the money economy a set of skills and resources that could just as easily be detached from it. Create something, share it, and link up with others.
c. Don’t try to do everything. Make friends who have the skills you don’t have to accomplish what you want. We need engineers, farmers, computer scientists, permaculture experts, listeners, singers, thieves, nurses, historians, visionaries, carpenters, plumbers, and a thousand other people who love the skills they’ve developed and want to share them. Make your skills available, and look at something you can’t do alone as an opportunity to meet someone new.
d. What passes for “political debate” today is a trap. Political discourse today is designed to pidgeon-hole us into pre-defined, easily manipulated categories. If you have a neighbor or a high school friend that is on opposite sides of the political spectrum, find a common practice or form of sharing material things that can create common ground for a relationship. Chart a course off the political spectrum with unpredictable friendships.
e. Build a culture of resistance. Non-cooperation with the police and the state, solidarity with those who resist. Turn out to demonstrations and make them true expressions of our collective capacity to transform life and the city, if even for a moment. Ask yourself how you can best contribute to creating or sustaining joyous chaos, a breakdown of the sad reign of normalcy, and make a plan with those you know.
f. Diversity is strength. Racial and class diversity, but also ideological, spiritual, age, and any other kinds. We want a world that values each of our perspectives and unique abilities to contribute, and this is an ethos that needs to be in the genetic code of our struggle. Keep in mind, the most effective tool of the powerful is division along racial, ethnic, or other lines. Within any identity, there is more difference than there is across its boundaries. The only lines that matter are ethical lines: how you are, not who you are; what you want, not where you come from.
g. Think ethically and strategically. Breaking out of the structures of this world is not something that will happen simply because it is a good idea. Good ideas lay buried in the brains of millions of dissidents. Similarly, rigid moral principles paralyze people from acting in a context where no action can be safe from a context of suffering. I type this on a computer, using electricity created from burning coal, which is warming the atmosphere and destroying the lungs of people around the globe. Morality creates guilt around these facts, which are beyond any of our control and therefore responsibility. Guilt paralyzes and brings out nastiness, resentment.
What is needed is a strategic ethics, which starts from what is practically possible in any given situation, and is oriented toward expanding those possibilities for the next moment.
Morality commands, whether it is from a church pulpit or a conscience. Ethics, in contrast, invites us to steer a course through the undesirable extreme consequences to grow more powerful in each unique situation.
For our broad situation, there are clear extremes we want to navigate between: on the one hand, we want to steer clear of what is normal, which is the destruction of the world at the hands of the economy. On the other hand, we don’t want to catalyze the outbreak of open civil war in a context where the state and right wing paramilitary forces can be deployed to crush everything we love. Veer too far from normal, without having built enough strength, and the reactionary forces will be shipping us off to the camps. Come too close to normal, and our projects will be captured in the economy and become a nightmare version of what we hope for, as has happened so many times before.
\section{6. Which Future Past?}
Fifty years ago, no one could have imagined the world we have now. Fifty years from now, the world will have transformed several times over in ways that we currently cannot imagine. This is beyond question. The only question is whether the terms of these changes will continue to be set by the interests of the wealthy and their political lackeys, or whether a new historical force will enter the equation.
Eclipses are useful to historians, because they allow the precise dating of events that otherwise may have been recorded unreliably. What will these eclipses mean to the future? A moment where the sublime movements of astronomical bodies was reduced to a marketing gimmick for a dying region? Or a moment when, however subtly, some otherwise inconsequential earthlings began seriously organizing to save themselves?
\chapter{vol. 2.1: Frozen in Place}
\section{Repairing Our Relation to Carbondale’s Rebellious History}
The following essay is a beginning to the second installment to \emph{The Next Eclipse,} the beginning of a longer, deeper project of repairing our relation to history. History, in order for us to have a relationship with it, must be local. But local history must be informed by an understanding of the broader political and economic transformations, of which the changes in a particular place are only an instance. The guiding existential hypothesis of this text is the following: if things feel meaningless, without sense or direction, it is because we have lost the capacity to understand the historical forces that control our present and shape our future. The aim, then, is to reconnect our existence with the historical forces that have shaped it, and to draw attention to what was lost along the way. This aim is \emph{strategic,} because it outlines our reality in terms of the power relations that define it.
\section{Introduction}
Southern Illinois University Carbondale is in crisis. The university is hemorrhaging students and the state has revealed itself to be an unreliable source of funds. Everyone agrees that something needs to change. Many have given up already: their applications are out, their houses are for sale, they are trying to find a way off a sinking ship.
There was a time when crises could be seen as moments of opportunity, moments when the problems with the existing social and economic system were revealed and genuine questions could be asked about new directions. Since the 1970s, however, a new form of thinking has become dominant, sometimes called “neoliberalism.” According to neoliberalism, \emph{there is no alternative} to the existing social system. The only possible world is a world where everything is evaluated according to one measure: that of the economy. Crises today, rather than an opportunity to reflect on new directions, are used as an opportunity to force more and more aspects of life into economic values. The only cure we are offered is more of the same poison.
Chancellor Montemagno’s plan is an exemplary case of this. Like so many other neoliberal gestures, it is an attempt to centralize power within the organization, and discipline it to make it attractive to capital investment. No values other than economic values count when it comes to attracting capital: drones that will surveil and kill, Homeland Security to deport our neighbors, police to lock people up, fossil fuels to continue the destruction of the conditions for human life on the planet? Anything, as long as its money. The only “solution” on offer for the institution is to more deeply collaborate with the institutions that are causing the problems.
But neoliberalism didn’t come out of nowhere: it emerged as a response to social movements that challenged the functioning of the American Empire to its core. It was a form of government that was developed to destroy the welfare state, build up the prison and policing system, and tame sites where rebellion had broken out during the 1960s and 1970s – among those sites, the University was one of the most powerful for generating a critique and opposition to capitalism and the wars that sustain it.
If we look closer at those social movements, we see that they were fighting against the same problems that we are concerned about today, and they were developing solutions that were based on principles that many of us hold today. Principles of egalitarianism, of autonomy, of community, and of ecological responsibility. We must rediscover and pick up the baton from those struggles, long repressed in our memory. Any proposed solutions that do not address the fundamental problems of our society – problems that have been evident for almost 50 years – will fail, and will continue us down a nightmare path of endless war, ecological catastrophe, and widespread immiseration.
The University can, and should, be a site where these problems are being faced head on. It should be a site where we develop the means to break free from the economy.
***
\section{CHAPTER 1: THE UNIVERSITY THAT SHOULDN’T HAVE HAPPENED, BUT DID}
Southern Illinois Normal College was opened in 1869, thirteen years after the first train stopped in the newly founded city of Carbondale. Carbondale had been founded by Daniel Brush, when he heard that there were plans for a railway to be constructed through the region. He hired a surveyor to determine what the most likely path of the railway would be, and planted Carbondale in that path so it could become the center of rail traffic for Little Egypt.
Little Egypt, the name for southern Illinois since the early days of European colonization, itself has always been a resource colony for business interests located in larger midwestern cities:
“In many ways Southern Illinois has a ‘colonial economy’, one controlled by outside financial interests. Outside interests have developed the regions mineral and timber resources, its shoe and work-clothing factories and the rail transport for such development. These companies have employed local labor, even recruited labor to come to the region to work, but have taken the profits from their operations elsewhere. To a degree, the corporate base of Chicago and St. Louis has been built on Southern Illinois labor and resources.” (Harper, 10)
This attitude of business interests toward the region, and the determination of southern Illinoisans, helped fuel massive and intense labor struggles throughout the 19th and early 20th centuries. For coal miners and their families, the fight for unionization was a life or death struggle, since non-unionized mines meant not just starvation wages, but lax safety protocol that time and again led to collapses or explosions that killed dozens of people at a time.
Throughout this era, Southern Illinois Normal College was a small teachers college a few thousand students at most. The city of Carbondale was the major connection with the rest of the world – which also meant the site from which the national guard would be deployed to beat up striking miners and protect scab laborers.
From the 1930s through the 50s, many mines began to close, leaving small towns throughout the region without any ability to participate in the money economy. Interestingly, the mine closures were not a result of coal running low, nor as a result of the ecological concerns that we have today. Rather, they were closed as a part of a global strategy to shift from coal to oil as the major industrial fuel source, a decision that was made specifically to break the power of the coal unions.
The coal unions played a decisive role in early 20th century labor struggles because they had the privileged ability to literally paralyze the economy. And they use this power to help striking workers around the country win basic labor rights. This power of coal workers was a vulnerability to industrial capitalists, who shifted their fuel to oil because it required less labor to both produce and distribute, and could be more easily rerouted around blockages posed by workers in any given area. The coal mines closing left the region, already “undeveloped” in capitalist terms, in a localized depression.
And this was the regional condition in which Southern Illinois Normal College would be transformed into a completely unlikely University, ten times its previous size. The fact that the region was viewed as backward and violent, combined with post world war 2 investment in higher education through the GI Bill, were seized upon by a man of some extraordinary talent: Delyte Morris.
Morris was appointed President of the new University in 1948, after a quick succession of unsuccessful Presidents. Morris had two big ideas that guided the remarkable growth of the University: first, to pitch the University to the State as a development project for a troubled region, and second, to draw upon alternative visions of higher education which were by no means well-established at the time.
Major research universities tend to be located in or near major cities. The idea that one could – or should – be built in what we would today call flyover country was unorthodox. But Delyte toured small towns throughout Little Egypt to pitch the idea of a “open university,” one that would be a resource for developing economic and cultural life throughout the whole region. His philosophy of education related to this: the University was not to prioritize inquiry and reflection detached from real life. Naturally, the classics of higher learning were to be on offer, but not the centerpiece. One of Delyte’s hires was Baker Brownell, a philosopher turned radical educator who developed regional educational programs for the University and author of the rhapsodic book \emph{The Other Illinois.} According to Brownell, in response to the stuffy, Ivory tower vision of education that privileges reason detached from experience,
Southern would reply, “Reason with a small r is the only useful kind of reason. The training in its method, its beauty, its triumphs, and its uses is surely important. But reason segregated from the community of men is sterile. Withdrawn from the experiences, the disasters, the problems, the delights of the human adventure it is cracked and futile. For these things are the crucible in which reason is created. Neither reason nor any other single function of our many-stranded life is the key to it all.” (241)
This unique philosophy of education is what gave rise to the first ecology program at touch of nature, a hodgepodge of classical academic and vocational training distributed throughout the region, as well as earlys teps toward racial integration and handicapped accessibility. But the program that most embodied this philosophy was the Division of Area Services, pioneered by Baker Brownell. This program sent out teams of academics and experts in various fields to conduct community inquiries and discussions about how to develop small impoverished towns in the area. The delegates from the University were not to impose their own ideas, but to listen to the needs and desires of the communities and figure out how to make their plans a reality.
Unfortunately, since many of those plans involved attracting outside capital in the form of factories, they were not able to be realized. But imagine for a moment if the task was to specifically develop the means for life that could allow for local production of basic needs – imagine if rather than the assumption that “development” meant “integration into the capitalist economy,” the aim instead was to help communities build their own autonomous infrastructure outside of it. If that path had been taken at the time, decades of poverty and all its attendant social problems could have been avoided.
But that’s not how it worked. Instead, the University did indeed become a center of capital investment in the region – the economic engine that we all know. And it did grow into an unlikely major research institution, responsive to the local region while attracting students and scholars from all over the world. And, in due time, the insistence on connecting reason with life came back to Delyte in a way that he couldn’t have expected, and ultimately led to his downfall.
***
\section{CHAPTER 2: REASON REBELS}
When reason is connected with life in a society that is hostile to life, reason leads to rebellion. This is what happened in universities across the country in the late 1960s, and SIU Carbondale saw some of the most intense outbreaks of a rebellious reason of anywhere else. In order to understand why the student movement was so intense, we should consider, among other things, the way SIU had encouraged students to think freely, outside the logics of the state and the economy. No single faculty member better embodied these values than Buckminster Fuller.
Fuller was a world renowned intellectual, hailed by some as the Leonardo Da Vinci of the 20th century. He was critical of both American capitalism and Russian state socialism, and argued that a political revolution was destined to fail. Instead, he encouraged his students and audiences the world over to initiate a design revolution: to redesign the conditions of life, to create \emph{livingry} instead of weaponry. Fuller would hold massive lectures, sometimes outdoors, speaking for hours on all subjects. His philosophy of education was a radical extension of Morris’s own vision of a university open to all:
“We should do away with the absolutely specious notion that everybody has to earn a living. It is a fact today that one in ten thousand of us can make a technological breakthrough capable of supporting all the rest. The youth of today are absolutely right in recognizing this nonsense of earning a living. We keep inventing jobs because of this false idea that everybody has to be employed at some kind of drudgery because, according to Malthusian Darwinian theory he must justify his right to exist. So we have inspectors of inspectors and people making instruments for inspectors to inspect inspectors. The true business of people should be to go back to school and think about whatever it was they were thinking about before somebody came along and told them they had to earn a living.”
Bucky and his ideas were a major influence on the counterculture of the sixties, his geodesic dome design springing up in communes around the country.
His ideas, and the wider counter-culture, was active on campus and around Carbondale. The aim of the counter-culture was not merely to do drugs and have long hair, as so many stereotypes today would lead us to believe. Actually, people were building organizations and forms of life that responded to their own needs, without asking for permission from those in power.
The Women’s Center, now an established non-profit, was begun by a group of women who saw a need for a home for those escaping domestic abuse. So they rented a house and created one. The Black Panther Party, whose Carbondale chapter began in 1968, created a free breakfast program for local children, a free medical clinic, and the first food co-op in Carbondale, which brought in weekly shipments of eggs, bacon, and vegetables from local farms. There was a health food store run by members of a commune located outside of town, a cheap dental clinic, endless music, radical newspapers, an LSD crisis-hotline, and even a drug testing collective that checked for toxic additives to recreational drugs coming into town. The drug testing collective was called “Synergy.”
On campus, students developed a Free School, open to anyone, where people could collectively pursue subjects oriented toward expanding their sense of joy and meaning. There were classes in Zen Buddhism, Yoga, philosophy, and skill shares in everything from building to “making love in the fields.”
And these expressions of the world people were trying to build – a world of local agricultural production, of sharing, of food for all, of a harm-reduction approach to drugs, of support for the most vulnerable in society and joy in one another’s presence – were connected with the struggle against the current system and its injustices. This was reason connected to life at its best: people freely coming together to creatively solve pressing problems in their communities, using the university’s resources – with or without permission – to improve the lives of everyday people.
In the late 60s, protests against racism and sexism on campus were building, as well as an anti-war movement that would eventually transform the course of the entire university. At bottom, the counter-culture students were rejecting not just the specific war in Vietnam, but an entire social system and economy that was premised upon war, racism, and destruction of the environment. And the strategy for taking on such a monstrous thing was the same as that of the coal miners 50 years earlier who fought, not merely for their own higher wages, but for the rights of working people everywhere: paralyze the functioning of everyday life that allowed the economy to operate. Also, just like in the coal miners struggles, arson, sabotage, and bombings were used to gum up the wheels of the system. In 1968, a bomb was placed in the Ag building – detonated in the middle of the night, so that no one would be injured. In 1969, Old Main was burnt to a crisp, presumably by student activists\Slash{}arsonists. Again, no one was hurt.
The focal point of the local anti-war movement was the Center for Vietnamese Studies, a research center funded by a million-dollar federal grant to advise and provide technical support for Vietnam when the war ended. Students had read about a similar center at the University of Michigan, in which it was revealed that there were CIA operatives working there. One of the faculty members associated with the CIA faction in Michigan, William Fischel, was hired for the center at SIU. This was the source of the allegation that the Center for Vietnamese Studies was a CIA front. Apart from that, it would have been opposed anyway as a symbol of colonial development in a country that America had been murdering people in daily. As one faculty member opposed to the Center put it, in reference to the center’s mission of post war “planning”: “you’ve planned enough already.”
The rebellion began after the Nixon administration expanded the war in Vietnam to Cambodia. Students marched, smashed some things, and about a hundred set up camp on the train lines, blocking train traffic through town. This action brought the Illinois national guard in – [the national guard which had been created in 1877 to beat up workers in a nationwide railroad strike, which had led to the first general strike in American history, which took place in St. Louis, where workers took control of the city for three days before being beaten and shot into submission by a small army raised by the ruling class (this ruling class victory was commemorated every year in the so-called “veiled prophet” parade, in which arms were displayed led by a Klan figure. The tradition continues to this day as an exclusive gala.)] When on May 4, 4 students at Kent State in Ohio were murdered by the national guard, students went on strike and took over the town.
Days of streetfighting ensued. Students, out of town rebels, and community members, took on the police and the national guard. Eight days of riots culminated in a march to the President’s house, which was smashed up. School was cancelled for the remainder of the semester, and all students received full credit for the classes they were enrolled in.
What needs to be understood is that this was not merely childish acting out or mere chaos: this was a rebellion that followed a conscious an coherent political strategy. In the face of a business that is exploiting and threatening the lives of its workers, the proper response is to strike for better conditions. In the face of a society is that is powering a war machine that is murdering people both at home and abroad, the proper response is to strike – to prevent that society from functioning.
This event spelled the end for Delyte Morris, who had already outstayed his welcome as far as members of the Board of Trustees were concerned. He was stripped of all his Presidential powers, and consigned to a marginal, symbolic role.
The irony is that the rebellion of May 1970 could be aptly described as the fruit of a philosophy of education that Morris endorsed in principle, but whose consequences he couldn’t see. To connect reason with life, in a society that produces horrors, is to invite reason to rebel. The students took risks – to their lives and livelihoods – based on their conviction that the world could be changed, their correct assessment that the official channels were not willing or able to change it, and their sense of justice that this change could not in good conscience be postponed. So they became what all great people become: historical actors, who recognize that \emph{now} is the only time to act in.
***
\section{CHAPTER 3: THE REACTION, OR, THE AGE OF DEPERSONALIZED AUTHORITY\Slash{}CONTROL}
[After the student rebellions from 1968 to 1970] the university’s development was sharply arrested\dots{} [T]o a large extent Southern Illinois University lost its momentum, its vision, its leader. It has been largely frozen in place since 1970. Its future became hostage to a frightened board of trustees, a restrictive state legislature, and false impressions created during the events of Morris’ downfall.” (Robert L. Harper, \emph{The University That Shouldn’t Have Happened, But Did!,} 4)
What could it mean for a university to be “frozen in place”? No doubt, things have happened, lives and careers have been led, time has passed and things have changed. And yet, this metaphor of being “frozen in place” somehow rings true: development has been stunted, the contradictions and tensions that a generation sought to resolve have been maintained by ever increasing levels of force and novel forms of control. The wrong things change, and the things that so many struggled to change remain the same.
In a sense, this is what the role of governing powers has always been: to freeze a society from developing beyond the need for them. In the 1920s, when the labor movement was at its most militant, the U.S. government pioneered a strategy of counter-revolution: use direct repression against organizers, associating them with foreign governments, killing them, deporting them. And then, to hamper the ability for communities to continue organizing, pass laws that allow the police the ability to raid and disrupt those communities. In the 1920s, this meant Prohibition of alcohol, which was used to target working class immigrant communities who were accused of being the most radical segments of the labor movement.
This drama played itself out in Williamson County, Illinois, with a catch: the police in Williamson County, at the time, were themselves “corrupt,” i.e., they tended to support the union over the federal government. As a result, the wealthy business interests of the county had to invite S. Glenn Young, a former federal agent and Klan organizer to lead a campaign of “cleaning up” Williamson county, targeting the immigrant labor movement under the veil of enforcing Prohibition. This led to the fracturing of the labor movement into bootlegging gangs, and waves of violence that recall the gang warfare under the War on Drugs today.
This strategy was how, in the wake of the first world war, the U.S. government managed to “freeze in place” the class relations that were intolerable to working people of that generation.
A similar strategy has been deployed nationally since the movements of the 1960s. This was famously admitted to by John Erlichman, the domestic policy advisor to Richard Nixon, after he was released from jail for his role in the Watergate scandal. In a 1994 interview with Harper’s Magazine, Erlichman said:
“You want to know what this was really all about?” he asked with the bluntness of a man who, after public disgrace and a stretch in federal prison, had little left to protect. “The Nixon campaign in 1968, and the Nixon White House after that, had two enemies: the antiwar left and black people. You understand what I’m saying? We knew we couldn’t make it illegal to be either against the war or black, but by getting the public to associate the hippies with marijuana and blacks with heroin, and then criminalizing both heavily, we could disrupt those communities. We could arrest their leaders, raid their homes, break up their meetings, and vilify them night after night on the evening news. Did we know we were lying about the drugs? Of course we did.”
This quote is a lens through which a whole, deliberately obfuscated, sequence of history becomes clear. But almost all instances in which it has been quoted focus solely on its meaning for race relations, its role in constructing a “colorblind racism” that persisted through the criminalization of black life. This is no doubt true, and significant. But what is left out of these interpretations is the fact that Erlichman points to \emph{two} enemies, the other of which is the “antiwar left.” Targeting Black radicals meant targeting urban areas for repressive restructuring, turning them into zones of police occupation. What did it mean, however, to target the anti-war left?
Simple: it meant targeting universities, turning them into sites that were adapted to the interests of capitalists. It meant “freezing them,” and freezing the capacity of thought to interrogate and intervene in the society more generally. It meant, as Ronald Reagan had proposed when running for Governor of California in 1968, creating a situation where students were more concerned about getting a job after school than about reflecting on the conditions of the society they were being asked to inherit and reproduce (Reagan’s plan to do this was to raise tuition). And it meant doing so in a way that was shielded from criticism of the movements that they were targeting, movements which had launched a devastating cultural critique of authoritarian power, just as the movements for Black freedom had launched a devastating moral critique of overt racism. For the latter, after key organizers were assassinated and organizations destroyed, a form of “colorblind racism” was invented that had the same effect of maintaining a racial caste system, but without overtly racial justification. Similarly, for the anti-war left, whose stronghold was universities across the country, a form of “politics-blind political repression” was created, as generations of students were burdened with debt in order to control the direction of their inquiries and action into avenues subdued by the economy.
At the national scale, this is partly how the “freezing” of social relations has been accomplished, and why we are left burdened with the same problems that the generation of the 1960s rebelled against, only in a different and more intensified form: racism, now in the form of the largest system of prison slavery in the history of the world; ecological devastation, now in the form of literal ecocide, or the destruction of habitable life on the planet; imperial wars, now in the form of endless global policing operations fought increasingly by people whose heroic warrior activity has been reduced to something barely distinguishable from playing video games.
Our task, then, is to repair our relation to this history, to the struggle for liberation from these conditions. Which means understanding, at a local level, the war that has been waged against us to maintain them.
**
So how did this happen \emph{here?}
Consistent with the wider FBI project of neutralizing the Black Panthers, in November of 1970 – the semester after the student rebellion – cops from Carbondale and other surrounding towns shot 778 bullets into the Black Panther house on the northeast corner of Washington St. and Allyn St. Shockingly, no one was killed, and, just as shockingly, a cease-fire was negotiated by members of the northeast community. Six Panthers – the Carbondale 6 – were arrested and none were convicted. But the legal battle lasted for a long time, and the attempted massacre by the Carbondale Police Department accomplished its presumed goal of neutralizing the organization’s activity.
The Black Panthers had been declared by FBI director J. Edgar Hoover to be the greatest threat to American democracy. The FBI’s counter-intelligence program, or COINTELPRO, engaged in assassinations, frame-ups, and misinformation campaigns to demonize and neutralize the group around the country. The Carbondale Police’s story that they had seen a “suspect” enter the Panther house on the night of the shoot-out is consistent with stories used to excuse assassinations around the country that destroyed the Panthers’ organization.
Apart from the Panthers, there were drug raids of high profile leftist activist houses, suspected at the time to be pretenses for repressing them. The house of Reverends Norman S. Bach and William E. Garrett, two of the many clergy involved in the anti-war movement, were raided on suspicion of marijuana possession. The Big Muddy Gazette interpreted this, at the time, as an act of repression, which is consistent with how we know the drug war was used. A chilling effect must have set in among public organizers: if you’re Black, the cops might shoot up your house; if you’re white, you may be publicly shamed and arrested on whatever charges can be cooked up. Step one of counter-revolution: target the organizers.
Next, there was the Horsely Commission, led by Senator Horsely to investigate the conditions that led to the student uprising. Initiated at the beginning of the semester after the riots, a few months before the Panther shootout, the commission blamed the uprising on an “international communist conspiracy,” and made the following recommendations to the University:
\begin{itemize}
\item\relax
introduction of student ID cards
\item\relax
that the administration be able to fire politically problematic professors, even if they are tenured.
\item\relax
Introduction of pornography legislation, presumably as an excuse to ban independent student newspapers
\item\relax
The banning of material “inciting violence,” presumably for the same reason
\item\relax
to cut off scholarship to students awaiting hearings for participation in the unrest.
\item\relax
Elimination of the difference between property destruction causing under \$150 in damages and damage in excess of that. In other words, punishment was not to be proportional to the economic damage, but rather the principle of property itself was what was to be protected, and any violation of it, no matter how economically small, was to be considered with equal seriousness.
\end{itemize}
Each of these recommendations, with the exception of the ability to fire “problematic” professors, may appear innocuous, or at least “reasonable.” They had to: there was a strong movement, and the measures taken to suppress it had to be careful not to trigger more resistance. In light of what has occurred – the construction of a hyper-controlled world, justified at each step with reasons that obscure its true aims – we can see these measures for what they are: excuses to expand the ability for police and administrators to intervene in and make trouble for the movements that had challenged their authority. Governments being what they are – organizations for maintaining hierarchical power – we should assume that the published recommendations of the Horsely Commission were only the visible surface of the policies that were being pursued.
The recommendation that the University fire problematic professors for political reasons was tested on Douglas Allen, a philosophy professor who was up for tenure. Allen had the support of his colleagues and department, but was denied tenure explicitly for his participation as a leader of the anti-war movement. The administration was sued by Allen and eventually had to offer him tenure. By that point, he had already found another position at the University of Maine, and did not return. Although they achieved the intended effect of rooting out a radical, it was clear that the method of overt political targeting would not stand up legally.
Another tactic for rooting out problematic professors and reshaping the university in the interest of the wealthy needed to be found. And, within a couple of years, it was: the tactic of the “budget-crisis.”
It has to be stressed that the first “budget crisis” that SIU experienced was a \emph{direct result} of the student rebellions. The Illinois Board of Higher Education was formed in response to the state’s sense that things had gotten out of hand down in Egypt, and they were no longer going to support Delyte’s dreams. They turned off the spigot, and demanded the university adapt.
In 1974, SIU President Derge fired 104 professors, a quarter of them tenured. The fired faculty were largely from departments of philosophy, history, english, sociology, and from the Division of Area Services, ending the latter program of community engagement. Adding insult to injury, Derge’s administration also tried to sue a number of the faculty that they were firing. The fired professors publicly declared that they saw this as a political purging of those departments that were most supportive of the anti-war movement. Derge denied this, and articulated for the first time what would be the standard justification for all university changes down to today. It wasn’t about politics, it was about budget cuts, failing to mention that those budget cuts themselves were about politics. In a statement that could have, and indeed has, come out of administrators from Derge to Montemagno, Derge said “decisions as to what departments should be cut were made according to enrollment trends.” This was the local application of a form of governance that would overtake the globe in the coming decades: political decisions imposed from above, justified not in political terms, but as necessary adaptations to the demands of “the economy.” This sleight of hand was first applied here as a repressive retaliation for a university that had brought thought together with life, and demanded that life change.
**
But the rebellious spirit of Carbondale and SIU didn’t die so easily. It continued for decades after the uprising, in a town in which the university administrations and the city government had become afraid of the students that were also their bread and butter. The city government and university administration have gone to quite extreme lengths to kill the rebellious energy of students and locals, only to find that it was this energy that kept the place alive. So they always look like idiots: destroying the conditions for collective joy, and yet begging people for “vibrancy” downtown. This was a vibrant town, but its vibrancy was connected to freedom, to the possibility of rebellion, to a counterculture. They have worked to police that out of existence, but also long for the flowers of the plants they have ripped out.
What were called the ‘riots’ were really just a ceremonial culmination of the life of the town, a moment of communion for the energies that had been released by the 60s, and denied their right to remake the world. From the party scene in the 80s that would shut down the strip on a weekly basis, to the Halloween riots that brought rebellious energy from all around the midwest. These events need to be understood, not simply as kids getting rowdy – though they are also that – but as the continuation of the rebellion launched in the 1960s, but within a new circumstance where the terrain of politics had shifted to undercut the possibility of this energy taking an explicitly political form. As a result, the measures of control, the process of policing existence, took a form that were similarly apolitical – as measures of crime reduction and safety.
Taking the strip was a collective gesture of transforming public space, of intervening in the order imposed by the police. Engaging in such acts, especially if connected with a party atmosphere, is what creates a genuine experience of community – the feeling of friends, neighbors, strangers, stepping outside of the roles and rules imposed upon them and creating their city on their own terms. It is ironic that today everyone is obsessed with “community,” but so few recognize how to build it: it comes from people having experiences together that are not pre-defined and constrained from above, from the moment when people engage with each other in recognition of their individual and collective capacity to shape their world and their futures. This is precisely what every act of government today is designed to destroy. The role of government, achieved through its police, its procedures, its regulations, its laws, is to \emph{lock all the exits} from the burning house that is this ecocidal\Slash{}prison society; to prevent the development of the very possibility of community life, and the sense of collective autonomy that it requires.
So it is worth stressing the extreme measures that were taken to destroy this spontaneous continuation of rebellious life. First, there were the riot police and their tear gas. Next, the city \emph{cancelled Halloween} for a few years in the 90s – an extraordinary step – blaming the riotous activity on “outside agitators.” After a few years they lifted the ban only to find they had not killed the spirit, and the town choked from tear gas for days. Thus began a decade and a half long ban on Halloween, a celebration that was in the process of becoming a midwestern Mardi Gras. Rather than recognizing this as a local culture in the making, the city government and reactionary forces clamped down for 15 years, finishing off the death of the public counter-culture. Now confined to basement shows, this culture, while it has nurtured musicians and a few rebels, suffers from the isolation it was forced into.
**
This has been the beginning of a sketch of a different history for Carbondale and SIU. It is not complete or authoritative: it is more of an invitation for others to speak up, to correct, to fill in the gaps, to value their own memory.
It is easy to see why people wouldn’t do so. The world appears to have changed into something unrecognizable, and it is hard to imagine how experiences 50, 30, even a decade ago feel relevant today. This too must be understood as a move a in a battle for control: the principle tool of American power is amnesia, the smothering of the possibility of collective memory. The story sketched here is an invitation for us to fight back, to recover a history that makes sense of where we are, to recognize that the official narrative is deaf and blind to all that is relevant for life, for our desires, and for the challenges we face. Reducing everything to the laws of economics and the government that imposes them, it systematically ignores that these laws, far from being natural, are tools for preventing the growth of an autonomous community power. Such a power was growing here in Carbondale, nourished and inspired by rebellion, by thousands of people recognizing that life as it was offered was intolerable, and who insisted that thought and life must be brought together against the forces that subject both to the superficial calculations of penny-counters, to the reign of the neurotic, the paranoid, their wealth and their police.
Our guiding thesis, hardly proven here, is this: we cannot understand the problems we face today – at the university, in Carbondale, or indeed nationally – unless we understand that the world we have was built to destroy the movements that sought to fundamentally change it. Here in Carbondale, that means that we need to remember that the roots of the long stretch of budget-crises have their origin in thinly veiled political repression, disciplining the university for producing students that were capable of asserting their power against a war machine. Unwilling to change, and now afraid of what young people were capable of, a process of “freezing” life began.
It is not, and never has been, money that makes the world go round. It is labor, love, friendship, desire. These forces must be mutilated and confined to money-relationships in order for the wealthy to stay in control. Today, here, the crisis is not really lack of money – that is only the crisis for those in power. The crisis for the rest of us is disconnection from our own sense of the world, disconnection from the power we have to build what we need and desire without the crutch of money and those who have it. We have a crisis of energy, and a crisis of struggle, a disconnection of our thought and our lives, a studied superficiality of our relationships, a paralyzing anxiety that holds us back from recognizing that all we need to chart a path out of this mess, and to repair our relationship to those who struggled before us, is here with us already.
1Fred Hampton, the 21 year-old revolutionary genius of Chicago, who had travelled to Carbondale and advised Reggie Brown to start the Panther chapter here, had been shot in his bed by Chicago Police. It was later learned that Chicago Police were working with the FBI and this was a targeted assassination, since the FBI was concerned Hampton could have been a “Messiah-figure,” linking struggles between black and poor white people. Indeed, this is exactly what he did with what would become the original “rainbow coalition,” in which the Panthers organized against the cops with displaced Appalachian white people, many of whom were racist and proudly wore their Confederate flags. This willingness to organize across the cultural\Slash{}color lines and against the state made Hampton in particular a target, and his brief life has been examined to an extent that other Panther chapters, like the one in Carbondale, have not.
\chapter{vol. 2.2: Introducing the Knights of the Flaming Circle}
During the 1920s, a nation-wide, secret organization called The Knights of the Flaming Circle took on the Ku Klux Klan in the streets. Little – far too little – is known about the organization. But we do know that there was a chapter in Williamson County.
This essay collects what little we do know about the “Red Knights,” and helps us to recognize that today’s antifascism is a part of a long, largely forgotten, tradition of giving no public forum to fascists.
\Slash{}
In late September 1923, a dynamite blast went off in the hills outside Steubenville, OH. Residents streamed out of their houses to see “white robed figures moving about in a strange ceremonial,” lit only by a gigantic, flaming circle.
Were these members of the Ku Klux Klan that had simply switched their flaming cross for a circle? Soon word spread through the town that, in fact, this was an anti-Klan group that was inaugurating its formation: The Knights of the Flaming Circle.
A month before, in Kane, Pennsylvania, a similar circle had burned, and the local paper, the Kane Republican, received an anonymous letter announcing the founding of the “Knights of the Burning Ring.” The letter stated: “Kane is selected as the starting point of a movement that will ring the earth with blazing justice to all. We are enemies of all clans or klans. We believe in liberty for every human being, black, white or yellow, regardless of race, religion or creed.” For reasons unknown, the “Burning Ring” name seems to have been subsequently dropped.
A short time after, a Klan parade in Steubenville, OH, a few hours away, led to a riot, during which “six or seven Klan cars were overturned by the Steubenville people. Flags were torn off the machines and their occupants were attacked with bricks and bottles and clubs and other flying objects.” The hillside dynamite blast and ceremony in Stuebenville followed the riot by about a month, announcing to western Ohio that there was more than just a raucous disruption of Klan demonstrations going on, but rather an organized effort.
A local dentist, Dr. W. F. McGuigan, claimed to be the founder of the Steubenville chapter of the Knights of the Flaming Circle and the Grand Supreme Monarch of the organization’s “central division,” stretching from Massachusetts to Illinois. A few days after the initial ceremony, McGuigan told reporters that “The Knights of the Flaming Circle is a non-sectarian society and its object is to combat religious, racial and political intolerance.” They wore no masks or hoods, but did wear white robes, embroidered with their official insignia: a red circle with the figure of the State of Liberty at the center.
But the very notion that there was an “organization” at all is disputed by one of the few oral histories that mentions the Flaming Circle. In an interview conducted in 1984 with Nicola Criscioni, of Youngstown, OH, Criscioni claims “there was no organization, it was the papers that dubbed them that, but it was no organization, just a thrown-together outfit\dots{}. What we did was we got a bunch of tires and put them around a circle and burned them, or bailed the hay and put them around a big circle and burned them. They burned the cross and we burned the circle. It was a hit-and-run outfit. There were no heads of anything\dots{} then when we heard that there was going to be a parade, by then we maybe put together a certain bunch and would try to disrupt it.”
This ambiguity – an organization with Klan-esque titles like Grand Supreme Monarch, or a rag-tag hit and run outfit with no meetings or dues – hints that this was a decentralized organization, one for which any group that wanted to take up the cause could do so on their own terms.
According to the 1923 A Dictionary of Secret and Other Societies, the Knights of the Flaming Circle “welcomes Catholics, Jews, and Negroes, but excludes Protestants. The members wear robes at the initiation ceremony, and each knight has a flaming circle over his heart, symbolic of the truth.” White protestants made up the base of the Klan, and were presumably excluded on that ground. According to the Klan, the Knights of the Flaming Circle were “a mob that proffered anarchism and sought to ruin the Republic.”
We have evidence that there were chapters of Knights of the Flaming Circle in Vermont, Pennsylvania, West Virginia, Ohio, Illinois, Iowa, and New Mexico. In the coming years, in various parts of the country, they used a diversity of rebellious tactics to confront the Klan. Many of those tactics are also practiced today by antifascists: pressure on meeting-halls to refuse to allow the Klan to meet there; publishing lists of Klan members, destroying the anonymity of the organization; organizing counter demonstrations to show mass opposition to the Klan and what it stood for; physically interrupting their parades and rallies; assaulting Klan members and damaging their property. In Youngstown, Criscioni recalls lining the road with roofing tacks before a Klan parade, popping their tires and getting some laughs at their expense.
They even, one could say, “trolled” the Klan. In addition to wearing illustrious garb of their own, sometimes white, sometimes red, they fought back with fire: in response to the Klan’s practice of burning crosses in front of the homes of immigrants and minorities, the Circlers’ would set tires alight on the yards of known Klansmen. It seems likely that McGuigan’s claim to be “Grand Supreme Monarch” was just another jab at the Invisible Empire’s ridiculous hierarchy.
But if indeed McGuigan was in some role of leadership in the midwest, he was certainly hard at work organizing. Numerous articles from the time repeat the Flaming Circle’s claims that they had organizers in every city in Ohio, and throughout Pennsylvania and West Virginia. And somehow, within a year, a chapter was formed in Williamson County, Illinois.
\Slash{}\Slash{}
Williamson County, known at the time as “Bloody Williamson,” had just been the site of one of the bloodiest labor battles in American history. The Herrin Massacre was the final major explosion of decades-long battles between coal-miners and mine-owners, and it had brought international infamy to the county. During the massacre, 19 scabs were killed by coal-miners. No one was convicted by a Williamson County jury.
A group of wealthy businessmen, interested in restoring the county’s reputation and affiliated with the Ku Klux Klan, hired a former Bureau of Investigations officer, S. Glenn Young, to lead their campaign. But the campaign wasn’t against the miner’s union. The Klan made the move characteristic of all fascist movements: it attempted to divide the working-class union movement along racial and national lines, targeting Italian-American immigrants.
Moreover, in a move that prefigured the War on Drugs, they targeted them not for political activity, but for violations of Prohibition. A “clean-up Williamson County” movement was underway, led by the Klan, which blamed the violence of a thirty year long class struggle between miners and mine-owners on immigrant communities in Herrin. S. Glenn Young’s raids targeted immigrants and anyone who opposed the Klan, ignoring the drinking of Protestants and flamboyantly ignoring the very laws he claimed to be enforcing. Eventually, Young even opened a “soft-drink parlour” of his own.
Prohibition, a constitutional amendment passed in 1919, didn’t go into effect until 1920 because it was well-known to be unenforceable by the American state-apparatus at the time. The Ku Klux Klan served as a para-military force, disproportionately targeting minority groups in the name of enforcing “law and order.” They defended their targeting of immigrants because of their unfamiliar culture and their supposed “predisposition to radicalism and anarchism”
And this might have gone well for them in Williamson County, IL, if they hadn’t encountered an unexpected adversary in the Knights of the Flaming Circle.
We don’t know how the Knights of the Flaming Circle made it to Williamson County. Perhaps word of the group travelled along lines of conspiratorial communication that the miner’s union had already established. If not, anyone reading \emph{The New York Times} would probably have encountered mention of the group in 1923. Perhaps Ora Thomas and E.E. Bowan, the rumored founders of the group in Herrin, decided they could take up the name without asking any permission from some Grand Supreme Monarch. That would have suited them.
The Flaming Circle in Williamson county was an alliance of miners, immigrants, bootleggers, and even law-enforcement who were none-too-happy to lock up their communities just because some new Prohibition law had been passed. The city of Herrin was almost completely integrated with the miner’s union, and what little wealth and safety miners knew at the time could be attributed only to the solidarity that union embodied. The union rightly saw the Klan as a threat, a ruling-class funded attempt to divide the strength of the working-class union along racial and ethnic lines, obscuring the actual conflict between the poor and the wealthy. For that reason, the UMWA issued a statement barring all Klan members from the union, and noting that the Klan’s efforts were aimed primarily at disrupting and dividing the power that working people had gained through Union organizing. It was later learned that S. Glenn Young, who was notoriously fast and loose with the facts about his own history, had worked as a scab-herder during the 1922 Railway Shopmen’s Strike – a feature of his past that he tried to conceal.
The Klan, under the leadership of S. Glenn Young, was so powerful in those years that it would have been very dangerous to make membership in the Circle known. Still, newspaper articles from the time attest that when the Klan would hold a parade, the next day you could be sure the Flaming Circle would, “neutralizing the effect of the Klan’s.”
But events did not remain at the level of competing parades for long. The first shooting occurred at an anti-Klan meeting, by pro-Klan police. While the first victim was recovering in the hospital, a constable, and member of the Klan, named Ceasar Cagle was shot and killed in retaliation. In response, the Klan laid siege to Herrin hospital, where Flaming Circle members were gathering with their wounded. The Klan fired into the hospital, and the Circlers’ that found themselves held up in there refusing to leave. The National Guard was called in. This was just the first round of what would be an all out war that would engulf Williamson and surrounding counties for the next year and a half.
The war came to an end when Ora Thomas entered a cigar shop at the Embassy Hotel in January of 1925, overhearing the familiar voice of S. Glenn Young threatening a young miner for spreading the story that Young had been a scab-herder prior to his becoming a Prohibition agent. Young had two men with him, and all three of them died in that cigar shop. As did Ora Thomas, the founder of Herrin’s Red Knights.
In the years after the Klan was defeated, many of these bootleggers would go on to engage in bloody battle with one another. Even the notorious Shelton and Birger gangs, who wreaked havoc throughout southern Illinois for the next decade, were momentarily allied in opposition to the Klan.
\Slash{}\Slash{}\Slash{}
The Knights of the Flaming Circle, whatever they were and whatever their shortcomings, are a sign that there has always been a counter-history to “America” on this continent, one full of people who, regardless of race, religion, or creed, have been quietly conspiring and jubilantly acting toward freedom for all. Today’s anti-fascists fall into a long tradition of those willing to risk everything to confront the racist forces who aim to re-create the “Founding Father’s” dream of a white ethno-state. That old American dream is recreated with new racist, nationalist lies in every generation that the wealthy feel their power threatened.
May we instead remember as our ancestors the brave people who fought to the death against the racist dreams of the wealthy, and against the stupid who accepted their lies.
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\begin{center}
The Anarchist Library
\smallskip
Anti-Copyright
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\bigskip
\end{center}
\strut
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\begin{center}
anonymous
The Next Eclipse
A Vision for Regional Autonomy
2018
\bigskip
Retrieved on July 25th, 2018 from https:\Slash{}\Slash{}thenexteclipse.wordpress.com\Slash{}
https:\Slash{}\Slash{}thenexteclipse.wordpress.com
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\textbf{theanarchistlibrary.org}
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|
https://dlmf.nist.gov/9.8.E13.tex | nist.gov | CC-MAIN-2021-49 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2021-49/segments/1637964362969.51/warc/CC-MAIN-20211204094103-20211204124103-00639.warc.gz | 288,670,326 | 707 | \[M\left(x\right)N\left(x\right)\sin\left(\theta\left(x\right)-\phi\left(x\right%
)\right)=\pi^{-1},\] |
https://dlmf.nist.gov/4.21.E12.tex | nist.gov | CC-MAIN-2022-40 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2022-40/segments/1664030337244.17/warc/CC-MAIN-20221002021540-20221002051540-00224.warc.gz | 260,413,000 | 677 | \[{\sin}^{2}z+{\cos}^{2}z=1,\] |
https://mirror.las.iastate.edu/tex-archive/macros/latex/contrib/shipunov/doc/biokey-doc-en.tex | iastate.edu | CC-MAIN-2023-14 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2023-14/segments/1679296945289.9/warc/CC-MAIN-20230324211121-20230325001121-00270.warc.gz | 464,031,234 | 2,522 | \documentclass{article}
\usepackage[bookmarks=false,colorlinks=true,hypertexnames=false]{hyperref}
\usepackage{biokey}
\author{A.\,Shipunov\footnote{e-mail: \texttt{dactylorhiza at gmail}}}
\title{\texttt{biokey}, the package for precious and flexible identification keys}
\date{}
\begin{document}
\maketitle
This package can be used for creating biological identification keys. Different layouts are available.
\section{General usage}
This is the textual key:
\begin{verbatim}
1. It is an animal ... 2.
- It is a plant ... 3.
2. It is spiny ... Hedgehog
- It is not very spiny ... Swift
= It is not spiny at all ... Siskin
3(1). Lots of wood ... Spruce
- No wood ... Daisy
\end{verbatim}
The interpretation in suggested language is follows:
\bigskip\hrule
\begin{verbatim}
\begin{biokey}
\Z1. It is an animal \T 2.
\AN It is a plant \T 3.
\Z2. It is spiny \TT Hedgehog
\AN It is not very spiny \TT Swift
\AAN It is not spiny at all \TT Siskin
\ZZ3(1). Lots of wood \TT Spruce
\AN No wood \TT Daisy
\end{biokey}
\end{verbatim}
\hrule\bigskip
\begin{biokey}
\Z1. It is an animal \T 2.
\AN It is a plant \T 3.
\Z2. It is spiny \TT Hedgehog
\AN It is not very spiny \TT Swift
\AAN It is not spiny at all \TT Siskin
\ZZ3(1). Lots of wood \TT Spruce
\AN No wood \TT Daisy
\end{biokey}
\bigskip\hrule\bigskip
For aesthetics, I recommend that text before \verb|\T| should not end with dot (with the exception of abbreviations). \verb|\T| and \verb|\TT| are just the same thing, but second is better to designate names, and first is better for numbers. Sometimes, these two commands cannot format the paragraph without overfulls, in these (rare) cases I recommend the \verb|\TTTT| or ``old-style'' \verb|\TTT| which results are less precious but require less handwork.
\verb|\Z| and \verb|\ZZ| are different only for the second is used for backreferences, or for typical in serial zoological keys references for theses and antitheses. These two commands along with \verb|\AN|, \verb|\AAN|, and (not used in the example above) \verb|\AAAN| are used also for aesthetic hanging indentation.
Commands \verb|\N|, \verb|\NN| and \verb|\NNN| are for end-level objects (species, for example). They did not produce leading dots, but justify following object right, next with some space, or on next line, respectively.
Command \verb|\VT| is for hanging number references. There is also starred variant, \verb|\VT*|, where dot leader are also protruding outside right text margin.
By default, all \verb|\T|-like commands along with \verb|\N| and \verb|\NN| have the declaration \verb|\samepage| inside. One can redefine that via \verb|\SameDecl| hook. The most obvious redefinition is \verb|\relax|.
\verb|\SHRIFTZ| and \verb|\SHRIFTN| are two hooks which are defined by default as \verb|\relax| (do nothing), so one can redefine them to change the representation of these number and end-level objects, respectively. For example,
\verb|\renewcommand{\SGRIFTZ}{\textbf}|
will result in boldface theses numbers.
Several commands designed for commentaries after theses (or antitheses). \verb|\FK| put the text in footnote size, \verb|\KOM| imitate these, but without number, and \verb|\VPRAVO| aligned its contents to the right. \verb|\OTSTUP| is a hook for indentation of first two kinds of comments. By default it is 2\,em, but one can easily redefine it.
\section{``Automatic'' keys}
This sort of key can put numbers automatically. The example (needs two \LaTeX\ runs):
\bigskip\hrule
\begin{verbatim}
\begin{biokey}
\TE{ani} It is an animal \SS{spi}
\AN It is a plant \SS{pla}
\TE{spi} It is spiny \TT Hedgehog
\AN It is not very spiny \TT Swift
\AAN It is not spiny at all \TT Siskin
\SE{pla}{ani} Lots of wood \TT Spruce
\AN No wood \TT Daisy
\end{biokey}
\end{verbatim}
\hrule\bigskip
\begin{biokey}
\TE{ani} It is an animal \SS{spi}
\AN It is a plant \SS{pla}
\TE{spi} It is spiny \TT Hedgehog
\AN It is not very spiny \TT Swift
\AAN It is not spiny at all \TT Siskin
\SE{pla}{ani} Lots of wood \TT Spruce
\AN No wood \TT Daisy
\end{biokey}
\bigskip\hrule\bigskip
The biggest advantage of this type of key is that it is much easier to correct. It is possible to convert ``ordinary'' key to ``automatic'' key and further to HTML, with the help of \texttt{biokey2html} scripts (see documentation). See also how hyper-references working here.
\section{Indented keys}
And, finally, the different key layout---so-called indented keys:
\bigskip\hrule
\begin{verbatim}
\begin{biokey}
\Z A. It is an animal
\begin{LE}
\Z AA. It is more or less spiny
\begin{LE}[2]
\Z AAA. It is very spiny \TT Hedgehog
\Z BBB. It is not very spiny \TT Swift
\end{LE}
\Z BB. It is not spiny at all \TT Siskin
\end{LE}
\Z B. It is a plant
\begin{LE}
\Z CC. Lots of wood \TT Spruce
\Z DD. No wood \TT Daisy
\end{LE}
\end{biokey}
\end{verbatim}
\hrule\bigskip
\begin{biokey}
\Z A. It is an animal
\begin{LE}
\Z AA. It is more or less spiny
\begin{LE}[2]
\Z AAA. It is very spiny \TT Hedgehog
\Z BBB. It is not very spiny \TT Swift
\end{LE}
\Z BB. It is not spiny at all \TT Siskin
\end{LE}
\Z B. It is a plant
\begin{LE}
\Z CC. Lots of wood \TT Spruce
\Z DD. No wood \TT Daisy
\end{LE}
\end{biokey}
\bigskip\hrule\bigskip
It is more complicated then previous examples, so one may to consider \texttt{dichokey} package, but it is much less flexible.
\end{document} |
http://tph.tuwien.ac.at/~svozil/publ/2019-s.tex | tuwien.ac.at | CC-MAIN-2022-33 | text/x-tex | text/x-matlab | crawl-data/CC-MAIN-2022-33/segments/1659882572286.44/warc/CC-MAIN-20220816090541-20220816120541-00662.warc.gz | 48,940,819 | 14,917 | % This is samplepaper.tex, a sample chapter demonstrating the
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\title{Quantum advantage by relational queries about equivalence classes}
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\author{Karl Svozil\orcidID{0000-0001-6554-2802}}
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\institute{Institute for Theoretical Physics,
Vienna University of Technology,
Wiedner Hauptstrasse 8-10/136,
1040 Vienna, Austria \\
\email{svozil@tuwien.ac.at}\\
\url{http://tph.tuwien.ac.at/\textasciitilde{}svozil}
}
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\begin{abstract}
Relational quantum queries are sometimes capable to effectively decide between collections of mutually exclusive elementary cases without completely resolving and determining those individual instances. Thereby the set of mutually exclusive elementary cases is effectively partitioned into equivalence classes pertinent to the respective query. In the second part of the paper, we review recent progress in theoretical certifications (relative to the assumptions made) of quantum value indeterminacy as a means to build quantum oracles for randomness.
\keywords{quantum computation, partitioning of cases, quantum parallelism, hidden subgroup problem, quantum random number generators.}
\end{abstract}
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%\title{Quantum advantage by queries associated with equivalence classes rather than individual cases}
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%\author{Karl Svozil}
%\email{svozil@tuwien.ac.at}
%\homepage{http://tph.tuwien.ac.at/~svozil}
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%Vienna University of Technology,
%Wiedner Hauptstrasse 8-10/136,
%1040 Vienna, Austria}
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%\begin{abstract}
%Depending on the query quantum information theory is sometimes capable of effectively deciding between classes of mutually exclusive elementary cases without completely resolving and determining those individual instances forming the respective equivalence class. Thereby the set of mutually exclusive elementary cases is effectively partitioned into equivalence classes pertinent to the respective query. In the last part of the paper, we review recent progress in theoretical certifications (relative to the assumptions made) of quantum value indeterminacy as a means to build quantum oracles for randomness.
%\end{abstract}
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%\maketitle
\section{Quantum (dis-)advantages}
Genuine quantum computations will be with us for a long time to come,
because the miniaturization of electronic circuits is pushing the processor physics into the coherent superposition/complementarity/entanglement/value-indefinite regime
(which has no sharp boundary just as the quantum--classical separation is fuzzy and means dependent).
Moore's law, insofar as it relates to classical ``paper and pencil''~\cite[p.~34]{Turing-Intelligent_Machinery} computation,
has reached its effective bottom ceiling approximately ten to five years ago; this is due to exhaustion of minimization
with respect to reasonably cooling, as well as by approaching the atomic scale.
Most recent performance increases are due to parallelization (if possible).
Alas, this upcoming kind of ``enforced'' quantum domain computing, imagined by Manin, Feynman, and others, still poses conceptual, theoretical and technological challenges.
Indeed, contemporary quantum information theory appears to be far from being fully comprehended, worked out and mature.
It is based on quantum mechanics, a theory whose semantics has been notoriously debated almost from its inception, while its syntax -- its formalism, and, in particular,
the rules of deriving predictions
-- are highly successful, accepted and relied upon.
Depending on temperament and metaphysical inclination, its proponents admit that nobody understands quantum mechanics~\cite{feynman-law,clauser-talkvie},
maintain that there is no issue whatsoever~\cite{Englert2013,fuchs-peres},
one should not bother too much~\cite{dirac,bell-a} about its meaning and foundations, and rather shut up and calculate~\cite{mermin-1989-shutup,mermin-2004-shutup}.
By transitivity or rather a reduction, quantum information theory inherits quantum mechanics'
apparent lack of consensus, as well as a certain degree of cognitive dissonance between applying the formalism while suffering from an absence of conceptual clarity~\cite{mermin-2019},
Strong hopes, claims and promises~\cite{Aaronson:2013:QCD:2487754,Dyakonov-2013,svozil-2016-quantum-hokus-pokus,Abbott-Calude-blog-2016-06-19,Dyakonov-2019,aaronson-Dyakonov} of quantum ``supremacy''~\cite{Wiesner-2017} are
accompanied by the pertinent question of what exactly, if at all, could make quantum information and computation outperform classical physical resources.
Surely many nonclassical quantum features present themselves as being useful or decisive in this respect; among them complementarity, coherence (aka parallelism), entanglement,
or value indeterminacy (aka contextuality).
But if and how exactly those features will contribute or enable future algorithmic advances still remains to be seen.
The situation is aggravated by the fact that, although the quantum formalism amounts to linear algebra and functional analysis,
some of its most important theorems are merely superficially absorbed by the community at large: take,
for example, Gleason's theorem~\cite{Gleason}, and extensions thereof~\cite{pitowsky:218,2015-AnalyticKS}.
Another example is Shor's factoring algorithm~\cite[Chapter~5]{nielsen-book10} whose presentations often suffer from the fact
that its full comprehension requires a nonsuperficial understanding of number theory,
analysis, as well as quantum mechanics; a condition seldom encountered in a single (wo)man.
Moreover, often one is confronted with confusing opinions: for instance, the claim that quantum computation is universal with respect to either unitary transformations
or first-order predicate calculus is sometimes confused with full Turing universality.
And the plethora of algorithms collected into a quantum algorithm zoo~\cite{jordan-zoo} is compounded by the quest of exactly why and how quantum algorithms may outperform classical ones.
Quantum advantages may be enumerated in four principal groups, reflecting potential non-classical quantum features:
\begin{itemize}
\item
quantum parallelism -- aka {\it coherent superposition} of classically mutually exclusive bit states,
associated with their simultaneous co-representation;
\item
quantum collectivism -- aka entanglement (involving possibly nonlocal correlations) in a multi-particle situation: information
is encoded only in {\it relational properties} among particles; individual particles have no definite property;
\item
quantum probabilities are vector-based (orthogonal projection operators), resulting in non-classical
expectation values rendering different (from classical value assignments) predictions;
\item
quantum complementarity: in general quantized systems forbid measurements of certain pairs of observables with arbitrary precision:
``you cannot eat a piece of the quantum cake \& have another one too;''
\item
quantum value indefiniteness: there cannot exist classical (true/false) value assignments on certain collections of (intertwining) quantum observables.
\end{itemize}
In what follows the first and the last feature -- parallelism and value indefiniteness -- will be discussed in more detail.
\section{Suitable partitioning of cases}
One quantum feature called ``quantum parallelism,''
which is often presented as a possible quantum resource not available classically,
is the capacity of $n$ quantum bits to encode $2^n$ classically
mutually exclusive distinct classical bit states at once, that is, simultaneously:
$
\vert \Psi \rangle = \sum_{i=0}^{2^n-1} \psi_i \vert i \rangle
$,
where the index $i$ runs through all $2^n$ possible combinations of $n$ classically mutually exclusive bit states $\{0,1\}$,
$\vert i \rangle $ are elements of an orthonormal basis in $2^n$-dimensional Hilbert space,
and $\psi_i$ represent probability amplitudes whose absolute squares sum up to $1$.
Quantum parallelism, often presented rather mystically,
may formally come about rather trivially: the alleged simultaneous quantum co-existence of classically mutually exclusive states is like
pretending that a vector in the plane may simultaneously point in both directions of the plane~\cite{Dyakonov-2019};
a sort of confusion between a vector and its components.
This seemingly absurd co-representability of contradicting classical states was the motivation for Schr\"odinger's cat paradox~\cite{schrodinger}.
Note also that, in order to maintain coherence throughout a quantum computation,
a {\em de facto} exponential overhead of ``physical stuff'' might be required.
This could well compensate or even outweigh the advantage; that is, the exponential simultaneous
co-representability of (coherent superpositions of) classical mutually exclusive cases of a computation.
The state
$
\vert \Psi \rangle
$
``carrying'' all these classical cases in parallel is not directly accessible or ``readable'' by any physical operational means.
And yet, it can be argued that its simultaneous representation of classically exclusive cases can be put to practical use indirectly if certain criteria are met:
\begin{itemize}
\item
first of all, there needs to be a quantum physical realizable grouping or partitioning of the
classical cases, associated with a particular query of interest; and
\item
second, this aforementioned query needs to be realizable by a quantum observable.
\end{itemize}
In that way, one may attain knowledge of a particular feature one is interested in; but,
unlike classical computation, (all) other features remain totally unspecified and unknown.
There is no ``free quantum lunch'' here, as a total specification of all observables would
require the same amount of quantum queries as with classical resources.
And yet, through coherent superposition (aka interference)
one might be able to ``scramble'' or re-encode the signal
in such a way that some features can be read off of it very efficiently --
indeed, with an exponential (in the number of bits) advantage over classical computations
which lack this form of rescrambling and re-encoding (through coherent superpositions).
However, it remains to be seen whether, say, classical analog computation with waveforms,
can produce similar advantages.
For the sake of a demonstration, the Deutsch algorithm~\cite[Chapter~2]{mermin-07} serves as a Rosetta stone of sorts
for a better understanding of the formalism and respective machinery at work in such cases.
It is based on the four possible binary functions $f_0, \ldots , f_3$ of a single bit $x \in \{0,1\}$:
the two constant functions $f_0(x)=1-f_3(x)=0$,
as well as the two nonconstant functions: the identity $f_1(x)=x$ and the not $f_3(x) = (x+1) \text{ mod } 2$, respectively.
Suppose that one is presented with a black box including in- and output interfaces,
realizing one of these classical functional cases, but it is unknown which one.
Suppose further that one is only interested in their parity; that is, whether or not the encoded black box function is a constant function of the argument.
Thereby, with respect to the corresponding equivalence relation of being ``(not) constant in the arguement''
the set of functions
$\{f_0, \ldots , f_3\}$
is partitioned into
$\{\{f_0,f_3\},\{f_1,f_2\}\}$.
A different way of looking at this relational encoding
is in terms of zero-knowledge proofs: thereby
nature is in the role of an agent
which is queried about a property/proposition, and issues a correct answer
without disclosing
all the details and the fine structure of the way this result is obtained.
Classically the only way of figuring this (``constant or not'') out
is to input the two bit-state cases, corresponding to two separate queries.
If the black box admits quantum states,
then the Deutsch algorithm presents a way to obtain the answer (``constant or not'')
directly in one query.
In order to do this one has to perform
three successive steps~\cite{svozil-2005-ko,2007-tkadlec-svozil-springer}:
\begin{itemize}
\item
first one needs to scramble the classical bits into a coherent superposition of the two classical bit states.
This can be done by a Hadamard transformation, or a quantum Fourier transformation;
\item
second, one has to transform the coherent superposition according to the binary function which is encoded in the box.
This has to be done while maintaining reversibility; that is, by taking ``enough'' auxiliary bits
to maintain bijectivity/permutation; even if the encoding function is many-to-one (eg, constant).
\item
third, one needs to unscramble this resulting state to produce a classical output signal which indicates the result of the query.
As all involved transformations need to be unitary and thus reversible
the latter task can again be achieved by an (inverse) Hadamard transformation, or an (inverse)
quantum Fourier transformation.
\end{itemize}
This structural pattern repeats itself in many quantum algorithms suggested so far.
It can be subsumed into the three- or rather fivefold framework:
``prepare a classical state; then
spread (the classical state into a coherent superposition of classical states)
---
transform (according to some functional form pertinent to the problem or query considered)
---
fold (into partitions of classical states which can be accessed via quantum queries and yield classical signals);
then detect that classical signal.''
Besides the (classical) pre- and post-processing of the data,
Shor's algorithm~\cite[Chapter~5]{nielsen-book10}
has a very similar structure in its quantum (order-finding) core:
It creates a superposition of classically mutually exclusive states $i$
{\it via} a generalized Hadamard transformation.
It then processes this coherent superposition of all $i$ by computing $x^i \text{ mod } n$,
for some (externally given) $x$ and $n$, the number to be factored.
And it finally ``folds back'' the expanded, processed state by applying an inverse quantum Fourier transform,
which then (with high probability) conveniently yields a piece of classical information (in one register) about the period or order; that is,
the least positive integer $k$ such that $x^k =1 (\text{mod } n)$ holds.
As far as Shor's factoring algorithm is concerned, everything else is computed classically.
Partitioning of states may be related to the hidden subgroup problem~\cite[Section~5.4.3]{nielsen-book10}:
thereby, a function maps from some group to a finite set and is
promised to be constant on cosets of the hidden subgroup.
If those cosets are identified with the transformations ``filtering'' and ``singling out''~\cite{DonSvo01,svozil-2002-statepart-prl,svozil-2003-garda,svozil-2005-ko}
the elements of a partition of states associated with the particular problem,
finding the hidden subgroup may yield an effective way of solving this problem (encoded by the state partition).
Whether or not this strategy to find ``quantum oracles'' corresponding to arbitrary partitions
of classical cases is quantum feasible remains to be seen. There appears to be an {\it ad hoc} counterexample,
as there is no speedup for generalized parity~\cite{Farhi-98}; at least with the means considered.
\section{Quantum oracles for random numbers}
Let me, for the sake of presenting another quantum resource mentioned in the beginning, contemplate one example for which, relative to the assumptions made,
quantum ``computation'' outperforms
classical recursion theory: the generation of (allegedly) irreducibly indeterministic numbers; or sequences thereof~\cite{2014-nobit}.
A recent extension of the
Kochen-Specker theorem~\cite{2012-incomput-proofsCJ,PhysRevA.89.032109,2015-AnalyticKS}
allowing partial value assignments suggests the following algorithm:
Suppose one prepares a quantized system capable of three or more mutually exclusive outcomes,
formalized by Hilbert spaces of dimension three and higher, in an arbitrary pure state.
Then,
relative to certain reasonable assumptions (for value assignments and noncontextuality),
this system cannot be in any defined, determined property in any other direction of Hilbert state not
collinear or orthogonal to the vector associated with the prepared state~\cite{pitowsky:218,hru-pit-2003}:
the associated classical truth assignment cannot be a total function.
The proof by contradiction is constructive and involves a configuration of intertwining quantum contexts (aka orthonormal bases).
Figure~\ref{2019-s} depicts a particular configuration of quantum observables, as well as a particular one of their faithful orthogonal representations~\cite{lovasz-79}
in which the prepared and measured states are an angle
$
\text{arccos } \langle {\bf a}\vert {\bf b} \rangle =
\text{arccos} \left[
\begin{pmatrix}
1,0,0
\end{pmatrix} \frac{1}{2}
\begin{pmatrix}
\sqrt{2},1,1
\end{pmatrix}^\intercal
\right] = \frac{\pi}{4}$ apart~\cite[Table~1]{2015-AnalyticKS}.
\newif\iflabel \labeltrue
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\begin{center}
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% Define positions of all observables
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\caption{Greechie orthogonality diagram of a logic~\cite[Fig.~2, p.~102201-8]{2015-AnalyticKS}
realizable in $\mathbb{R}^3$
with the true--implies--value indefiniteness (neither true nor false) property on the atoms $\vert {\bf a} \rangle $ and $\vert {\bf b} \rangle $,
respectively.
The 8 classical value assignments require $\vert {\bf a} \rangle $ to be false.
Therefore, if one prepares the quantized system in state $\vert {\bf a} \rangle $,
the second state $\vert {\bf b} \rangle $ cannot have any consistent classical value assignment -- it must be value indeterminate/indefinite.
}
\label{2019-s}
\end{figure}
Whenever one approaches quantum indeterminacy from the empirical, inductive side,
one has to recognize that, without {\it a priori} assumptions, formal proofs of (in)computability,
and more so algorithmic incompressibility (aka randomness~\cite{ml:70})
are blocked by reduction to the halting problems and similar~\cite{svozil-2016-pu-book}.
The best one can do is to run
tests, such as Borel normality and other criteria, on finite sequences of random number generators~\cite{PhysRevA.82.022102,Abbott_2019}
which turn out to be consistent with the aforementioned value indefiniteness and
quantum indeterminacy.
\section{Afterthoughts on assumptions}
Let me, as a substitute for a final discussion, mention a {\it caveat}: as all results and certifications hold true relative to the assumptions made,
different assumptions and axioms may change the perceptual framework and results entirely.
One might, for instance, disapprove of the physical existence of states and observables beyond a single vector or context~\cite{svozil-2018-whycontexts,Auffeves-Grangier-2018}.
Thereby, the problem of measuring other contexts would be relegated to the general measurement problem of coherent superpositions~\cite{london-Bauer-1983}.
In this case, as von Neumann, Wigner and Everett have pointed out, by ``nesting'' the measurement objects and the measurement apparatus in larger and larger systems~\cite{everett-collw},
the assumption of the universal validity of the quantum state evolution would
result in mere epistemic randomness; very much like the randomness encountered in, and the second law of~\cite{Myrvold2011237}, classical statistical physics.
From that perspective, quantum randomness might turn out to be valid ``for all practical purposes''~\cite{bell-a} through interaction with a huge number of (uncontrollable) degrees of freedom
in the environment of a quantized system in a coherent state, ``squeezing'' out this coherence very much like a balloon losing gas~\cite{Zyczkowski-balloon}.
\section*{Acknowledgments}
I kindly acknowledge enlightening discussions with Cristian Calude about many of the subjects mentioned.
All misconceptions and errors are mine.
I declare that I have no conflict of interest.
%\begin{acknowledgments}
%I kindly acknowledge enlightening discussions with Cristian Calude on many of the subjects mentioned.
%All misconceptions and errors are mine.
%\end{acknowledgments}
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\providecommand{\url}[1]{\texttt{#1}}
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\bibitem{aaronson-Dyakonov}
Aaronson, S.: Happy new year! {M}y response to {M}. {I}. {D}yakonov (1999),
\url{http://www.scottaaronson.com/writings/bignumbers.html}, accessed March
16th, 2017
\bibitem{Aaronson:2013:QCD:2487754}
Aaronson, S.: Quantum Computing Since {D}emocritus. Cambridge University Press,
New York, NY, USA (2013). \doi{10.1017/CBO9780511979309},
\url{https://doi.org/10.1017/CBO9780511979309}
\bibitem{Abbott-Calude-blog-2016-06-19}
Abbott, A.A., Calude, C.S.: Limits of quantum computing: A sceptic's view,
\url{http://www.quantumforquants.org/quantum-computing/limits-of-quantum-computing/},
jun 19th, 2016, accessed June 19th, 2016
\bibitem{2012-incomput-proofsCJ}
Abbott, A.A., Calude, C.S., Conder, J., Svozil, K.: Strong {K}ochen-{S}pecker
theorem and incomputability of quantum randomness. Physical Review A
\textbf{86}, 062109 (Dec 2012). \doi{10.1103/PhysRevA.86.062109},
\url{https://doi.org/10.1103/PhysRevA.86.062109}
\bibitem{Abbott_2019}
Abbott, A.A., Calude, C.S., Dinneen, M.J., Huang, N.: Experimentally probing
the algorithmic randomness and incomputability of quantum randomness. Physica
Scripta \textbf{94}(4), 045103 (feb 2019). \doi{10.1088/1402-4896/aaf36a},
\url{https://doi.org/10.1088/1402-4896/aaf36a}
\bibitem{PhysRevA.89.032109}
Abbott, A.A., Calude, C.S., Svozil, K.: Value-indefinite observables are almost
everywhere. Physical Review A \textbf{89}, 032109 (Mar 2014).
\doi{10.1103/PhysRevA.89.032109},
\url{https://doi.org/10.1103/PhysRevA.89.032109}
\bibitem{2014-nobit}
Abbott, A.A., Calude, C.S., Svozil, K.: On the unpredictability of individual
quantum measurement outcomes. In: Beklemishev, L.D., Blass, A., Dershowitz,
N., Finkbeiner, B., Schulte, W. (eds.) Fields of Logic and Computation II,
Lecture Notes in Computer Science, vol.~9300, pp. 69--86. Springer, Cham,
Heidelberg, New York, Dordrecht, London (2015).
\doi{10.1007/978-3-319-23534-9\_4},
\url{https://doi.org/10.1007/978-3-319-23534-9\_4}
\bibitem{2015-AnalyticKS}
Abbott, A.A., Calude, C.S., Svozil, K.: A variant of the {K}ochen-{S}pecker
theorem localising value indefiniteness. Journal of Mathematical Physics
\textbf{56}(10), 102201 (2015). \doi{10.1063/1.4931658},
\url{https://doi.org/10.1063/1.4931658}
\bibitem{Auffeves-Grangier-2018}
Auff\'eves, A., Grangier, P.: Extracontextuality and extravalence in quantum
mechanics. Philosophical Transactions of the Royal Society {A}: Mathematical,
Physical and Engineering Sciences \textbf{376}(2123), 20170311 (2018).
\doi{10.1098/rsta.2017.0311}, \url{https://doi.org/10.1098/rsta.2017.0311}
\bibitem{bell-a}
Bell, J.S.: Against `measurement'. Physics World \textbf{3}, 33--41 (1990).
\doi{10.1088/2058-7058/3/8/26},
\url{https://doi.org/10.1088/2058-7058/3/8/26}
\bibitem{Zyczkowski-balloon}
Bengtsson, I., Zyczkowski, K.: Geometry of quantum states - addendum (2018),
\url{http://chaos.if.uj.edu.pl/\textasciitilde{}karol/decoh18.pdf}, accessed
on March 24th, 2019
\bibitem{PhysRevA.82.022102}
Calude, C.S., Dinneen, M.J., Dumitrescu, M., Svozil, K.: Experimental evidence
of quantum randomness incomputability. Phys. Rev. A \textbf{82}(2), 022102
(Aug 2010). \doi{10.1103/PhysRevA.82.022102},
\url{https://doi.org/10.1103/PhysRevA.82.022102}
\bibitem{clauser-talkvie}
Clauser, J.: Early history of {B}ell's theorem. In: Bertlmann, R., Zeilinger,
A. (eds.) Quantum (Un)speakables: {F}rom {B}ell to Quantum Information, pp.
61--96. Springer, Berlin (2002). \doi{10.1007/978-3-662-05032-3\_6},
\url{https://doi.org/10.1007/978-3-662-05032-3\_6}
\bibitem{dirac}
Dirac, P.A.M.: The Principles of Quantum Mechanics. Oxford University Press,
Oxford, fourth edn. (1930, 1958)
\bibitem{DonSvo01}
Donath, N., Svozil, K.: Finding a state among a complete set of orthogonal
ones. Physical Review A \textbf{65}, 044302 (2002).
\doi{10.1103/PhysRevA.65.044302},
\url{https://doi.org/10.1103/PhysRevA.65.044302}
\bibitem{Dyakonov-2013}
Dyakonov, M.I.: State of the Art and Prospects for Quantum Computing, chap.~20,
pp. 266--285. John Wiley \& Sons, Ltd (2013).
\doi{10.1002/9781118678107.ch20},
\url{https://doi.org/10.1002/9781118678107.ch20}
\bibitem{Dyakonov-2019}
Dyakonov, M.I.: When will we have a quantum computer? (2019),
\url{https://arxiv.org/abs/1903.10760}, talk at the conference ``Future
trends in microelectronics'', Sardinia (2018). To be published in a special
issue of Solid State Electronics
\bibitem{Englert2013}
Englert, B.G.: On quantum theory. The European Physical Journal D
\textbf{67}(11), 1--16 (2013). \doi{10.1140/epjd/e2013-40486-5},
\url{https://doi.org/10.1140/epjd/e2013-40486-5}
\bibitem{everett-collw}
{Everett III}, H.: The {E}verett interpretation of quantum mechanics: Collected
works 1955-1980 with commentary. Princeton University Press, Princeton, NJ
(2012), \url{http://press.princeton.edu/titles/9770.html}
\bibitem{Farhi-98}
Farhi, E., Goldstone, J., Gutmann, S., Sipser, M.: Limit on the speed of
quantum computation in determining parity. Physical Review Letters
\textbf{81}, 5442--5444 (1998). \doi{10.1103/PhysRevLett.81.5442},
\url{https://doi.org/10.1103/PhysRevLett.81.5442}
\bibitem{feynman-law}
Feynman, R.P.: The Character of Physical Law. MIT Press, Cambridge, MA (1965)
\bibitem{fuchs-peres}
Fuchs, C.A., Peres, A.: Quantum theory needs no `interpretation'. Physics Today
\textbf{53}(4), 70--71 (March 2000). \doi{10.1063/1.883004},
\url{https://doi.org/10.1063/1.883004}, further discussions of and reactions
to the article can be found in the September issue of Physics Today, {\it
53}, 11-14 (2000)
\bibitem{Gleason}
Gleason, A.M.: Measures on the closed subspaces of a {H}ilbert space. Journal
of Mathematics and Mechanics (now Indiana University Mathematics Journal)
\textbf{6}(4), 885--893 (1957). \doi{10.1512/iumj.1957.6.56050},
\url{https://doi.org/10.1512/iumj.1957.6.56050}
\bibitem{hru-pit-2003}
Hrushovski, E., Pitowsky, I.: Generalizations of {K}ochen and {S}pecker's
theorem and the effectiveness of {G}leason's theorem. Studies in History and
Philosophy of Science Part B: Studies in History and Philosophy of Modern
Physics \textbf{35}(2), 177--194 (2004). \doi{10.1016/j.shpsb.2003.10.002},
\url{https://doi.org/10.1016/j.shpsb.2003.10.002}
\bibitem{jordan-zoo}
Jordan, S.: Quantum algorithm zoo (2011-2019),
\url{http://quantumalgorithmzoo.org/}, accessed March 26, 2019
\bibitem{london-Bauer-1939}
London, F., Bauer, E.: La theorie de l'observation en m\'ecanique quantique;
{N}o.~775 of Actualit\'es scientifiques et industrielles: Expos\'es de
physique g\'en\'erale, publi\'es sous la direction de {P}aul {L}angevin.
Hermann, Paris (1939), english translation in~\cite{london-Bauer-1983}
\bibitem{london-Bauer-1983}
London, F., Bauer, E.: The theory of observation in quantum mechanics. In:
Quantum Theory and Measurement, pp. 217--259. Princeton University Press,
Princeton, NJ (1983), consolidated translation of French
original~\cite{london-Bauer-1939}
\bibitem{lovasz-79}
Lov\'asz, L.: On the {S}hannon capacity of a graph. IEEE Transactions on
Information Theory \textbf{25}(1), ~1--7 (January 1979).
\doi{10.1109/TIT.1979.1055985}
\bibitem{ml:70}
Martin-L{\"{o}}f, P.: On the notion of randomness. In: Kino, A., Myhill, J.,
Vesley, R.E. (eds.) Intuitionism and Proof Theory, p.~73. North-Holland,
Amsterdam and London (1970)
\bibitem{mermin-2004-shutup}
Mermin, D.N.: Could {F}eynman have said this? Physics Today \textbf{57},
10--11 (1989). \doi{10.1063/1.1768652},
\url{https://doi.org/10.1063/1.1768652}
\bibitem{mermin-1989-shutup}
Mermin, D.N.: What's wrong with this pillow? Physics Today \textbf{42}, 9--11
(1989). \doi{10.1063/1.2810963}, \url{https://doi.org/10.1063/1.2810963}
\bibitem{mermin-07}
Mermin, D.N.: Quantum Computer Science. Cambridge University Press, Cambridge
(2007). \doi{10.1017/CBO9780511813870},
\url{https://doi.org/10.1017/CBO9780511813870}
\bibitem{mermin-2019}
Mermin, D.N.: Making better sense of quantum mechanics (2019),
\url{https://arxiv.org/abs/1809.01639}
\bibitem{Myrvold2011237}
Myrvold, W.C.: Statistical mechanics and thermodynamics: A {M}axwellian view.
Studies in History and Philosophy of Science Part B: Studies in History and
Philosophy of Modern Physics \textbf{42}(4), 237--243 (2011).
\doi{10.1016/j.shpsb.2011.07.001},
\url{https://doi.org/10.1016/j.shpsb.2011.07.001}
\bibitem{nielsen-book10}
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information.
Cambridge University Press, Cambridge (2010). \doi{10.1017/CBO9780511976667},
\url{https://doi.org/10.1017/CBO9780511976667}, 10th Anniversary Edition
\bibitem{pitowsky:218}
Pitowsky, I.: Infinite and finite {G}leason's theorems and the logic of
indeterminacy. Journal of Mathematical Physics \textbf{39}(1), 218--228
(1998). \doi{10.1063/1.532334}, \url{https://doi.org/10.1063/1.532334}
\bibitem{schrodinger}
Schr{\"{o}}dinger, E.: {D}ie gegenw\"artige {S}ituation in der
{Q}uantenmechanik. Naturwissenschaften \textbf{23}, 807--812, 823--828,
844--849 (1935). \doi{10.1007/BF01491891, 10.1007/BF01491914,
10.1007/BF01491987}, \url{https://doi.org/10.1007/BF01491891,
https://doi.org/10.1007/BF01491914, https://doi.org/10.1007/BF01491987}
\bibitem{svozil-2002-statepart-prl}
Svozil, K.: Quantum information in base $n$ defined by state partitions.
Physical Review A \textbf{66}, 044306 (2002).
\doi{10.1103/PhysRevA.66.044306},
\url{https://doi.org/10.1103/PhysRevA.66.044306}
\bibitem{svozil-2003-garda}
Svozil, K.: Quantum information via state partitions and the context
translation principle. Journal of Modern Optics \textbf{51}, 811--819
(2004). \doi{10.1080/09500340410001664179},
\url{https://doi.org/10.1080/09500340410001664179}
\bibitem{svozil-2005-ko}
Svozil, K.: Characterization of quantum computable decision problems by state
discrimination. In: Adenier, G., Khrennikov, A., Nieuwenhuizen, T.M. (eds.)
Quantum Theory: Reconsideration of Foundations---3. vol.~810, pp. 271--279.
American Institute of Physics (2006). \doi{10.1063/1.2158729},
\url{https://doi.org/10.1063/1.2158729}
\bibitem{svozil-2016-quantum-hokus-pokus}
Svozil, K.: Quantum hocus-pocus. Ethics in Science and Environmental Politics
(ESEP) \textbf{16}(1), 25--30 (2016). \doi{10.3354/esep00171},
\url{https://doi.org/10.3354/esep00171}
\bibitem{svozil-2018-whycontexts}
Svozil, K.: New forms of quantum value indefiniteness suggest that incompatible
views on contexts are epistemic. Entropy \textbf{20}(6), 406(22) (2018).
\doi{10.3390/e20060406}, \url{https://doi.org/10.3390/e20060406}
\bibitem{svozil-2016-pu-book}
Svozil, K.: Physical [A]Causality. {D}eterminism, Randomness and Uncaused
Events. Springer, Cham, Berlin, Heidelberg, New York (2018).
\doi{10.1007/978-3-319-70815-7},
\url{https://doi.org/10.1007/978-3-319-70815-7}
\bibitem{2007-tkadlec-svozil-springer}
Svozil, K., Tkadlec, J.: On the solution of trivalent decision problems by
quantum state identification. Natural Computing \textbf{in print}, in print
(2009). \doi{10.1007/s11047-009-9112-5},
\url{https://doi.org/10.1007/s11047-009-9112-5}
\bibitem{Turing-Intelligent_Machinery}
Turing, A.M.: Intelligent machinery. In: Evans, C.R., Robertson, A.D.J. (eds.)
{C}ybernetics. {K}ey Papers, pp. 27--52. Butterworths, London (1968)
\bibitem{Wiesner-2017}
Wiesner, K.: The careless use of language in quantum information,
\url{https://arxiv.org/abs/1705.06768}
\end{thebibliography}
\end{document}
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\title{Ditirambi di Dioniso}
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\author{Friedrich Nietzsche}
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\section{Nota introduttiva}
Se non scritte al di là della soglia di non ritorno, queste poesie sono state riassettate e preparate per la stampa in piena crisi. Nietzsche scrive ormai biglietti e lettere che, ai più, sono sembrati privi di senso. Lo erano veramente? Non più di quanto appaia il tentativo realizzato nel consegnare agli assennati facitori di teorie, che ormai si era lasciato alla spalle, queste riflessioni poetiche, che tali sono, in linea con quanto aveva scritto di filosofico nella sua non lunga vita.
Il fatto è che qui agisce la logica del tutto e subito, la stessa che rendeva non solo “incomprensibili” le menadi, ma che sconvolgeva l’assetto ben ordinato del mondo apollineo il quale, fra l’altro, costringeva le donne a mantenersi all’interno delle regole della cosiddetta buona creanza. E siccome tutto ciò che esce dalle regole causa fastidio, deve essere ricondotto, a ogni costo, all’interno di una spiegazione logica plausibile.
Ecco, i ditirambi di Nietzsche non sono plausibili, sono un viaggio nell’inverosimile, nell’intuizione dell’immenso che sta “oltre”, al di là del muro di cinta, dove per i commensali del limitato e del conteggiato è indigestione.
Non ho letto mai, fra le centinaia di pagine sull’opera di Nietzsche che mi è piaciuto affrontare, un solo rigo degno di rispetto riguardo i ditirambi. Nessun filosofo ha mai ardito avventurarsi al di là dell’irreversibile, ogni buon uomo tiene alla propria incolumità.
Sarà lo stesso per i pochi lettori di questi libretto? Spero di no.
\bigskip
Trieste, 20 novembre 2011
\begin{flushright}
Alfredo M. Bonanno
\end{flushright}
\chapter{Soltanto stolto! Soltanto poeta!}
\begin{verse}
Nell’aria rischiarata,\forcelinebreak
quando già la consolazione della rugiada stilla\forcelinebreak
sopra la terra, invisibile e inudita\forcelinebreak
– poiché come tutti i dolci consolatori indossa\forcelinebreak
la confortatrice rugiada delicati calzari –\forcelinebreak
allora ricordi, ricordi, cuore ardente,\forcelinebreak
come fosti assetato, un tempo, come, stanco e riarso,\forcelinebreak
fosti assetato di lacrime celesti e gocce di rugiada,\forcelinebreak
mentre su gialli sentieri d’erba\forcelinebreak
tra neri alberi ti correvano intorno\forcelinebreak
malvagi sguardi serali del sole,\forcelinebreak
accecanti, ardenti, maligni sguardi del sole.
Il pretendente della verità tu? così schernivano\forcelinebreak
no! soltanto un poeta!\forcelinebreak
un astuto, rapace, strisciante animale\forcelinebreak
che deve mentire,\forcelinebreak
che sapendo, volendo, deve mentire,\forcelinebreak
bramoso di preda,\forcelinebreak
variamente mascherato,\forcelinebreak
maschera egli stesso,\forcelinebreak
egli stesso preda\forcelinebreak
\emph{questo} – il pretendente della verità?\dots{}\forcelinebreak
Soltanto stolto! Soltanto poeta!\forcelinebreak
Che parla in modo variopinto,\forcelinebreak
che dalle maschere di stolto parla confusamente,\forcelinebreak
arrampicandosi su menzogneri ponti di parole,\forcelinebreak
girovagando, strisciando\forcelinebreak
su arcobaleni di menzogne tra falsi cieli –\forcelinebreak
\emph{soltanto} stolto! \emph{soltanto} poeta!\dots{}
Questo – il pretendente della verità?\dots{}
Non quieto, rigido, piano, freddo,\forcelinebreak
divenuto immagine,\forcelinebreak
pilastro di dio,\forcelinebreak
non innalzato dinanzi ai templi,\forcelinebreak
un guardiano di dio:\forcelinebreak
no! ostile a simili statue di virtù,\forcelinebreak
più nelle selve che nei templi di casa,\forcelinebreak
colmo di una felina spavalderia\forcelinebreak
che salta oltre ogni finestra\forcelinebreak
hop! in ogni azzardo,\forcelinebreak
fiutando ogni foresta vergine,\forcelinebreak
tu che corresti nelle foreste vergini\forcelinebreak
tra variegati e arruffati animali da preda\forcelinebreak
empiamente sano e bello e variopinto,\forcelinebreak
con labbra vogliose,\forcelinebreak
beato di scherno, beato d’inferno, beato di brama di sangue,\forcelinebreak
predando, strisciando, \emph{mentendo} corresti\dots{}
Oppure simile all’aquila che a lungo,\forcelinebreak
a lungo immobile fissa gli abissi,\forcelinebreak
i suoi abissi\dots{}\forcelinebreak
– oh, come quaggiù essi\forcelinebreak
si inanellano in basso, in dentro,\forcelinebreak
in sempre più fonde profondità! –\forcelinebreak
Poi,\forcelinebreak
d’un tratto,\forcelinebreak
con volo diritto\forcelinebreak
e slancio improvviso\forcelinebreak
gettarsi su \emph{agnelli}\forcelinebreak
a precipizio,\forcelinebreak
affamato, bramoso di agnelli,\forcelinebreak
adirato con tutte le anime d’agnello\forcelinebreak
furiosamente adirato con tutto ciò che ha\forcelinebreak
sguardi virtuosi, di pecora, sguardi dal vello ricciuto,\forcelinebreak
ottusi, muniti della benevolenza del latte d’agnello\dots{}
Così\forcelinebreak
come di aquila, di pantera\forcelinebreak
sono le bramosie del poeta,\forcelinebreak
sono, dietro mille maschere,\forcelinebreak
le tue bramosie, tu stolto! tu poeta!\dots{}
Tu che vedesti l’uomo\forcelinebreak
come \emph{dio} e come \emph{pecora} –;\forcelinebreak
\emph{sbranare} il dio nell’uomo\forcelinebreak
come la pecora nell’uomo\forcelinebreak
e \emph{ridere} sbranando –\forcelinebreak
\emph{questa}, \emph{questa} è la tua beatitudine,\forcelinebreak
la beatitudine di una pantera e di un’aquila,\forcelinebreak
la beatitudine di un poeta e di uno stolto!\dots{}
Nell’aria rischiarata,\forcelinebreak
quando già la falce della luna\forcelinebreak
verde tra rossi di porpora\forcelinebreak
invidiosa s’insinua,\forcelinebreak
– avversa al giorno,\forcelinebreak
a ogni passo segretamente\forcelinebreak
falciando amache di rose,\forcelinebreak
fino a quando esse cadono,\forcelinebreak
pallide cadono verso la notte:
così io stesso caddi, una volta,\forcelinebreak
dalla mia follia di verità,\forcelinebreak
dalle mie bramosie del giorno,\forcelinebreak
stanco del giorno, sofferente per la luce,\forcelinebreak
– caddi in giù, verso la sera, verso l’ombra,\forcelinebreak
bruciato da una sola\forcelinebreak
verità e assetato\forcelinebreak
– ricordi ancora, ricordi, cuore ardente,\forcelinebreak
com’eri assetato allora? –\forcelinebreak
\emph{che io sia bandito}\forcelinebreak
\emph{da ogni verità}!\forcelinebreak
\emph{Soltanto} stolto! soltanto poeta!\dots{}
\end{verse}
\chapter{Tra figlie del deserto}
\begin{verse}
\emph{Il deserto cresce}: \emph{guai a colui che cela deserti}\dots{}
Ah!\forcelinebreak
Solenne!\forcelinebreak
un degno inizio!\forcelinebreak
africanamente solenne!\forcelinebreak
d’un leone degno\forcelinebreak
o di una morale scimmia urlatrice\dots{}\forcelinebreak
ma nulla per voi,\forcelinebreak
voi dilette amiche,\forcelinebreak
ai cui piedi è concesso\forcelinebreak
a me, a un Europeo sotto le palme,\forcelinebreak
di sedere. Sela.
Meraviglioso invero!\forcelinebreak
Qui siedo ora,\forcelinebreak
prossimo al deserto e già\forcelinebreak
nuovamente al deserto tanto lontano,\forcelinebreak
ma in nulla ancora desolato:\forcelinebreak
inghiottito infatti\forcelinebreak
da questa minuscola oasi\forcelinebreak
essa spalancò sbadigliando\forcelinebreak
la sua graziosa bocca,\forcelinebreak
la più odorosa tra le boccucce:\forcelinebreak
io vi caddi attraverso,\forcelinebreak
giù dentro – tra voi,\forcelinebreak
voi dilette amiche! Sela.
Salute, salute a quella balena,\forcelinebreak
se essa fece star comodo\forcelinebreak
il suo ospite! – intendete\forcelinebreak
la mia dotta allusione?\dots{}\forcelinebreak
Salute al suo ventre dunque,\forcelinebreak
se esso era\forcelinebreak
un leggiadro ventre di oasi\forcelinebreak
simile a questo: del che tuttavia dubito.\forcelinebreak
Dal momento che vengo dall’Europa\forcelinebreak
che è la più scettica tra tutte le sposine.\forcelinebreak
Voglia dio migliorarla!\forcelinebreak
Amen!
Qui siedo dunque,\forcelinebreak
In quest’oasi minuscola,\forcelinebreak
simile a un dattero,\forcelinebreak
bruno, zuccherato, gocciolante oro,\forcelinebreak
bramoso di una rotonda bocca di fanciulla,\forcelinebreak
ma più ancora di virginei, gelidi,\forcelinebreak
taglienti incisivi bianchi come neve:\forcelinebreak
dei quali infatti\forcelinebreak
è avido il cuore di tutti i datteri ardenti. Sela.
Simile, troppo simile\forcelinebreak
ai nominati frutti del sud\forcelinebreak
giaccio qui circondato\forcelinebreak
dai giochi e dalle danze di piccoli\forcelinebreak
scarabei alati,\forcelinebreak
e insieme da ancor più piccoli\forcelinebreak
più stolti e più malvagi\forcelinebreak
desideri e capricci, –\forcelinebreak
circondato da voi,\forcelinebreak
voi mute, voi presaghe\forcelinebreak
fanciulle-gatto\forcelinebreak
Dudù e Suleika\forcelinebreak
– \emph{racchiuso da una sfinge}, per imbottire\forcelinebreak
una parola di molti sentimenti\forcelinebreak
(– dio mi perdoni\forcelinebreak
questo peccato linguistico!\dots{})\forcelinebreak
– siedo qui, annusando l’aria migliore,\forcelinebreak
aria di paradiso, in verità,\forcelinebreak
aria chiara e leggera, striata d’oro,\forcelinebreak
l’aria più buona che mai\forcelinebreak
sia caduta dalla luna,\forcelinebreak
fu per caso\forcelinebreak
o avvenne per superbia?\forcelinebreak
raccontano gli antichi poeti.\forcelinebreak
Ma io scettico ne dubito,\forcelinebreak
dal momento che vengo\forcelinebreak
dall’Europa,\forcelinebreak
la più scettica tra tutte le sposine.\forcelinebreak
Voglia dio migliorarla!\forcelinebreak
Amen.
Respirando questa bellissima aria,\forcelinebreak
con nari rigonfie come calici,\forcelinebreak
senza futuro, senza ricordi,\forcelinebreak
così qui siedo,\forcelinebreak
voi dilette amiche,\forcelinebreak
e guardo la palma,\forcelinebreak
come essa simile a una danzatrice,\forcelinebreak
si pieghi e si fletta e si culli sull’anca\forcelinebreak
sì fa lo stesso se la si osserva a lungo\dots{}\forcelinebreak
simile a una danzatrice che, mi pare,\forcelinebreak
già troppo a lungo, pericolosamente a lungo,\forcelinebreak
sempre, sempre si erge su una gambetta sola?\forcelinebreak
– mi pare perciò che abbia dimenticato\forcelinebreak
l’altra gambetta?\forcelinebreak
Invano almeno\forcelinebreak
cercai il mancante\forcelinebreak
gioiello gemello\forcelinebreak
– cioè l’altra gambetta –\forcelinebreak
nelle sacre vicinanze\forcelinebreak
del suo leggiadrissimo, graziosissimo gonnellino\forcelinebreak
a ventaglio, svolazzante di lustrini.\forcelinebreak
Sì, se voi, mie belle amiche,\forcelinebreak
vorrete credermi fino in fondo\forcelinebreak
essa l’ha \emph{perduta}\dots{}\forcelinebreak
Uh! uh! uh! uh! uh!\forcelinebreak
È svanita,\forcelinebreak
per sempre svanita,\forcelinebreak
l’altra gambetta!\forcelinebreak
Oh, che peccato per quest’altra graziosa gambetta!\forcelinebreak
Dove – si troverà mai e languirà abbandonata,\forcelinebreak
questa solitaria gambetta?\forcelinebreak
Nel terrore forse\forcelinebreak
di un mostruoso, rabbioso, giallo\forcelinebreak
leone dalla bionda criniera? o addirittura\forcelinebreak
già rosicchiata, scarnificata –\forcelinebreak
miseramente ah! ah! scarnificata! Sela.
Oh non piangete,\forcelinebreak
teneri cuori!\forcelinebreak
Non piangete, voi\forcelinebreak
cuori di dattero! seni di latte!\forcelinebreak
voi sacchetti dal cuore\forcelinebreak
di liquirizia!\forcelinebreak
Sii uomo, Suleika! Coraggio! Coraggio!\forcelinebreak
Non piangere più\forcelinebreak
pallida Dudù!\forcelinebreak
– O non sarebbe\forcelinebreak
qui forse il caso di qualcosa di tonificante\forcelinebreak
di tonificante per il cuore?\forcelinebreak
una consacrata sentenza?\forcelinebreak
un solenne conforto?\dots{}
Ah!\forcelinebreak
Innalzati, dignità!\forcelinebreak
Soffia, soffia ancora\forcelinebreak
mantice della virtù!\forcelinebreak
Ah!\forcelinebreak
Ancora una volta ruggire,\forcelinebreak
moralmente ruggire,\forcelinebreak
ruggire da leone morale dinanzi alle figlie del deserto!.\forcelinebreak
– Poiché il latrato della virtù,\forcelinebreak
voi fanciulle dilette,\forcelinebreak
di ogni cosa\forcelinebreak
zelo da Europei, voracità da Europei!\forcelinebreak
E qui io resto già,\forcelinebreak
come Europeo,\forcelinebreak
non posso fare altrimenti, che dio m’aiuti!\forcelinebreak
Amen!
Il deserto cresce: guai a colui che cela deserti!\forcelinebreak
Pietra stride contro pietra, il deserto divora e strangola.\forcelinebreak
La mostruosa morte guarda rovente, bruna\forcelinebreak
e \emph{mastica}, – la sua vita è il suo masticare\dots{}\forcelinebreak
\emph{Uomo che la voluttà ha bruciato}, \emph{non dimenticare} –\forcelinebreak
\emph{tu sei la pietra}, \emph{il deserto}, \emph{sei la morte}\dots{}
\end{verse}
\chapter{Ultima volontà}
\begin{verse}
Morire così,\forcelinebreak
come un giorno lo vidi morire –,\forcelinebreak
l’amico, che saette e sguardi divinamente gettò\forcelinebreak
nella mia oscura giovinezza.\forcelinebreak
Sventato e profondo,\forcelinebreak
danzatore nella battaglia –,
tra guerrieri il più sereno,\forcelinebreak
tra vincitori il più arduo,\forcelinebreak
un destino ritto sul suo destino,\forcelinebreak
duro, riflessivo, pensieroso di ciò che sarà –:
tremante \emph{perché} aveva vinto,\forcelinebreak
esultante perché \emph{morendo} aveva vinto –:
ordinava, mentre moriva\forcelinebreak
e ordinò che si \emph{annientasse}\dots{}
Morire così,\forcelinebreak
come un giorno lo vidi morire:\forcelinebreak
vincendo, \emph{annientando}\dots{}
\end{verse}
\chapter{Tra uccelli predatori}
\begin{verse}
Chi volge in basso qui,\forcelinebreak
come presto\forcelinebreak
lo inghiotte l’abisso!\forcelinebreak
Ma tu, Zarathustra,\forcelinebreak
ami ancora l’abisso\forcelinebreak
fai come l’\emph{abete}?
Esso mette radici, dove\forcelinebreak
il dirupo stesso rabbrividendo\forcelinebreak
guarda il profondo –,\forcelinebreak
esita sopra precipizi\forcelinebreak
intorno ai quali tutto\forcelinebreak
volge verso il fondo:\forcelinebreak
tra l’impazienza\forcelinebreak
di selvaggia frana, di impetuoso ruscello\forcelinebreak
sopportando paziente, duro, silente,\forcelinebreak
solo\dots{}
\emph{Solo}!\forcelinebreak
Chi osò mai\forcelinebreak
essere ospite qui,\forcelinebreak
essere ospite \emph{tuo}?\dots{}\forcelinebreak
Forse un uccello predatore:\forcelinebreak
questi si aggrappa\forcelinebreak
volentieri ai capelli\forcelinebreak
di chi saldo pazienta,\forcelinebreak
maligno, con riso folle,\forcelinebreak
il riso di un uccello predatore\dots{}\forcelinebreak
\emph{Perché} così saldo?\forcelinebreak
– schernisce egli spietato:\forcelinebreak
bisogna avere ali, se si ama l’abisso\dots{}\forcelinebreak
non restare appesi\forcelinebreak
come te, impiccato! –
Oh Zarathustra,\forcelinebreak
crudelissimo Nimrod!\forcelinebreak
Poc’anzi ancora cacciatore di dio,\forcelinebreak
la rete che cattura ogni virtù,\forcelinebreak
la freccia del male!\forcelinebreak
Ora –\forcelinebreak
da te stesso catturato,\forcelinebreak
tua propria preda,\forcelinebreak
penetrato in te stesso\dots{}
Ora –\forcelinebreak
con te stesso solo,\forcelinebreak
duplice nel tuo sapere,\forcelinebreak
tra cento specchi\forcelinebreak
falso dinanzi a te stesso,\forcelinebreak
tra cento ricordi\forcelinebreak
incerto,\forcelinebreak
stanco di ogni ferita,\forcelinebreak
freddo per ogni gelo,\forcelinebreak
dalle tue stesse funi strangolato,\forcelinebreak
\emph{conoscitore di te stesso}!\forcelinebreak
\emph{carnefice di te stesso}!
Perché mai ti legasti\forcelinebreak
con la fune della tua saggezza?\forcelinebreak
Perché mai attirasti te stesso\forcelinebreak
nel paradiso del vecchio serpente?\forcelinebreak
Perché mai ti insinuasti strisciando\forcelinebreak
in \emph{te} – in \emph{te}?\dots{}
Ora un malato,\forcelinebreak
reso infermo dal veleno del serpente;\forcelinebreak
un prigioniero ora,\forcelinebreak
cui toccò in sorte il più duro destino:\forcelinebreak
che lavora curvo nel proprio pozzo,\forcelinebreak
vuoto in se stesso come una caverna\forcelinebreak
che scava in se stesso\forcelinebreak
maldestro,\forcelinebreak
rigido,\forcelinebreak
una salma –\forcelinebreak
sovrastato da cento gravami sovrastanti,\forcelinebreak
sovraccarico di te,\forcelinebreak
un \emph{sapiente}!\forcelinebreak
un \emph{conoscitore di se stesso}!\forcelinebreak
il \emph{sapiente} Zarathustra!\dots{}
Tu cercasti il carico più pesante:\forcelinebreak
e lì trovasti \emph{te} stesso –,\forcelinebreak
non ti libererai di te\dots{}
In agguato,\forcelinebreak
rannicchiato,\forcelinebreak
incapace di stare ritto in piedi!\forcelinebreak
Mi appari aggrovigliato alla tua tomba,\forcelinebreak
spirito \emph{deforme}!\dots{}\forcelinebreak
E poc’anzi così orgoglioso,\forcelinebreak
su tutti i trampoli del tuo orgoglio\forcelinebreak
poc’anzi l’anacoreta senza dio,\forcelinebreak
che il suo eremo divide con il diavolo,\forcelinebreak
il principe scarlatto di ogni superbia!\dots{}
Ora –\forcelinebreak
in mezzo a due nulla\forcelinebreak
rannicchiato,\forcelinebreak
un punto interrogativo,\forcelinebreak
uno stanco enigma –\forcelinebreak
un enigma da \emph{uccelli predatori}\dots{}
– essi di certo ti “risolveranno”,\forcelinebreak
già bramano la tua “risoluzione”,\forcelinebreak
svolazzano intorno a te, il loro enigma,\forcelinebreak
intorno a te, impiccato!\dots{}\forcelinebreak
Oh Zarathustra!\dots{}\forcelinebreak
\emph{Conoscitore di te stesso}!\dots{}\forcelinebreak
\emph{Carnefice di te stesso}!\dots{}
\end{verse}
\chapter{Il segnale di fuoco}
\begin{verse}
Qui, dove tra mari l’isola crebbe,\forcelinebreak
pietra sacrificale erta e svettante,\forcelinebreak
qui sotto nero cielo accende\forcelinebreak
Zarathustra i suoi fuochi d’altura,\forcelinebreak
segnali di fuoco per naviganti sperduti,\forcelinebreak
interrogativi per coloro che hanno risposte\dots{}
Questa fiamma dal ventre grigio chiaro\forcelinebreak
– in fredde lontananze guizza la sua brama,\forcelinebreak
verso sempre più pure altezze essa piega il collo –\forcelinebreak
un serpente che si erge ritto per l’impazienza:\forcelinebreak
questo segno io posi innanzi a me.
La mia anima stessa è questa fiamma,\forcelinebreak
insaziabile di nuove lontananze\forcelinebreak
divampa alto, alto il suo quieto fuoco.\forcelinebreak
Perché mai Zarathustra fuggì animali e uomini?\forcelinebreak
Perché d’un tratto sfuggì alla terra ferma?\forcelinebreak
\emph{Sei} solitudini già egli conosce –,\forcelinebreak
ma neanche il mare fu per lui abbastanza solitario,\forcelinebreak
l’isola lo lasciò salire, sul monte divenne fiamma,\forcelinebreak
cercando una settima solitudine\forcelinebreak
egli getta ora l’amo sopra il capo.
Sperduti naviganti! Macerie d’antichi astri!\forcelinebreak
Voi mari del futuro! Cieli insondati!\forcelinebreak
A tutti i solitari ora getto l’amo:\forcelinebreak
rispondete all’impazienza della fiamma,\forcelinebreak
prendete a me, pescatore su alti monti,\forcelinebreak
la mia settima, \emph{ultima} solitudine! –
\end{verse}
\chapter{Il sole declina}
\begin{verse}
Non più a lungo avrai sete\forcelinebreak
~~~~riarso cuore!\forcelinebreak
Una promessa è nell’aria,\forcelinebreak
soffia da bocche sconosciute a me\forcelinebreak
~~~~– la grande frescura viene\dots{}
Stava nel meriggio ardente su di me il mio sole:\forcelinebreak
siate i benvenuti, voi che venite\forcelinebreak
~~~~venti improvvisi\forcelinebreak
voi freschi spiriti pomeridiani!
Va l’aria estranea e pura.\forcelinebreak
Non mi sogguarda\forcelinebreak
~~~~con occhi obliqui\forcelinebreak
di seduttrice la notte?\dots{}\forcelinebreak
Stai forte, mio cuore ardito!\forcelinebreak
Non domandare: perché? –
Giorno della mia vita!\forcelinebreak
il sole declina.\forcelinebreak
Già sta dorata\forcelinebreak
~~~~la piatta marea.\forcelinebreak
Calda respira la rupe:\forcelinebreak
~~~~dormì forse qui nel meriggio\forcelinebreak
la felicità il suo sonno pomeridiano?\forcelinebreak
~~~~Tra verdi luci\forcelinebreak
il bruno abisso innalza ancora un gioco felice.
Giorno della mia vita!\forcelinebreak
Il sole declina!\forcelinebreak
Già arde il tuo occhio\forcelinebreak
~~~~spezzato in due,\forcelinebreak
già gocciano lacrime stillanti\forcelinebreak
~~~~della tua rugiada,\forcelinebreak
già scorre silenziosa su bianchi mari\forcelinebreak
la porpora del tuo amore,\forcelinebreak
la tua ultima, esitante beatitudine\dots{}
Serenità, dorata, vieni!\forcelinebreak
~~~~tu della morte\forcelinebreak
più segreto, più dolce assaggio!\forcelinebreak
– Corsi troppo veloce la mia strada?\forcelinebreak
Soltanto ora che il piede si stancò,\forcelinebreak
~~~~mi raggiunge ancora il tuo sguardo,\forcelinebreak
~~~~mi raggiunge ancora la tua \emph{felicità}.
Tutt’intorno soltanto onda e gioco.\forcelinebreak
~~~~Ciò che fu un tempo pesante\forcelinebreak
sprofondò in azzurro oblio,\forcelinebreak
inoperosa è ora la mia barca.\forcelinebreak
Tempesta e viaggio – come essa disimpara!\forcelinebreak
~~~~Annegò desiderio e speranza,\forcelinebreak
~~~~lisci giacciono anima e mare.\forcelinebreak
Settima solitudine!\forcelinebreak
~~~~Mai sentii a me\forcelinebreak
più vicina una dolce certezza,\forcelinebreak
più caldo lo sguardo del sole.\forcelinebreak
– Non arde ancora il ghiaccio della mia vetta?\forcelinebreak
~~~~Argentea, lieve, come un pesce\forcelinebreak
~~~~nuota ora al largo la mia barca\dots{}
\end{verse}
\chapter{Lamento di Arianna}
\begin{verse}
Chi mi riscalda, chi mi ama ancora?\forcelinebreak
~~~~Date mani ardenti,\forcelinebreak
~~~~date bracieri del cuore!\forcelinebreak
Già prostrata, colta da brividi,\forcelinebreak
una moribonda quasi, cui si scaldano i piedi,\forcelinebreak
scossa, ah!, da febbri sconosciute\forcelinebreak
tremante per freddi, gelidi dardi acuminati,\forcelinebreak
~~~~da te inseguita, pensiero!\forcelinebreak
Innominabile! Celato! Tremendo!\forcelinebreak
~~~~Tu cacciatore oltre le nubi!\forcelinebreak
Prostrata dai tuoi fulmini,\forcelinebreak
tu occhio beffardo, che dall’oscurità mi osservi!\forcelinebreak
~~~~Così io giaccio,\forcelinebreak
mi piego, mi dibatto, tormentata\forcelinebreak
da tutti gli eterni martiri,\forcelinebreak
~~~~colpita\forcelinebreak
da te, spietatissimo cacciatore,\forcelinebreak
sconosciuto – \emph{dio}\dots{}
Colpisci più in fondo!\forcelinebreak
Colpisci una volta ancora!\forcelinebreak
Trafiggi, infrangi questo cuore!\forcelinebreak
A che questa tortura\forcelinebreak
con frecce spuntate?\forcelinebreak
Perché guardi di nuovo\forcelinebreak
inappagato del tormento umano,\forcelinebreak
con maligni, divini occhi lampeggianti?\forcelinebreak
Non vuoi uccidere,\forcelinebreak
torturare solo, torturare?\forcelinebreak
A che – torturar\emph{mi},\forcelinebreak
un maligno dio sconosciuto?
Ah! Ah!\forcelinebreak
Ti avvicini furtivo\forcelinebreak
in questa mezzanotte?\dots{}\forcelinebreak
Che cosa vuoi?\forcelinebreak
Parla!\forcelinebreak
Tu mi premi, mi incalzi\forcelinebreak
ah! troppo da presso!\forcelinebreak
Mi ascolti respirare,\forcelinebreak
il tuo orecchio spia il mio cuore,\forcelinebreak
geloso!\forcelinebreak
~~~~– ma geloso di che?
Via! via!\forcelinebreak
perché la scala?\forcelinebreak
Vuoi entrare\forcelinebreak
\emph{nel} cuore, salire,\forcelinebreak
nei miei\forcelinebreak
più segreti pensieri?\forcelinebreak
Impudico! Sconosciuto! Ladro!\forcelinebreak
Cosa vorresti rubare?\forcelinebreak
Cosa vorresti ascoltare?\forcelinebreak
Che cosa estorcere,\forcelinebreak
torturatore!\forcelinebreak
Tu – dio carnefice!\forcelinebreak
O devo io, simile al cane,\forcelinebreak
rotolare dinanzi a te?\forcelinebreak
Abbandonata, esaltata fuori di me\forcelinebreak
per te amore – scodinzolare?
Invano!\forcelinebreak
Trafiggi ancora!\forcelinebreak
Crudelissima spina!\forcelinebreak
Non cane – solo tua preda sono,\forcelinebreak
crudelissimo cacciatore!\forcelinebreak
La tua più fiera prigioniera,\forcelinebreak
tu rapinatore oltre le nubi\dots{}\forcelinebreak
Parla infine!\forcelinebreak
Tu nascosto dal fulmine! Sconosciuto! parla!\forcelinebreak
Che cosa vuoi tu, bandito, da – \emph{me}?\dots{}
Come?\forcelinebreak
Prezzo del riscatto?\forcelinebreak
Quanto vuoi per il riscatto?\forcelinebreak
Chiedi molto – suggerisce il mio orgoglio!\forcelinebreak
e parla poco – suggerisce l’altro mio orgoglio!\forcelinebreak
Ah! Ah!\forcelinebreak
Me – vorresti? me?\forcelinebreak
me – tutta?\dots{}
Ah! Ah!\forcelinebreak
E mi tormenti, pazzo che non sei altro,\forcelinebreak
martirizzi il mio orgoglio?\forcelinebreak
~~~~Dammi \emph{amore} chi mi riscalda ancora?\forcelinebreak
~~~~chi mi ama ancora?\forcelinebreak
Da’ mani ardenti,\forcelinebreak
da’ bracieri del cuore,\forcelinebreak
da’ a me, la più sola,\forcelinebreak
cui ghiaccio, ah!, ghiaccio dalle sette forme\forcelinebreak
insegna a bramare nemici,\forcelinebreak
persino nemici,\forcelinebreak
datti a me, \emph{te},\forcelinebreak
crudelissimo nemico,\forcelinebreak
arrenditi! \dots{}
Via!\forcelinebreak
Anch’egli fuggi ora,\forcelinebreak
mio solo compagno,\forcelinebreak
mio grande nemico,\forcelinebreak
mio sconosciuto,\forcelinebreak
mio dio-carnefice!\dots{}\forcelinebreak
No!\forcelinebreak
ritorna\forcelinebreak
Con tutte le tue torture!\forcelinebreak
Le mie lacrime tutte\forcelinebreak
corrono verso te\forcelinebreak
e l’ultima fiamma del mio cuore\forcelinebreak
risplende per te.\forcelinebreak
Oh, ritorna,\forcelinebreak
mio dio sconosciuto! mio \emph{dolore}!\forcelinebreak
~~~~mia ultima felicità!\dots{}
(\emph{Un lampo}. \emph{Appare Dioniso in una bellezza smeraldina})
\emph{Dioniso}:
Sii saggia Arianna!\dots{}\forcelinebreak
Hai orecchie piccole, hai le mie orecchie:\forcelinebreak
poni in esse una saggia parola! –\forcelinebreak
Non ci si deve odiare, prima, se ci si vuole amare?\dots{}\forcelinebreak
\emph{Io sono il tuo labirinto}\dots{}
\end{verse}
\chapter{Gloria ed eternità}
\begin{verse}
Da quanto tempo già stai seduto\forcelinebreak
~~~~sul tuo destino avverso?\forcelinebreak
Fa’ attenzione! tu mi covi ancora\forcelinebreak
~~~~un uovo,\forcelinebreak
~~~~un uovo di basilisco\forcelinebreak
nel tuo lungo affanno.
Perché mai Zarathustra striscia lungo il monte? –
Diffidente, ulceroso, cupo,\forcelinebreak
a lungo in agguato –,\forcelinebreak
ma, d’improvviso, un lampo\forcelinebreak
chiaro, terribile, un colpo\forcelinebreak
contro il cielo dall’abisso:\forcelinebreak
– al monte stesso si scuotono\forcelinebreak
le viscere\dots{}
Dove odio e folgore\forcelinebreak
si unirono, una \emph{maledizione}\forcelinebreak
sui monti dimora adesso l’ira di Zarathustra,\forcelinebreak
come nube di tempesta striscia sulla sua strada.
Si rintani chi ha un’ultima coperta!\forcelinebreak
A letto, voi esseri delicati!\forcelinebreak
Rotolano i tuoni ora sulle volte,\forcelinebreak
trema ora tutto ciò che è trave e muro,\forcelinebreak
sussultano ora lampi e verità giallo-zolfo –\forcelinebreak
~~~~Zarathustra \emph{maledice}\dots{}
Questa moneta con cui\forcelinebreak
il mondo intero paga,\forcelinebreak
\emph{gloria} –,\forcelinebreak
afferro con i guanti questa moneta,\forcelinebreak
con schifo la calpesto \emph{sotto} di me.
\emph{Chi} vuole esser pagato?\forcelinebreak
Coloro che si possono comprare\dots{}\forcelinebreak
Chi è \emph{in vendita}, protende\forcelinebreak
grasse mani verso\forcelinebreak
questo comodo tintinnio di latta, gloria!
– \emph{Vuoi} tu comprarli?\forcelinebreak
tutti si possono comprare.\forcelinebreak
Ma offri molto!\forcelinebreak
fai tintinnare una borsa piena!\forcelinebreak
~~~~– li \emph{rinforzeresti}, altrimenti,\forcelinebreak
rinforzeresti altrimenti le loro \emph{virtù}\dots{}
Sono tutti virtuosi.\forcelinebreak
Gloria e virtù – si accordano.\forcelinebreak
Sin quando vivrà il mondo,\forcelinebreak
pagherà il cicaleccio della virtù\forcelinebreak
con lo strepitio della gloria –\forcelinebreak
il mondo vive di questo chiasso\dots{}\forcelinebreak
Dinanzi a tutti i virtuosi\forcelinebreak
~~~~voglio essere colpevole,\forcelinebreak
colpevole esser chiamato di ogni grande colpa!\forcelinebreak
Dinanzi a tutti i megafoni della gloria\forcelinebreak
la mia ambizione diventa verme –,\forcelinebreak
tra costoro mi prende il desiderio\forcelinebreak
di essere l’\emph{infimo}\dots{}
Questa moneta con cui\forcelinebreak
il mondo intero paga,\forcelinebreak
\emph{gloria} –,\forcelinebreak
afferro con i guanti questa moneta,\forcelinebreak
con schifo la calpesto sotto di me.
Silenzio! –\forcelinebreak
Di grandi cose – io \emph{vedo} cose grandi! –\forcelinebreak
bisogna tacere\forcelinebreak
o parlare con grandezza:\forcelinebreak
parla con grandezza, mia estasiata saggezza!
Io guardo in alto\forcelinebreak
lì scorrono mari di luce:\forcelinebreak
– oh notte, oh silenzio, oh strepito silenzioso come la morte!\dots{}\forcelinebreak
Io vedo un segno –,\forcelinebreak
dalle più remote lontananze\forcelinebreak
– cala verso di me lenta, scintillante una costellazione\dots{}
Supremo astro dell’essere!\forcelinebreak
Tavola di eterne immagini!\forcelinebreak
\emph{tu} vieni a me? –\forcelinebreak
Ciò che nessuno ha scorto,\forcelinebreak
la tua muta bellezza, –\forcelinebreak
come? non fugge essa dinanzi ai miei sguardi?
Stemma della necessità!\forcelinebreak
Tavola di eterne immagini!\forcelinebreak
– ma tu lo sai:\forcelinebreak
ciò che tutti odiano,\forcelinebreak
ciò che \emph{io} solo amo,\forcelinebreak
che tu sei \emph{eterno}!\forcelinebreak
che tu sei \emph{necessario}!\forcelinebreak
Il mio amore si accende in eterno\forcelinebreak
solo alla fiamma della necessità.
Stemma della necessità!\forcelinebreak
Supremo astro dell’essere!\forcelinebreak
– che nessun desiderio raggiunge,\forcelinebreak
che nessun no imbratta,\forcelinebreak
eterno sì dell’essere,\forcelinebreak
eternamente sono io il tuo sì:\forcelinebreak
\emph{perché io ti amo}, \emph{oh eternità}! –
\end{verse}
\chapter{Della povertà del più ricco}
\begin{verse}
Passarono dieci anni –\forcelinebreak
non una goccia mi giunse,\forcelinebreak
né vento umido, né rugiada d’amore\forcelinebreak
– una terra \emph{senza pioggia}\dots{}\forcelinebreak
Ora prego la mia saggezza\forcelinebreak
di non farsi avida in questa aridità:\forcelinebreak
trabocca, stilla tu stessa rugiada\forcelinebreak
sii tu stessa pioggia alla selva ingiallita!
Ordinai un tempo alle nubi\forcelinebreak
di andar via dai miei monti –\forcelinebreak
dissi un tempo «più luce, voi oscure!»\forcelinebreak
Oggi le attiro perché vengano:\forcelinebreak
fate buio intorno a me con le vostre mammelle!\forcelinebreak
– voglio mungervi\forcelinebreak
voi, mucche superne.\forcelinebreak
Riverso su questa terra\forcelinebreak
calda saggezza di latte,\forcelinebreak
dolce rugiada d’amore.
Via, via, voi verità\forcelinebreak
che oscure guardate!\forcelinebreak
Non voglio vedere sui miei monti\forcelinebreak
verità acerbe, impazienti.\forcelinebreak
Indorata dal sorriso\forcelinebreak
mi si avvicini oggi la verità,\forcelinebreak
addolcita dal sole, brunita dall’amore –\forcelinebreak
coglierò dall’albero solo una verità \emph{matura}.
Oggi tendo la mano\forcelinebreak
verso le chiome del caso,\forcelinebreak
saggio abbastanza per condurlo,\forcelinebreak
simile a un bimbo, e ingannarlo.\forcelinebreak
Oggi voglio essere ospitale\forcelinebreak
verso ciò che è sgradito,\forcelinebreak
con il destino stesso non voglio essere spinoso\forcelinebreak
– non è un riccio Zarathustra.
La mia anima,\forcelinebreak
con la sua lingua insaziabile,\forcelinebreak
ha già leccato ogni cosa buona e cattiva,\forcelinebreak
si è immersa in ogni profondità.\forcelinebreak
Ma sempre, simile al sughero,\forcelinebreak
essa torna a nuotare in superficie,\forcelinebreak
volteggia giocando come olio su mari bruni:\forcelinebreak
in virtù di questa anima mi si chiama beato.
Chi mi è padre, chi madre?\forcelinebreak
Mi è padre il principe abbondanza\forcelinebreak
e mi è madre il quieto ridere?\forcelinebreak
Non generò l’unione di costoro\forcelinebreak
me, animale enigmatico,\forcelinebreak
me, demone della luce,\forcelinebreak
me, dissipatore di tutta la saggezza, Zarathustra?
Malato, oggi di tenerezza,\forcelinebreak
un vento di disgelo,\forcelinebreak
siede in attesa Zarathustra, in attesa sui suoi monti, –\forcelinebreak
nella sua stessa linfa
teso dolce e cotto,\forcelinebreak
sotto la sua vetta\forcelinebreak
sotto il suo ghiaccio,\forcelinebreak
stanco e felice,\forcelinebreak
un creatore nel suo settimo giorno.
– Silenzio!\forcelinebreak
Una verità vaga sopra di me\forcelinebreak
come una nube –\forcelinebreak
con invisibili folgori mi coglie. Su\forcelinebreak
ampie, lente scalinate\forcelinebreak
sale la sua fortuna verso di me:\forcelinebreak
vieni, vieni, amata verità!
– Silenzio! –\forcelinebreak
È la \emph{mia} verità! –\forcelinebreak
Da occhi esitanti,\forcelinebreak
da vellutati brividi\forcelinebreak
il suo sguardo mi coglie,\forcelinebreak
ridente, malvagio, uno sguardo di fanciulla\dots{}\forcelinebreak
Essa indovinò il \emph{fondo} della mia felicità,\forcelinebreak
\emph{mi} indovinò – ah! che cosa trama? –\forcelinebreak
Sta un drago purpureo in agguato\forcelinebreak
nell’abisso del suo sguardo di fanciulla.
– Silenzio! Parla la mia verità! –
Guai a te, Zarathustra!\forcelinebreak
Hai l’aspetto di uno\forcelinebreak
che abbia inghiottito oro:\forcelinebreak
ti squarceranno il ventre!\dots{}\forcelinebreak
Sei troppo ricco,\forcelinebreak
corruttore di molti!\forcelinebreak
Troppi rendi invidiosi,\forcelinebreak
troppi poveri\dots{}\forcelinebreak
Su me pure getta ombra la tua luce –\forcelinebreak
rabbrividisco: va’ via, tu ricco,\forcelinebreak
va’, Zarathustra, via dal tuo sole!\dots{}
Vorresti donare, dare via la tua abbondanza,\forcelinebreak
ma sei tu stesso il più superfluo!\forcelinebreak
Sii saggio, ricco!\forcelinebreak
\emph{Dona via prima te stesso}, o Zarathustra!
Passarono dieci anni –\forcelinebreak
e non una goccia ti raggiunse?\forcelinebreak
né vento umido né rugiada d’amore?\forcelinebreak
Ma \emph{chi} dovrebbe amarti,\forcelinebreak
tu troppo ricco?\forcelinebreak
La tua fortuna inaridisce all’intorno,\forcelinebreak
rende poveri d’amore\forcelinebreak
– una terra \emph{senza pioggia}\dots{}
Nessuno più ti ringrazia.\forcelinebreak
Ma tu ringrazi chiunque\forcelinebreak
prenda da te:\forcelinebreak
da ciò ti riconosco,\forcelinebreak
tu troppo ricco,\forcelinebreak
\emph{il più povero} dei ricchi!
Tu ti sacrifichi, ti \emph{tormenta} la tua ricchezza –,\forcelinebreak
ti dedichi,\forcelinebreak
non ti risparmi, non ti ami:\forcelinebreak
tarde tormento sempre ti stringe,\forcelinebreak
il tormento di granai \emph{traboccanti}, di un cuore traboccante –\forcelinebreak
ma nessuno più ti ringrazia\dots{}
Devi farti \emph{più povero},\forcelinebreak
saggio insipiente!\forcelinebreak
se vuoi essere amato.\forcelinebreak
Solo chi soffre è amato,\forcelinebreak
solo a chi ha fame si dà amore:\forcelinebreak
\emph{Dona via prima te stesso}, o Zarathustra!
– Io sono la tua verità\dots{}
\end{verse}
% begin final page
\clearpage
% new page for the colophon
\thispagestyle{empty}
\begin{center}
\bigskip
\includegraphics[width=0.25\textwidth]{anarchismologo.pdf}
\bigskip
\end{center}
\strut
\vfill
\begin{center}
Friedrich Nietzsche
Ditirambi di Dioniso
\bigskip
Prima edizione: novembre 2013\forcelinebreak Opuscoli provvisori N. 50
\bigskip
\textbf{www.edizionianarchismo.net}
\end{center}
% end final page with colophon
\end{document}
|
http://ftp.twaren.net/Unix/TeX/CTAN/fonts/vicentino/kilfiger/testvic.tex | twaren.net | CC-MAIN-2023-06 | text/x-tex | application/x-tex | crawl-data/CC-MAIN-2023-06/segments/1674764500384.17/warc/CC-MAIN-20230207035749-20230207065749-00670.warc.gz | 13,221,683 | 887 | \documentclass{article}
\usepackage{vicent}
\begin{document}
\Large\raggedright
\textcursive{This is the `cursive' shape, \textbf{in Bold series}
The Quick Brown Fox Jumps Over The Lazy Dog.}
\textmodernscript{This is the `modern script' shape, \textbf{in Bold
series} The Quick Brown Fox Jumps Over The Lazy Dog.}
\texttwist{This is the `twist' shape \textbf{in Bold
series} The Quick Brown Fox Jumps Over The Lazy Dog.}
%example of using low level font selection to get a swash `r'
\raggedleft{\LARGE\fontfamily{vc}\fontshape{ui}\selectfont
James Kilfige\fontshape{its}\selectfont r }
\end{document}
|
https://www.zentralblatt-math.org/matheduc/en/?id=236&type=tex | zentralblatt-math.org | CC-MAIN-2019-26 | text/plain | application/x-tex | crawl-data/CC-MAIN-2019-26/segments/1560627999853.94/warc/CC-MAIN-20190625152739-20190625174739-00234.warc.gz | 1,004,010,083 | 1,334 | \input zb-basic
\input zb-matheduc
\iteman{ZMATH 2016f.01354}
\itemau{Ju, Mi-Kyung; Moon, Jong-Eun; Song, Ryoon-Jin}
\itemti{History of mathematics in Korean mathematics textbooks: implication for using ethnomathematics in culturally diverse school.}
\itemso{Int. J. Sci. Math. Educ. 14, No. 7, 1321-1338 (2016).}
\itemab
Summary: From a multicultural perspective, this research investigated to what extent Korean mathematics textbooks use history of mathematics. The results show even though educational use of history presented in Korean mathematics textbooks may provide a rich outlook, it does not encourage a fundamental change in the educational practice of school mathematics that has traditionally been entrenched in the Eurocentric narrative of mathematics. This suggests that the mathematics textbooks were not organized effectively to promote students' understanding of diversity. Based on the results, we discuss the implications for the development of mathematics textbook from multicultural perspectives.
\itemrv{~}
\itemcc{U20 D30 A30 C60}
\itemut{diversity; ethnomathematics; equity; history of mathematics; multicultural competence}
\itemli{doi:10.1007/s10763-015-9647-0}
\end |
https://www.hep.princeton.edu/~mcdonald/mumu/palmer/pr_88.tex | princeton.edu | CC-MAIN-2022-21 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2022-21/segments/1652662525507.54/warc/CC-MAIN-20220519042059-20220519072059-00641.warc.gz | 929,358,642 | 1,700 | \section{NEUTRINO RADIATION}
It has been shown\cite{ref41} that the surface radiation dose $D_B(Sv)$
at a time $t(s)$, in the plane of a bending magnet of field B(T), in
a circular collider with beam energy $E(TeV)$, average bending field
$<B(T)>$, at a depth $d(m)$ (assuming a spherical earth), with muon
current (of each sign) of $I\textrm{(muons/sec/sign)}$ is given by:
$$
D_B\ \approx\ 4.4\ 10^{-24}\ {I_\mu \ E^3\ t \over d}\ {<B> \over B}\ t
$$
and that the dose $D_S$ at a location on the surface, in line with a high
beta straight section of length $\ell$ is:
$$
D_S\ \approx\ 6.7\ 10^{-24}\ {I_\mu \ E^3\ t \over d}\ {\ell <B>}\ t
$$
The first formula has been confirmed by a Monte Carlo simulation using
the MARS code\cite{mokhovrad}.
In all cases it is assumed that the average divergence angles satisfy the
condition: $\sigma_\theta << {1\over \gamma}.$
This condition is not satisfied in the straight sections approaching the IP,
and these regions, despite their length, do not contribute a significant dose.
For the 3 TeV parameters given in Tb.~\ref{sum} (muon currents
$I=6\times 10^{20}\,\mu^-/yr,$ $<B>= 6\, T,$ $B= 10\, T,$ and taking the federal limit on off site
radiation Dose/year, $D_{Fed}$ to be 1 mSv/year (100 mrem/year), then the
dose $D_B$ per year (defined as $10^7$ s), in the plane of a bending dipole
is:
$$
D_B = 1.07 \ 10^{-5}\ \ (\textrm{Sv})\ \approx 1 \% \ D_{Fed}
$$
and for a straight section of length 0.6 m is:
$$
D_B = 9.7 \ 10^{-5}\ \ (\textrm{Sv})\ \approx 10 \% \ D_{Fed}
$$
which may be taken to be a reasonable limit.
Special care will be required in the lattice design to assure that no
field free region longer than this is present. But it may be noted that the
presence of a field of even 1 T over any length, is enough to reduce the dose to the 10
\% Federal limit standard. For machines above 3 TeV, the muon current would probably have to be reduced.
For lower energy machines, the requirements get rapidly easier: a 0.5
TeV machine at 500 m depth could have 130 m straight sections, or if at 100 m depth
25 m lengths, for the same surface dose. For a 100 GeV machine the doses are
negligible.
|
https://anorien.csc.warwick.ac.uk/CTAN/fonts/ps-type1/starfont/starfont.tex | warwick.ac.uk | CC-MAIN-2023-14 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2023-14/segments/1679296945368.6/warc/CC-MAIN-20230325161021-20230325191021-00530.warc.gz | 126,905,141 | 3,939 | \documentclass{article}
\usepackage{starfont}
\usepackage{url}
\usepackage{hyperref}
\newcommand{\showboth}[1]{\starfontsans #1 & \starfontserif #1}
\begin{document}
\title{The \texttt{starfont} package for \LaTeX, version 1.2}
\author{Matthew Skala\thanks{\url{mailto:mskala@ansuz.sooke.bc.ca}}}
\date{29 September 2010}
\maketitle
\section{Introduction}
This package is designed to provide two fonts named StarFont Sans and
StarFont Serif in \LaTeX. These fonts contain a wide variety of glyphs
suitable for typesetting astrological documents. Astrological support in
previous \LaTeX\ packages is inadequate for a number of reasons that include
incomplete coverage of the popular glyph set, inconsistent style between
glyphs that need to work well when used together, simply ugly glyphs, wide
variation in widths of glyphs (which makes trouble in tables), no
availability in outline form to make well-behaved PDFs, and so on. These
glyphs aren't perfect either, but they are certainly the best ones I've
found for typesetting astrological material in \LaTeX.
Given the typical use of \LaTeX\ in the scientific community and the
relationship between the scientific community and astrology, it amuses me to
have \LaTeX\ used for astrology. It's also convenient because I write both
astrological and scientific documents and want to use the same tools for
both.
This is version 1.2 of the package, adding support for StarFont Serif and
changing the commentary on copying restrictions now that it's confirmed the
fonts are public domain. Version 1.1 dated from 29~June 2006; version 1.0
was never widely distributed but first existed around 2003 or 2004.
The fonts were designed, and distributed in TrueType form, by
Anthony~I.P. Owen. The packaging for TeX and LaTeX was done by Matthew
Skala. Both these authors have released their contributions to the public
domain. As such, the contents of this package are provided ``as is,'' with
no warranties. See the file \texttt{COPYING} for more information.
\section{Using \texttt{starfont}}
Install the fonts. Installing fonts is a black art; I have included, in the
\texttt{README} file, hints on where to put the files involved, but I do not
really understand how \LaTeX\ (and \TeX, and \texttt{dvips}, and so on)
finds font files and I cannot give meaningful instruction to others on it.
The fonts should end up installed with the names ``\texttt{fstr8x}'' for
StarFont Sans, and `\texttt{fsts8x}'' for StarFont Serif. The
\texttt{starfont} package defines NFSS families named ``\texttt{stf}'' and
`\texttt{sts}''. The general approach used imitates the way the
\texttt{marvosym} package works, and this package is to some degree
compatible with \texttt{marvosym}.
StarFont Sans is the default and recommended choice; I believe it mixes
better with other fonts typically used in \LaTeX\ documents. However, the
StarFont Serif version is also available via the \texttt{starfontserif}
package option. A corresponding \texttt{starfontsans} option will be
accepted for clarity but has no actual effect because the Sans version is
default anyway. These options have verbose names to make it easier for them
to inherit from a higher-level package like my \texttt{horoscop} package.
You can also switch between the two styles inside a document using the
\verb|\starfontsans| and \verb|\starfontserif| macros; each of these will
change the mode for any subsequent uses of the character macros below. Both
are shown in the sample tables below.
\subsection{Luminaries and traditional planets}
Here are the basics:
\begin{tabular}{llll|llll}
\verb|\Sun| & \showboth{\Sun} & Sun &
\verb|\Jupiter| & \showboth{\Jupiter} & Jupiter \\
\verb|\Moon| & \showboth{\Moon} & Moon &
\verb|\Saturn| & \showboth{\Saturn} & Saturn \\
\verb|\Mercury| & \showboth{\Mercury} & Mercury &
\verb|\Uranus| & \showboth{\Uranus} & Uranus \\
\verb|\Venus| & \showboth{\Venus} & Venus &
\verb|\Neptune| & \showboth{\Neptune} & Neptune \\
\verb|\Terra| & \showboth{\Terra} & Earth (planet) &
\verb|\Pluto| & \showboth{\Pluto} & Pluto \\
\verb|\Mars| & \showboth{\Mars} & Mars
\end{tabular}
The planet Earth is referred to as ``Terra'' in the command name to
prevent a collision with the glyph for the element Earth. Since the
element is much more commonly referred to in astrology than the
planet, it takes precedence for the more straightforward name. There
are also variants of some of these glyphs:
\begin{tabular}{llll|llll}
\verb|\varMoon| & \showboth{\varMoon} & Moon &
\verb|\varUranus| & \showboth{\varUranus} & Uranus \\
\verb|\varTerra| & \showboth{\varTerra} & Earth (planet) &
\verb|\varPluto| & \showboth{\varPluto} & Pluto
\end{tabular}
\subsection{Signs of the zodiac}
\begin{tabular}{llll|llll}
\verb|\Aries| & \showboth{\Aries} & Aries &
\verb|\Libra| & \showboth{\Libra} & Libra \\
\verb|\Taurus| & \showboth{\Taurus} & Taurus &
\verb|\Scorpio| & \showboth{\Scorpio} & Scorpio \\
\verb|\Gemini| & \showboth{\Gemini} & Gemini &
\verb|\Sagittarius| & \showboth{\Sagittarius} & Sagittarius \\
\verb|\Cancer| & \showboth{\Cancer} & Cancer &
\verb|\Capricorn| & \showboth{\Capricorn} & Capricorn \\
\verb|\Leo| & \showboth{\Leo} & Leo &
\verb|\Aquarius| & \showboth{\Aquarius} & Aquarius \\
\verb|\Virgo| & \showboth{\Virgo} & Virgo &
\verb|\Pisces| & \showboth{\Pisces} & Pisces
\end{tabular}
The command
\verb|\varCapricorn| produces ``\varCapricorn'' or
``\starfontserif\varCapricorn,'' a variant symbol for
Capricorn. This package also
provides a \verb|\Zodiac| command similar to the one in \texttt{marvosym}:
\verb|\Zodiac{1}|\ldots\verb|\Zodiac{12}| produce
\starfontsans\Zodiac{1}\ldots\Zodiac{12} or
\starfontserif\Zodiac{1}\ldots\Zodiac{12}.
\subsection{Asteroids}
\begin{tabular}{llll|llll}
\verb|\Ceres| & \showboth{\Ceres} & Ceres &
\verb|\Amor| & \showboth{\Amor} & Amor \\
\verb|\Pallas| & \showboth{\Pallas} & Pallas &
\verb|\Eros| & \showboth{\Eros} & Eros \\
\verb|\Juno| & \showboth{\Juno} & Juno &
\verb|\Hidalgo| & \showboth{\Hidalgo} & Hidalgo \\
\verb|\Vesta| & \showboth{\Vesta} & Vesta &
\verb|\Hygiea| & \showboth{\Hygiea} & Hygiea \\
\verb|\Chiron| & \showboth{\Chiron} & Chiron &
\verb|\Psyche| & \showboth{\Psyche} & Psyche \\
& & & & \verb|\Sappho| & \showboth{\Sappho} & Sappho
\end{tabular}
\subsection{Uranian hypothetical planets}
\begin{tabular}{llll|llll}
\verb|\Cupido| & \showboth{\Cupido} & Cupido &
\verb|\Apollon| & \showboth{\Apollon} & Apollon \\
\verb|\Hades| & \showboth{\Hades} & Hades &
\verb|\Admetos| & \showboth{\Admetos} & Admetos \\
\verb|\Zeus| & \showboth{\Zeus} & Zeus &
\verb|\Vulkanus| & \showboth{\Vulkanus} & Vulkanus \\
\verb|\Kronos| & \showboth{\Kronos} & Kronos &
\verb|\Poseidon| & \showboth{\Poseidon} & Poseidon
\end{tabular}
\subsection{Derived points}
\begin{tabular}{llll|llll}
\verb|\NorthNode| & \showboth{\NorthNode} & North~Node &
\verb|\SouthNode| & \showboth{\SouthNode} & Sout~Node \\
\verb|\Lilith| & \showboth{\Lilith} & Lilith &
\verb|\Fortune| & \showboth{\Fortune} & Fortune
\end{tabular}
\subsection{Aspects}
\begin{tabular}{llll|llll}
\verb|\Conjunction| & \showboth{\Conjunction} & Conjunction &
\verb|\Quincunx| & \showboth{\Quincunx} & Quincunx \\
\verb|\Opposition| & \showboth{\Opposition} & Opposition &
\verb|\Semisextile| & \showboth{\Semisextile} & Semisextile \\
\verb|\Trine| & \showboth{\Trine} & Trine &
\verb|\Semisquare| & \showboth{\Semisquare} & Semisquare \\
\verb|\Square| & \showboth{\Square} & Square &
\verb|\Sesquiquadrate| & \showboth{\Sesquiquadrate} & Sesquiquadrate \\
\verb|\Sextile| & \showboth{\Sextile} & Sextile
\end{tabular}
\subsection{Angles}
\begin{tabular}{llll|llll}
\verb|\ASC| & \showboth{\ASC} & Ascendant &
\verb|\DSC| & \showboth{\DSC} & Descendant \\
\verb|\MC| & \showboth{\MC} & Midheaven &
\verb|\IC| & \showboth{\IC} & Nadir \\
& & & (Medium C\oe li) & & & & (Imum C\oe li) \\
\verb|\Vertex| & \showboth{\Vertex} & Vertex &
\verb|\EastPoint| & \showboth{\EastPoint} & East Point
\end{tabular}
\subsection{Directions}
\begin{tabular}{llll|llll}
\verb|\Retrograde| & \showboth{\Retrograde} & Retrograde &
\verb|\Station| & \showboth{\Station} & Station \\
\verb|\Direct| & \showboth{\Direct} & Direct
\end{tabular}
\subsection{Elements}
\begin{tabular}{llll|llll}
\verb|\Fire| & \showboth{\Fire} & Fire &
\verb|\Earth| & \showboth{\Earth} & Earth (element) \\
\verb|\Air| & \showboth{\Air} & Air &
\verb|\Water| & \showboth{\Water} & Water
\end{tabular}
\subsection{Other symbols}
\begin{tabular}{llll|llll}
\verb|\Natal| & \showboth{\Natal} & Natal &
\verb|\Radix| & \showboth{\Radix} & Radix \\
\verb|\Pentagram| & \showboth{\Pentagram}
\end{tabular}
There are many other symbols in the font which I don't recognize,
including a bunch that are probably from Cosmobiology. It should be
possible to add them easily enough by following the examples in
\texttt{starfont.sty}. There is an encoding table (made by
\texttt{testfont.tex}) provided in the file \texttt{table.pdf}. I
would appreciate hearing from readers who know of good names for the
unknown symbols.
\end{document}
|
https://dlmf.nist.gov/2.10.E11.tex | nist.gov | CC-MAIN-2020-29 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2020-29/segments/1593657138718.61/warc/CC-MAIN-20200712113546-20200712143546-00185.warc.gz | 375,921,651 | 748 | \[S(\alpha,\beta,n)=\sum_{j=1}^{n-1}e^{ij\beta}j^{\alpha},\] |
http://www.mathematik.tu-dortmund.de/lsiii/cms/bibtex/40001043.tex | tu-dortmund.de | CC-MAIN-2023-14 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2023-14/segments/1679296949678.39/warc/CC-MAIN-20230331175950-20230331205950-00589.warc.gz | 78,858,977 | 923 | <br />
<b>Strict Standards</b>: Non-static method BibtexComponent::generateBibtex() should not be called statically, assuming $this from incompatible context in <b>/web/www/webdev1/nobackup/database/apache/wei/fomcms/apps/cms/controllers/cms_controller.php</b> on line <b>625</b><br />
@TECHREPORT{Reimer1976,
author = {Reimer, M.},
title = {Auswertungsalgorithmen bester numerischer Stabilit\"{a}t f\"{u}r Poynome},
year = {1976},
institution = {Fakult\"{a}t f\"{u}r Mathematik, TU Dortmund},
note = {Ergebnisberichte des Instituts f\"{u}r Angewandte Mathematik, Nummer 002},
}
|
http://barsamian.am/2de/TP1_Fete_maximum.tex | barsamian.am | CC-MAIN-2019-09 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2019-09/segments/1550247511174.69/warc/CC-MAIN-20190221213219-20190221235219-00254.warc.gz | 23,705,318 | 2,263 | \documentclass[a4paper,11pt]{article}
\setlength{\textwidth } {17cm}
\setlength{\textheight } {25cm}
\addtolength{\topmargin}{-2.50cm}
\setlength{\oddsidemargin} {-.81cm}
\setlength{\evensidemargin} {-0.01cm}
\usepackage[latin1]{inputenc}
\usepackage[french]{babel}
\usepackage{graphicx}
\usepackage{amsfonts, amsmath}
\pagestyle{empty}
\usepackage{eurosym}
\DeclareInputText{128}{\euro}% on assigne \EUR à €
\begin{document}
\newcommand{\hbra}{
\hbox to .998\textwidth{\vrule width 0.3mm height 1.8mm depth-0.3mm
\leaders\hrule height1.8mm depth-1.5mm\hfill
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\renewcommand{\labelitemi}{$\bullet$}
\renewcommand{\labelitemii}{$\diamond$}
\noindent Algorithmique : travail en groupe \hfill Lundi 20 février 2012\\
Voici un algorithme rédigé en français pour l'organisation de l'anniversaire de Sophie. Les phrases qui sont précédées de "//" sont des commentaires qui ne sont là que pour aider à la compréhension.
\begin{center}
\begin{minipage}{\textwidth}
\textbf{Une soirée d'anniversaire.}\\[-.8ex]
\begin{footnotesize}
\begin{tabular}{llll}
\multicolumn{4}{c}{\hbra}\\
\multicolumn{4}{l}{Variables :}\\
\multicolumn{4}{l}{$invites$ est un entier.}\\
\multicolumn{4}{l}{$cout$ est un entier.}\\
\multicolumn{4}{l}{$horaire$ est une heure.}\\
& & &\\
\multicolumn{4}{l}{Corps de l'algorithme :}\\
1 & \multicolumn{3}{l}{$invites$ {\bf prend la valeur} 3}\\
2 & \multicolumn{3}{l}{$cout$ {\bf prend la valeur} 200}\\
3 & \multicolumn{3}{l}{$horaire$ {\bf prend la valeur} $19^h30$}\\
4 & {\bf Si} & \multicolumn{2}{l}{$horaire \geq 19^h00$}\\
5 & & {\bf Alors} & $invites$ {\bf prend la valeur} $invites + 1$\\
6 & & & \textit{// Y. ne vient que si la fête commence après $19^h$.}\\
7 & & {\bf Sinon} & $cout$ {\bf prend la valeur} $cout + 50$\\
8 & & & \textit{// Il doit rapporter la boisson ; s'il ne vient pas, il faut l'acheter.}\\
9 & \multicolumn{3}{l}{{\bf Fin\_Bloc\_Si}}\\
10 & {\bf Si} & \multicolumn{2}{l}{$horaire \geq 19^h30$}\\
11 & & {\bf Alors} & $invites$ {\bf prend la valeur} $invites + 2$\\
12 & & & \textit{// J. \& A. ne viennent que si la fête commence après $19^h30$.}\\
13 & & {\bf Sinon} & $cout$ {\bf prend la valeur} $cout + 80$\\
14 & & & \textit{// Ils doivent rapporter le dessert ; s'ils ne viennent pas, il faut l'acheter.}\\
15 & \multicolumn{3}{l}{{\bf Fin\_Bloc\_Si}}\\
16 & {\bf Si} & \multicolumn{2}{l}{$horaire \geq 20^h00$}\\
17 & & {\bf Alors} & $invites$ {\bf prend la valeur} $invites + 2$\\
18 & & & \textit{// M. \& L. ne viennent que si la fête commence après $20^h$.}\\
19 & & {\bf Sinon} & $cout$ {\bf prend la valeur} $cout + 70$\\
20 & & & \textit{// Ils doivent rapporter l'entrée ; s'ils ne viennent pas, il faut l'acheter.}\\
21 & \multicolumn{3}{l}{{\bf Fin\_Bloc\_Si}}\\
22 & \multicolumn{3}{l}{{\bf Afficher le message} "Ce soir il y aura "}\\
23 & \multicolumn{3}{l}{{\bf Afficher la variable} $invites$}\\
24 & \multicolumn{3}{l}{{\bf Afficher le message} " invités à l'anniversaire de Sophie. La fête coûtera "}\\
25 & \multicolumn{3}{l}{{\bf Afficher la variable} $cout$}\\
26 & \multicolumn{3}{l}{{\bf Afficher le message} " €."}\\
\multicolumn{4}{c}{\hket}\\
\end{tabular}
\end{footnotesize}
\end{minipage}
\end{center}
\begin{enumerate}
\item Transcrire dans Algobox l'algorithme \og Une soirée d'anniversaire \fg. Qu'affiche le programme quand on le lance ?
\item Le tableau ci-après montre les valeurs des variables $invites$ et $cout$ au fil de l'algorithme. Il y a une nouvelle ligne à chaque fois qu'une de ces valeurs change. Ainsi, à la ligne 1, la valeur de la variable $invites$ est changée en 3 ; à la ligne 2, la valeur de la variable $cout$ est changée en 200. A la ligne 3, ces deux valeurs ne changent pas. Reproduire et terminer ce tableau. En déduire le nombre d'invités et le coût de la fête.
\begin{tabular}{|l|l|l|}
\hline
& $invites$ & $cout$\\
\hline
Ligne 1 & 3 & -\\
\hline
Ligne 2 & 3 & 200\\
\hline
... & ... & ...
\end{tabular}
\item Ecrire en français un algorithme avec trois variables : un nombre $a$, un nombre $b$ et un nombre $maximum$. Les nombres $a$ et $b$ sont donnés en entrée à l'algorithme (par ex. en Algobox avec "Lire variable"), et l'algorithme doit alors enregistrer dans la variable $maximum$ le maximum des deux nombres $a$ et $b$. Il doit enfin afficher le message "Le maximum des deux nombres est : " suivi de la valeur de la variable $maximum$.
\end{enumerate}
\end{document}
|
http://pcfm-ma.iecl.univ-lorraine.fr/communication-2.tex | univ-lorraine.fr | CC-MAIN-2018-43 | text/x-tex | text/x-matlab | crawl-data/CC-MAIN-2018-43/segments/1539583509690.35/warc/CC-MAIN-20181015184452-20181015205952-00103.warc.gz | 276,177,147 | 2,725 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\usepackage{amsfonts}
\usepackage{xcolor}
\usepackage{fancyhdr}
\usepackage{fancybox}
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\def\titre#1{\begin{center}{\Large{ \sf
#1}}\end{center}}
\def\orateur#1#2{\begin{center}{{\large{\sc
#1}}}, {#2}\end{center}}
\def\orateurAdr#1#2{\begin{center}{{\large{\it
#1}}}, {#2}\end{center}}
\def\auteur#1#2{\begin{center}{{\large{\sc
#1}}}, {#2}\end{center}}
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% PRIERE DE NE RIEN MODIFIER CI-DESSUS %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% DANS TOUTE LA SUITE NOUS PRIONS LES AUTEURS DE BIEN VOULOIR UTILISER
% LA SYNTAXE TeX STRICTE POUR LES LETTRES ACCENTUEES.
% ON PEUT AU BESOIN LES REMPLACER APR\'ES LA FRAPPE DU DOCUMENT
% PAR LEUR \'EQUIVALENT TeX.
% DANS LE CAS CONTRAIRE LES LETTRES ACCENTU\'ES N'APPARA\^ITRONT PAS
% DANS LE DOCUMENT FINAL.
%
% ORATEUR ET CO-AUTEURS
%---------------------------------------------------------------
%
% LES AUTEURS SONT PRIES DE FOURNIR LES BONS ARGUMENTS AUX MACROS CI-DESSOUS :
% \Titre : Titre de la communication
% \NomOrateur : Pr\'enom(s) NOM de l'Orateur
% \AdresseCourteOrateur : Exemple : Universit\'e de Lorraine
% \AdresseLongueOrateur : Exemple : Universit\'e cadi Ayyad..
% \EmailOrateur : Adresse electronique
%
% ET DE MEME POUR LES EVENTUELS CO-AUTEURS :
% \NomAuteurI ...
% \AdresseCourteAuteurI ...
%---------------------------------------------------------------
% DEFINIR ICI LE TITRE DE VOTRE COMMUNICATION
%\def\Titre{Titre de la communication ici }
\def\Titre{Titre de la communication ici}
%
% DEFINIR ICI LES NOMS, ADRESSES, ... DE l'ORATEUR OU UNIQUE AUTEUR
%\def\NomOrateur{Pr\'enom NOM ici }
%\def\AdresseCourteOrateur{Adresse ici }
%\def\EmailOrateur{Email ici }
\def\NomOrateur{\underline{Pr\'enom NOM}}
\def\AdresseCourteOrateur{Adresse}
\def\EmailOrateur{Email }
%
% DEFINIR ICI LES NOMS, ADRESSES, ... DES EVENTUELS CO-AUTEURS
\def\NomAuteurI{Pr\'enom NOM de co-auteur}
\def\AdresseCourteAuteurI{Adresse de co-auteur}
\def\EmailAuteurI{Email de co-auteur}
%\def\NomAuteurI{En collaboration avec : Pr\'enom NOM ici }
%\def\AdresseCourteAuteurI{Adresse ici}
%\def\EmailAuteurI{Email ici}
%=== et ainsi de suite II, III, IV, V ... pour les suivants
%
%=== Liste des mots-cles separes par des virgules si besoin
% N'enlever le signe % que si necessaire
%\def\listmotcles{mot-cle-1, mot-cle-2, ...}
%
%
% DEBUT DE LA COMMUNICATION
%---------------------------------------------------------------
% NE PAS MODIFIER LA LIGNE SUIVANTE
% Le titre est a definir dans la macro \Titre (23 lignes plus haut)
\titre{\Titre}%
%---------------------------------------------------------------
% TITRE & AUTEUR(S)
% RETIRER LES SIGNES % SI NECESSAIRE ET PLACER DANS L'ORDRE SOUHAITE
% DANS LES LIGNES SUIVANTES NE MODIFIER QUE LES SIGNES COMMENTAIRES '%'
% Les noms, adresses, email de l'orateur et des co-auteurs sont a definir
% dans les macros \NomOrateur, \AdresseCourteOrateur etc. plus haut
%---------------------------------------------------------------
\orateur{\NomOrateur}{}
\orateurAdr{\AdresseCourteOrateur}{}
\orateurAdr{\EmailOrateur}{}
% NE PAS MODIFIER LES 4 LIGNES SUIVANTES sauf a retirer le signe commentaire '%'
\auteur{\NomAuteurI}{}
\auteurAdr{\AdresseCourteAuteurI}{}
\auteurAdr{\EmailAuteurI}{}
%\auteur{\NomAuteurII}{\AdresseCourteAuteurII}
%\auteur{\NomAuteurIII}{\AdresseCourteAuteurIII}
%\auteur{\NomAuteurIV}{\AdresseCourteAuteurIV}
%
\vspace*{1cm}
\noindent {\bf Abstract.}
In the present paper,
\vspace*{0.5cm}
\noindent {\bf Key words:}
%---------------------------------------------------------------
% TEXTE DE LA COMMUNICATION
%---------------------------------------------------------------
\setcounter{equation}{0}
\section{Introduction}
1) Motivation du probl\`eme ; \\
2) Historiques des r\'esultats connus\\ \\
Texte de la communication ici avec ses r\'ef\'erences
bibliographiques \'even\-tuelles \cite{ref1,ref2}.\\
\setcounter{equation}{0}
\section{Main Results}
%*******************************************************************
3) Le(s) nouveau(x) r\'esultat(s) ;\\
4) Des id\'ees de d\'emonstrations ; \\
\section{Conclusion}
...
%---------------------------------------------------------------
% REFERENCES BIBLIOGRAPHIQUES
%---------------------------------------------------------------
% NE PAS MODIFIER LES 2 LIGNES SUIVANTES
\bibliographystyle{plain}
\begin{thebibliography}{99}
\bibitem{ref1} {\sc Auteur}, {\sl Titre}, Editeur, ann\'ee.
\bibitem{ref2} {\sc Auteur}, {\sl Titre}, Revue, r\'ef\'erences, ann\'ee.
% NE PAS MODIFIER LA LIGNE SUIVANTE
\end{thebibliography}
\end{document}
|
http://wicky-math.fr.nf/pdf_2015/courssuites_1S.tex | fr.nf | CC-MAIN-2019-04 | text/x-tex | application/x-tex | crawl-data/CC-MAIN-2019-04/segments/1547583659654.11/warc/CC-MAIN-20190118005216-20190118031216-00537.warc.gz | 251,855,140 | 21,878 | \documentclass[4apaper,10pt,french]{article}
\linespread{1}
\newcommand{\ch}{Chapitre 2}
\newcommand{\Ch}{Les suites, en particulier les suites arithm\'etiques et g\'eom\'etriques}
\newcommand{\Cl}{1S}
\newcommand{\Annee}{2012-2013}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Package
\input macrodwicky.tex
\geometry{hmargin=2cm,vmargin=2cm}
\setcounter{NumLecon}{2}
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\begin{document}
\ddwicky{separation.eps}{Ashgar Farhadi}{Une séparation} % Image + titre + Auteur
{Si les gens ne croient pas que les mathématiques sont simples, c’est seulement parce qu’ils ne réalisent pas combien la vie est compliquée !}{John Louis von Neumann} % Citation + Auteur
{Asghar Farhadi a fait ses études de théâtre, avec un diplôme du 1er cycle en arts dramatiques et une maîtrise de mise en scène théâtrale à l’Université de Téhéran et l’Université Tarbiat Modarres. Farhadi a tourné des courts métrages de 8 mm et 16 mm au Département de la société du cinéma de jeunesse d’Ispahan avant d’entamer l’écriture des pièces de théâtre et des scénarios pour la télévision iranienne, IRIB. Danse dans la poussière est son premier film réalisé, suivi par le film acclamé par les critiques, Les enfants de Belle Ville. Son troisième film, La Fête du feu obtient le Hugo d'or au Festival international du film de Chicago en 2006.
À propos d'Elly, pour lequel il reçoit l’Ours d'argent du meilleur réalisateur à Berlin en 2009, prend pour sujet le voyage d’un groupe d’Iraniens au bord de la mer Caspienne tournant à la catastrophe. En 2011, Farhadi revient à la Berlinale pour y présenter Une séparation. Le film gagne l'Ours d'or et les Prix d'interprétation féminine et masculine pour l'ensemble de la distribution. Puis il reçoit, en 2012, le Golden Globe, le César et l'Oscar du meilleur film étranger.
} % Présentation auteur
{0.25} % Ratio portrait
{0.3} % Ratio Image
{
\item Calculer les termes d'une suite générée par récurrence.
\item Construire et exploiter la représentation graphique d'une suite définie par récurrence
\item Algorithme
}
\TITRE{fibo.eps}{0.5} % Image 1ere page + ratio
%\begin{abstract}
\begin{Intro}{Au fil du temps}{
Vous allez dans ce chapitre, découvrir les suites, qui sont présentes dans bien des sciences, par exemple en biologie
des populations pour décrire le cycle de reproduction des lapins, en astronomie dans les loirs de répartition
des planètes, en physique dans la théorie des particules élémentaires, en informatique dans les algorithmes
et simulations (et via les ordinateurs, dans toutes nos activités numériques). Mais cette omniprésence n'est pas
un hasard, car tous ces domaines se servent d'équations mathématiques. Or les suites occupent une place de choix
en mathématiques depuis plus de 2000 ans.\\
Pourquoi un tel intêret, alors qu'il s'agit simplement de ranger une succession de nombres liés par un loi, comme
quand on énumère les jours du mois ? Parce que cette simplicité n'est qu'apparente : l'étrange n'est jamais loin.\\
Prenons par exemple la suite des \og puissances de un demi \fg : $1 ; \dfrac12 ; \dfrac14 ; \dfrac18 ; \dfrac1{16} ; \dots ; \dfrac1{2n} ; \dots$
et la série associée $1 + \dfrac12 + \dfrac14 + \dfrac18 + \dfrac1{16} + \dots + \dfrac1{2n} + \dots$ Si ces nombres
représentaient des tiges en bois mesurant chacune la moitié de la précédente (en commençant par 1 mètre), n'est-ce
pas étonnant que la longueur maximale qu'on puisse atteindre en les mettant bout à bout ne dépasse pas 2 mètres,
même avec une infinité de tiges ? Cela a stupéfait les savants qui l'ont découvert au $XVIII^e$ siècle.
Comment admettre que l'infini (le nombre de tiges) puisse être contenu dans le fini (2 mètres) ?
Il s'en est suivi de violentes disputes entre les pro-infini et les contre, qui n'ont fait que s'amplifier
jusqu'au $XX^e$ siècle. Bref, ce sont les suites qui ont introduit l'infini dans l'arithmétique et l'analyse ...\\
Mais si le $XVIII^e$ siècle est un tournant dans l'histoire des suites et de l'infini, leur origine remonte à Archimède
de Syracuse, le mathématicien grec du $III^e$ siècle avant JC. Archimède voulait résoudre une question qui n'avait rien
à voir avec l'infini, le problème de la quadrature du cercle, grande énigme des maths anciennes : étant donné un cercle,
comment construire une figure de même surface mais composée de carrés ou de triangles (figures que les Grecs savaient
bien mesurer). Tel était le but d'Archimède ... Mais à la place, il a découvert les suites et, sans le savoir,
il a mis les mathématiciens sur la voie de l'infini.\\
Comment cela s'est-il produit ? Archimède pensait que la bonne méthode pour \og quarrer \fg le cercle était
de l'encadrer entre deux figures faites de triangles, puis de faire converger la taille de ces triangles jusqu'à
les faire coïncider (comme si l'on cherchait à emprisonner un objet entre des murs qui se rapprochent). Archimède
choisit comme figures connues et quarrables pour coïncer le cercle, les polygones réguliers, faits de triangles
disposés en pétales de fleur, en commençant par l'hexagone (six côtés, six triangles équilatéraux) : il encadre le cercle
entre l'hexagone inscrit et l'hexagone circonscrit. Ensuite, il passe au dodécagone (12 côtés), puis il enchaîne
sur le polygone à 24 côtés, puis 48 et enfin 96. A chaque pas, les mesures se rapprochent, mais jamais elles
ne s'égalent ... Il obtient ainsi une suite illimitée de nombres
connus dont la limite est $2\pi$ et qui fournissent très rapidement une bonne approximation de $\pi$.\\
Las, Archimède ne résoudra jamais le problème de la quadrature du cercle, et pour cause. Les mathématiciens
du $XIX^e$ siècle démontreront qu'il n'a pas de solution, d'où l'expression \og C'est la quadrature du cercle ! \fg.
Mais Archimède a bel et bien inauguré l'histoire des suites, car dans sa méthode, il montre comment calculer
la surface du polygone $n$ en fonction de celui qui précède (le $n-1^{eme}$).
Le terme $u_n$ défini par le terme $u_{n-1}$, c'est bien là une suite, la première du genre, et qui peut être
prolongée autant que l'on veut ... jusque dans l'infini.\\
Plus tard, les suites furent formalisées par Cauchy, la maîtrise de cet outil a été grandement facilitée
par l'adoption de la notation indicielle au $XIX^e$ siècle qui consiste à noter chaque nombre d'une suite
par une même lettre affectée d'un indice. \newline
On doit à Péano la définition d'une suite numérique telle qu'elle est enseigné en première S.
}
\end{Intro}
\pagebreak
\section{Introduction}
\subsection{Introduction historique}
L'un des premiers travaux portant sur les suites de nombres semble provenir d’un certain Archimède (j’en entends déjà se dire d’ici : \og encore lui ! \fg, eh oui. . . ). Dans son traité La mesure du cercle,
pour trouver une valeur approchée de $\pi$, il inscrit dans un cercle de rayon $1$ un triangle équilatéral dont il calcule le périmètre. Puis en doublant le nombres de côtés, il calcule le périmètre d'un hexagone, puis celui d'un dodécagone et ainsi de suite, indéfiniment. Il obtient ainsi une suite illimitée de nombres connus dont la limite est $2\pi$ et qui fournissent très rapidement une bonne approximation de $\pi$.\newline
Plus tard, les suites furent formalisées par Cauchy, la maîtrise de cet outil a été grandement facilitée par l'adoption de la notation indicielle au $XIX^e$ siècle qui consiste à noter chaque nombre d'une suite par une même lettre affectée d'un indice. \newline
On doit à Péano la définition d'une suite numérique telle qu'elle est enseigné en première S.
\subsection{Introduction}
Il arrive que l'on demande, lors de tests psychotechniques par exemple, de compl\'eter "logiquement" une suite de nombres, comme par exemple:
$$1 , 2 , 4 , 8 , 16 , \dots\dots , \dots\dots , \dots\dots$$
$$1 , 4 , 9 , 16 , 25 , \dots\dots , \dots\dots , \dots\dots$$
$$-3 , 1 , 5 , 9 , \dots\dots , \dots\dots , \dots\dots$$
$$ \text{suite de Fibonacci} \qquad 0, 1, 1, 2, 3, 5, 8, 13 , \dots\dots , \dots\dots , \dots\dots$$
$$ \text{suite de Stern} \qquad 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, , \dots\dots , \dots\dots , \dots\dots$$
En math\'ematiques, une \textbf{suite} $u$ est une \textbf{liste ordonn\'ee de nombres r\'eels}: les \'el\'ements de cette liste :
\begin{itemize}
\item Sont appel\'es \textbf{termes}
\item Sont rep\'er\'es par leur rang dans la liste
\end{itemize}
\begin{center}
Le $1^{er}$ terme de la suite $u$ est souvent not\'e $u_0$ (ou $u_1$),\\
Le $2^{\`eme}$ terme de la suite $u$ est souvent not\'e $u_1$ (ou $u_2$)\\
\dots \dots\dots\dots\dots \dots\dots\dots\dots \dots\dots\dots\dots \dots\dots \dots\dots\dots\dots\dots \\
\dots \dots\dots\dots\dots \dots\dots\dots\dots \dots\dots\dots\dots \dots\dots \dots\dots\dots\dots\dots \\
Le $n^{\`eme}$ terme de la suite $u$ est souvent not\'e $u_{n-1}$ (ou $u_{n}$)\\
\end{center}
Le terme pr\'ec\`edent $u_n$ est $u_{n-1}$, le suivant $u_{n+1}$.
On note $u=(u_n)_{n \in \N}$ pour signifier que le rang d'un terme de la suite $u$ est un entier naturel (sans "fin" de liste). On a donc:
\begin{center}
$\overbrace{u}^{\text{nom de la suite}}=\quad(\overbrace{u_0}^{\text{1\up{er} terme}};\overbrace{u_1}^{\text{2\up{nd} terme}};\hspace{.5cm}u_2\hspace{.5cm};\hspace{.5cm}\dots\hspace{.5cm};\hspace{.5cm}u_{n-1}\hspace{.5cm};\overbrace{u_n}^{\text{terme de rang $n$}};\hspace{.5cm}u_{n+1}\hspace{.5cm};\hspace{.5cm}\dots\hspace{.5cm})$
\end{center}
\Expl{En reprenant les exemples précédents :
\begin{itemize}
\item La première suite est la suite des puissances de $2$, on définit alors cette suite $u$ par :
$$ u_n=2^n$$
Une autre manière de définir cette suite est de remarquer que chaque terme est le double du précédent ; on peut alors définir cette suite par :
$$ \left\{ \begin{array}{l} u_0=1 \\ u_{n+1}=2\times u_n \end{array} \right.$$
\item La seconde suite est la suite des carrés des premiers entiers, ainsi :
$$ u_n=n^2$$
\item La troisième suite admet pour premier terme $-3$ et pour calculer le suivant on ajoute toujours $4$ :
$$ \left\{ \begin{array}{l} u_0=-3 \\ u_{n+1}= u_n +4 \end{array} \right.$$
On peut aussi la définir de la manière suivante :
$$ u_n=-3+4n$$
\item La suite de Fibonacci se définit par :
$$ \left\{ \begin{array}{l} u_0=0\\u_1=1\\ u_{n+2}= u_n +u_{n+1} \end{array} \right. $$
\item La suite de Stern se définit par :
\begin{center}
\includegraphics[scale=0.7]{stern.eps}
\\
Construction de la suite de Stern. La suite s'obtient en lisant chaque ligne successivement de gauche à droite. Les 1 de la colonne de droite sont à identifier avec les 1 de la colonne de gauche et ne sont pas pris en compte dans la liste des éléments de la suite.
\end{center}
$$\left\{ \begin{array}{l} u_0=0\\u_1=1\\ u_{2n}= u_n \\ u_{2n+1}=u_n+u_{n+1} \end{array} \right. $$
\end{itemize}}
\newpage
\section{Suites numériques}
\subsection{Définition}
\begin{defi}
Une suite numérique est une suite liste ordonnée de nombre réels. \\
Soit $p\in \N$. Une suite $u$ est en fait une fonction de $\N$ dans $\R$ définie à partir d'un certain entier $p$ . A chaque
entier $n\geq p$, la suite $u$ associe un réel $u (n )$, que l’on note $u_n$.\\
$u_n$ est appelé terme d’indice $n$ ou de rang $n$ de la suite.
$u_p$ est le premier terme, ou le terme initial de la suite. On note $(u_n )_{n\geq p}$ l’ensemble des termes de la
suite.
\end{defi}
\Exoi{Déterminer le rang à partir duquel la suite $u$ suivante est définie :
$$ u_n=\sqrt{n-4}$$}
\subsection{Mode de génération d'une suite numérique}
On distingue principalement deux manières de définir les suites : de manière explicite ou par récurrence. \\
\begin{defi}[Formule explicite]
Soit $p\in\N$. Une suite $(u_n)_{n\geq p}$ est définie de manière explicite lorsqu'il existe une fonction $f$
définie sur $[p ; +\infty[$ telle que :
\begin{center}
$\forall n \geq p$, on a $u_n=f(n)$
\end{center}
\end{defi}
\Expl{
On se donne $u_n=-2n+1$ pour $n \geqslant0$ \qquad (ici $u_n=f(n)$ avec $f$ d\'efinie sur $\R$ par $f(x)=-2x+1$.)\\
On a ainsi $u_0=-2 \times 0 +1 = 1$, $u_1=-2 \times 1 + 1 = -1$, $u_2 = -2\times 2 +1 = -3$,
$u_3 = -6+1 = -5$, $u_4=-8 +1 = -7$, \dots $u_{100}=-199\dots$, etc
}
\Rq{
On peut alors calculer chaque terme de la suite par rapport à son indice.
}
\begin{defi}[Par récurrence]
Soit $f$ une fonction définie sur un ensemble $I$ telle que si $x\in I$ alors $f(x)\in I$.\\
Soit $a$ un nombre réel de $I$ et $p \in \N$.\\
On peut alors définir une suite $u$ en posant :
$\left\{ \begin{array}{l} u_p=a \\ u_{n+1}=f(u_n)\quad \forall n \geq p \end{array} \right.$
\end{defi}
\Expl{
On se donne $\left\{ \begin{array}{l} u_0=1 \\ u_{n+1}=-2u_n+1 \end{array} \right.$
\qquad (ici $u_n=f(n)$ avec $f$ d\'efinie sur $\R$ par $f(x)=-2x+1$.)\\
On a ainsi $u_1=-2u_0+1=-2\times 1+1=-1$, $ u_2=-2u_1+1=-2\times(-1)+1=3$ , $u_3=-2u_2+1=-2\times 3+1=-5$,
etc
}
\Rqs{
\item En fait on se donne la valeur du premier terme et un procédé appelé \textbf{relation de récurrence} qui permet
de calculer un terme à partir du précédent.
\item On visualise ainsi facilement le lien logique entre les termes.
\item Dans l'exemple pr\'ec\'edent, pour calculer $u_{100}$, il faut conna\^itre $u_{99}$, et pour calculer $u_{99}$, il faut conna\^itre $u_{98}$, ainsi de suite \dots Il est alors pr\'ef\'erable d'exprimer $u_n$ en fonction de $n$ pour calculer $u_{100}$ directement.
}
\Cadre[Avec une calculatrice]{
\begin{tabular}{cc|cc}
\begin{minipage}[t]{7.5cm}
\begin{center}
\textbf{Avec une TI :}
\end{center}
Par défaut, la calculatrice est en mode fonction. Il faut passer en mode \textit{suite} en appuyant sur
\fbox{\textbf{Mode}} puis mettre \fbox{\texttt{Suite}} en surbrillance.\\
Pour entrer l'expression de la suite $(u_n)$, on procède désormais comme pour une fonction :
on appuie sur \fbox{$f(x)$} ce qui nous permet d'entrer le premier
indice, l'expression de la suite et éventuellement son premier terme. \\
\textit{Le $n$ s'obtient avec la touche \fbox{$x$, $t$, $\theta$, $n$} et le $u$ s'obtient
en appuyant sur \fbox{\textbf{2nde}} + \fbox{$7$} (on met l'indice entre parenthèses).}\\
On obtient le tableau de valeurs dans
\begin{center}
\fbox{\textbf{Table}}= \fbox{\textbf{2nde}} + \fbox{\textbf{Graphe}}.
\end{center}
\end{minipage}
&&&
\begin{minipage}[t]{7.5cm}
\begin{center}
\textbf{Avec une Casio :}
\end{center}
On choisit le mode \textit{suite} en sélectionnant le menu \fbox{\textbf{\texttt{Recur}}}.\\
On choisit ensuite le type de suite (explicite ou récurrente) grâce à la touche \fbox{\textbf{F3 : \texttt{Type}}}
puis la touche \fbox{\textbf{F1}} (explicite) ou \fbox{\textbf{F2}} (récurrente).\\
On entre ensuite l'expression de la suite et on appuie sur \fbox{\textbf{F5 : \texttt{SET}}}
pour paramétrer le tableau, notamment donner le premier indice et/ou premier terme si nécessaire.\\
\textit{Le $n$ s'obtient avec la touche \fbox{\textbf{F1 : $n$}} et le $a_n$ s'obtient
avec la touche \fbox{\textbf{F2 : $a_n$}}}\\
On peut alors afficher les valeurs de la table grâce à \fbox{\textbf{F6 : \texttt{TABL}}}
\end{minipage}
\\
\end{tabular}
}
\Exoi{Soit la suite $(v_n)_{\N}$ par
$\left\{ \begin{array}{l} v_0=2 \\ v_{n+1}=2v_n+3n\quad \forall n \in\N \end{array} \right.$.
\begin{enumerate}
\item Calculer $v_1$, $v_{2}$ et $v_{3}$.
\item Exprimer $v_{n}$, $v_{n-1}$, $v_{2n}$ et $v_{3n-1}$ en fonction du terme approprié de la suite $(v_n)$.
\end{enumerate}
}
\Exoi{Soit la suite $(u_n)_{\N}$ définie par $u_n= (-2)^n+3$ et la suite $(v_n)_{\N}$ par
$\left\{ \begin{array}{l} v_0=4 \\ v_{n+1}=-2v_n+9\quad \forall n \in\N \end{array} \right.$.
\begin{enumerate}
\item Pour chacune des suites $u$ et $v$ :
\begin{enumerate}
\item Déterminer les valeurs des trois premiers termes.
\item Vérifier à la calculatrice les réponses de la question précédente.
\end{enumerate}
\item Quelle conjecture peut-on émettre sur les suites $u$ et $v$ ? Démontrer cette conjecture.
\end{enumerate}
}
%\subsection{Représentation graphique}
%\subsubsection{Suites explicites}
%\begin{defi}
%On se place dans un repère $(O;\vec i, \vec j)$.
%La représentation graphique d'une suite définie explicitement $(u_n)$ est l'ensemble des points de
%coordonnées $(n;u_n)$
%\end{defi}
%
%\Expl{Soit $(u_n)$ la suite définie, pour $n\geq 1$, par $$u_n=\dfrac{1}{n} $$
%Sa représentation graphique est donc l'ensemble des points \textbf{isolés} de coordonnées $\left(1;1\right)$,
%$\left(2,\dfrac{1}{2}\right)$, $\left(3,\dfrac{1}{3}\right)$, $\left(4,\dfrac{1}{4}\right)$,
%$\left(5,\dfrac{1}{5}\right)$, etc$\dots$}
%\begin{center}
%\psset{xunit=2cm , yunit=3cm}
%\begin{pspicture*}(-1.1,-0.35)(5.35,1.2)
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%\end{pspicture*}
%\end{center}
%
%\Exoi{
%\begin{multicols}{2}
%Soit $f$ la fonction définie par sa courbe représentative $\mathscr C_f$ ci-contre et la suite $u$ de terme général $u_n=f(n)$.
%\begin{enumerate}
% \item Lire une valeur approchée des termes de $u_0$ à $u_5$.
%\item Que peut-on dire du comportement des premiers termes de $u$ ?
%\end{enumerate}
%\begin{center}
%%\scalebox{0.8} % Change this value to rescale the drawing.
%{
%\begin{pspicture}(-1,-0.50)(7.02,4.0)
%\psset{xunit=1.0cm,yunit=0.7cm}
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%\curveto(1.6,4.4)(1.7,4)(2,3.5)
%\curveto(2.5,2.75)(2.75,3.8)(3,4)
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%\end{multicols}
%}
%
%
%
%
%\subsubsection{Suites récurrentes}
%
%\Exoi{
%On considère la fonction $f$ définie sur $[0;+\infty[$ par $f(x)=\sqrt{x}$.\\
%La suite $(u_n)$ est définie par $u_0=3$ et pour tout $n\geq 0$ on a $u_{n+1}=f(u_n)=\sqrt{u_n}$.\\
%\partieBac{Tracer les premiers termes sur l'axe des abscisses}
%\begin{enumerate}
% \item Tracer soigneusement la courbe $\mathscr C$ représentant $f$ et la droite $\Delta$ d'équation $y=x$ sur $[0;3]$
%dans un repère orthonormé avec pour unité 5 cm.
%\item \begin{enumerate}
% \item Placer $u_0$ sur l'axe des abscisses. Placer $u_1=f(u_0)$ sur l'axe des ordonnées.
% \item Placer le point $A_1$ de $\Delta$ d'ordonnée $u_1$. Quelle est son abscisse ?\\
%Placer alors $u_1$ sur l'axe des abscisses.
%\item Sachant que $u_2=f(u_1)$, expliquer comment construire $u_2$ sur l'axe des abscisses. Le construire.
%\end{enumerate}
%\item Construire ainsi, pas à pas, sur l'axe des abscisses, les premiers termes de la suite jusqu'à $u_5$.
% \item Comment se poursuivrait le tracé si on pouvait agrandir le graphique ?\\
% Emettre des conjectures sur le comportement de la suite $(u_n)$.
%%Quelles conjectures peut-on faire sur le sens de variation de $(u_n)$ et sur sa limite éventuelle ?
%\end{enumerate}
%\partieBac{ Influence du premier terme}
%\begin{enumerate}
% \item Sur votre calculatrice, afficher de même les premiers termes de la suite $(v_n)$ définie par $v_0=0.1$ et
%pour tout $n$, $v_{n+1}=f(v_n)$.\\
%\textit{Dans }\fbox{\textbf{Fenêtre}}, \textit{choisir $X$ et $Y$ entre 0 et 1.}
%\item Emettre des conjectures sur le comportement de la suite $(v_n)$.
%\end{enumerate}
%}
%
%
%Dans le cas d'une suite récurrente, on ne cherche pas en général à représenter graphiquement la suite
%comme pour les suites explicites (mais on pourrait très bien le faire). \\
%On préfère représenter ses premiers termes sur l'axe des abscisses en s'appuyant sur la représentation
%graphique de la fonction définissant la relation de récurrence. \\
%On obtient alors un diagramme \og en escalier \fg ou en \og en escargot \fg.
%%On peut alors faire des conjectures sur le sens de variation, etc.
%
%\Expl{On considère la suite $(u_n)$ définie pour $n\geq 0$ par $u_{n+1}=2 \sqrt{u_n}+2$ et $u_0=1$\newline
%On considère la fonction $f$ vérifiant $u_{n+1}=f(u_n)$ définie par $f : x\longmapsto 2 \sqrt{x}+2$.
%}
%\begin{multicols}{2}
%\begin{enumerate}
% \item On trace la courbe $\mathscr C_f$ représentative de $f$
% \item On place $u_0$ sur l'axe des abscisses et $u_1$, image de $u_0$ par $f$, sur l'axe des ordonnées
% \item Comme $u_2$ est l'image de $u_1$ par $f$, on veut avoir $u_1$ sur l'axe des abscisses.\\
%Pour cela, on utilise la droite $\Delta$ d'équation $y=x$, que l'on prendra soin de tracer.
%\item On reporte alors $u_1$ sur l'axe des abscisses, à l'aide de $\Delta$
%\item On place $u_2$ image de $u_1$ par $f$, puis on reporte $u_2$ sur l'axe des abscisses, etc.
%\end{enumerate}
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%\uput[180](0,6){\small $u_2$}
%\uput[-90](6,0){\small $u_2$}
%\uput[180](0,6.89897){\small $u_3$}
%\uput[-90](6.89897,0){\small $u_3$}
%\uput[180](0,7.25318){\small $u_4$}
%\uput[-90](7.25318,0){\small $u_4$}
%\uput[ur](7.5,8){\small $\Delta$}
%\end{pspicture*}
%\end{center}
%\end{multicols}
%
%\Rq{Dans l'exemple précédent, on constate que les termes de la suite semblent augmenter et se rapprocher
% d'une valeur \og limite \fg : celle de l'abscisse du point d'intersection entre $\mathscr C_f$ et de $\Delta$. \\
%On dira que la suite est croissante et qu'elle \textit{converge} vers cette valeur $l$, appelée limite de la suite $(u_n)$.\\
%Pour la trouver, on résout l'équation $f(l)=l$ :
%$$f(l)=l \iff 2\sqrt{l}+2=l \iff 2\sqrt{l}=l-2 \iff 4l=l^2-4l+4 \quad\text{ et }\quad \left\{\begin{array}{l}
% l>0 \\ l-2>0
% \end{array}\right.
%\iff l^2 -8l+4=0\quad \text{ et } \quad l>2$$
%$\Delta = 64-4\times 1 \times 4 = 48$. \quad Donc $l_1=\dfrac{8+4\sqrt{3}}{2}=4+2\sqrt{3}$ et $l_2=4-2\sqrt{3}<2$.
%Donc $l=4+2\sqrt{3}$. \\
%On note $\lim\limits_{n \to + \infty} u_n = 4+2\sqrt{3}$
%}
%
%\Expl{On considère la suite $(u_n)$ définie pour $n\geq 0$ par $u_{n+1}=-\dfrac{2}{3} u_n-1$ et
%$u_0=7$\newline
%On considère la fonction $f$ vérifiant $u_{n+1}=f(u_n)$ définie par $f : x\longmapsto -\dfrac{2}{3}x-1$. \\
%On a représenté ci-dessous la représentation graphique $\mathscr C_f$ de $f$ et la droite $\Delta$ d'équation $y=x$,
%puis on a suivi les mêmes étapes que pour l'exemple précédent.}
%\begin{center}
%\psset{xunit=0.9cm , yunit=0.9cm}
%\begin{pspicture*}(-8.5,-6.6)(8.5,4.6)
%\def\xmin{-8} \def\xmax{8} \def\ymin{-6} \def\ymax{4}
%\newrgbcolor{couleurcadre}{0.99 0.99 0.99}
%\psframe[linewidth=0.3pt,linecolor=couleurcadre](-8.5,-6.6)(8.5,4.6)
%\def\pshlabel#1{\psframebox*[framesep=1pt]{\small #1}}
%\def\psvlabel#1{\psframebox*[framesep=1pt]{\small #1}}
%\psclip{%
%\psframe[linestyle=none](\xmin,\ymin)(\xmax,\ymax)
%}
%\newrgbcolor{couleur1}{0.6549 0.6549 0}
%\newrgbcolor{couleur2}{0 0.3176 0.4745}
%\newrgbcolor{couleur3}{0.0941 0.647 0.0196}
%\psline[linewidth=0.8pt,linecolor=blue,linestyle=dashed]{-}(7,0)(7,-5.66667)(-5.66667,-5.66667)
%(-5.66667,2.77777)(2.77777,2.77777)(2.77777,-2.85186)(-2.85186,-2.85186)(-2.85186,0.90123)(0.90123,0.90123)
%(0.90123,-1.60083)(-1.60083,-1.60083)(-1.60083,0.06721)(0.06721,0.06721)(0.06721,-1.04482)
%(-1.04482,-1.04482)(-1.04482,0)
%\def\F{0 2 x mul 3 div sub 1 sub}
%\psplot[linecolor=gray,linewidth=0.5pt,linestyle=solid]{-8}{8}{x}
%\psplot[linewidth=1.2pt,linecolor=red,linestyle=solid,plotpoints=1000]{-8}{8}{\F}
%\uput[0](4.2,-3.5){$\mathscr C_f$}
%\endpsclip
%\psaxes[labels=none,labelsep=1pt,Dx=1,Dy=1,Ox=0,Oy=0]{->}(0,0)(\xmin,\ymin)(\xmax,\ymax)
%\uput[dl](0,0){0}
%\pcline[linewidth=1pt]{->}(0,0)(1,0) \uput[d](0.5,0){\small $\vec i$}
%\pcline[linewidth=1pt]{->}(0,0)(0,1) \uput[l](0,0.5){\small $\vec j$}
%\uput[u](7,0){\small $u_0$}
%\uput[ul](0,-5.66667){\small $u_1$}
%\uput[dl](-5.66667,0){\small $u_1$}
%\uput[ul](0,2.77777){\small $u_2$}
%\uput[dr](2.77777,0){\small $u_2$}
%\uput[dr](0,-2.85186){\small $u_3$}
%\uput[dl](-2.85186,0){\small $u_3$}
%\uput[ul](0,0.90123){\small $u_4$}
%\uput[dr](0.90123,0){\small $u_4$}
%\uput[dl](0,-1.60083){\small $u_5$}
%\uput[u](-1.60083,0){\small $u_5$}
%\uput[dl](4.5,4){\small $\Delta$}
%%\uput[130](0,0.06721){\small $u_6$}
%%\uput[-30](0.06721,0){\small $u_6$}
%%\uput[130](0,-1.04482){\small $u_7$}
%%\uput[-30](-1.04482,0){\small $u_7$}
%\end{pspicture*}
%\end{center}
%
%\Rq{Contrairement à l'exemple précédent, les éléments de la suite ne semblent pas faire qu'augmenter ou diminuer. Cette
%suite n'est ni croissante, ni décroissante. Mais cette suite semblent également convergente vers l'abscisse $l$ du point d'intersection
%de $\mathscr C_f$ et $\Delta$.\\
%Pour trouver $l$, on résout $f(l)=l \iff -\dfrac23l-1=l \iff \dfrac53l=-1 \iff l=-\dfrac35$.
%}
%
%\Exoi{
%\begin{multicols}{2}
%On a tracé ci-contre la courbe représentative d'une fonction $g$ et la droite $\Delta : y=x$.\\
%On a représenté les quatre premiers termes de la suite $t$ définie par son terme initial $t_0$ et la relation
%$$t_{n+1}=g(t_n) \qquad \text{
%pour tout entier } n\geq 0$$
%Donner le terme initial $t_0$ et lire des valeurs approchées de $t_1$, $t_2$ et $t_3$.
%\begin{center}
% \newrgbcolor{ttttff}{0.2 0.2 1}
%\newrgbcolor{qqzzqq}{0 0.6 0}
%\psset{xunit=1.0cm,yunit=1.0cm}
%\begin{pspicture*}(-6,-1)(4,4)
%\psgrid[subgriddiv=0,gridlabels=0,gridcolor=lightgray](0,0)(-6,-1)(4,4)
%\psset{xunit=1.0cm,yunit=1.0cm,algebraic=true,dotstyle=o,dotsize=3pt 0,linewidth=0.8pt,arrowsize=3pt 2,arrowinset=0.25}
%\psaxes[labelFontSize=\scriptstyle,xAxis=true,yAxis=true,Dx=1,Dy=1,ticksize=-2pt 0,subticks=2]{->}(0,0)(-6,-1)(4,4)
%\psplot[linewidth=1.2pt,linecolor=red]{-6}{4}{(-0--1*x)/1}
%\psplot[linewidth=1.2pt,linecolor=ttttff,plotpoints=200]{-6.0}{4.0}{sqrt(x+6)}
%\psline[linewidth=1.2pt,linestyle=dashed,dash=1pt 1pt,linecolor=qqzzqq](-5,0)(-5,1)
%\psline[linewidth=1.2pt,linecolor=qqzzqq](-5,1)(1,1)
%\psline[linewidth=1.2pt,linecolor=qqzzqq](1,1)(1,2.65)
%\psline[linewidth=1.2pt,linecolor=qqzzqq](1,2.65)(2.65,2.65)
%\psline[linewidth=1.2pt,linecolor=qqzzqq](2.65,2.65)(2.65,2.94)
%\psline[linewidth=1.2pt,linecolor=qqzzqq](2.65,2.94)(2.94,2.94)
%\psline[linewidth=1.2pt,linestyle=dashed,dash=1pt 1pt,linecolor=qqzzqq](1,0)(1,1)
%\psline[linewidth=1.2pt,linestyle=dashed,dash=1pt 1pt,linecolor=qqzzqq](2.65,2.65)(2.65,0)
%\psline[linewidth=1.2pt,linestyle=dashed,dash=1pt 1pt,linecolor=qqzzqq](2.94,2.94)(2.94,0)
%\rput[bl](2,3.5){\red{$\Delta:y=x$}}
%\rput[bl](-5.64,1.13){\ttttff{$\mathscr C_g$}}
%\end{pspicture*}
%\end{center}
%\end{multicols}
%}
%
%\Cadre[Avec une calculatrice]{
%%\begin{tabular}{cc|cc}
%%\begin{minipage}[t]{10cm}
%\begin{center}
%\textbf{Avec une TI : }
%\end{center}
%Se mettre en Mode \fbox{\texttt{Suite}}.
%\begin{itemize}
% \item[$\blacktriangleright$] \textbf{Pour une suite explicite} :
% \begin{itemize}
% \item Mettre en surbrillance le Mode \fbox{\texttt{NonRelié}}
%afin que les points ne soient pas reliés entre eux.
%\item Rentrer la suite dans \fbox{$f(x)$} en précisant l'indice de départ.
%\item Dans \fbox{\textbf{Format} : 2nde + Zoom} mettre en surbrillance \fbox{\texttt{f(n)}}.\\
%\end{itemize}
%\item[$\blacktriangleright$] \textbf{Pour une suite récurrente} :
% \begin{itemize}
%\item Mettre en surbrillance le \textit{Mode} \fbox{\texttt{Relié}}.
%\item Rentrer la suite dans \fbox{$f(x)$} en précisant l'indice de départ, \texttt{u(n)} en fonction des termes précédents appropriés
%et le premier terme.
%\item Aller dans \fbox{\textbf{Format} : 2nde + Zoom} et mettre en surbrillance \fbox{\texttt{Esc}} (en escalier).\\
%\end{itemize}
%\end{itemize}
%Ensuite, appuyer sur \fbox{\textbf{Graphe}}, puis \fbox{\textbf{Trace}} et les flèches \fbox{$\rhd$} et \fbox{$\lhd$}
%pour voir les termes de la suite.\\
%Afin d'ajuster la fenêtre automatiquement, appuyer sur \fbox{\textbf{Zoom}} et choisir \fbox{\texttt{ZMinMax}}.\\
%%\end{minipage}
%%&&&
%%\begin{minipage}[t]{5cm}
%\begin{center}
%\textbf{Avec une Casio :}
%\end{center}
%Se mettre en \textit{Mode} \textit{suite}.\\
%Enregistrer la suite dans le bon \textit{Type}. \\
%Appuyer ensuite sur la touche \fbox{\textbf{F4 : \texttt{WEB}}}
%ou encore \fbox{\textbf{F6 : \texttt{TABL}}} + \fbox{\textbf{F6 : \texttt{G-PLT}}}.\\
%
%Afin d'ajuster la fenêtre automatiquement, appuyer sur \fbox{\textbf{F2 : \texttt{Zoom}}} et choisir \fbox{\texttt{AUTO}}.
%%\end{minipage}
%%\\
%%\end{tabular}
%}
%
%\Exoi{\begin{enumerate}
% \item Soit la suite $u$ définie sur $\N$ par $\left\{\begin{array}{l}
% u_0=-1 \\ u_{n+1}=\sqrt{2u_n+6}
% \end{array}\right.$\\
%Afficher sur votre calculatrice une représentation graphique de la suite $u$.
% \item Même question pour la suite $v$ définie sur $\N$ par $v_{n}=\sqrt{2n+6}$.
% \end{enumerate}
%}
%
%
%
%\section{Sens de variation d'une suite numérique}
%
%\subsection{Définition}
%
%\Exoi{Soient les suites $(u_n)$, $(v_n)$, $(w_n)$ et $(t_n)$ définies sur $\N$ par :
%$$u_n=2n+3 \qquad \qquad v_n=5 \times 0.8^n \qquad \qquad w_n=5 \times (-0.8)^n \qquad \text{ et } \qquad
%\left\{\begin{array}{l}
%t_0=4 \\ t_{n+1}= t_n-3
% \end{array}\right.
%$$
%Comparer pour tout $n\in\N$ les termes suivants :
%\begin{enumerate}
%\begin{multicols}{4}
% \item $u_{n+1}$ et $u_n$.
% \item $v_{n+1}$ et $v_n$.
% \item $w_{n+1}$ et $w_n$.
%\item $t_{n+1}$ et $t_n$.
%\end{multicols}
%\end{enumerate}
%}
%
%\begin{defi}Soit $(u_n)$ une suite de nombre réels. On dit que la suite $(u_n)$ est
%\begin{itemize}
%\item \textbf{croissante} (à partir du rang $p$) si et seulement $u_n\leq u_{n+1}$, $\forall n\geq p$.
%\item \textbf{décroissante} (à partir du rang $p$) si et seulement $u_n\geq u_{n+1}$, $\forall n\geq p$.
%\item \textbf{monotone} (à partir du rang $p$) si et seulement elle est croissante ou décroissante
%(à partir du rang $p$)
%\item \textbf{stationnaire} (à partir du rang $p$) si et seulement si $u_n=u_{n+1}$ pour tout entier
%$n\geq p$ (si la suite est définie à partir du rang $p$ alors on dit que la suite est \textbf{constante})
%\end{itemize}
%\end{defi}
%
%\Rq{
%%\item
%On définit la stricte croissance ou décroissance à l'aide des inégalités strictes suivantes :
%$$u_n<u_{n+1} \text{ ou } u_n>u_{n+1}$$
%%\item Les intervalles d'entiers sont souvent notés à l'aide de crochets doubles. Par exemple
%%$\text{\textlbrackdbl 2,5 \textrbrackdbl}=\{2;3;4;5\}$.
%%Si bien qu'on pourra écrire, par exemple, qu'une suite est croissante sur \textlbrackdbl $0,+\infty[$
%}
%\subsection{Méthode : Comment étudier le sens de variation d'une suite ?}
%
%\Cadre[Méthodes pour étudier les variations d'une suite]{
%\begin{itemize}
%\item[$\blacktriangleright$] On \'etudie g\'en\'eralement le signe de $u_{n+1}-u_n$ selon les valeurs de $n$.
%\item[$\blacktriangleright$] Si tous les termes de la suite $u$ sont \textbf{strictement positifs},
%on peut comparer le quotient $\dfrac{u_{n+1}}{u_n}$ avec 1.\\
%\textit{Ceci se révèle souvent pratique dans le cas où il y a des exposants $n$ dans l'expression de la suite.}
%\end{itemize}}
%
%
%
%\Expls{
%\begin{enumerate}
%\item Soit la suite $(u_n)_{n\in\N}$ est d\'efinie par $u_n=n^2+2$, alors on a
%$$u_{n+1}=(n+1)^2+2=n^2+2n+3$$
%Ainsi pour tout $n$ on a $u_{n+1}-u_n=2n+1 > 0$ pour tout $n>0$.\\
%Donc $u_{n+1} > u_n$ pour tout $n$ : la suite est donc strictement croissante sur $\N$.
%\item Soit $(v_n)_{n\in\N}$ d\'efinie par $v_n=2\times5^n$. \\
%On a $v_n>0$ pour tout entier naturel $n$ et $$v_{n+1}=2\times 5^{n+1}$$
%Ainsi pour tout $n$ on a $$\dfrac{v_{n+1}}{v_n}=\cfrac{5^{n+1}}{5^{n} }=5 >1$$
%Donc $v_{n+1}>v_n$ pour tout $n$ : la suite est donc strictement croissante sur \textlbrackdbl $0,+\infty[$
%\item Etudier de deux manières différentes le sens de variation de la suite $(w_n)_{n\geq 3}$ définie par $$ w_n=\dfrac{3n-1}{n+2}$$
% %\item On considère la suite $u$ définie par $u_n=2n+\sin n$\newline
%%Étudions, pour tout entier $n$, le signe de la différence de deux termes consécutifs :
%%$$ u_{n+1}-u_n=2(n+1)+\sin (n+1)-2n-\sin n=2+\sin (n+1) - \sin n$$
%%Or, $\forall x\in \R$ on a : $-1\leq \sin x \leq 1$, par conséquent :
%%$$ 2+\sin (n+1)-\sin n>0\Longleftrightarrow u_{n+1}>u_n$$
%%La suite $u$ est donc strictement croissante.
%\end{enumerate}
%}
%
%\begin{theo}On considère la suite $(u_n)_{n\geq p}$ définie \textbf{explicitement} par $u_n=f(n)$, avec $f$ définie sur
%l'intervalle $[p;+\infty[$.\newline
%Si la fonction $f$ est monotone (resp. strictement monotone) sur $[p;+\infty[$ alors la suite $(u_n)$ est monotone
% (resp. strictement monotone) et possède le même sens de variation que la fonction $f$
% \end{theo}
%
%\Rqs{
%\item On a déjà vu graphiquement que ce théorème était faux pour les suites définies par récurrence.
%\item La réciproque de ce théorème est fausse i.e que l'on peut trouver une suite croissante,
%par exemple, définie par une fonction non croissante, comme sur le dessin ci-dessous :
%\begin{center}
%\begin{pspicture}(-1,-0.50)(7,4.50)
%\psset{xunit=1.0cm,yunit=0.6cm}
%\psgrid[subgriddiv=0,gridlabels=0,gridcolor=lightgray](0,0)(-1,-1)(7,7)
%\psaxes[labelFontSize=\scriptstyle,xAxis=true,yAxis=true,Dx=1,Dy=1,ticksize=-2pt 0]{->}(0,0)(-1,-1)(7,7)
%\pscustom[linewidth=0.04]
%{
%\newpath
%\moveto(0,1)
%\curveto(0,1)(0.25,0.1)(0.5,1.)
%\curveto(0.6,1.7)(1,2)
%\curveto(1.1,2.1)(1.4,4.4)(1.5,4.5)
%\curveto(1.6,4.4)(1.7,4)(2,3.5)
%\curveto(2.5,2.75)(2.75,3.8)(3,4)
%\curveto(3.5,4.2)(3.7,4.3)(4,4.5)
%\curveto(4.5,4.2)(4.8,4.5)(5,5)
%\curveto(5.2,5.5)(5.5,6.5)(6,6)
%}
%\end{pspicture}
%\end{center}
%}
%
%\Dem{On a $p \leq n <n+1$ donc si $f$ est strictement croissante sur $[p;+\infty[$, on a par définition :
%$$f(n)<f(n+1)\Longleftrightarrow u_n<u_{n+1}$$
%Par conséquent, $(u_n)$ est strictement croissante.\\
%De la même manière, si $f$ est strictement décroissante sur $[p;+\infty[$, on a
%$$f(n)>f(n+1)\Longleftrightarrow u_n>u_{n+1}$$
%Par conséquent, $(u_n)$ est strictement décroissante.
%}
%
%\Expls{Etudier avec cette troisième méthode le sens de variation des suites $(u_n)_{n\in\N}$ et $(w_n)_{n\geq 3}$ définies
%dans l'exemple précédent.
%\begin{itemize}
% \item Soit $f : x \longmapsto x^2+2$ ; définie sur $[0 ; + \infty[$.\\
%$f$ est une fonction trinôme et sait qu'elle est strictement croissante sur $[0 ; + \infty[$.\\
%Donc $(u_n)$ est aussi strictement croissante sur $\N$.
%\item Soit $g:x\longmapsto \dfrac{3x-1}{x+2}$ ; définie sur $[3 ; +\infty[$.\\
%On a $g(x)=\dfrac{3x}{x+2}-\dfrac1{x+2}=3\dfrac1{1+\dfrac{2}{x}}+\left(-\dfrac1{x+2}\right)$.\\
%Or on a
%\begin{center}
% \begin{tikzpicture}
%\tkzTabInit[espcl=2]{$x$/0.5, Variations de $1+\dfrac2x$/1.5, Variations de $\dfrac1{1+\frac2x}$/1.5,
%Variations de $3\dfrac1{1+\frac2x}$/1.5}{$3$,$+\infty$}
%\tkzTabVar{+ /, -/ }
%%\tkzTabIma{}{4}{3}{$0$}
%\tkzTabVar{- / , +/ }
%\tkzTabVar{- / , +/ }
%\end{tikzpicture}
%et
% \begin{tikzpicture}
%\tkzTabInit[espcl=2]{$x$/0.5, Variations de $x+2$/1.5, Variations de $\dfrac1{x+2}$/1.5,
%Variations de $-\dfrac1{x+2}$/1.5}{$3$,$+\infty$}
%\tkzTabVar{- /, +/ }
%%\tkzTabIma{}{4}{3}{$0$}
%\tkzTabVar{+ / , -/ }
%\tkzTabVar{- /, +/ }
%\end{tikzpicture}
%\end{center}
%Or la somme de fonctions croissantes est croissante. Donc $g$ est croissante sur $[3 ; + \infty[$.
%On en conclut que $(w_n)_{n\geq 3}$ est aussi strictement croissante pour $n\geq 3$.
%\end{itemize}
%}
%
%
%\section{Notion de limite d'une suite numérique}
%
%\subsection{Etude d'un exemple}
%
%\Exoi{Soient les suites $(u_n)$, $(v_n)$ et $(w_n)$ définies sur $\N$ par :
%$$u_n=\dfrac1n \qquad \qquad v_n=n^2-3 \qquad \qquad w_n=(-1)^n$$
%\begin{enumerate}
% \item Etudier le sens de variation de chacune de ces suites.
% \item %Calculer pour chacune des suites les termes de rang $100$, $1000$, $10^6$ et $10^{6}+1$.\\
%Conjecturer graphiquement le \og comportement à l'infini \fg de ces suites.
%\item \begin{enumerate}
% \item Déterminer un entier $p$ tel que pour tout entier $n\geq p$, on ait $0 \leq u_n \leq 10^{-6}$.
%\item Peut-on faire de même en remplaçant $10^{-6}$ par n'importe quel réel $\varepsilon >0$ ?
% \end{enumerate}
%\item \begin{enumerate}
% \item Déterminer un entier $p'$ tel que pour tout entier $n\geq p'$, on ait $v_n \geq 10^{10}$.
%\item Peut-on faire de même en remplaçant $10^{10}$ par n'importe quel réel $M$ ?
% \end{enumerate}
%\end{enumerate}
%}
%\subsection{Suite convergente, suite divergente}
%
%
%
%
%\begin{defi}
%On dit qu'une suite \textbf{admet une limite réelle $\ell$} (ou \textbf{converge vers le réel $\ell$}) lorsque tous les termes de
%la suite $(u_n)$ sont aussi proches de $\ell$ que l'on veut à partir d'un certain rang.
%\\
%Autrement dit une suite converge vers le réel $\ell$ si tout intervalle du type $]\ell -\varepsilon; \ell +\varepsilon[$ (avec $\varepsilon>0$) contient tous les termes de la suite à partir d'un certain rang $N$.
%On note $\lim\limits_{n \to + \infty} u_n = \ell$.
%\end{defi}
%
%\Rq{Autrement dit, quelque soit le nombre $\varepsilon$ choisi (aussi petit que l'on veut),
%il existe un rang $N$ (dépendant de $\varepsilon$) à partir duquel
%tous les termes de la suite $(u_n)$ sont contenus dans l'intervalle $]\ell-\varepsilon ; \ell+ \varepsilon[ $).
%}
%\Expl{
%Graphiquement, cela se traduit ainsi :
%\begin{center}
%%\usepackage{pstricks,pst-plot,pst-text,pst-tree,pst-eps,pst-fill,pst-node,pst-math}
%\psset{xunit=0.7cm , yunit=10cm}
%\begin{pspicture*}(0,0.95)(25.1,1.8)
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%\def\psvlabel#1{\psframebox*[framesep=1pt]{\small #1}}
%\psclip{%
%\psframe[linestyle=none](\xmin,\ymin)(\xmax,\ymax)
%}
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%\newrgbcolor{couleur3}{0.0941 0.647 0.0196}
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%\psplot[linecolor=blue,linestyle=solid,plotpoints=1000]{0}{25}{\F}
%\def\G{1.55}
%\psplot[linecolor=black,linestyle=solid,plotpoints=1000]{0}{25}{\G}
%\def\H{1.45}
%\psplot[linecolor=black,linestyle=solid,plotpoints=1000]{0}{25}{\H}
%\pscustom[fillstyle=hlines,hatchwidth=0.3pt,hatchsep=12pt,hatchcolor=gray,linestyle=solid]
%{
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%}
%\psdot(1,1)
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%\psdot(4,1.625)
%\psdot(5,1.4)
%\psdot(6,1.58)
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%\psdot(14,1.53)
%\psdot(15,1.47)
%\psdot(16,1.53125)
%\psdot(17,1.471)
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%\psdot(19,1.473)
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%\psline[linecolor=black]{<->}(1,1.5)(1,1.55)
%\uput[ul](1,1.5){$\varepsilon$}
%\uput[ul](1,1.45){$\varepsilon$}
%\uput[ur](10,1.3){$10$ est le rang à partir duquel tous les termes}
%\uput[ur](10,1.2){de la suite sont dans la bande hachurée dépaisseur choisie}
% \uput[ur](5,1.7){Illustration avec la suite définie pour tout $n\geq 1$ par $u_n=\dfrac{3n+(-1)^n}{2n}$ }
%\endpsclip
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%\end{center}
%}
%\begin{itemize}
%\item Le graphique permet de conjecturer que la suite $(u_n)$ converge vers $\ell= \dfrac{3}{2}$
%\item Ici on a choisi $\varepsilon = 0.05$ et on a trouvé que pour $N=10$, tous les termes de la suite $(u_n)$
%étaient dans l'intervalle $]1.45; 1.55[$ pour $n\geq 10$.
%\item Si on avait choisi $\varepsilon = 0.1$, on aurait trouvé que pour $N=5$, tous les termes de la suite $(u_n)$
%étaient dans l'intervalle $]1.4; 1.6[$ pour $n\geq 5$.
%\item Si on avait choisi $\varepsilon = 0.04$, on aurait trouvé que pour $N=13$, tous les termes de la suite $(u_n)$
%étaient dans l'intervalle $]1.46; 1.54[$ pour $n\geq 13$.\\
%\end{itemize}
%
%
%\begin{defi}
%On dit qu'une suite est \textbf{divergente} si elle n'est pas convergente.\\
%C'est le cas des suites qui n'admettent pas de limite, et des suites qui sont
%aussi grandes que l'on veut, dans les positifs ou négatifs, à partir d'un certain rang.\\
%Dans ce dernier cas, on dit que la suite diverge vers $+ \infty$ ou $-\infty$ et on note $\lim\limits_{n \to +\infty} u_n = +\infty$ ou
%$\lim\limits_{n \to +\infty} u_n = -\infty$.
%\end{defi}
%
%\Expls{
%Conjecturer graphiquement les limites éventuelles des suites $(u_n)$, $(v_n)$, $(w_n)$ et $(t_n)$ définies sur $\N$ par :
%$$u_n=4n^2+5n-1 \qquad \qquad v_n=-\dfrac{1}{n+2}+1 \qquad \qquad w_n=-2n^2+2 \qquad \text{ et } \qquad
%t_n=\cos(n)+1$$
%%Déterminer par le calcul le rang à partir duquel : $u_n \geq 10^{6}$.
%}
%
%
%\subsection{Application : limites et algorithmes}
%
%\subsubsection{Une suite qui diverge vers $-\infty$}
%
%\Exoi{On considère la suite $u$ définie pour tout entier naturel $n$ par :
% $$\left\{ \begin{array}{l} u_0=1 \\ u_{n+1}=2u_n-2\end{array} \right.$$
% \begin{enumerate}
%\item A l'aide des droites $\mathscr D :y=x$ et $\mathscr D' :y=2x-2$ donnée ci-dessous, placer sur l'axe des abscisses les termes de $u_0$ à $u_3$.
%\item Conjecturer la limite de la suite $u$.
%\item Calculer les $4$ premiers termes de la suite $u$.
%\item \begin{center}
%\Algo{8cm}{
%\Entree{
%$u$ est un nombre réel.\\
%$p$ est un nombre entier naturel.\\
%$A$ est un nombre réel strictement positif.
%}
%{
%$u:=1$ et $p:=0$ \\
%Entrer $A$ \\
% \While{ $u>-A$ }
%{$u:=2u-2$ et $ p:=p+1$}
%Afficher $p$.
%}
%}
%\end{center}
%\begin{enumerate}
%\item Qu'affiche cet algorithme si l'utilisateur entre $A=30$ ?
%\item Qu'affiche cet algorithme si l'utilisateur entre $A=100$ ? s'il entre $A=10000$ ?
%\end{enumerate}
%\end{enumerate}
%}
%
%\begin{center}
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%\subsubsection{Une suite qui converge vers un réel $\ell$}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Le cours
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0. Position du pb
%\Exoi{On considère la suite $u$ définie pour tout entier naturel $n$ par :
% $$u_n=2-\dfrac{1}{n+1}$$
% \begin{enumerate}
% \item Calculer les premiers termes de la suite, conjecturer son sens de variation et sa limite $\ell$.
% \item Montrer que $$ u_{n+1}-u_n=\dfrac{1}{n+1}$$
% \item En déduire que la suite est strictement croissante.
%\item On considère l'algorithme suivant :
% \begin{center}
%\Algo{8cm}{
%\Entree{
%$u$ est un nombre réel.\\
%$p$ est un nombre entier naturel.\\
%$\varepsilon$ est un nombre réel strictement positif.
%}
%{
%$u:=1$ et $p:=0$ \\
%Entrer $\varepsilon$ \\
% \While{ $u\notin \left]2-\varepsilon;2+\varepsilon\right[$ }
%{$p:=p+1$ et $ u:=2-\dfrac{1}{p+1}$}
%Afficher $p$.
%}
%}
%\end{center}
%\begin{enumerate}
%\item Qu'affiche cet algorithme si l'utilisateur entre $\varepsilon=0,3$ ?
%\item Qu'affiche cet algorithme si l'utilisateur entre $\varepsilon=0,1$ ? s'il entre $\varepsilon=0,01$ ?
%\item Soit $\varepsilon >0$. Déterminer le rang $p$ à partir duquel $$u_p\in \left]2-\varepsilon;2+\varepsilon\right[$$
%\item Conclure que :
%$$ \lim\limits_{n\to +\infty} u_n=2$$
%\end{enumerate}
%\end{enumerate}
%}
\pagebreak
\section{Suite Arithmétique}
\subsection{Découverte des suites arithmétiques au travers d'un exemple}
\Exoi{Dans le pays des merveilles d'Alice, le lapin blanc, depuis le temps, a fait des enfants (enfin des adolescents plutôt...). Du plus vieux au plus jeune : le lapin bleu, le lapin rouge, le lapin vert et le lapin noir. A l'adolescence chacun des 4 lapins a réclamé de l'argent de poche. Noter que les lapins du pays des merveilles sont adolescents de $0$ à $4$ ans, ils deviennent enfants par la suite et n'ont jamais été adultes.\\
Le lapin blanc a décidé de donner au lapin bleu dès sa naissance et jusqu'au jour de ses 4 ans des carottes de la manière suivante :
\begin{itemize}
\item $3$ carottes la première semaine ;
\item Chaque semaine deux carottes de plus que la semaine précédente.
\end{itemize}
\textit{On admet qu'au pays des merveilles chaque année est constituée d'exactement $52$ semaines et chaque mois de $4$ semaines. Remarquons que les lapins du pays des merveilles ont un treizième mois...}
\\
On note $u_0=3$ et $u_n$ le nombre de carottes reçues par le lapin bleu le jour où il fête ses $n$ semaines.
\begin{enumerate}
\item Exprimer $u_{n+1}$ en fonction de $u_n$ ; calculer $u_1$ ; $u_2$ et $u_3$. Combien de carottes le lapin bleu a-t-il reçu le premier mois ?
\item Proposer une formule donnant $u_n$ en fonction de $n$. Vérifier cette formule en recalculant $u_1$ ; $u_2$ et $u_3$.
\item Calculer le nombre de carottes reçues par le lapin bleu le jour de ses $1$ an, de ses $2$ ans, de ses $3$ ans et enfin le jour de ses $4$ ans.
\item Pour leur seule consommation personnelle les lapins du pays des merveilles ont besoin de $300$ carottes par semaine.
\begin{enumerate}
\item A partir de quel âge le lapin bleu peut-il se nourrir à satiété ?
\item Déterminer le nombre total de carottes que le lapin blanc a donné au lapin bleu au cours de son adolescence. On devra donc calculer :
$$ S=u_0+u_1+\dots+u_{207}=\sum_{i=0}^{i=207}u_i$$
\item Dès qu'il reçoit plus de $300$ carottes, le lapin bleu (fort économe) met toutes les autres de côté. \\
Déterminer le nombre de carottes économiser par le lapin bleu.
\item Grand amateur de montre, le lapin bleu décide de troquer ses carottes contre des montres au cours suivant, $1$ montre contre $540$ carottes.
Déterminer le nombre de montres que le lapin bleu a pu acquérir grâce aux carottes économisées.
\end{enumerate}
\end{enumerate}
}
\pagebreak
\subsection{Définition}
\begin{defi}
Une suite arithmétique est une suite de nombres dans laquelle chaque terme permet de déduire le suivant en lui ajoutant la même constante appelée raison.\\
Si on note $u$ une suite arithmétique de raison $r$ définie pour tout entier $n$ on a donc, pour tout entier naturel $n$ :
$$ u_{n+1}=u_n+r$$
\end{defi}
\Expl{La suite des entiers naturels pairs est une suite arithmétique de premier terme 0 et de raison 2}
\Rq{Si $u$ est suite arithmétique de raison $r$ alors pour tout $n$ on a :
$$ u_{n+1}=u_n+r\Longleftrightarrow u_{n+1}-u_n=r$$
Si la raison $r>0$ alors la suite arithmétique est strictement croissante, au contraire si $r<0$ la suite arithmétique est strictement décroissante. Dans le cas où $r=0$ il s'agit d'une suite constante.
}
\Exoi{Les suites suivantes sont-elles arithmétiques ? Dans le cas d'une réponse positive préciser leur raison et leur sens de variation.
\begin{multicols}{3}
\begin{enumerate}
\item $u_n=3n-2$
\item $u_n=n^2-3$
\item $u_n=-4n+1$
\end{enumerate}
\end{multicols}
}
\subsection{Expression explicite en fonction de $n$}
On considère une suite arithmétique $u$ de raison $r$ et de premier terme $u_0$, on a alors :
\begin{eqnarray*}
& & u_1=u_0+r\\
& \Longrightarrow & u_2=u_1+r=u_0+2r\\
& \Longrightarrow & u_3=u_2+r=u_0+3r\\
& \Longrightarrow & u_4=u_3+r =u_0+3r+r=u_0+4r\\
& \Longrightarrow & \dots\dots\dots\\
&\Longrightarrow & u_n=u_{n-1}+r=u_0+(n-1)r+r=u_0+nr
\end{eqnarray*}
\begin{prop}
Soit $(u_n)$ une suite arithmétique de raison $r$, alors $$u_n=u_0+nr$$
\end{prop}
\Exoi{$(u_n)$ est la suite arithmétique de premier terme $u_0=3$ et de raison $2$. \newline
Calculer $u_{2013}$}
\begin{theo}Soit $(u_n)$ une suite arithmétique de premier terme $u_0$ et de raison $r$, alors pour tous $p$ et $n$ de $\N$ :
$$ u_n=u_p+(n-p)r$$
\end{theo}
\Dem{D'après la propriété précédente on a pour tous $p$ et $n$ de $\N$ :
$$ u_p=u_0+pr \qquad \text{ et }\qquad u_n=u_0+nr$$
Par conséquent $$ u_n-u_p=u_0+nr-u_0-pr=(n-p)r\Longleftrightarrow u_n=u_p+(n-p)r$$}
\Exoi{Considérons une suite arithmétique $(v_n)$ telle que $v_{27}=6$ et $v_{39}=10$\newline
Calculer $v_7$ et $v_{74}$
}
\begin{theo}
On considère une suite $(u_n)$ définie par $u_n=an+b$ où $a$ et $b$ sont deux réels. \newline
$(u_n)$ est une suite arithmétique de raison $a$
\end{theo}
\Dem{Soit $n\in\N$, on a alors :
$$ u_{n+1}-u_n=a(n+1)+b-an-b=a$$}
\subsection{Somme de termes successifs}
\Rq{Soit $(u_n)$ une suite. La somme $u_1+u_2$ comporte deux termes, de même la somme $u_1+u_2+u_3$ en comporte $3$. De manière générale la somme $u_1+u_2+\dots u_p$ comporte $p$ termes. \newline
Combien en comporte la somme :$u_{14}+u_{15}+\dots +u_{25}$ ? On peut remarquer que cette somme s'écrit encore :
$$ u_{1+13}+u_{2+13}+\dots +u_{13+12} $$
Par conséquent elle comporte $12$ termes, i.e $25-14+1$ termes.}
\begin{prop}La somme $u_p+u_{p+1}+\dots+u_q$ comporte donc $q-p+1$ termes ($p$ et $q$ sont des nombres entiers tels que : $p<q$)
\end{prop}
\begin{prop}[Somme des $n$ premiers entiers]$$ 1+2+\dots+n-1+n=\dfrac{n(n+1)}{2}$$\end{prop}
\Dem{Notons $S=1+2+\dots+n-1+n$, on a $2S=1+2+\dots+n+1+2+\dots+n=(1+n)+(2+n-1)+(3+n-2)+\dots +(n-2+3)+(n-1+2)+(n+1)=n(n+1)$ donc $S=\dfrac{n(n+1)}{2}$}
\Expl{La somme des $100$ premiers entiers est donc :
$$ \dfrac{100\times 101}{2}=\dfrac{10100}{2}=5050$$}
\begin{theo}On considère une suite arithmétique $u$ et $S$ la somme des termes successifs (à partir de celui de rang $p$ jusqu'à celui de rang $n$) que l'on note :
$$ S=u_p+u_{p+1}+\dots+u_n=\sum_{i=p}^{i=n}u_i$$
On a alors :
$$S=\dfrac{(n-p+1)(u_p+u_d)}{2} $$
\end{theo}
\Dem{On a : $$ S=u_p+u_{p+1}+u_{p+2}\dots+u_{n-2}+u_{n-1}+u_n$$
En notant $r$ la raison on obtient :
$$ S=u_p+(u_p+r)+(u_p+2r)+\dots + (u_n-2r)+(u_n-r)+u_n$$
En inversant l'ordre des termes de cette somme, $S$ s'écrit aussi :
$$ S=u_n+(u_n-r)+(u_n-2r)+\dots+(u_p+2r)+(u_p+r)+u_p$$
Effectuons alors la somme, membre à membre terme à terme, des deux égalités précédentes :
$$ 2S=(u_p+u_n)+(u_p+r+u_n-r)+(u_p+2r+u_n-2r)+\dots+(u_n-2r+u_p+2r)+(u_n-r+u_p+r)+(u_n+u_p)$$
Cette somme comporte $n-p+1$ termes tous égaux à $u_p+u_n$, par conséquent :
$$ 2S=(n-p+1)(u_p+u_n)\Longleftrightarrow S=\dfrac{(n-p+1)(u_p+u_n)}{2} $$}
\Exoi{
\begin{enumerate}
\item Calculer la somme des $50$ premiers entiers impairs.
\item Calculer la somme des $50$ premiers entiers pairs en partant de $12$
\end{enumerate}}
\pagebreak
\Exoi{En reprenant le contexte de l'exercice introductif. La lapin blanc décide pour son second, le lapin rouge de donner dès sa naissance et jusqu'au jour de ses 4 ans des carottes de la manière suivante :
\begin{itemize}
\item $417$ carottes la première semaine ;
\item Chaque semaine deux carottes de moins que la semaine précédente.
\end{itemize}
On note $v$ la suite telle que $v_n$ vaut le nombre de carottes reçues par le lapin rouge le jour de sa $n-$ième semaine. Notons que $v_1=417$ et que $v_0$ n'existe pas.
\begin{enumerate}
\item Justifier que $v_n$ est une suite arithmétique ; préciser sa raison et son sens de variation.
\item Exprimer $v_n$ en fonction de $n$.
\item Calculer le nombre de carottes reçues par le lapin bleu le jour de ses $1$ an, de ses $2$ ans, de ses $3$ ans et enfin le jour de ses $4$ ans.
\begin{enumerate}
\item Jusqu'à quel âge le lapin bleu peut-il se nourrir à satiété ?
\item Déterminer le nombre total de carottes que le lapin blanc a donné au lapin rouge au cours de son adolescence. On devra donc calculer :
$$ S=v_1+v_2+\dots+v_{208}=\sum_{i=1}^{i=208}v_i$$
\item Dès qu'il reçoit plus de $300$ carottes, le lapin rouge (fort économe comme son frère) met toutes les autres de côté. \\
Déterminer le nombre de carottes économiser par le lapin rouge.
\item Grand amateur de montre, le lapin rouge décide de troquer ses carottes contre des montres mais l'inflation existe au pays des merveilles. Il faut $10\%$ de carottes supplémentaires pour obtenir une montre qu'au temps du lapin bleu.
Le lapin rouge est-il perdant par rapport à son frère ?
\end{enumerate}
\item Le lapin blanc constatant l'injustice subit par le lapin rouge décide d'utiliser une autre méthode pour les \og carottes de poches \fg{} du lapin suivant, le lapin vert. Il le rémunère de sa naissance et jusqu'au jour de ses 4 ans de la manière suivante :
\begin{itemize}
\item $1$ carotte la première semaine ;
\item Chaque semaine trois carottes de plus que la semaine précédente ;
\item $100$ carottes les $6$ derniers mois.
\end{itemize}
On note $w$ la suite telle que $w_0=1$ et $w_n$ désigne le nombre de carottes reçues par le lapin rouge le jour où il fête ses $n$ semaines.
\begin{enumerate}
\item La suite $w$ est-elle arithmétique ?
\item Plus précisément déterminer le rang jusqu'au quel $w$ se comporte comme une suite arithmétique.
\item Identique à ses frères le lapin rouge économise dès qu'il reçoit plus de $300$ carottes par semaine. Mais durant les $6$ derniers mois il mange un peu de ses économies de manière à manger $300$ carottes exactement par semaine. Sachant que le cours de la carotte a encore augmenté de $50\%$ déterminer le nombre de montre que le lapin rouge possèdera au moment de devenir enfant.
\end{enumerate}
\end{enumerate}
}
\pagebreak
\section{Suite Géométrique}
\subsection{Découverte des suites géométriques au travers d'un exemple}
\Exoi{Vient le tour du derrnier né du lapin blanc, le lapin noir. Détestant les habitudes le lapin blanc modifie une nouvelle fois le système des \og carottes de poches \fg{} et le lapin noir se voit proposer le système suivant :
\begin{itemize}
\item $3$ carottes la première semaine ;
\item Chaque semaine $3,5\%$ de carottes en plus de la semaine précédente (le lapin blanc donnera s'il le faut des morceaux de carottes...)
\end{itemize}
On note $t$ la suite telle que $t_n$ vaut le nombre de carottes reçues par le lapin rouge le jour de sa $n-$ième semaine. Notons que $t_1=3$ et que $t_0$ n'existe pas.
\begin{enumerate}
\item Calculer $t_1$ ; $t_2$ et $t_3$ puis exprimer $t_{n+1}$ en fonction de $t_n$. Combien de carottes le lapin noir a-t-il reçu le premier mois ?
\item Proposer une formule donnant $t_n$ en fonction de $n$. Vérifier cette formule en recalculant $t_1$ ; $t_2$ et $t_3$.
\item Calculer le nombre de carottes reçues par le lapin noir le jour de ses $1$ an, de ses $2$ ans, de ses $3$ ans et enfin le jour de ses $4$ ans.
\item Pour leur seule consommation personnelle les lapins du pays des merveilles ont besoin de $300$ carottes par semaine.
\begin{enumerate}
\item A partir de quel âge le lapin noir peut-il se nourrir à satiété ?
\item Déterminer le nombre total de carottes que le lapin blanc a donné au lapin noir au cours de son adolescence. On devra donc calculer :
$$ S=t_1+t_2+\dots+t_{208}=\sum_{i=1}^{i=208}t_i$$
\item Dès qu'il reçoit plus de $300$ carottes, le lapin noir (comme les autres) met toutes les autres de côté. \\
Déterminer le nombre de carottes économiser par le lapin noir.
\item Par rapport au lapin précédent, le cours de la carotte a encore augmenté de $10\%$.
Déterminer le nombre de montres que le lapin noir a pu acquérir grâce aux carottes économisées.
\end{enumerate}
\end{enumerate}
}
\subsection{Définition}
\begin{defi}Une suite \underline{g\'eom\'etrique} est une suite de nombres dans laquelle chaque terme permet de déduire le suivant par multiplication par un coefficient constant appelé raison. Ainsi, une suite géométrique $u$ de raison $q$ et de premier terme $a$ a la forme suivant :
$$ a\quad aq\qquad aq^2\qquad aq^3\qquad aq^4$$
La définition peut s'écrire sous la forme d'une relation de récurrence, c'est-à-dire que pour chaque entier naturel $n$ :
$$ u_{n+1}=q\times u_n$$
\end{defi}
\Expl{La suite des puissances de $2$ est une suite géométrique de raison $2$ : $u_{n+1}=2\times u_n$\\
Donner les premiers termes de la suite géométrique de premier terme $2$ et de raison $0,5$.}
\Exoi{\begin{enumerate}
\item Montrer que la suite $(u_n)$ définie par $u_n=\dfrac{2}{3^n}$ est géométrique
\item La suite $(v_n)$ est définie par $v_0=6$ et $v_{n+1}=3v_n+4$ pour tout $n\in\N$.\newline
On note $$w_n=v_n+2$$
Montrer que $(w_n)$ est une suite géométrique
\end{enumerate}}
\Exoi{Montrer que la suite $(u_n)$ définie, pour tout $n\in\N$ par $u_n=2\times (-1)^n$ est géométrique. On précisera sa raison.}
\subsection{Expression explicite en fonction de $n$}
\begin{theo}On considère une suite $(u_n)$ définie par $u_n=aq^n$ où $a$ et $q$ sont deux réels non nuls. \newline
$(u_n)$ est une suite géométrique de raison $q$\end{theo}
\Dem{Pour tout $n\in\N$ on a $u_{n+1}=aq^{n+1}=aq^n\times q=q u_n $. Par conséquent la suite est géométrique de raison $q$}
\begin{theo}Soit $(u_n)$ une suite géométrique de raison $q\neq 0$ et de premier terme $u_0$ alors $$u_n=u_0 \times q^n$$\end{theo}
\Dem{On peut raisonner de proche en proche. On a :
\begin{eqnarray*}
&& u_1=u_0q\\
&& u_2=u_1q=u_0q^2\\
&& u_3=u_2q=u_0q^3\\
&& \dots \\
&& u_{n-1}=u_{n-2}q=u_0q^{n-2}\\
&& u_n=u_{n-1}q=u_0q^{n-1}\\
\end{eqnarray*}
}
\Expl{Soit $(u_n)$ la suite géométrique de premier terme $u_0=2$ et de raison $3$. On a alors :
$$ u_n=2 \times 3^n$$
On peut, par exemple calculer directement $u_5=2\times 3^5=2\times 243=486$}
\begin{theo}$(u_n)$ est une suite géométrique de raison $q\neq 0$ alors quels que soient les entiers naturels $n$ et $p$ on a :
$$u_n=q^{n-p}\times u_p$$ \end{theo}
\Dem{D'après le théorème précédent, on a :
$$ u_n=u_0q^n \qquad \text{ et }\qquad u_p=u_0q^p$$
donc, puisque $q\neq 0$, $u_0= \dfrac{u_p}{q^p}$ ; d'où $u_n=\dfrac{u_p}{q^p}q^n=u_p\times q^{n-p}$ }
\Exoi{$(u_n)$ et $(v_n)$ sont deux suites géométriques. Déterminer $u_5$, $u_8$, $v_7$ et $v_{15}$ sachant que :
\begin{enumerate}
\item $u_0=6$ et $q=-\dfrac{1}{3}$
\item $v_5=1$ et $v_{10}=32$
\end{enumerate}}
\subsection{Somme de termes successifs}
On s'interesse à la somme des $n$ premiers termes de la suite géométrique de premier terme $1$ et de raison $q$, avec $q\neq 1$
\begin{prop}[Cas particulier $u_n=q^n$, avec $q\neq 1$]$$ 1+q+q^2+\dots+q^{n-2}+q^{n-1}=\dfrac{1-q^n}{1-q}$$\end{prop}
\Dem{Notons $S=1+q+q^2+\dots+q^{n-2}+q^{n-1}$, on a $qS=q+q^2+\dots+q^{n-2}+q^{n-1}+q^n$\newline
Par conséquent $$(1-q)S=S-qS=1-q^n\Longleftrightarrow S=\dfrac{1-q^n}{1-q}$$}
\Expl{La somme des $10$ premiers termes de cette suite géométrique lorsque $q=2$ est donc :
$$ \dfrac{1-2^{10}}{1-2}=1023$$}
\begin{theo}La somme des termes consécutifs, du terme de rang $p$ au terme de rang $n$, d'une suite géométrique de raison $q$ ($q\neq 1$) est égale à :
$$ u_p+u_{p+1}+\dots+u_n=u_p \dfrac{1-q^{n-p+1}}{1-q}$$
\end{theo}
\Dem{On calcule donc $S$, la somme des $n-p+1$ termes consécutifs, de premier terme $u_p$, d'une suite géométrique de raison $q$ où $q\neq 1$
$$ S=u_p+u_{p+1}+\dots+u_n=u_p+u_p\times q+u_p\times q^2+\dots +u_p\times q^{n-p+1-1}=u_p(1+q+q^2+\dots+q^{n-p+1-1})=u_p \dfrac{1-q^{n-p}}{1-q}$$
}
\Rq{Le cas $q=1$ est trivial, en notant le premier terme de la somme $a$ :
$$a+aq+aq^2+\dots +aq^{n-1}=a+a+\dots+a=na$$}
\Exoi{
Soit $(u_n)$ la suite géométrique de premier terme $u_0=\dfrac{1}{2}$ et de raison $q=\dfrac{3}{2}$. Calculer $S=u_4+u_5+\dots+u_{14}$}
\subsection{Convergence}
\begin{theo}Soit $(u_n)$ une suite définie par : $u_n=q^n$ alors :
\begin{itemize}
\item Si $q \in ]-1;1[$ la suite $(u_n)$ est convergente vers $0$
\item Si $q=1$ alors la suite $(u_n)$ est constante et donc convergente vers $1$, si $q=-1$ la suite diverge (elle vaut tantôt $1$ tantôt $-1$).
\item Si $q>1$ alors la suite $(u_n)$ est divergente (vers $+\infty$), enfin si $q<-1$ la suite diverge (un terme sur deux est négatif, l'autre est positif).
\end{itemize}
\end{theo}
Pour cette démonstration, nous n'étudierons que le cas où $q>0$, nous allons utiliser le résultat suivant \footnote{un résultat servant une démonstration est usuellement appelé Lemme}
\begin{lem}[Inégalité de Bernoulli]Pour tout réel $x$ positif et pour tout entier $n$, on a :$$(1+x)^n\geq 1+nx$$\end{lem}
\Dem[du lemme]{Notons $\mathscr P(n)$ la propriété $(1+x)^n\geq 1+nx$ est vraie\newline
$\mathscr P(0)$ et $\mathscr P(1)$ sont évidentes\newline
Montrons que $\mathscr P(n)\Longrightarrow \mathscr P(n+1)$.\newline
On suppose donc que $(1+x)^n\geq 1+nx$ et on souhaite montrer que : $(1+x)^{n+1}\geq 1+(n+1)x$\newline
On a alors, pour tout $x\geq0$ :
\begin{eqnarray*}
&& (1+x)^n\geq 1+nx \\
&\Longleftrightarrow & (1+x)^{n+1}\geq (1+nx)(1+x) \qquad \text{en multipliant membre à membre par }(1+x)>0\\
&\Longleftrightarrow & (1+x)^{n+1}\geq 1+nx+x+nx^2\\
& \Longleftrightarrow & (1+x)^{n+1}\geq 1+(n+1)x+nx^2 \\
& \Longleftrightarrow & (1+x)^{n+1}\geq 1+(n+1)x \qquad \text{puisque }nx^2\geq 0\\
\end{eqnarray*}
Résumons : On a donc $\mathscr P(0)$ mais aussi, $\forall n\in \N$, $\mathscr P(n)\Longrightarrow \mathscr P(n+1)$, par conséquent on a : pour tout réel $x$ positif et pour tout entier $n$, on a :$$(1+x)^n\geq 1+nx$$}
\Rq{Le type de raisonnement que l'on vient d'effectuer s'appelle le \underline{raisonnement par récurrence}, il sera étudié amplement en terminale.}
\Dem[du théorème]{
\begin{itemize}
\item $q>1$\newline
Posons $x=q-1$, on a alors $x>0$, et d'après l'inégalité de Bernoulli :
$$ q^n=(1+x)^n \geq 1+nx$$
Or, $\lim\limits_{n\to +\infty} 1+nx=+\infty$, par comparaison on en déduit : $$ \lim\limits_{n \to +\infty} q^n=+\infty$$
La suite $(u_n)$ diverge donc vers $+\infty$
\item $q\in [0;1[$\newline
Si $q=0$ le résultat est évident, sinon posons $q'=\dfrac{1}{q}$, dans ce cas $q' \in ]1;+\infty[$\newline
D'après le résultat précédent : $$ \lim\limits_{n \to +\infty} q'^n=+\infty$$
Par passage à l'inverse nous obtenons donc : $$ \lim\limits_{n \to +\infty} q^n=0$$
La suite $(u_n)$ converge donc vers $0$
\item $q=1$, le résultat est alors évident.
\end{itemize}}
\Exoi{$(u_n)$ est la suite géométrique de premier terme $u_0=3$ et de raison $ \dfrac{1}{2}$. On note $s_n$ la somme $u_0+u_1+u_2+\dots+u_n$
\begin{enumerate}
\item Exprimer $s_n$ en fonction de $n$
\item Calculer $\lim\limits_{n\to +\infty}s_n$
\end{enumerate} }
\pagebreak
\subsection{Application}
\Exoi{Un étudiant loue une chambre pour $3$ ans. On lui propose deux types de bails. \\
\underline{1$^\text{er}$ contrat} : Un loyer de $200\euro$ pour le premier mois puis une augmentation de $5\euro$ par mois jusqu'à la fin du bail.
\\
\underline{2$^\text{ème}$ contrat} : Un loyer de $200\euro$ pour le premier mois puis une augmentation de $2\%$ par mois jusqu'à la fin du bail\footnote{Un bail est un contrat de location}.
\begin{enumerate}
\item Calculer, pour chacun des deux contrats, le loyer du deuxième mois puis le loyer du troisième mois.
\item Calculer, pour chacun des deux contrats, le loyer du dernier mois, i.e le loyer du $36^\text{ème}$ mois.
\item Quel est le contrat globalement le plus avantageux pour un bail de $3$ ans ? (\textit{Justifier par des calculs})
\end{enumerate}
}
\Exoi{On considère la suite géométrique définie de la façon suivante :
$$ u_1=1\qquad \text{et}\qquad u_{n+1}=2u_n\qquad \forall n\geq 1$$
\begin{enumerate}
\item Calculer $u_2$ ; $u_3$ ; $u_4$.
\item Exprimer $u_n$ en fonction de $n$ ; en déduire $u_{64}$.
\item \textbf{La légende du jeu d'échec} :\textit{ Le roi demanda à l'inventeur du jeu d'échec de choisir lui-même sa récompense. Celui-ci répondit : \og place 1 grain de blé sur la première case de l'échiquier, deux grains sur la deuxième case, quatre sur la troisième case, et ainsi de suite jusqu'à la $64^\text{ième}$ case. Le roi sourit de la modestie de la demande.}
\\
Calculer une valeur approchée du nombre total de grains de blé que le roi devra placer sur l'échiquier.
\end{enumerate}
}
\Exoi{Les rayons cosmiques produisent continuellement dans l'atmosphère du carbone $14$, qui est un élément radioactif. Durant leur vie, les tissus animaux et végétaux contiennent la même proportion de carbone $14$ que l'atmosphère. Cette proportion de carbone $14$ décroît après la mort du tissu de $1,24\%$ en $100$ ans.
\begin{enumerate}
\item Déterminer les pourcentages de la proportion initiale de carbone $14$ contenu dans le tissu au bout de $1000$ ans, de $2000$ ans et de $10000$ ans.
\item Exprimer le pourcentage de la proportion initiale de carbone $14$ contenu dans le tissu au bout de $k\times 10^3$ années.
\item Un fossile ne contient plus que $10\%$ de ce qu'il devrait contenir en carbone $14$. Estimer son âge.
\end{enumerate}
}
\Exoi{Premières étapes de la construction du triangle de Sierpinski :
\begin{center}
\includegraphics[scale=1]{Sierpinski.eps}
\end{center}
\begin{enumerate}
\item On note $u$ la suite qui donne le nombre de triangle noir à l'étape $n$. Quelle est la nature de $u$ ; préciser ses éléments caractéristiques.
\item On note $v$ la suite qui donne la longueur d'un côté du triangle noir à l'étape $n$. Quelle est la nature de $v$ ; préciser ses éléments caractéristiques.
\item On note $w$ la suite qui donne l'aire d'un triangle noir à l'étape $n$. Quelle est la nature de $w$ ; préciser ses éléments caractéristiques.
\item On note $t$ la suite qui donne l'aire du domaine couvert par les triangles noirs à l'étape $n$. Quelle est la nature de $t$ ; préciser ses éléments caractéristiques.
\end{enumerate}
}
\pagebreak
\section{Suite Arithmético-géométrique}
\Exoi{Comme vous le savez tous, le Schblurb commun à aillette mouchetée est l’animal emblématique de la Syldavie. Aussi
paisible que les habitants de ce bucolique pays, le Schblurb se nourrit exclusivement des baies du bleurtschzrn, arbre
qui pousse en abondance dans les verts sous-bois syldaves.
\\
On suppose que la population $u$ lors de l'année $n$ de Schblrurbs suit la loi suivante :
$$ u_{n+1}=au_n+b$$
L’effectif des Schblurbs,
exprimé en millions d’individus, est approché pour l’année $n$ par un nombre réel $u_n$. Par
exemple, si pour l’année zéro il y a $300 000$ Schblurbs, on prendra $u_0= 0,3$.\\
Le but de l’exercice est d’étudier le comportement de la suite $u$ pour différentes valeurs de la population initiale $u_0$
et des paramètres $a$ et $b$.\\
On cherche à estimer la population de Schblurbs dans l'avenir lointain, par deux techniques différentes dont l'une utilise la suite auxiliaire suivante :\\
la suite $v$ est définie, pour $n\in\N$, par :
$$ v_n=u_n-\dfrac{b}{1-a}$$
\begin{enumerate}
\item \textbf{Cas 1} : $u_0=0,7$ ; $a=-0,2$ et $b=0,4$.
\begin{enumerate}
\item Calculer la population de Schblurbs présent aux années $1$ ; $2$ et $3$.
\item \begin{enumerate}
\item Préciser la fonction $f$ telle que $u_{n+1}=f(u_n)$.
\item A l'aide de la représentation graphique de la fonction $f$ et de la droite d'équation $y=x$ représenter les $5$ premiers termes de la suite $u$.
\item Que pouvez-vous conjecturer sur la limite de la suite $u$.
\item Déterminer cette limite par le calcul.
\end{enumerate}
\item Vérifier que, pour tout entier $n$, on a :
$$ v_{n}=u_n-\dfrac{1}{3}$$
\item Montrer que $v$ est une suite géométrique ; on précisera sa raison.
\item Exprimer $v_n$ en fonction de $n$.
\item En déduire que $$ u_n=\dfrac{11}{30}\times \left(-\dfrac{1}{5}\right)^n+\dfrac{1}{3}$$
\item En déduire la limite $\ell$ de la suite $u$.
\end{enumerate}
\item \textbf{Cas 2} : $u_0=0,7$ ; $a=1,5$ et $b=-0,2$.
\begin{enumerate}
\item Calculer la population de Schblurbs présent aux années $1$ ; $2$ et $3$.
\item \begin{enumerate}
\item Préciser la fonction $f$ telle que $u_{n+1}=f(u_n)$.
\item A l'aide de la représentation graphique de la fonction $f$ et de la droite d'équation $y=x$ représenter les $5$ premiers termes de la suite $u$.
\item Que pouvez-vous conjecturer sur la limite de la suite $u$.
\end{enumerate}
\item Vérifier que, pour tout entier $n$, on a :
$$ v_{n}=u_n-\dfrac{2}{5}$$
\item Montrer que $v$ est une suite géométrique ; on précisera sa raison.
\item Exprimer $v_n$ en fonction de $n$.
\item En déduire que $$ u_n=\dfrac{3}{10}\times \left(\dfrac{3}{2}\right)^n+\dfrac{2}{5}$$
\item En déduire la limite $\ell$ de la suite $u$.
\end{enumerate}
\item \textbf{Cas 3} : $u_0=0,3$ ; $a=1,5$ et $b=-0,2$.
\begin{enumerate}
\item Calculer la population de Schblurbs présent aux années $1$ ; $2$ et $3$.
\item \begin{enumerate}
\item Préciser la fonction $f$ telle que $u_{n+1}=f(u_n)$.
\item A l'aide de la représentation graphique de la fonction $f$ et de la droite d'équation $y=x$ représenter les $5$ premiers termes de la suite $u$.
\item Que pouvez-vous conjecturer sur la limite de la suite $u$.
\end{enumerate}
\item Vérifier que, pour tout entier $n$, on a :
$$ v_{n}=u_n-\dfrac{2}{5}$$
\item Montrer que $v$ est une suite géométrique ; on précisera sa raison.
\item Exprimer $v_n$ en fonction de $n$.
\item En déduire que $$ u_n=-\dfrac{1}{10}\times \left(\dfrac{3}{2}\right)^n+\dfrac{2}{5}$$
\item En déduire la limite $\ell$ de la suite $u$. Conclure.
\end{enumerate}
\item \textbf{Cas 4} : $u_0=0,3$ ; $a=-0,5$ et $b=7$.
\begin{enumerate}
\item Calculer la population de Schblurbs présent aux années $1$ ; $2$ et $3$.
\item \begin{enumerate}
\item Préciser la fonction $f$ telle que $u_{n+1}=f(u_n)$.
\item A l'aide de la représentation graphique de la fonction $f$ et de la droite d'équation $y=x$ représenter les $5$ premiers termes de la suite $u$.
\item Que pouvez-vous conjecturer sur la limite de la suite $u$.
\item Déterminer cette limite par le calcul.
\end{enumerate}
\item Vérifier que, pour tout entier $n$, on a :
$$ v_{n}=u_n-\dfrac{14}{3}$$
\item Montrer que $v$ est une suite géométrique ; on précisera sa raison.
\item Exprimer $v_n$ en fonction de $n$.
\item En déduire que $$ u_n=-\dfrac{131}{30}\times \left(-\dfrac{1}{2}\right)^n+\dfrac{14}{3}$$
\item En déduire la limite $\ell$ de la suite $u$. Conclure.
\end{enumerate}
\end{enumerate}
}
\epigraphe{La physique est bien trop dure pour les phycisiens}
{David Hilbert}
{mathématicien}
\end{document}
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{\gtfamily\bfseries 計算欄}
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\rotatebox{180}{{\normalsize\gtfamily\bfseries 数学プリント\#32}\scriptsize
{\normalsize\ajKaku{5}}~\( -6,-1,2,3,2,-1 \)\
{\normalsize\ajKaku{6}}~\( 11,6,3,2,3,6 \)\qquad
\( x=-1,(-1,-3)\quad
x=2,(2,0)\quad
x=1,(1,3)\quad
x=2,(2,4)\quad
x=1,(1,3)\quad
x=2,(2,2)\)
}
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\newpage
%zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz222222222222222
\def\siki{y=2x^2-4x+5}
\toi \( \siki \) について次の表を完成させ，グラフをかきなさい。\kotae{21,11,5,3,5,11}\\[1ex]
\def\arraystretch{1.5}
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& \mb{2} & \mb{3} \\ \hline
\ifnum\DisplayToiFig>0
$y$ & \textcolor{red}{$21$} &
\textcolor{red}{$11$} &
\textcolor{red}{$5$} &
\textcolor{red}{$3$} &
\textcolor{red}{$5$} &
\textcolor{red}{$11$} \\ \hline
\else
$y$ & & & & & & \\ \hline
\fi
\end{tabular}
\vskip-10ex
\mbox{}\hfill
\begin{tikzpicture}[scale=0.3, >=stealth, baseline=(current bounding box.north)]
\tiny
\draw[->](-4,0) -- (4,0);
\draw[->](0,-3) -- (0,24);
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\draw(-0.4,-0.4) node {O};
\draw(4,-0.3) node {$x$};
\draw(-0.3,24) node {$y$};
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\fill[red](\x,{2*(\x)^2-4*\x+5}) circle(4pt);
}
\draw[red,thick]({1-sqrt(10)},23)
parabola bend (1,3) (3.8,{2*(3.8)^2-4*3.8+5});
\fi
\end{tikzpicture}
\hspace*{2zw}\mbox{}
\vskip-20zh
{\gtfamily\bfseries 計算欄}
\nidangumi{$\bullet \quad x=-2$ のとき\\ \hspace*{2.8ex} \(\siki\)}
{$\bullet \quad x=-1$ のとき\\ \hspace*{2.8ex} \(\siki\)}
\vfill
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{$\bullet \quad x=3$ のとき\\ \hspace*{2.8ex} \(\siki\)}
\vfill
\ifnum\make_pdf_with_insatsu=0
\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\fi
\def\siki{y=-3x^2+12x-8}
\toi \( \siki \) について次の表を完成させ，グラフをかきなさい。\kotae{-8,1,4,1,-8,-23}\\[1ex]
\def\arraystretch{1.5}
\def\mb#1{\makebox[3ex]{#1}}
\begin{tabular}[t]{|c||c|c|c|c|c|c|} \hline
$x$ & \mb{0} & \mb{1} & \mb{2} & \mb{3} & \mb{4}
& \mb{5} \\ \hline
\ifnum\DisplayToiFig>0
$y$ & \textcolor{red}{$-8$} &
\textcolor{red}{$1$} &
\textcolor{red}{$4$} &
\textcolor{red}{$1$} &
\textcolor{red}{$-8$} &
\textcolor{red}{$-23$} \\ \hline
\else
$y$ & & & & & & \\ \hline
\fi
\end{tabular}
\vskip-13ex
\mbox{}\hfill
\begin{tikzpicture}[scale=0.3, >=stealth, baseline=(current bounding box.north)]
\tiny
\draw[->](-2,0) -- (7,0);
\draw[->](0,-26) -- (0,6);
\foreach \x in {-1,...,6}{\foreach \y in {-25,...,5}{\fill (\x,\y) circle (2pt);}}
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{\gtfamily\bfseries 計算欄}
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\vfill
\newpage
%3333333333333333333333333333333333333333333333333333333333333333333
\def\siki{y=-x^2+2x+2}
\toi \( \siki \) について次の表を完成させ，グラフをかきなさい。\kotae{-6,-1,2,3,2,-1}\\[1ex]
\def\arraystretch{1.5}
\def\mb#1{\makebox[3ex]{#1}}
\begin{tabular}[t]{|c||c|c|c|c|c|c|} \hline
$x$ & \mb{$-2$} & \mb{$-1$} & \mb{0} & \mb{1} & \mb{2}
& \mb{3} \\ \hline
\ifnum\DisplayToiFig>0
$y$ & \textcolor{red}{$-6$} &
\textcolor{red}{$-1$} &
\textcolor{red}{$2$} &
\textcolor{red}{$3$} &
\textcolor{red}{$2$} &
\textcolor{red}{$-1$} \\ \hline
\else
$y$ & & & & & & \\ \hline
\fi
\end{tabular}
\vskip-15ex
\mbox{}\hfill
\begin{tikzpicture}[scale=0.4, >=stealth, baseline=(current bounding box.north)]
\tiny
\draw[->](-3,0) -- (4,0);
\draw[->](0,-8) -- (0,6);
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{\gtfamily\bfseries 計算欄}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\def\siki{y=x^2-4x+6}
\toi \( \siki \) について次の表を完成させ，グラフをかきなさい。\kotae{11,6,3,2,3,6}\\[1ex]
\def\arraystretch{1.5}
\def\mb#1{\makebox[3ex]{#1}}
\begin{tabular}[t]{|c||c|c|c|c|c|c|} \hline
$x$ & \mb{$-1$} & \mb{0} & \mb{1} & \mb{2} & \mb{3} & \mb{4}
\\ \hline
\ifnum\DisplayToiFig>0
$y$ & \textcolor{red}{$11$} &
\textcolor{red}{$6$} &
\textcolor{red}{$3$} &
\textcolor{red}{$2$} &
\textcolor{red}{$3$} &
\textcolor{red}{$6$} \\ \hline
\else
$y$ & & & & & & \\ \hline
\fi
\end{tabular}
\vskip-10ex
\mbox{}\hfill
\begin{tikzpicture}[scale=0.4, >=stealth, baseline=(current bounding box.north)]
\tiny
\draw[->](-2,0) -- (5,0);
\draw[->](0,-2) -- (0,12);
\foreach \x in {-1,...,4}{\foreach \y in {-1,...,11}{\fill (\x,\y) circle (2pt);}}
\draw(-0.4,-0.4) node {O};
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\draw(-0.3,12) node {$y$};
\foreach \x in {5,10}{\draw(-0.3,\x) node {$\x$};}
%\draw(-0.3,5) node {$5$};
%\draw(-5,-0.3) node {$-5$};
\ifnum\DisplayToiFig>0
\foreach \x in {-1,...,4}{%
\fill[red](\x,{(\x)^2-4*\x+6}) circle(4pt);
}
\draw[red,thick](-1.1,{(-1.1)^2-4*(-1.1)+6})
parabola bend (2,2) (4.5,{(4.5)^2-4*4.5+6});
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\end{tikzpicture}
\hspace*{2zw}\mbox{}
\vskip-10zh
{\gtfamily\bfseries 計算欄}
\nidangumi{$\bullet \quad x=-1$ のとき\\ \hspace*{2.8ex} \(\siki\)}
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\vfill
\nidangumi{$\bullet \quad x=1$ のとき\\ \hspace*{2.8ex} \(\siki\)}
{$\bullet \quad x=2$ のとき\\ \hspace*{2.8ex} \(\siki\)}
\vfill
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\rotatebox{180}{{\normalsize\gtfamily\bfseries 数学プリント\#32}\scriptsize
{\normalsize\ajKaku{1}}~\( 5,-1,-3,-1,5 \)\
{\normalsize\ajKaku{2}}~\( 9,4,1,0,1,4 \)\
{\normalsize\ajKaku{3}}~\( 21,11,5,3,5,11 \)\
{\normalsize\ajKaku{4}}~\( -8,1,4,1,-8,-23 \)
}
\fi
\newpage
\unitlength=1mm
\( y=2x^2+4x-1 \) の軸と頂点を求めなさい（\ajKaku{1}の式です）
\kotae{x=-1,\quad (-1,-3)}
\begin{picture}(80,40)(0,0)
\put(35,32){\( {\ \bbox\ \over \bbox}=\bbox \)}
\put(54,29){\vector(0,-1){5}}
\put(50.5,19){\bbox}
\put(54,16){\vector(0,-1){5}}
\put(50.5,6){\bbox}
\put(60,26){プラス・マイナスを逆にする}
\put(60,13){2で割る}
\put(60,4){\gtfamily\bfseries この
値を\(\boldsymbol{y=2x^2+4x-1}\)に代入する}
\put(16,42){\line(0,-1){5}}
\put(16,37){\vector(1,0){19}}
\put(7.5,42){\line(0,-1){12}}
\put(7.5,30){\vector(1,0){27}}
\end{picture}
\( y=x^2-4x+4 \)の軸と頂点を求めなさい（\ajKaku{2}の式です）
\kotae{x=2,\quad (2,0)}
\unitlength=1mm
\begin{picture}(80,40)(0,0)
\put(35,32){\( {\ \bbox\ \over \bbox}=\bbox \)}
\put(54,29){\vector(0,-1){5}}
\put(50.5,19){\bbox}
\put(54,16){\vector(0,-1){5}}
\put(50.5,6){\bbox}
\put(60,26){プラス・マイナスを逆にする}
\put(60,13){2で割る}
\put(60,4){\gtfamily\bfseries この
値を\(\boldsymbol{y=x^2-4x+4}\)に代入する}
\put(15,42){\line(0,-1){5}}
\put(15,37){\vector(1,0){19}}
\put(6.5,42){\line(0,-1){12}}
\put(6.5,30){\vector(1,0){27}}
\end{picture}
\( y=2x^2-4x+5 \)の軸と頂点を求めなさい（\ajKaku{3}の式です）
\kotae{x=1,\quad (1,3)}
\unitlength=1mm
\begin{picture}(80,40)(0,0)
\put(35,32){\( {\ \bbox\ \over \bbox}=\bbox \)}
\put(54,29){\vector(0,-1){5}}
\put(50.5,19){\bbox}
\put(54,16){\vector(0,-1){5}}
\put(50.5,6){\bbox}
\put(60,4){\gtfamily\bfseries この
値を\(\boldsymbol{y=2x^2-4x+5}\)に代入する}
\put(15,42){\line(0,-1){5}}
\put(15,37){\vector(1,0){19}}
\put(7,42){\line(0,-1){12}}
\put(7,30){\vector(1,0){27}}
\end{picture}
\( y=-3x^2+12x-8 \)の軸と頂点を求めなさい（\ajKaku{4}の式です）
\kotae{x=2,\quad (2,4)}
\unitlength=1mm
\begin{picture}(80,40)(0,0)
\put(35,32){\( {\ \bbox\ \over \bbox}=\bbox \)}
\put(54,29){\vector(0,-1){5}}
\put(50.5,19){\bbox}
\put(54,16){\vector(0,-1){5}}
\put(50.5,6){\bbox}
\put(60,4){\gtfamily\bfseries この
値を\(\boldsymbol{y=-3x^2+12x-8}\)に代入する}
\put(20,42){\line(0,-1){5}}
\put(20,37){\vector(1,0){15}}
\put(8,42){\line(0,-1){12}}
\put(8,30){\vector(1,0){27}}
\end{picture}
\( y=-x^2+2x+2 \)の軸と頂点を求めなさい（\ajKaku{5}の式です）
\kotae{x=1,\quad (1,3)}
\bigskip
\( y=x^2-4x+6 \)の軸と頂点を求めなさい（\ajKaku{6}の式です）
\kotae{x=2,\quad (2,2)}
\vfill
\end{document}
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https://anarhija.info/library/italia-germania-aggiornamenti-sul-processo-a-riccardo-imprigionato-ad-amburgo-05-10-it.tex | anarhija.info | CC-MAIN-2020-29 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2020-29/segments/1593655937797.57/warc/CC-MAIN-20200711192914-20200711222914-00082.warc.gz | 278,106,391 | 3,101 | \documentclass[DIV=12,%
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\title{Italia \Slash{} Germania: Aggiornamenti sul processo a Riccardo, imprigionato ad Amburgo (05\Slash{}10\Slash{}2017)}
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{\usekomafont{title}{\huge Italia \Slash{} Germania: Aggiornamenti sul processo a Riccardo, imprigionato ad Amburgo (05\Slash{}10\Slash{}2017)\par}}%
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Il processo che vedrà imputato \href{https://anarhija.info/category/topic/riccardo}{Riccardo} si terrà il 5 di ottobre alle h.9.00 presso il tribunale di Altona – Amburgo (Max Bauer Allee 91.)
Sarà a porte aperte ma non ci è ancora dato di sapere se avverrà la sentenza nello stesso giorno o se slitterà ad un’altra data. Dipende dall’iter processuale (in molti casi hanno sentenziato in un solo giorno anche perché gli imputati hanno confessato).
Sarà giudicato tramite il secondo grado di una corte che prevede pene dai due anni in su (in Germania le corti sono divise in 3 livelli in base alla pena richiesta, non è una corte speciale).
I capi di accusa formalizzati sono: interruzione della pace pubblica, attacco tramite assalto (che equivale a lesioni – concorso in Italia) e resistenza.
Per quanto riguarda la censura alla posta non ci sono stati blocchi sistematici ma qualche lettera viene bloccata (fin ora sono 3, diluite nel tempo: una cartolina, una lettera, una busta contenente giornali da Amburgo). Poi sono state bloccate buste contenenti materiale controinformativo e opuscoli.
\emph{Indirizzo}: \textbf{Riccardo Lupano – Jva Billwerder – Dweerlandweg 100 – 22113 Hamburg – Germany}
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Anarhija.info
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Italia \Slash{} Germania: Aggiornamenti sul processo a Riccardo, imprigionato ad Amburgo (05\Slash{}10\Slash{}2017)
\bigskip
via mail
\bigskip
\textbf{anarhija.info}
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\end{document}
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http://jovens.ime.unicamp.br/sessoes-timetable.tex | unicamp.br | CC-MAIN-2021-10 | text/x-tex | application/x-tex | crawl-data/CC-MAIN-2021-10/segments/1614178362899.14/warc/CC-MAIN-20210301182445-20210301212445-00039.warc.gz | 47,752,623 | 1,146 |
\documentclass[a4paper]{article} %
\usepackage{graphicx,amssymb} %
\textwidth=15cm \hoffset=-1.2cm %
\textheight=25cm \voffset=-2cm %
\pagestyle{empty} %
\date{} %
\def\keywords#1{\begin{center}{\bf Keywords}\\{#1}\end{center}} %
\def\titulo#1{\title{#1}} %
\def\autores#1{\author{#1}} %
% Please, do not change any of the above lines
%#begin-user-packages
% HERE YOU CAN INCLUDE SOME LaTeX PACKAGES YOUR ABSTRACT NEEDS
% END OF THE SPACE FOR INCLUDING LaTeX PACKAGES
%#end-user-packages
%#begin-of-user-defined-commands
% HERE YOU CAN INCLUDE SOME CUSTOM LaTeX COMMANDS
% END OF THE SPACE FOR DEFINING LaTeX COMMANDS
%#end-of-user-defined-commands
\begin{document}
\thispagestyle{empty}
\noindent {\large \bf Programa\c c\~ao das palestras}\\
\noindent {\large \bf Sess\~ao especial:} Futebol.
\bigskip
\noindent {\bf Segunda-feira}\\
\noindent\begin{tabular}{ll}
14:00 - 14:30& Edson Arantes\\
14:30 - 15:00& T\'ulio Costa.\\
15:00 - 15:30& Nome (sem t\'itulo)\\
\end{tabular}
\bigskip
\noindent {\bf Ter\c ca-feira}\\
\noindent\begin{tabular}{ll}
14:00 - 14:30& Nome\\
14:30 - 15:00& Nome\\
15:00 - 15:30& Nome\\
\end{tabular}
\bigskip
\noindent {\bf Quarta-feira}\\
\noindent\begin{tabular}{ll}
14:00 - 14:30& Nome\\
14:30 - 15:00& Nome\\
15:00 - 15:30& Nome\\
\end{tabular}
\end{document}
|
https://www.zentralblatt-math.org/matheduc/en/?id=39598&type=tex | zentralblatt-math.org | CC-MAIN-2019-39 | text/plain | application/x-tex | crawl-data/CC-MAIN-2019-39/segments/1568514573289.83/warc/CC-MAIN-20190918131429-20190918153429-00545.warc.gz | 1,087,186,518 | 1,327 | \input zb-basic
\input zb-matheduc
\iteman{ZMATH 2009e.00193}
\itemau{Vollrath, Hans-Joachim}
\itemti{Towards an authentic teaching of mathematics: Hans-Georg Steiner's contribution to the reform of mathematics teaching.}
\itemso{ZDM, Int. J. Math. Educ. 39, No. 1-2, 39-50 (2007).}
\itemab
Summary: Hans-Georg Steiner was the ``motor of the reform'' of mathematics education in Germany. His main concern was to promote authentic teaching. His suggestions for teaching mathematical structures stimulated the process of reform, but were criticised as well. Two controversies are studied in this paper. The controversy with Detlef Laugwitz in 1965 was about the dichotomy ``axiomatics vs. constructiveness''. Another controversy with Alexander Wittenberg in 1964 was about the problem of ``elementary''. The following considerations can show the need for fundamental didactical analyses in mathematics education, as they were initiated by Hans-Georg Steiner.
\itemrv{~}
\itemcc{D30 A30}
\itemut{reform of mathematics education; axiomatics vs. constructiveness; didactical analyses; history of mathematics education}
\itemli{doi:10.1007/s11858-006-0013-0}
\end |
https://ctan.math.utah.edu/tex-archive/graphics/pgf/contrib/pgfornament-han/xiaoshan-sample.tex | utah.edu | CC-MAIN-2022-49 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2022-49/segments/1669446710237.57/warc/CC-MAIN-20221127105736-20221127135736-00463.warc.gz | 237,696,003 | 1,298 | % !TEX program = xelatex
\documentclass{ctexbeamer}
\usetheme{Xiaoshan}
\author{林莲枝}
\title{萧山Beamer主题}
\subtitle{\texttt{pgfornament-han}附录福利}
\begin{document}
\begin{frame}
\maketitle
\end{frame}
\section{简介}
\begin{frame}
\frametitle{其实是 Metropolis 主题的魔改}
\begin{itemize}
\item 改了颜色（用了 \texttt{cncolours.sty}）
\item 加入 \texttt{pgfornament-han} 汉风纹样元素
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{为什么叫「萧山」？}
\begin{itemize}
\item 以城市名字命名主题，是 Beamer 的一个传统
\item 作为\texttt{pgfornament-han}的实战尝试，用在了 \LaTeX{} Studio 工作室的一次直播活动的材料上
\item 直播在{\kaishu 杭州萧山区}进行
\end{itemize}
\end{frame}
\begin{frame}[standout]
作为强调的一个 standout 页面
\end{frame}
\section{充版面}
\begin{frame}[allowframebreaks]
\frametitle{各种 block}
\begin{block}{Metropolis 走极简风}
因此「萧山」主题也走极简风。
\end{block}
\begin{exampleblock}{Metropolis 走极简风}
因此「萧山」主题也走极简风。
\end{exampleblock}
\begin{alertblock}{Metropolis 走极简风}
因此「萧山」主题也走极简风。
\end{alertblock}
\begin{theorem}[Metropolis 走极简风]
因此「萧山」主题也走极简风。
\end{theorem}
\begin{proof}[Metropolis 走极简风]
因此「萧山」主题也走极简风。
\end{proof}
\end{frame}
\end{document}
|
https://www.zentralblatt-math.org/matheduc/en/?id=141656&type=tex | zentralblatt-math.org | CC-MAIN-2019-51 | text/plain | application/x-tex | crawl-data/CC-MAIN-2019-51/segments/1575540496492.8/warc/CC-MAIN-20191207055244-20191207083244-00012.warc.gz | 935,003,186 | 1,205 | \input zb-basic
\input zb-matheduc
\iteman{ZMATH 1985h.01579}
\itemau{Comte, M.L.; Gasser, E.; Guignard, N.; Hutin, R.; Leutenegger, F. (Service de la Recherche Pedagogique du Departement de l'Instruction Publique, Geneva (Switzerland).Groupe Mathematique)}
\itemti{Approaching mathematics at the age of 5 years. Annaeherung an die Mathematik mit 5 Jahren(Approcher la mathematique a cinq ans).}
\itemso{Mar 1983. 395 p. Ser. Title: Collection SRP. no. 26.}
\itemab
\itemrv{~}
\itemcc{F21 U11}
\itemut{Pre-School Education; Games; Numbers From 1 To 20; Spatial Ability; Social Learning; Topology; Set Theory; ; Elementarbereich; Spiel; Zahlenraum 1-20; Raumvorstellung; Soziales Lernen; Topologie; Mengenlehre}
\itemli{}
\end |
https://flamechallenge.authorea.com/users/496357/articles/580945/download_latex | authorea.com | CC-MAIN-2022-49 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2022-49/segments/1669446711162.52/warc/CC-MAIN-20221207121241-20221207151241-00472.warc.gz | 271,012,359 | 2,858 | \documentclass[10pt]{article}
\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}
\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
linkcolor = blue,
urlcolor = blue,
citecolor = blue,
anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
\errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother
\usepackage{natbib}
\renewenvironment{abstract}
{{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
{\bigskip}
\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}
\usepackage{authblk}
\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%
\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{float}
\begin{document}
\title{Exposure to weak opioids and risk of gastrointestinal tract cancers: A
series of nested case-control studies.}
\author[1]{Martin Houston}%
\author[1]{Una McMenamin}%
\author[2]{Brian Johnston}%
\author[1]{Ronald McDowell}%
\author[3]{Carmel Hughes}%
\author[4]{Peter Murchie}%
\author[1]{C Cardwell}%
\affil[1]{Queen's University Belfast Centre for Public Health}%
\affil[2]{Royal Victoria Hospital}%
\affil[3]{Queen's University of Belfast School of Pharmacy}%
\affil[4]{University of Aberdeen Institute of Applied Health Sciences}%
\vspace{-1em}
\date{\today}
\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup
\selectlanguage{english}
\begin{abstract}
Background There is evidence gastrointestinal (GI) motility may play a
role in the development of GI cancers. Weak opioids (codeine and
dihydrocodeine) decrease GI motility, but their effect on GI cancer risk
has not been assessed. Aim To assess the association between weak
opioids and cancers of the GI tract. Methods A series of nested
case-control studies was conducted using Scottish general practice
records from the Primary Care Clinical Informatics Unit Research
database. Oesophageal (n=2,432), gastric (n=1,443), and colorectal
cancer (n=8,750) cases, diagnosed between 1999 and 2011, were identified
and matched with up to five controls. Weak opioid use was identified
from prescribing records. Odds ratios (OR) and 95\% confidence intervals
(CI) were calculated using conditional logistic regression, adjusting
for relevant comorbidities and medication use. Results There was no
association between weak opioids and colorectal cancer (adjusted
OR=0.96, CI 0.90, 1.02, p=0.15). There was an increased risk of
oesophageal (adjusted OR=1.16, CI 1.04, 1.29, p=0.01) and gastric cancer
(adjusted OR=1.26, CI 1.10, 1.45, p=0.001). The associations for
oesophageal cancer, but not gastric cancer, were attenuated when weak
opioid users were compared with users of another analgesic (adjusted
OR=1.03 CI 0.86, 1.22, p=0.76 and adjusted OR=1.29 CI 1.02, 1.64, p=0.04
respectively). Conclusion In this large population-based study, there
was no consistent evidence of an association between weak opioids and
oesophageal or colorectal cancer risk, but a small increased risk of
gastric cancer. Further investigation is required to determine whether
this association is causal or reflects residual confounding or
confounding by indication.%
\end{abstract}%
\sloppy
\textbf{Hosted file}
\verb`Weak opioids and GI cancer BJP.docx` available at \url{https://authorea.com/users/496357/articles/580945-exposure-to-weak-opioids-and-risk-of-gastrointestinal-tract-cancers-a-series-of-nested-case-control-studies}
\selectlanguage{english}
\FloatBarrier
\end{document}
|
https://www.dickimaw-books.com/gallery/acronym-lang.tex | dickimaw-books.com | CC-MAIN-2021-25 | application/x-tex | text/x-matlab | crawl-data/CC-MAIN-2021-25/segments/1623487610841.7/warc/CC-MAIN-20210613192529-20210613222529-00639.warc.gz | 641,426,950 | 1,302 | % arara: pdflatex
% arara: makeglossaries
% arara: pdflatex
\documentclass{article}
\usepackage[colorlinks]{hyperref}
\usepackage[nopostdot,% suppress dot after description
toc,% add glossary to table of contents
acronym,% create the "acronym" glossary
nomain% don't create the "main" glossary
]{glossaries}
\makeglossaries
% define an acronym style for the acronyms with a translation:
\newacronymstyle{acronymslang}%
{%
\GlsUseAcrEntryDispStyle{long-short}%
}
{%
\GlsUseAcrStyleDefs{short-long}%
\renewcommand*{\genacrfullformat}[2]{%
\glsentrylong{##1}##2\space
(\protect\firstacronymfont{\glsentryshort{##1}}%
\ifglshasfield{useri}{##1}%
{, English: \glsentryuseri{##1}}{})%
}%
\renewcommand*{\Genacrfullformat}[2]{%
\Glsentrylong{##1}##2\space
(\protect\firstacronymfont{\glsentryshort{##1}}%
\ifglshasfield{useri}{##1}%
{, English: \glsentryuseri{##1}}{})%
}%
\renewcommand*{\genplacrfullformat}[2]{%
\glsentrylongpl{##1}##2\space
(\protect\firstacronymfont{\glsentryshortpl{##1}}%
\ifglshasfield{useri}{##1}%
{, English: \glsentryuseri{##1}}{})%
}%
\renewcommand*{\Genplacrfullformat}[2]{%
\Glsentrylongpl{##1}##2\space
(\protect\firstacronymfont{\glsentryshortpl{##1}}%
\ifglshasfield{useri}{##1}%
{, English: \glsentryuseri{##1}}{})%
}%
}
\setacronymstyle{acronymslang}
\loadglsentries[acronym]{example-glossaries-acronyms-lang}
% glossary style for acronyms with a translation
\newglossarystyle{acronymslang}
{%
\setglossarystyle{long}%
\renewcommand*{\glsgroupskip}{}%
\renewcommand{\glossentry}[2]{%
\glsentryitem{##1}\glstarget{##1}{\glossentryname{##1}} &
\glossentrydesc{##1}\glspostdescription
\ifglshasfield{useri}{##1}{ (English: \glsentryuseri{##1})}{}%
\space ##2\tabularnewline
}%
}
\begin{document}
\section{Sample}
First use:
\forglsentries{\thislabel}{\gls{\thislabel}. }
Next use:
\forglsentries{\thislabel}{\gls{\thislabel}. }
\printglossary[type=acronym,style=acronymslang]
\end{document}
|
http://ftp.fi.debian.org/mirror/CTAN/documentation/visualtikz/Source/tkzchains.tex | debian.org | CC-MAIN-2022-40 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2022-40/segments/1664030335448.34/warc/CC-MAIN-20220930082656-20220930112656-00153.warc.gz | 16,027,932 | 2,564 | \SbSbSSCT{Création d'une chaine de n\oe euds}{Starting and Continuing a Chain}
\maboite{\BS{usetikzlibrary}\AC{chains}}
\label{lib-chains}
\begin{center}
\RRR{46-2}
\end{center}
\bigskip
\begin{tabular}{|l|} \hline
\BS{begin}\AC{tikzpicture}[\RDD{start chain}] \\
\BS{node} [\RDD{on chain}] \AC{A};\\
\BS{node} [\RDD{on chain}] \AC{B};\\
\BS{node} [\RDD{on chain}] \AC{C};\\
\BS{end}\AC{tikzpicture} \\ \hline
\begin{tikzpicture}[start chain]
\node [on chain] {A};
\node [on chain] {B};
\node [on chain] {C};
\end{tikzpicture}
\\ \hline
\end{tabular}
\bigskip
\begin{tabular}{|c|} \hline
\BS{begin}\AC{tikzpicture}[start chain, \RDD{node distance}= 0.5 cm]
\\ \hline
\begin{tikzpicture}[start chain, node distance= .5 cm]
\node [on chain] {A};
\node [on chain] {B};
\node [on chain] {C};
\end{tikzpicture}
\\ \hline
\end{tabular}
\bigskip
\begin{tabular}{|c|} \hline
\BS{begin}\AC{tikzpicture}[start chain=\rouge {going below} ]
\\ \hline
\begin{tikzpicture}[start chain=going below]
\node [on chain] {A};
\node [on chain] {B};
\node [on chain] {C};
\end{tikzpicture}
\\ \hline
\end{tabular}
\bigskip
\begin{tabular}{|c|} \hline
\BS{begin}\AC{tikzpicture}[start chain=\rouge {going left} ]
\\ \hline
\rule[0cm]{0pt}{.7cm}
\begin{tikzpicture}[start chain=going left]
\node [on chain] {A};
\node [on chain] {B};
\node [on chain] {C};
\end{tikzpicture}
\\ \hline
\end{tabular}
\bigskip
\begin{tabular}{|c|} \hline
\BS{begin}\AC{tikzpicture}[start chain, \rouge{every node/.style=draw} ]
\\ \hline
\rule[0cm]{0pt}{.7cm}
\begin{tikzpicture}[start chain, every node/.style=draw]
\node [on chain] {A};
\node [on chain] {B};
\node [on chain] {C};
\end{tikzpicture}
\\ \hline
\end{tabular}
\bigskip
\begin{tabular}{|c|c|}\hline
\begin{tikzpicture}[start chain=1 going right,
start chain=2 going left]
\node [draw,on chain=1] {A};
\node [draw,on chain=1] {B};
\node [draw,on chain=1] {C};
\node [draw,on chain=2] at (3,1) {0};
\node [draw,on chain=2] {1};
\node [draw,on chain=2] {2};
\node [draw,on chain=1] {D};
\end{tikzpicture}
&
\parbox{10cm}{
\BS{begin}\AC{tikzpicture}[\rouge{start chain=1} going right , \\
\blll{start chain=2} going left] \\
\BS{node} [draw,\rouge{on chain=1}] \AC{A}; \\
\BS{node} [draw,\rouge{on chain=1}] \AC{B}; \\
\BS{node}[draw,\rouge{on chain=1}] \AC{C}; \\
\BS{node} [draw,\blll{on chain=2}] at (3,1) \AC{0}; \\
\BS{node} [draw,\blll{on chain=2}] \AC{1}; \\
\BS{node} [draw,\blll{on chain=2}] \AC{2}; \\
\BS{node}[draw,\rouge{on chain=1}] \AC{D}; \\
\BS{end}\AC{tikzpicture}}
\\ \hline
\end{tabular}
\bigskip
\begin{tabular}{|c|c|} \hline
\rule[-2cm]{0pt}{4cm}
\begin{tikzpicture}[start chain=going right,baseline=-1.5cm]
\node [draw,on chain] {A};
\node [draw,on chain] {B};
\node [draw,continue chain=going below,on chain] {C};
\node [draw,on chain] {D};
\node [draw,continue chain=going right,on chain] {E};
\end{tikzpicture}
&
\parbox{11cm}{
\BS{begin}\AC{tikzpicture}[start chain going right]
\BS{node} [draw,on chain] \AC{A}; \\
\BS{node} [draw,on chain] \AC{B}; \\
\BS{node} [draw,\RDD{continue chain}=going below,on chain] \AC{C}; \\
\BS{node}[draw,on chain] \AC{D}; \\
\BS{node} [draw,\RDD{continue chain}=going right,on chain] \AC{E}; \\
\BS{end}\AC{tikzpicture}}
\\ \hline
\end{tabular}
\bigskip
\begin{tabular}{|c|c|} \hline
\begin{tikzpicture}[every node/.style=draw,baseline=-1.5cm]
{ [start chain=1]
\node [on chain] {A};
\node [on chain] {B};
\node [on chain] {C};
}
{ [start chain=2 going below]
\node [on chain=2] at (0.5,-.5) {0};
\node [on chain=2] {1};
\node [on chain=2] {2};
}
{ [continue chain=1]
\node [on chain] {D};
}
\end{tikzpicture}
&
\parbox{10cm}{
\BS{begin}\AC{tikzpicture}[start chain going right] \\
\{ [\RDD{start chain}=1] \\
\BS{node} [draw,on chain] \AC{A}; \\
\BS{node} [draw,on chain] \AC{B}; \\
\BS{node} [draw,on chain] \AC{C}; \\
\} \\
\{ [\RDD{start chain}=2] \\
\BS{node}[draw,on chain=2] \AC{0}; \\
\BS{node}[draw,on chain=2] \AC{1}; \\
\BS{node}[draw,on chain=2] \AC{2}; \\
\} \\
\{ [\RDD{continue chain}=1] \\
\BS{node} [draw,on chain] \AC{D}; \\
\} \\
\BS{end}\AC{tikzpicture}}
\\ \hline
\end{tabular}
\bigskip
\SbSbSSCT{N\oe uds sur la chaine}{Nodes on a Chain}
\begin{center}
\RRR{46-3}
\end{center}
\bigskip
\begin{tabular}{|c|c|} \hline
\begin{tikzpicture}[start chain=XXX placed {at=(\tikzchaincount*-30+90:1.5)},baseline=0pt]
\foreach \i in {1,...,12}
\node [on chain] {\i};
\draw (0,0) -- (XXX-10);
\draw (0,0) -- (XXX-2);
\end{tikzpicture}
&
\parbox{11cm}{
\BS{begin}\AC{tikzpicture}[start chain=\blll{XXX} \RDD{placed} \\ \AC{at=(\BSS{tikzchaincount}*-30+90:1.5)}] \\
\BS{foreach} \BS{i} in \AC{1,...,12} \\
\BS{node} [on chain] \AC{\BS{i}}; \\
\BS{draw }(0,0) -- \blll{(XXX-10)}; \\
\BS{draw }(0,0) -- \blll{(XXX-2)}; \\
\BS{end}\AC{tikzpicture}}
\\ \hline
\end{tabular}
\bigskip
\begin{tabular}{|c|c|} \hline
\begin{tikzpicture}[start chain,baseline=-1cm]
\node [draw,on chain] {A};
\node [draw,on chain] {B};
\node [draw,on chain=going below] {C};
\node [draw,on chain] {D};
\node [draw,on chain] {E};
\end{tikzpicture}
&
\parbox{11cm}{
\BS{begin}\AC{tikzpicture}[start chain] \\
\BS{node} [draw,on chain] \AC{A}; \\
\BS{node} [draw,on chain] \AC{B}; \\
\BS{node} [draw,on chain=\rouge{going below}] \AC{C}; \\
\BS{node} [draw,on chain] \AC{D}; \\
\BS{node} [draw,on chain] \AC{E}; \\
\BS{end}\AC{tikzpicture}}
\\ \hline
\end{tabular}
\bigskip
\begin{tabular}{|c|c|} \hline
\begin{tikzpicture}[start chain=going {at=(\tikzchainprevious),shift=(30:1)},baseline=1cm]
\node [draw,on chain] {A};
\node [draw,on chain] {B};
\node [draw,on chain] {C};
\node [draw,on chain] {D};
\end{tikzpicture}
&
\parbox{11cm}{
\BS{begin}\AC{tikzpicture}[start chain=going \\ \AC{at=(\BSS{tikzchainprevious},shift=(30:1)}] \\
\BS{node} [draw,on chain] \AC{A}; \\
\BS{node} [draw,on chain] \AC{B}; \\
\BS{node} [draw,on chain] \AC{C}; \\
\BS{node} [draw,on chain] \AC{D}; \\
\BS{end}\AC{tikzpicture}}
\\ \hline
\end{tabular}
\bigskip
\begin{tabular}{|c|c|} \hline
\begin{tikzpicture}[baseline=1cm]
\node[draw,red] (A) at (0,2) {A};
{ [start chain]
\node [draw,on chain] {B};
\node [draw,on chain] {C};
\chainin (A) [join];
\node [draw,on chain] {D};
\node [draw,on chain] {E};
}
\end{tikzpicture}
&
\parbox{11cm}{
\BS{begin}\AC{tikzpicture} \\
\BS{node} [draw,red] (A) at (0,2) \AC{A}; \\
\{ [start chain] \\
\BS{node} [draw,on chain] \AC{B}; \\
\BS{node} [draw,on chain] \AC{C}; \\
\BSS{chainin} (A) [join]; \\
\BS{node} [draw,on chain] \AC{D}; \\
\BS{node} [draw,on chain] \AC{E}; \\
\} \\
\BS{end}\AC{tikzpicture}}
\\ \hline
\end{tabular}
\bigskip
\begin{tabular}{|c|c|} \hline
\begin{tikzpicture}[baseline=-1cm]
\matrix [matrix of nodes,column sep=1cm,row sep=1cm,every node/.style=draw]
{
|(a) | A & |(b) | B & |(c) | C \\
|(d) | D & |(e) | E & |(f) | F \\
};
{ [start chain,every on chain/.style={join=by ->}]
\chainin (a);
\chainin (b);
\chainin (d);
\chainin (c);
\chainin (f);
\chainin (e);
}
\end{tikzpicture}
&
\parbox{11cm}{
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|
http://voodoo-circle.sourceforge.net/doc_for_developers/latex/c__func__arg_8cpp.tex | sourceforge.net | CC-MAIN-2018-05 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2018-05/segments/1516084891196.79/warc/CC-MAIN-20180122073932-20180122093932-00626.warc.gz | 378,664,144 | 938 | \hypertarget{c__func__arg_8cpp}{
\section{c\_\-func\_\-arg.cpp File Reference}
\label{c__func__arg_8cpp}\index{c\_\-func\_\-arg.cpp@{c\_\-func\_\-arg.cpp}}
}
Class 'c\_\-func\_\-arg'.
{\ttfamily \#include \char`\"{}../params.h\char`\"{}}\par
{\ttfamily \#include \char`\"{}../utils/memleak.h\char`\"{}}\par
{\ttfamily \#include \char`\"{}../utils/my\_\-assert.h\char`\"{}}\par
{\ttfamily \#include \char`\"{}../compat.h\char`\"{}}\par
{\ttfamily \#include \char`\"{}c\_\-func\_\-arg.h\char`\"{}}\par
{\ttfamily \#include \char`\"{}../utils/precomp.h\char`\"{}}\par
Include dependency graph for c\_\-func\_\-arg.cpp:
\nopagebreak
\begin{figure}[H]
\begin{center}
\leavevmode
\includegraphics[width=162pt]{c__func__arg_8cpp__incl}
\end{center}
\end{figure}
\subsection{Detailed Description}
Class 'c\_\-func\_\-arg'.
Definition in file \hyperlink{c__func__arg_8cpp_source}{c\_\-func\_\-arg.cpp}.
|
https://www.authorea.com/users/248886/articles/368879/download_latex | authorea.com | CC-MAIN-2020-45 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2020-45/segments/1603107893402.83/warc/CC-MAIN-20201027052750-20201027082750-00717.warc.gz | 613,108,651 | 3,158 | \documentclass[10pt]{article}
\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
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\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
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\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%
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\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\begin{document}
\title{Enjoy the Benefits of Nature Gardening~}
\author[1]{permaculturecourse}%
\affil[1]{Affiliation not available}%
\vspace{-1em}
\date{\today}
\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup
\sloppy
You should know that Permaculture is a technique of gardening which is
completely based on biological and ecological principles. It is a
natural technique of gardening which works along with nature to improve
the natural resources which exist to advantage growth of the plant,
along with decreasing the amount of physical labor required to get a
thriving garden simultaneously.
One of the most excellent parts of
\href{https://www.permaculturecourseonline.com/}{\textbf{Permaculture
Education Online}} gardening is that it can be directly adapted to and
rural, environment, urban and suburban areas, along with having the
skill of being any specific size. Box type gardens, together with window
boxes, to all other traditional techniques of gardening can utilize the
principles of \textbf{Permaculture Australia} in their landscape or
gardening practices.
\par\null
To perfectly fit in the process of \textbf{Permaculture Design Course
Online} in the practice of your gardening, you must have some kind of
knowledge of ecological systems, with complete type of theory, to make a
perfect and healthy environment. At the time, you are going to design a
\textbf{Online Permaculture Course} system, each and every element of it
have to be advantageous to the system, and even the connections between
these possible elements act to manage it. A well managed system with
positive associations of elements will get better the situation of the
land you are developing your crops on, get the most out of productivity,
and confirm that the land can be used for an indefinite period.
\par\null
To get this, recycling wastage of plant, animal, or some particular
activity of the
\href{https://www.permaculturecourseonline.com/}{\textbf{Online
Permaculture Design}} system to be utilized to benefit any other part of
the system same as nature does naturally. Studying the manner nature
works in a natural manner in your area is the best method to get the
information of how an ecosystem is formed. It is a completely natural
procedure that nutrients are refilled back again into the system in a
natural manner without the requirement to add them to the soil by
reproduction means. It is not just reasonable, it is even a technique of
preventing pollution.
\par\null
You should understand that diversity is a main part of permaculture, not
like modern agricultural practices which produce mass amount of one
crop. Permaculture completely depends on a lot of different animals and
crops to support each other. So in case any one species comes under
touch by a pest or predator, there is a wonderful possibility that
within the system there would be a natural technique in place to keep
secure it, or defend it earlier than the crop is spoiled. In latest
agriculture, in case a crop is attacked by any type of pest, the
complete crop can be lost.
\par\null
Carefully thinking on how we utilize our energy, resources, food,
non-material, material needs, and shelter, you would see it is very
feasible to get a lot more out of life by utilizing less. Permaculture
offers you the skill to be more creative, with less possible effort, and
simultaneously advantage from the atmosphere and ourselves nowadays and
for ages to come.
\selectlanguage{english}
\FloatBarrier
\end{document}
|
http://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/Directory_LHCb-PAPER-2011-023/Table_1.tex | cern.ch | CC-MAIN-2019-47 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2019-47/segments/1573496668539.45/warc/CC-MAIN-20191114205415-20191114233415-00307.warc.gz | 94,084,999 | 909 |
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\usepackage{standalone}
\usepackage{ifthen}
\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{upgreek}
\usepackage{xspace}
\usepackage{color}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{bm}
\usepackage{dcolumn}
\usepackage{mciteplus}
\begin{document}
\begin{ruledtabular}
\begin{tabular}{lc}
Source & Uncertainty \\
\colrule
Fiducial requirement & 0.01\% \\
Peaking background asymmetry & 0.04\% \\
Fit procedure & 0.08\% \\
Multiple candidates & 0.06\% \\
Kinematic binning & 0.02\% \\
\hline
Total & 0.11\% \\
\end{tabular}
\end{ruledtabular}
\end{document}
|
https://authorea.com/users/339139/articles/465391/download_latex | authorea.com | CC-MAIN-2020-40 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2020-40/segments/1600400198213.25/warc/CC-MAIN-20200920125718-20200920155718-00709.warc.gz | 299,255,603 | 11,321 | \documentclass[10pt]{article}
\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}
\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
linkcolor = blue,
urlcolor = blue,
citecolor = blue,
anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
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\usepackage{authblk}
\usepackage{graphicx}
\usepackage[space]{grffile}
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\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
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% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%
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\usepackage[utf8]{inputenc}
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\begin{document}
\title{Meta-Analysis of mutual information applied in EBM diagnostics}
\author[1]{Athanasios Tsalatsanis}%
\author[2]{Iztok Hozo}%
\author[3]{Benjamin Djulbegovic}%
\affil[1]{University of South Florida}%
\affil[2]{Indiana University Northwest}%
\affil[3]{City of Hope National Medical Center}%
\vspace{-1em}
\date{\today}
\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup
\selectlanguage{english}
\begin{abstract}
Rationale Assessing the performance of diagnostic tests requires
evaluation of the amount of diagnostic uncertainty the test reduces
(i.e. 0\% - useless test, 100\% - perfect test). Statistical measures
currently dominating the evidence-based medicine (EBM) field and
particularly meta-analysis (e.g. sensitivity and specificity), cannot
explicitly measure this uncertainty reduction. Mutual information (MI),
an information theory statistic, is a more appropriate metric for
evaluating diagnostic tests as it explicitly quantifies uncertainty and,
therefore, facilitates natural interpretation of a test's value. In this
paper, we propose the use of MI as a single measure to express
diagnostic test performance and demonstrate how it can be used in
meta-analysis of diagnostic test studies. Methods We use two cases from
the literature to demonstrate the applicability of MI meta-analysis in
assessing diagnostic performance. These cases are: 1) Meta-analysis of
studies evaluating ultrasonography (US) to detect endometrial cancer and
2) meta-analysis of studies evaluating magnetic resonance angiography to
detect arterial stenosis. Results Results produced by the MI
meta-analyses are comparable to the results of meta-analyses based on
traditionally used statistical measures. However, the results of MI are
easier to understand as it relates directly to the extent of uncertainty
a diagnostic test can reduce. For example, a US test diagnosing
endometrial cancer is 40\% specific and 94\% sensitive. The combination
of these values is difficult to interpret and may lead to inappropriate
assessment (e.g. one could favour the test due to its high sensitivity,
ignoring its low specificity). In terms of MI however, the test reduces
diagnostic uncertainty by 10\%, which is marginal and thus the test is
clearly not very useful. Conclusions We have demonstrated the
suitability of MI in assessing the performance of diagnostic tests,
which can facilitate easier interpretation of the true utility of
diagnostic tests.%
\end{abstract}%
\sloppy
\textbf{Meta-Analysis of mutual information applied in EBM diagnostics}
Athanasios Tsalatsanis\textsuperscript{1}, Iztok
Hozo\textsuperscript{2}and Benjamin Djulbegovic\textsuperscript{3,4,5}
\textsuperscript{1}Department of Internal Medicine, University of South
Florida, Tampa, FL
\textsuperscript{2}Department of Mathematics, Indiana University
Northwest, Gary, IN
\textsuperscript{3} Department of Supportive Care Medicine, City of
Hope, 1500 East Duarte Rd, Duarte, CA
\textsuperscript{4}Department of Hematology, City of Hope, 1500 East
Duarte Rd, Duarte, CA;
\textsuperscript{5}Evidence-based Analytics \& Program for Comparative
Effectiveness Research and Evidence-based Medicine, 1500 East Duarte Rd,
Duarte, CA;
\textsuperscript{*}Corresponding author
Email addresses:
AT: atsalats@usf.edu
IH: ihozo@iun.edu
BD: bdjulbegovic@coh.org
\textbf{Abstract}
\textbf{Rationale}
Assessing the performance of diagnostic tests requires evaluation of the
amount of diagnostic uncertainty the test reduces (i.e. 0\% - useless
test, 100\% - perfect test). Statistical measures currently dominating
the evidence-based medicine (EBM) field and particularly meta-analysis
(e.g. sensitivity and specificity), cannot explicitly measure this
uncertainty reduction. Mutual information (MI), an information theory
statistic, is a more appropriate metric for evaluating diagnostic tests
as it explicitly quantifies uncertainty and, therefore, facilitates
natural interpretation of a test's value. In this paper, we propose the
use of MI as a single measure to express diagnostic test performance and
demonstrate how it can be used in meta-analysis of diagnostic test
studies.
\textbf{Methods}
We use two cases from the literature to demonstrate the applicability of
MI meta-analysis in assessing diagnostic performance. These cases are:
1) Meta-analysis of studies evaluating ultrasonography (US) to detect
endometrial cancer and 2) meta-analysis of studies evaluating magnetic
resonance angiography to detect arterial stenosis.
\textbf{Results}
Results produced by the MI meta-analyses are comparable to the results
of meta-analyses based on traditionally used statistical measures.
However, the results of MI are easier to understand as it relates
directly to the extent of uncertainty a diagnostic test can reduce. For
example, a US test diagnosing endometrial cancer is 40\% specific and
94\% sensitive. The combination of these values is difficult to
interpret and may lead to inappropriate assessment (e.g. one could
favour the test due to its high sensitivity, ignoring its low
specificity). In terms of MI however, the test reduces diagnostic
uncertainty by 10\%, which is marginal and thus the test is clearly not
very useful.
\textbf{Conclusions}
We have demonstrated the suitability of MI in assessing the performance
of diagnostic tests, which can facilitate easier interpretation of the
true utility of diagnostic tests.
\textbf{Introduction}
It is widely acknowledged that the purpose of diagnostic testing is to
reduce diagnostic uncertainty (e.g. by 0\%, if the test is useless , or
up to 100\%, when the test is perfect) \textsuperscript{1}. However, the
current metrics of diagnostic performance {[}i.e. sensitivity (S),
specificity (C), positive and negative likelihood ratios (LR+; LR-),
diagnostic odds ratio (DOR), and area under curve (AUC){]} cannot
provide a direct assessment of the amount by which diagnostic
uncertainty is reduced. Despite lacking this crucial clinical
usefulness, these ``traditional'' diagnostic metrics are widely used as
the preferred evidence-based medicine (EBM) diagnostic test
measures\textsuperscript{2,3}.
Meanwhile, there is a long tradition of quantifying diagnostic test
performance in the field of information theory \textsuperscript{4} .
Although, conceptually speaking, the problems associated with medical
diagnostic testing are similar to the problems faced in communication
and information theory, for some reasons the field of EBM diagnostics
has not embraced measures typically found in information theory.
One such measure, mutual information (MI) \textsuperscript{5}, used to
evaluate association between two random variables, is considered the
best metric to quantify diagnostic uncertainty and therefore test
performance. \textsuperscript{6} It has been used in a number of studies
in medicine to explain the relationship between test results and disease
states \textsuperscript{7-14}. Yet it has been surpassingly missing from
the EBM literature.
The most significant properties that establish MI as superior to
traditional measures of diagnostic performance can be summarized as
follows:
\begin{itemize}
\tightlist
\item
MI quantifies the average amount of information that can be obtained
about the value of a random variable (i.e. probability of disease
before the diagnostic test) provided the value of another random
variable is available (i.e. probability of disease after the
diagnostic test) \textsuperscript{15};
\item
MI quantifies the expected value of the amount of information a
diagnostic test provides about the disease state, i.e. it takes into
account all possible states that can be associated with the test
results weighted by the likelihood of disease \textsuperscript{16,17}.
This number is particularly useful when comparing different diagnostic
tests;
\item
MI summarizes test performance with a single meaningful number that
corresponds to the average amount of information obtained by the
diagnostic test and unlike the ROC it does not require a specified
diagnostic cut-off point (threshold). The larger the MI value is, the
greater the amount of diagnostic uncertainty reduced through the
diagnostic test;
\item
MI can be applied to situations in which different test results are
associated with different probabilities of
disease\textsuperscript{6,16};
\item
Unlike ROC and AUC, MI can be applied to a broad spectrum of testing
situations ranging from the simple binary case (two test results and
two disease states) to much more complicated situations in which a
large number of test results (or a continuum of test results) are
associated with multiple possible disease
states\textsuperscript{7-14};
\item
The maximal value of MI, formally referred to as channel capacity, can
be used to identify the range of disease prevalence at which a
diagnostic test is most useful;
\item
One way MI expresses information is in bits that range from 0 to
infinity. In the simplest, binary case, where we are concerned if
disease is present or not, the maximum number of bits is equal to
1\textsuperscript{6};
\item
Finally, the relative expression of MI indicates the percentage of
diagnostic information that can be reduced by a diagnostic test and it
can range from 0\% (a useless test) to 100\% (a perfect test).
\end{itemize}
In this paper, we promote the notion that MI is a better measure for
evaluation of diagnostic performance \textsuperscript{8}, both on
theoretical and practical grounds. We extent the current work by
explaining how MI can be meta-analyzed, and provide two illustrative
examples of diagnostic test meta-analysis using MI.
\textbf{Methods}
\textbf{Mutual information and diagnostic testing primer}
Assume that a test (T) is used to examine whether a disease (D) is
present in a group of \emph{N} patients. For a diagnostic test, the
values of specificity, sensitivity as well as the counts of true
positive (TP), true negative (TN), false positive (FP), and false
negative (FN) results depend on whether the test turns out to be
positive \(\left(T+\right)\), with probability \emph{t} , or
negative\(\left(T-\right)\), and whether the disease is
present\(\left(D+\right)\), with probability \emph{p} , or
absent\(\left(D-\right)\). To assist the reader, Table 1 summarizes the
calculations of specificity, sensitivity, TP, TN, FP, and FN. Unabridged
derivations are presented in the appendix.
The uncertainty of the state of disease \emph{prior} to performing the
diagnostic test is best expressed as entropy \textsuperscript{4,15,18}:
\(H\left(D\right)=-\left(p\operatorname{}p+\left(1-p\right)\operatorname{}\left(1-p\right)\right)\),
where \(p\) is the probability of disease. The uncertainty
due to the test is:
\begin{equation}
H\left(T\right)=-\left(\text{\ t}\operatorname{}t+\left(1-t\right)\operatorname{}\left(1-t\right)\right),\nonumber \\
\end{equation}
where \(t\) is the probability of disease estimated by the
diagnostic test T.
The MI is computed as:
\begin{equation}
I\left(D,T\right)=H\left(D\right)+H\left(T\right)-H\left(D,T\right).\nonumber \\
\end{equation}
where \(H\left(D,T\right)\) is the joint entropy of disease and diagnostic
test. MI can also be expressed in terms of the conditional entropy as
well as the conditional probabilities of every test/disease outcome
combination:
\begin{equation}
H\left(D\middle|T\right)=H\left(D,T\right)-H\left(T\right)\nonumber \\
\end{equation}
Hence, the mutual information is also defined as:
\begin{equation}
I\left(D,T\right)=H\left(D\right)-H\left(D\middle|T\right)\nonumber \\
\end{equation}
From the latter expression it is evident that MI explicitly describes
the amount of diagnostic uncertainty that can be reduced by the
diagnostic test. Clinically, it is particularly useful to express MI in
relative terms, as it can indicate explicitly the percentage of
diagnostic uncertainty a diagnostic test can reduce. Relative MI (RMI)
is defined as:
\begin{equation}
I_{R}\left(D,T\right)=\frac{I\left(D,T\right)}{H\left(D\right)}=1-\frac{H(D|T)}{H(D)}\nonumber \\
\end{equation}
The quantity \(\frac{H(D|T)}{H(D)}\), is the relative entropy associated
with the test result (i.e. the percentage of uncertainty reduced by the
test result).
\textbf{Interpretation of uncertainty reduction}
The amount of reduction of uncertainty defines the usefulness of a
diagnostic test. Ideally, it would be defined in decision analytic
context when the ``useful'' test is the one that affect our decisions
and its downstream consequences. This, however, require case-specific
decision modeling, which is not the focus of this paper. Alternatively,
usefulness of a test can be defined according to magnitude of reduction
of diagnostic uncertainty analogously to treatment effects as small,
moderate or large\textsuperscript{19}. Thus, we define small reduction
of diagnostic uncertainty if it is less than 10\%, moderate reduction
between 20-30\% and large reduction of diagnostic uncertainty if it
exceeds 40-50\%.
\textbf{Sensitivity and specificity}
As the majority of diagnostic studies express diagnostic performance
results in terms of sensitivity (\emph{S} ) and specificity (\emph{C} ),
we show how MI relates to these measures.
\begin{equation}
I\left(D,T\right)=H\left(D\right)+H\left(T\right)-H\left(D,T\right)=Sp\left(\log_{2}\left(\frac{S\left(\left(1-S\right)p+C\left(1-p\right)\right)}{\left(1-S\right)\left(Sp+\left(1-C\right)\left(1-p\right)\right)}\right)\right)+C\left(1-p\right)\left(\log_{2}\left(\frac{C\left(Sp+\left(1-C\right)\left(1-p\right)\right)}{\left(1-C\right)\left(\left(1-S\right)p+C\left(1-p\right)\right)}\right)\right)\ \ \ \ \ \ \ \ +p\log_{2}\left(\frac{\left(1-S\right)\left(Sp+\left(1-C\right)\left(1-p\right)\right)}{\left(1-C\right)\left(\left(1-S\right)p+C\left(1-p\right)\right)}\right)+\log_{2}\left(\frac{\left(1-C\right)}{\left(Sp+\left(1-C\right)\left(1-p\right)\right)}\right)\nonumber \\
\end{equation}
\textbf{Meta-Analysis of entropy and mutual information}
In most cases, decision-makers are not interested in evaluating the
performance of a diagnostic test in a single study. Instead, they would
like to know the totality of evidence generated in a series of studies
evaluating the particular test. In such cases, a meta-analysis of
summary statistics is employed.
Meta-analysis is initiated with the computation of a summary statistic
for each study \textsuperscript{20}. In our case, this summary statistic
is the value of MI associated with the diagnostic test under
investigation. The next step in meta-analysis is to compute the weighted
average of MI, where the weights used are typically the inverse of the
MI variance, which is related to sample size \textsuperscript{20}.
According to Roulston \textsuperscript{21}, the variance of the entropy
is given by
\begin{equation}
\text{Var}\left(H\left(D\right)\right)=\left[\left(\operatorname{}p+H\left(D\right)\right)^{2}+\left(\operatorname{}\left(1-p\right)+H\left(D\right)\right)^{2}\right]\cdot\frac{p\left(1-p\right)}{N}\ \nonumber \\
\end{equation}
which is valid for study sample size greater than 10.
Solving for the variance of MI we derive the expression:
\begin{equation}
{\text{Var}\left(I\left(D,T\right)\right)=\left(\operatorname{}\left(p_{11}+p_{12}\right)+\operatorname{}\left(p_{11}+p_{21}\right)-\operatorname{}p_{11}+I\left(D,T\right)\right)^{2}\left(\frac{p_{11}\left(1-p_{11}\right)}{N}\right)\backslash n}{+\left(\operatorname{}\left(p_{11}+p_{12}\right)+\operatorname{}\left(p_{12}+p_{22}\right)-\operatorname{}p_{12}+I\left(D,T\right)\right)^{2}\left(\frac{p_{12}\left(1-p_{12}\right)}{N}\right)\backslash n}{+\left(\operatorname{}\left(p_{21}+p_{22}\right)+\operatorname{}\left(p_{11}+p_{21}\right)-\operatorname{}p_{21}+I\left(D,T\right)\right)^{2}\left(\frac{p_{21}\left(1-p_{21}\right)}{N}\right)\backslash n}{+\left(\operatorname{}\left(p_{21}+p_{22}\right)+\operatorname{}\left(p_{12}+p_{22}\right)-\operatorname{}p_{22}+I\left(D,T\right)\right)^{2}\left(\frac{p_{22}\left(1-p_{22}\right)}{N}\right)}\nonumber \\
\end{equation}
See, table 1 for definitions of \(p_{11},\ p_{12},\ p_{21},\)
and\(p_{22}\). Unabridged derivations are presented in the
appendix. Numerical examples of these derivations are shown in Table 2.
\textbf{Results}
We present the application of MI meta-analysis based on two cases
previously published in literature.
Case 1. Detection of endometrial cancer using endovaginal
ultrasonography (US).
For this case, we used data presented in Deeks \textsuperscript{22},
originally published in Smith-Bindman et al \textsuperscript{23}. The
dataset is the result of a systematic review process on 35 papers
presenting the diagnostic performance of endovaginal US in the detection
of endometrial cancer. Evidence synthesis tables on test sensitivity and
specificity are provided in Deeks \textsuperscript{22}.
Figure 1 displays the meta-analytic summary plots based on US studies.
It includes the summary ROC curve, individual study estimate, and
summary point estimate of the ``traditional'' measures of performance of
endovaginal US in the detection of endometrial cancer. It is difficult
to interpret, how ``good'' the test is, and in particular how much
uncertainty the test reduced in each study where US was evaluated. For
example, a US test diagnosing endometrial cancer is 40\% specific and
94\% sensitive. The combination of these values is difficult to
interpret and may lead to inappropriate assessment (e.g. one could
favour the test due to its high sensitivity, ignoring its low
specificity). In terms of MI however, the test reduces diagnostic
uncertainty by 10\%, which is marginal and thus the test is clearly not
very useful.
Figure 2 demonstrates meta-analysis of MI. We can clearly see that the
US results provided only 0.05 (0.04 to 0.07) bits of information
(recall, that the maximum amount information in the binary diagnostic
case is 1). Although this gives us an estimate about overall diagnostic
performance of US for diagnosis of endometrial cancer, what we really
want to know is the amount of diagnostic uncertainty the US can possibly
reduce (on scale 0 to 100\%). This can be expressed by calculating RMI.
Figure 3a shows the performance of US expressed in terms of RMI. The
information presented is much clearer: a decision-maker has much better
understanding on how much diagnostic uncertainty was reduced in each
study. The pooled estimate of the reduction in diagnostic uncertainty is
13\% for pre-test probability of disease 14\%. That is, US can reduce
the uncertainty related to \emph{endometrial cancer} by 13\%. Figure 3b
presents the sample size of each study.
Case 2: Contrast-enhanced magnetic resonance angiography (MRA) for
arterial stenosis disease
In this case, we use meta-analysis data from the study of Menke and
Larsen\textsuperscript{24} summarizing evidence about how well MRA
detects arterial stenosis. A total of 32 studies were included in the
analysis.
Figure 4 depicts the meta-analytic summary plots. It includes the
summary ROC curve, individual study estimate, and summary point estimate
of the ``traditional'' measures of performance of MRA in diagnosis of
arterial stenosis. As with figure 1, the interpretation of traditional
statistics in terms of test performance is difficult. For example, an
MRA test diagnosing arterial stenosis is 96\% specific and 78\%
sensitive. The combination of these values is difficult to interpret and
may lead to inappropriate assessment. In terms of MI however, the test
reduces diagnostic uncertainty by 49\%, which indicates a clearly useful
test.
Figure 5, demonstrates the meta-analysis of MI, in which it is shown
that the information content of MRA in diagnosis of arterial stenosis is
0.53 (CI: 0.48, 0.57).
Figure 6 depicts the RMI for reported by each study as well as the pool
estimate, which is approximately 67\% for pre-test probability of
disease 25\%. That is, the MRA reduces uncertainty related to arterial
stenosis by 67\%.
\textbf{Discussion}
Many authors have outlined a number of problems with the use of
``traditional'' measures of diagnostic
performance\textsuperscript{6,16,25-27}. These problems relate to the
biases that plague studies evaluating diagnostic studies, and to the
metrics themselves \textsuperscript{28}. In this paper, we focus on the
latter. In particular, we focus on the measurement of diagnostic
accuracy as opposed to the impact of diagnostic tests on health
outcomes, which depends on consideration of down-stream effects of
testing such as the choice of treatment and will not be considered here.
With regards to diagnostic accuracy, it has been
argued\textsuperscript{6,8,29,30} that utilization of information
theory, and particularly MI, has theoretical and practical advantages
over the traditional measures at assessing the performance of a
diagnostic test. Notably, MI and RMI can be used to explicitly quantify
the amount of diagnostic uncertainty a test reduces. Such a direct
measure can easily be used to evaluate test performance not only by
trained researchers but also by any EBM literate practitioner. Here, we
summarized the MI advantages over traditional measures and demonstrated
how MI can be meta-analyzed using two cases from the literature.
The MI meta-analysis results presented in both cases show the
superiority of MI and RMI over other metrics in conveying arguably the
most useful clinical indicators of diagnostic test performance, namely
the amount of diagnostic uncertainty reduced by the test. Clearly,
consideration of other ethical and personal dilemmas is also involved in
the administration of a diagnostic test. However, for the EBM community
and the evidence synthesis practitioners , reduction of uncertainty is
of outmost importance. In terms of derivation, MI is easily computed and
meta-analyzed. In addition, although we have not emphasized it here, MI
has particular advantages over other metrics when it comes to analysis
of tests with continuous measurements such as PSA, blood pressure etc.
Analysis of such tests with traditional metrics requires dichotomization
of the test results discarding useful information \textsuperscript{31}.
On the other hand, MI can be computed both for discrete and continuous
variables \textsuperscript{32}.
One limitation of MI is its reliance on prevalence, which even though
represents theoretical advantages it introduces heterogeneity in
meta-analysis. To solve this problem, we propose meta-analyzing RMI
instead of MI, but at this time we know of no derivation of standard
error for RMI. Further development in the field of research synthesis of
diagnostic test performance may lie in the opportunity to develop robust
meta-analytic techniques for RMI.
In summary, we believe that MI is the most meaningful measure for both
decision makers and EMB researchers as it provides intuitive, easy to
understand metrics that quantify diagnostic tests information content.
We therefore, argue that the field of evidence-based diagnostics should
adopt MI as its most useful metric.
References
1. Sox HC, Blatt MA, Higgins MC, Marton MC. Medical Decision Making.
Boston: Butterworths; 1988.
2. Leeflang MM, Deeks JJ, Takwoingi Y, Macaskill P. Cochrane diagnostic
test accuracy reviews. Syst Rev 2013;2:82.
3. Leeflang MM, Deeks JJ, Gatsonis C, Bossuyt PM, Cochrane Diagnostic
Test Accuracy Working G. Systematic reviews of diagnostic test accuracy.
Ann Intern Med 2008;149:889-97.
4. Shannon CE, Waever W. The mathematical theory of communication.
Urbana: The University of Illinois Press; 1962.
5. Shannon C. A mathematical theory of communication, bell System
technical Journal 27: 379-423 and 623--656. Mathematical Reviews
(MathSciNet): MR10, 133e 1948.
6. Benish WA. Intuitive and axiomatic arguments for quantifying
diagnostic test performance in units of information. Methods Inf Med
2009;48:552-7.
7. Somoza E, Mossman D. Comparing and optimizing diagnostic tests: an
information-theoretical approach. Med Decis Making 1992;12:179-88.
8. Benish W. Mutual information as an index of diagnostic test
performance. Methods of information in medicine 2003;42:260-4.
9. Mossman D, Somoza E. Diagnostic tests and information theory. J
Neuropsychiatry Clin Neurosci 1992;4:95-8.
10. Somoza E, Soutullo-Esperon L, Mossman D. Evaluation and optimization
of diagnostic tests using receiver operating characteristic analysis and
information theory. International journal of bio-medical computing
1989;24:153-89.
11. Benish W. The use of information graphs to evaluate and compare
diagnostic tests. Methods of information in medicine 2002;41:114-8.
12. Nelson GW, O'Brien SJ. Using mutual information to measure the
impact of multiple genetic factors on AIDS. JAIDS Journal of Acquired
Immune Deficiency Syndromes 2006;42:347-54.
13. Meyer CR, Boes JL, Kim B, et al. Demonstration of accuracy and
clinical versatility of mutual information for automatic multimodality
image fusion using affine and thin-plate spline warped geometric
deformations. Medical image analysis 1997;1:195-206.
14. Diamond GA, Hirsch M, Forrester JS, et al. Application of
information theory to clinical diagnostic testing. The
electrocardiographic stress test. Circulation 1981;63:915-21.
15. Cover TM, Thomas JA. Elements of information theory: John Wiley \&
Sons; 2012.
16. Hughes G. Application of Information Theory to Epidemiology:
American Phytopathological Society; 2012.
17. Hughes G, McRoberts N. The structure of diagnostic information.
Australasian Plant Pathology 2014:1-20.
18. Djulbegovic B, Hozo I, Abdomerovic I, Hozo S. Diagnostic entropy as
a function of therapeutic benefit/risk ratio. Med Hyoptheses
1995;45:503-9.
19. Djulbegovic B, Glasziou P, Chalmers I. The importance of randomised
vs non-randomised trials. The Lancet 2019;394:634-5.
20. Deeks JJ, Altman DG, Bradburn MJ. Statistical methods for examining
heterogeneity and combining results from several studies in
meta-analysis. Systematic Reviews in Health Care: Meta-Analysis in
Context, Second Edition 2001:285-312.
21. Roulston MS. Estimating the errors on measured entropy and mutual
information. Physica D: Nonlinear Phenomena 1999;125:285-94.
22. Deeks JJ. Systematic reviews in health care: Systematic reviews of
evaluations of diagnostic and screening tests. BMJ 2001;323:157-62.
23. Smith-Bindman R, Kerlikowske K, Feldstein VA, et al. Endovaginal
ultrasound to exclude endometrial cancer and other endometrial
abnormalities. JAMA 1998;280:1510-7.
24. Menke J, Larsen J. Meta-analysis: Accuracy of contrast-enhanced
magnetic resonance angiography for assessing steno-occlusions in
peripheral arterial disease. Ann Intern Med 2010;153:325-34.
25. Knottnerus JA. The evidence base of clinical diagnosis. London: BMJ
Books; 2002.
26. Hilden J. The area under the ROC curve and its competitors. Med
Decis Making 1991;11:95-101.
27. Lee WC, Hsiao CK. Alternative summary indices for the receiver
operating characteristic curve. Epidemiology 1996;7:605-11.
28. Bossuyt PM, Reitsma JB, Bruns DE, et al. The STARD Statement for
reporting of studies of diagnostic accuracy: explanation and
elaboration. Clin Chem 2003;49:7-18.
29. Benish WA. Relative entropy as a measure of diagnostic information.
Medical decision making 1999;19:202-6.
30. Wu Y, Alagoz O, Ayvaci MU, et al. A comprehensive methodology for
determining the most informative mammographic features. Journal of
digital imaging 2013;26:941-7.
31. Shapiro DE. The interpretation of diagnostic tests. Stat Methods Med
Res 1999;8:113-34.
32. Ross BC. Mutual Information between Discrete and Continuous Data
Sets. PloS one 2014;9:e87357.
Appendix - Unabridged derivations of MI, RMI and Var(MI)
Entropy is expressed as:
\begin{equation}
H\left(D\right)=-\left(P(D+)\operatorname{}{P(D+)}+\left(1-P(D+)\right)\operatorname{}\left(1-P(D+)\right)\right)\nonumber \\
\end{equation}
The uncertainty due to the diagnostic test is:
\begin{equation}
H\left(T\right)=-\left(\ P(D+|T+)\operatorname{}{P(D+|T+)}+\left(1-P(D+|T+)\right)\operatorname{}\left(1-P(D+|T+)\right)\right)\nonumber \\
\end{equation}
The mutual information is computed as:
\begin{equation}
I\left(D,T\right)=H\left(D\right)+H\left(T\right)-H\left(D,T\right)=H\left(D\right)-H\left(D\middle|T\right)\nonumber \\
\end{equation}
The relative mutual information is computed as:
\begin{equation}
I_{R}\left(D,T\right)=\frac{I\left(D,T\right)}{H\left(D\right)}=1-\frac{H(D|T)}{H(D)}\nonumber \\
\end{equation}
In terms of sensitivity and specificity, mutual information is derived
as:
\begin{equation}
I\left(D,T\right)=H\left(D\right)+H\left(T\right)-H\left(D,T\right)=P\left(T+\middle|D+\right)P(D+)\left(\log_{2}\left(\frac{P\left(T+\middle|D+\right)\left(\left(1-P\left(T+\middle|D+\right)\right)P\left(D+\right)+P\left(T-\middle|D-\right)\left(1-P\left(D+\right)\right)\right)}{\left(1-P\left(T+\middle|D+\right)\right)\left(P\left(T+\middle|D+\right)P\left(D+\right)+\left(1-P\left(T-\middle|D-\right)\right)\left(1-P\left(D+\right)\right)\right)}\right)\right)+P\left(T-\middle|D-\right)\left(1-P(D+)\right)\ \left(\log_{2}\left(\frac{P(T-|D-)\left(P(T+|D+)P(D+)+\left(1-P(T-|D-)\right)\left(1-P(D+)\right)\right)}{\left(1-P(T-|D-)\right)\left(\left(1-P(T+|D+)\right)P(D+)+P(T-|D-)\left(1-P(D+)\right)\right)}\right)\right)\ \ \ \ \ \ \ \ +P(D+)\log_{2}\left(\frac{\left(1-P(T+|D+)\right)\left(P(T+|D+)P(D+)+\left(1-P(T-|D-)\right)\left(1-P(D+)\right)\right)}{\left(1-P(T-|D-)\right)\left(\left(1-P(T+|D+)\right)P(D+)+P(T-|D-)\left(1-P(D+)\right)\right)}\right)+\log_{2}\left(\frac{\left(1-P(T-|D-)\right)}{\left(P(T+|D+)P(D+)+\left(1-P(T-|D-)\right)\left(1-P(D+)\right)\right)}\right)\nonumber \\
\end{equation}
The variance of mutual information is computed as:
\begin{equation}
\text{Var}\left(H\left(D\right)\right)=\left[\left(\operatorname{}{P(D+)}+H\left(D\right)\right)^{2}+\left(\operatorname{}\left(1-P(D+)\right)+H\left(D\right)\right)^{2}\right]\frac{P(D+)\left(1-P(D+)\right)}{N}\nonumber \\
\end{equation}
and:
\begin{equation}
{\text{Var}\left(I\left(D,T\right)\right)=\left(\operatorname{}\left(P\left(T+\middle|D+\right)P(D+)+\left(1-P\left(T+\middle|D+\right)\right)P(D+)\right)+\operatorname{}\left(P\left(T+\middle|D+\right)P(D+)+(1-P\left(T-\middle|D-\right))(1-P\left(D+\right))\right)-\operatorname{}{(P\left(T+\middle|D+\right)P\left(D+\right))}+I\left(D,T\right)\right)^{2}\left(\frac{P\left(T+\middle|D+\right)P(D+)\left(1-P\left(T+\middle|D+\right)P(D+)\right)}{N}\right)\backslash n}{+\left(\operatorname{}\left(P\left(T+\middle|D+\right)P(D+)+\left(1-P\left(T+\middle|D+\right)\right)P(D+)\right)+\operatorname{}\left(\left(1-P\left(T+\middle|D+\right)\right)P\left(D+\right)+P\left(T-\middle|D-\right)(1-P\left(D+\right))\right)-\operatorname{}{(\left(1-P\left(T+\middle|D+\right)\right)P\left(D+\right))}+I\left(D,T\right)\right)^{2}\left(\frac{\left(1-P\left(T+\middle|D+\right)\right)P(D+)\left(1-\left(1-P\left(T+\middle|D+\right)\right)P(D+)\right)}{N}\right)\backslash n}{+\left(\operatorname{}\left((1-P\left(T-\middle|D-\right))(1-P\left(D+\right))+P\left(T-\middle|D-\right)(1-P\left(D+\right))\right)+\operatorname{}\left(P\left(T+\middle|D+\right)P(D+)+(1-P\left(T-\middle|D-\right))(1-P\left(D+\right))\right)-\operatorname{}{((1-P\left(T-\middle|D-\right))(1-P\left(D+\right)))}+I\left(D,T\right)\right)^{2}\left(\frac{(1-P\left(T-\middle|D-\right))(1-P\left(D+\right))\left(1-(1-P\left(T-\middle|D-\right))(1-P\left(D+\right))\right)}{N}\right)\backslash n}{+\left(\operatorname{}\left((1-P\left(T-\middle|D-\right))(1-P\left(D+\right))+P\left(T-\middle|D-\right)(1-P\left(D+\right))\right)+\operatorname{}\left(\left(1-P\left(T+\middle|D+\right)\right)P(D+)+P\left(T-\middle|D-\right)(1-P\left(D+\right))\right)-\operatorname{}{(P\left(T-\middle|D-\right)\left(1-P\left(D+\right)\right))}+I\left(D,T\right)\right)^{2}\left(\frac{P\left(T-\middle|D-\right)(1-P\left(D+\right))\left(1-P\left(T-\middle|D-\right)(1-P\left(D+\right))\right)}{N}\right)}\nonumber \\
\end{equation}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-1/Figure-1}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-2/Figure-2}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-3a/Figure-3a}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-3b/Figure-3b}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-4/Figure-4}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-5/Figure-5}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-6/Figure-6}
\end{center}
\end{figure}
\textbf{Hosted file}
\verb`Table 1.docx` available at \url{https://authorea.com/users/339139/articles/465391-meta-analysis-of-mutual-information-applied-in-ebm-diagnostics}
\textbf{Hosted file}
\verb`Table 2.docx` available at \url{https://authorea.com/users/339139/articles/465391-meta-analysis-of-mutual-information-applied-in-ebm-diagnostics}
\selectlanguage{english}
\FloatBarrier
\end{document}
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# | Part of LaTeXML : http://dlmf.nist.gov/LaTeXML/ | #
# | Copyright (c) 2006 arXMLiv group | #
# | Released under the GNU Public License | #
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package LaTeXML::Package::Pool;
use strict;
use LaTeXML::Package;
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http://dlmf.nist.gov/27.14.E7.tex | nist.gov | CC-MAIN-2016-22 | application/x-tex | null | crawl-data/CC-MAIN-2016-22/segments/1464053252010.41/warc/CC-MAIN-20160524012732-00226-ip-10-185-217-139.ec2.internal.warc.gz | 81,706,969 | 628 | \[n\mathop{p\/}\nolimits\!\left(n\right)=\sum_{k=1}^{n}\mathop{\sigma_{1}\/}%
\nolimits\!\left(n\right)\mathop{p\/}\nolimits\!\left(n-k\right),\] |
https://dlmf.nist.gov/13.7.E4.tex | nist.gov | CC-MAIN-2018-17 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2018-17/segments/1524125944851.23/warc/CC-MAIN-20180421012725-20180421032725-00245.warc.gz | 596,454,610 | 749 | \[U\left(a,b,z\right)=z^{-a}\sum_{s=0}^{n-1}\frac{{\left(a\right)_{s}}{\left(a-b%
+1\right)_{s}}}{s!}(-z)^{-s}+\varepsilon_{n}(z),\] |
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\begin{vitae}{\british}{Assoc. Prof. Mgr. Radová}
\nadpis{Curriculum vit\ae}
\vspace{0.8cm}
\podnadpis{\textbf{Name, first names, scientific degrees} }
\begin{ul}
\item Assoc. Prof. Mgr. Radová, Irena, Ph.D;
\item married, two children
\end{ul}
\podnadpis{\textbf{Department/Faculty/University} }
\begin{ul}
\item Department of Classical Studies\\
Faculty of Arts of Masaryk University (= FF MU)\\
A. Nováka 1\\
660 88 Brno
\end{ul}
\podnadpis{\textbf{Function, current position} }
\begin{ul}
\item Associate professor\\
since 2004 head of the Department of Classical Studies\\
\end{ul}
\podnadpis{\textbf{Education and academic qualifications} }
\begin{ul}
\item 2010 \quad Associate professor in Classical Philology (Masaryk University);
\item 2003 \quad PhD. in Classical Philology (Masaryk University);
\item 2000 \quad Mgr. in Ancient Greek Language and Literature (Masaryk University);
\item 1989 \quad Mgr. in Latin Language and Literature ? German Language and Literature (Masaryk University).
\end{ul}
\podnadpis{\textbf{Professional experience} }
\begin{ul}
\item 1999 \quad Department of Classical Studies FF MU
\end{ul}
\podnadpis{\textbf{Teaching activities} }
\begin{ul}
\item Proseminar and Seminar of Ancient Greek literature;
\item History of the Classical Literature;
\item Reading Herodotus;
\item Reading Xenophon;
\item Reading The New Testament;
\item Classical Mythology;
\item Classical Metrics
\item Ancient Topics in Movies
\end{ul}
\podnadpis{\textbf{Research activities} }
\begin{ul}
\item 2007?2011 Centre for the Interdisciplinary Research of Ancient Languages and Older Stages of Modern Languages (MSM 0021622435) (project team member);
\item 2006?2008 Research Project ? together with D. Bartoňková (Grant Agency of Academy of Sciences of Czech Republic, GAAV IAA901640603): Ancient Scriptural Records of the History of Our Territory;
\item 2005?2007: Research Project (Grant Agency of CR, n. 405/05/P134): Scholia on Apollonius Rhodius: Methodology of Ancient Scientific Approach to a Literary Work (principal investigator);
\item 2005 \quad Project of Ministry of Education of CR (n. 2954/2005/F5/a): New Approach to Classical Metrics (principal investigator).
\end{ul}
\podnadpis{\textbf{Professional stays abroad} }
\begin{ul}
\item 1993--1994 \quad University of Vienna;
\item 2000--2001 \quad The Aristotle University of Thessaloniki;
\item 2003 \quad Ruprecht Karls University Heidelberg;
\item 2003, 2005 Istituto Universitario Orientale.
\end{ul}
\podnadpis{\textbf{Other academic activities, research projects, grants} }
\begin{ul}
\item since 2004 (with breaks in 2007 and 2010/2011 for maternity leave) head of the Department of Classics;
\item in 2006--2014 (with breaks in 2007 and 2010/2011 for maternity leave) vice--dean of the Faculty of Arts.
\item
\end{ul}
\podnadpis{\textbf{Non--university activities} }
\begin{ul}
\item Member of the Society for Modern Greek Studies;
\item Memebr of the Society for Classical Studies;
\item 2018-- \quad Honorary member of the ???????? ???????? ??????????? ??????????? (National Society of Greek Authors)
\item
\end{ul}
\podnadpis{\textbf{Major publications}}
\begin{ul}
\item RADOVÁ, Irena, Juraj FRANEK and Tomáš JENIŠ. \textit{Tomáš Špidlík. Z pokladnice otců. Patristická čítanka na každý den. Přeloženo z řeckých, latinských a francouzských textů (Tomáš Špidlík. Patristic breviary : Ancient wisdom for today's world. Translated from Greek, Latin and French texts)\/}. Vydání první. Olomouc: nakladatelství Centra Aletti Refugium Velehrad--Roma, 2019. 461 pp. Dílo Tomáše Špidlíka; XXV. ISBN 978--80--7412--333--7. info
\item RADOVÁ, Irena. Médeia jako protagonistka uprchlické krize (Medea as the Protagonist of a Refugee Crisis). In BUZÁSSYOVÁ, Ľudmila; JURÍKOVÁ, Erika; GRUSKOVÁ, Jana. \textit{Ideológia v premenách času v pamiatkach gréckej a latinskej tradície\/}. Bratislava: Univerzita Komenského v Bratislave, 2018. p. 66--74. ISBN 978--80--223--4626--9. info
\item RADOVÁ, Irena. Hera and Juno in the Argonautica. \textit{Acta antiqua Academiae scientiarum Hungaricae\/}. Akademiai Kiado, 2017, vol. 57, 2--3, p. 207--214. ISSN 0044--5975. doi:10.1556/068.2017.57.2--3.6. info
\item RADOVÁ, Irena. The Argonauts as Dysfunctional Indo--European Heroes? In \textit{Emotional Trauma in Greek and Roman Culture : Representations and Reactions, European Cultural Center of Delphi (ECCD), June 23?25, 2016, Delphi, Greece\/}. 2016. URL info
\item RADOVÁ, Irena. Médeia jako protagonistka uprchlické krize (Medea in a refugee crisis). In \textit{Ideológia v premenách času v pamiatkach gréckej a latinskej tradície: Medzinárodná konferencia pri príležitosti sedemdesiatin profesora Daniela Škovieru; 18.?19. novembra 2016, FiF UK Bratislava\/}. 2016. info
\item RADOVÁ, Irena. \textit{Valerius Flaccus. Argonautica\/}. 1. vyd. Praha: Arista, Baset, 2015. 408 pp. Antická knihovna ; sv. 84. ISBN 978--80--86410--72--2. info
\item RADOVÁ, Irena and Katarina PETROVIĆOVÁ. \textit{Laetae segetes IV\/}. 2014. info
\item RADOVÁ, Irena. Médeia na prahu novověku ? dvě případové studie (Medea on the Threshold of Modern Times ? Two Case Studies). \textit{Historica Olomucensia\/}. Olomouc: Univerzita Palackého v Olomouci, 2014, vol. 34, Supplementum I, p. 305--313. ISSN 1803--9561. info
\item RADOVÁ, Irena and Holman PETR. \textit{Otokar Březina / Ottocarus Březina. Básnické spisy / Opera poetica. Latinis litteris expressit Iohannes Šprincl (Otokar Březina / Ottocarus Březina. Poetry / Opera poetica. Latin transl. Jan Šprincl)\/}. Červený Kostelec: Pavel Mervart, 2013. 467 pp. ISBN 978--80--7465--083--3. info
\item RADOVÁ, Irena. Mytologie a antická rodina ve vzájemném vztahu (Classical mythology and family interrelated). In Frýdek, Miroslav a kol. \textit{Právní, náboženské a politické aspekty starověké římské rodiny\/}. Vyd. 1. Ostrava: Key Publishing, 2012. p. 6--12. Právo. ISBN 978--80--7418--157--3. info
\item RADOVÁ, Irena. The influence of antiquity on Czech--written literature of the 19th and 20th centuries. In Aleksejeva, Brigita; Lams, Ojars; Rumniece, Ilze. \textit{Hellenic Dimension : Materials of the Riga 3rd International Conference of Hellenic Studies\/}. Riga: University of Latvia, 2012. p. 203--209. ISBN 978--9984--45--469--6. info
\item RADOVÁ, Irena. \textit{Altgriechische Scholien. Ein typologischer Versuch (Ancient Greek Scholia. A typological Attempt)\/}. Prag: Koniasch Latin Press, 2011. 216 pp. Laborinthus. ISBN 978--80--86791--58--6. info
\item RADOVÁ, Irena. Sprachwissenschaftliche Disziplinen in den altgriechischen Scholien (Linguistics in the Ancient Greek Scholia). In \textit{Early European Languages in the Eyes of Modern Linguistics\/}. 2009. ISBN 978--80--210--4944--4. info
\item PETROVIĆOVÁ, Katarina and Irena RADOVÁ. \textit{Graeco--Latina Brunensia. Erant in quadam civitate... Na počest Daši Bartoňkové. (Graeco--Latina Brunensia. Erant in quadam civitate... To Honour of Daša Bartoňková.)\/}. 1st ed. Brno: Masarykova univerzita, 2009. 412 pp. ISBN 978--80--210--5000--6. info
\item RADOVÁ, Irena. Vzdělávání v řecko--římském Egyptě na základě školních papyrů (Education in the Graeco--Roman Egypt on the Basis of the School Papyri). In \textit{Latina v církevním a světském školství\/}. Praha: Filosofický ústav Akademie věd České republiky, v.v.i. ? Kabinet pro klasická studia, 2009. p. 7--20, 19 pp. ISBN 978--80--254--4080--3. info
\item RADOVÁ, Irena. Sprachwissenschaftliche Disziplinen in den altgriechischen Scholien (The Linguistic Disciplines in the Ancient Greek Scholia). In \textit{Early European Languages in the Eyes of Modern Linguistics\/}. 1. vyd. Brno: Masarykova univerzita, 2009. p. 253--256, 8 pp. ISBN 978--80--210--4944--4. info
\item RADOVÁ, Irena and Nina JAŠKOVÁ. Výběrová bibliografie Daši Bartoňkové (Selective Bibliography of Daša Bartoňková). \textit{Graeco--Latina Brunensia\/}. Brno: Masarykova univerzita, 2009, vol. 2009, No 14, p. 5--9. ISSN 1803--7402. info
\item RADOVÁ, Irena. Mythology in the scholia to Apollonius Rhodius. In \textit{The 8th International Conference on Greek Research\/}. 2009. info
\item RADOVÁ, Irena. \textit{(ed.). Laetae segetes iterum (Laetae segetes iterum)\/}. Brno: Masarykova univerzita, 2008. 448 pp. ISBN 978--80--210--4775--4. info
\item RADOVÁ, Irena. Bibliografie (Bibliography). In CONTE, G. B. \textit{Dějiny římské literatury\/}. Praha: Koniasch Latin Press, 2008. p. 682--704. Druhé, revidované a doplněné vydání. ISBN 978--80--86791--57--9. info
\item BARTOŇKOVÁ, Daša, Petr KYLOUŠEK, Irena RADOVÁ and Helena SEKAVOVÁ. \textit{(transl.) Luciano Canfora: Gaius Iulius Caesar. Demokratický diktátor. Praha: Vyšehrad, 2007, 448s. ISBN 978--80--7021--901--0. ((transl.) Luciano Canfora: Gaius Iulius Caesar. Democratic Dictator. Praha: Vyšehrad, 2007, 448s. ISBN 978--80--7021--901--0.)\/}. Praha: Vyšehrad, 2007. 448 pp. ISBN 978--80--7021--901--0. info
\item RADOVÁ, Irena. Racionalistický výklad mýtů (Rationalistic interpretation of myths). In \textit{Vademecum Graeco--Latinum Brunense\/}. Brno: Masarykova univezita, 2006. p. 49--55. ISBN 80--210--3969--8. info
\item PFAFFEL, Wilhelm, Katarina PETROVIĆOVÁ and Irena RADOVÁ. \textit{Armilla -- Interaktive Übungssoftware (Armilla -- interactive tutorial software)\/}. 1st ed. Bamberg: C. C. Büchner, 2006. ISBN 3--7661--9592--1. info
\item RADOVÁ, Irena. Plautus redivivus. In EDD: KRMÍČKOVÁ, Helena, Anna PUMPROVÁ, Dana RŮŽIČKOVÁ and Libor ŠVANDA. \textit{Querite primum regnum Dei\/}. Brno: Filozofická fakulta MU; Matice moravská, 2006. p. 161--167. ISBN 80--86488--35--7. info
\item NECHUTOVÁ, Jana and Irena (edd.) RADOVÁ. \textit{Laetae segetes\/}. 1st ed. Brno: Masarykova univerzita, 2006. 196 pp. Laetae segetes I. ISBN 80--210--4069--6. info
\item RADOVÁ, Irena. Argonauti na cestách časem (The Argonauts Travelling through the Times). In ED. KEPARTOVÁ, Jana. \textit{Antika? Zajděte do kina, přečtěte román...\/} Praha: Nakladatelství Lidové noviny, 2006. p. 11--22. ISBN 80--7106--850--0. info
\item RADOVÁ, Irena. Einige Aspekte des Abenteuers auf Lemnos in griechischer und römischer Auffassung (Some Aspects of the Lemnos--adventure in the Greek and Roman Conception). \textit{Graecolatina Pragensia (Acta Universitatis Carolinae, Philologica)\/}. Praha: Univerzita Karlova, 2006, vol. 2006, No 20, p. 163--168. ISSN 0567--8269. info
\item RADOVÁ, Radová. Jana Nechutová (ed.), Druhý život antického mýtu, Brno 2004\duv{. \textit{Iliteratura\/}. 2005. ISSN 1214--309X. URL info
\item BEDNAŘÍKOVÁ, Jarmila and Irena RADOVÁ. \textit{Besedy o demokracii v minulosti a dnes (The talking about the democracy in antiquity and today)\/}. Lubor Kysučan. 2005. info
\item RADOVÁ, Irena, Jana NECHUTOVÁ and Katarina PETROVIĆOVÁ. \textit{Laetae segetes\/}. 2005. info
\item RADOVÁ, Irena. \textit{Palaifatos: O neuvěřitelných příbězích (Palaifatos: Unbelievable Tales)\/}. Praha: Koniasch Latin Press, 2005. 96 pp. Koniaschova knihovna klasiků, sv. 1. ISBN 80--86791--30--0. info
\item RADOVÁ, Irena and Jiří K. KROUPA. Slovníček řeckých a latinských pojmů (Vocabulary of greek and latin terms). In \textit{Luciano Canfora. Dějiny řecké literatury.\/} Druhé vydání. Praha: Koniasch Latin Press, 2004. p. 863--871. Dějiny evropských literatur, 2. ISBN 80--86791--10--6. info
\item RADOVÁ, Irena. \textit{Dobrodružství Argonautů: Řecko versus Řím (Adventure of Argonauts: Greece versus Rome)\/}. Praha: Koniasch Latin Press, 2004. 159 pp. Primitiae, 1. sv. ISBN 80--86791--15--7. info
\item RADOVÁ, Irena. Imitatio des Valerius Flaccus (Imitatio of Valerius Flaccus). \textit{Sborník prací Filozofické fakulty brněnské univerzity, řada klasická N, Graeco--Latina Brunensia\/}. Brno: Masarykova univerzita v Brně, 2003, vol. 8, No 1, p. 39--45, 6 pp. ISSN 1211--6335. info
\item RADOVÁ, Irena and Jiří K. KROUPA. Slovníček řeckých a latinských pojmů (Vocabulary of greek and latin terms). In \textit{Dějiny řecké literatury\/}. Praha: Koniasch Latin Press, 2001. p. 855--863. Dějiny evropských literatur, 2. ISBN 80--85917--69--6. info
\item RADOVÁ, Irena. Literarische Vorbilder von Valerius Flaccus (Literary inspiration of Vlaerius Flaccus). In \textit{SPFFBU\/}. 6--7. Brno: Masarykova Univerzita, 2001. p. 263--267. info
\item RADOVÁ, Irena. Nepoetická poezie? (Non--poetic poetry?). In \textit{Vademecum Graeco--Latinum Brunense\/}. Brno: Ústav klasických studií FF MU, 2001. p. 63--71. info
\item RADOVÁ, Irena. Non omnis mortuus est. \textit{Universitas\/}. Brno: Masarykova Univerzita, 2001, vol. 2001, No 4, p. 36--37. ISSN 1211--3384. info
\item RADOVÁ, Irena. Literární vzory Valeria Flakka (Literary Inspiration of Valerius Flaccus). In \textit{Philosophia 2000: }Klasická studia na prahu nového milénia"\/}. Ed. T. Klůsová. Litomyšl: Muzeum antického sochařství a architektury FF UK, 2000. p. 57--59. info
\end{ul}
\vspace{0.5cm} 2018/02/07
\vspace{0.5cm} \end{vitae}
\end{document}
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(31)--(43) (32)--(43) (34)--(44) (28)--(44) (31)--(44) (34)--(45) (36)--(45)
(29)--(45) (32)--(45) (34)--(46) (35)--(46) (30)--(46) (33)--(46) (37)--(47)
(38)--(47) (39)--(47) (40)--(47) (37)--(48) (41)--(48) (42)--(48) (43)--(48)
(45)--(49) (40)--(49) (43)--(49) (44)--(49) (46)--(50) (39)--(50) (42)--(50)
(44)--(50) (38)--(51) (41)--(51) (44)--(51) (47)--(52) (48)--(52) (49)--(52)
(50)--(52) (51)--(52);
\node[cnj=3] {120};
\node[cnj=7] {60};
\node[cnj=8] {60};
\node[cnj=10] {40};
\node[cnj=12] {24};
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\node[cnj=45] {2};
\node[cnj=46] {2};
\node[cnj=47] {5};
\node[cnj=48] {3};
\end{tikzpicture}
\end{document}
|
http://porocila.imfm.si/2017/mat/clani/dolinarfe.tex | imfm.si | CC-MAIN-2023-14 | text/x-tex | application/x-tex | crawl-data/CC-MAIN-2023-14/segments/1679296948756.99/warc/CC-MAIN-20230328011555-20230328041555-00725.warc.gz | 36,936,168 | 2,306 | \clan {Gregor Dolinar}
%--------------------------------------------------------
% A. objavljene znanstvene monografije
%--------------------------------------------------------
%\begin{skupina}{A}
%\disertacija
% {NASLOV}
% {UNIVERZA}
% {FAKULTETA}
% {ODDELEK}
% {KRAJ} {DRZAVA} {LETO}
%\magisterij
% {NASLOV}
% {UNIVERZA}
% {FAKULTETA}
% {ODDELEK}
% {KRAJ} {DRZAVA} {LETO}
%\monografija
% {AVTORJI}
% {NASLOV}
% {ZALOZBA}
% {KRAJ} {DRZAVA} {LETO}
%\end{skupina}
% Ni podatkov za to sekcijo
%--------------------------------------------------------
% B. raziskovalni clanki sprejeti v objavo v znanstvenih
% revijah in v zbornikih konferenc
%--------------------------------------------------------
\begin{skupina}{B}
%\sprejetoRevija
% {AVTORJI}
% {NASLOV}
% {REVIJA}
%\sprejetoZbornik
% {AVTORJI}
% {NASLOV}
% {KONFERENCA}
% {KRAJ} {DRZAVA} {MESEC} {LETO}
\sprejetoRevija
{\crta, B.~Kuzma, J.~Marovt}
{A note on commutativity preserving maps on $M_{n}(\mathbb{R})$}
{Oper.\ Matrices}
\sprejetoRevija
{\crta, B.~Kuzma, N.~Stopar}
{Characterization of orthomaps on the Cayley plane}
{Aequationes Math.}
\end{skupina}
% Ni podatkov za to sekcijo
%--------------------------------------------------------
% C. raziskovalni clanki objavljeni v znanstvenih revijah
% in v zbornikih konferenc
%--------------------------------------------------------
%\begin{skupina}{C}
%\objavljenoRevija
% {AVTORJI}
% {NASLOV}
% {REVIJA} {LETNIK} {LETO} {STEVILKA} {STRANI}
%\objavljenoZbornik
% {AVTORJI}
% {NASLOV}
% {KONFERENCA}
% {KRAJ} {DRZAVA} {MESEC} {LETO}
% {ZBORNIK} {STRANI}
%\end{skupina}
\begin{skupina}{C}
\objavljenoRevija
% 1.01: {\bf 1}. CRUZ, Henrique F. da, DOLINAR, Gregor, FERNANDES, Ros\'{a}rio, KUZMA, Bojan. Maximal doubly stochastic matrix centralizers. {\it Linear Algebra Appl.}, 2017, vol. 532, str. 387-396. $[$COBISS.SI-ID 18079577$]$\\
{H.~F.~Da Cruz, \crta, R.~Fernandes, B.~Kuzma}
{Maximal doubly stochastic matrix centralizers}
{Linear Algebra Appl.} {532} {2017} {} {387--396}
\objavljenoRevija
{\crta, B.~Kuzma, J.~Marovt}
{Lie product preserving maps on $M_{n}(\mathbb{F})$}
{Filomat} {31} {2017} {16} {53{3}5--534{4}}
\end{skupina}
%--------------------------------------------------------
% D. urednistvo v znanstvenih revijah in zbornikih
% znanstvenih konferenc
%--------------------------------------------------------
%\begin{skupina}{D}
%\urednikRevija
% {OPIS}
% {REVIJA}
%\urednikZbornik
% {OPIS}
% {KONFERENCA}
% {KRAJ} {DRZAVA} {MESEC} {LETO}
%\end{skupina}
\begin{skupina}{D}
\urednikRevija
{\v{C}lan uredni\v{s}kega odbora}
{Mathematica Slovaca}
\urednikRevija
{\v{C}lan uredni\v{s}kega odbora}
{Matematika i Informatika}
\end{skupina}
%--------------------------------------------------------
% E. organizacija mednarodnih in domacih znanstvenih
% srecanj
%--------------------------------------------------------
%\begin{skupina}{E}
%\organizacija
% {OPIS}
% {KONFERENCA}
% {KRAJ} {DRZAVA} {MESEC} {LETO}
%\end{skupina}
% Ni podatkov za to sekcijo
%--------------------------------------------------------
% F. vabljena predavanja na tujih ustanovah in
% mednarodnih konferencah
%--------------------------------------------------------
%\begin{skupina}{F}
%\predavanjeUstanova
% {NASLOV}
% {OPIS}
% {USTANOVA}
% {KRAJ} {DRZAVA} {MESEC} {LETO}
%\predavanjeKonferenca
% {NASLOV}
% {OPIS}
% {KONFERENCA}
% {KRAJ} {DRZAVA} {MESEC} {LETO}
%\end{skupina}
% Ni podatkov za to sekcijo
%--------------------------------------------------------
% G. aktivne udelezbe na mednarodnih in domacih
% konferencah
%--------------------------------------------------------
%\begin{skupina}{G}
%\konferenca
% {NASLOV}
% {KONFERENCA}
% {KRAJ} {DRZAVA} {MESEC} {LETO}
%\end{skupina}
\begin{skupina}{G}
\konferenca
% 3.15: {\bf 2}. Preservers Everywhere, Bolyai Institute, University of Szeged, Szeged, Hungary, 19-23 June 2017, DOLINAR, Gregor{\it . Maximal doubly stochastic matrix centralizers : Szeged, 20. 6. 2017}. $[$COBISS.SI-ID 18053721$]$\\
{Maximal doubly stochastic matrix centralizers}
{Preservers Everywhere}
{Szeged} {Madžarska} {junij} {2017}
\end{skupina}
%--------------------------------------------------------
% H. strokovni clanki
%--------------------------------------------------------
%\begin{skupina}{H}
%\clanekRevija
% {AVTORJI}
% {NASLOV}
% {REVIJA} {LETNIK} {LETO} {STEVILKA} {STRANI}
%\clanekZbornik
% {AVTORJI}
% {NASLOV}
% {KONFERENCA}
% {KRAJ} {DRZAVA} {MESEC} {LETO}
% {ZBORNIK} {STRANI}
%\end{skupina}
% Ni podatkov za to sekcijo
%--------------------------------------------------------
% I. razno
%--------------------------------------------------------
%\begin{skupina}{I}
%\razno
% {OPIS}
%\end{skupina}
%\begin{skupina}{I}
%POZOR: Bibliografija2017.tex > 2017\mat\clani\dolinarfe.tex 1781/203: Stevilo neopredeljenih zadetkov: 3
%\razno
% Ured: {\bf 3}. {\it Matematika i informatika}. Dolinar, Gregor (\v{c}lan uredni\v{s}kega sveta 2012-). Sofija: Ministerstvo na obrazovanieto i naukata: Nacionalno izdatelstvo za obrazovanie i nauka Az Buki, 1994-. ISSN 1310-2230. $[$COBISS.SI-ID 16290137$]$\\
%\razno
% Ured: %list {\bf 4}. {\it Mathematica slovaca}. Dolinar, Gregor (\v{c}lan uredni\v{s}kega odbora 2011-). Bratislava: Mathematical Institute of the Slovac Academy of Sciences, 1976-. ISSN 0139-9918. $[$COBISS.SI-ID 27357184$]$\\
%\razno
% Rece: {\bf 5}. OBLAK, Polona{\it . Matematika}. 2. izd. Ljubljana: Zalo\v{z}ba FRI, cop. 2017. 175 str., ilustr. ISBN 978-961-6209-93-9. $[$COBISS.SI-ID 290485504$]$\\
%\end{skupina}
%--------------------------------------------------------
% tuji gosti
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%\begin{seznam}
%\gost {IME} {TRAJANJE} {USTANOVA} {KRAJ} {DRZAVA} {MESEC} {LETO} {POVABILO}
%\end{seznam}
%--------------------------------------------------------
% gostovanja
%--------------------------------------------------------
%\begin{seznam}
%\gostovanje {IME} {TRAJANJE} {USTANOVA} {KRAJ} {DRZAVA} {MESEC} {LETO}
%\end{seznam}
|
http://cs.ru.nl/~freek/talks/leiden.tex | ru.nl | CC-MAIN-2020-50 | text/x-tex | application/x-tex | crawl-data/CC-MAIN-2020-50/segments/1606141672314.55/warc/CC-MAIN-20201201074047-20201201104047-00457.warc.gz | 28,890,609 | 6,864 | \documentclass[a4]{seminar}
\usepackage{advi}
\usepackage{advi-graphicx}
\usepackage{color}
\usepackage{amssymb}
\slideframe{none}
\definecolor{slideblue}{rgb}{0,0,.5}
\definecolor{slidegreen}{rgb}{0,.4,0}
\definecolor{slidered}{rgb}{1,0,0}
\definecolor{slidegray}{rgb}{.5,.5,.5}
\newpagestyle{fw}{}{\hfil\textcolor{slideblue}{\sf\thepage}\qquad\qquad}
\slidepagestyle{fw}
\newcommand{\sectiontitle}[1]{\centerline{\textcolor{slideblue}{\textbf{#1}}}
\par\medskip}
\newcommand{\slidetitle}[1]{{\textcolor{slideblue}{#1}}\par
\vspace{-1.2em}{\color{slideblue}\rule{\linewidth}{0.04em}}}
\newcommand{\dashskip}{\strut\enskip{ }}
\newcommand{\exclspace}{\hspace{.45pt}}
\begin{document}\sf
\renewcommand{\sliderightmargin}{0mm}
\renewcommand{\slideleftmargin}{20mm}
\renewcommand{\slidebottommargin}{6mm}
\setcounter{slide}{-1}
\begin{slide}
\slidetitle{\Large formal mathematics}
Freek Wiedijk \\
Nijmegen University
Leiden University \\
2002-10-10, 16:00
\end{slide}
\begin{slide}
\sectiontitle{proof checking}
\slidetitle{the best of two worlds}
a wonderful computer game\exclspace!
\adviwait
proof checking is like
\begin{itemize}
\item[$\bullet$]
\textbf{programming} \\ but no bugs, and not as trivial\exclspace!
\item[$\bullet$]
\textbf{doing mathematics} \\ but completely transparent, and the computer helps\exclspace!
\end{itemize}
\adviwait
(currently closer to programming than to doing mathematics)
\vfill
\end{slide}
\begin{slide}
\slidetitle{proof checking $\;\leftrightarrow\;$ mathematical assistants}
computer can help with:
\begin{itemize}
\item[$\bullet$]
the discovery of mathematics
\item[\advirecord{reg1}{$\bullet$}]
\advirecord{reg2}{the registration of mathematics}
\adviplay{reg1}\adviplay{reg2}
\end{itemize}
\adviwait
\adviplay[slidered]{reg1}\adviplay[slidered]{reg2}
here only interested in the formalization of already existing mathematics
\medskip
\adviwait
\textbf{analogy}
\begin{center}
\begin{tabular}{rcl}
mathematician & $\leftrightarrow$ & proof checker \\
\advirecord{h1a}{violin player}\advirecord{h2a}{\llap{music composer}} & $\leftrightarrow$ & \advirecord{h1b}{\rlap{hifi sound technician}}\advirecord{h2b}{violin player}
\adviplay{h1a}\adviplay{h1b}
\adviwait
\adviplay[white]{h1a}\adviplay[white]{h1b}
\adviplay{h2a}\adviplay{h2b}
\end{tabular}
\end{center}
\vfill
\end{slide}
\begin{slide}
\slidetitle{what does proof checking buy me as a mathematician?}
currently:
\begin{itemize}
\item[$\bullet$]
\textbf{nothing} \\
the gains are not worth the effort yet
\end{itemize}
\adviwait
in the (near? far?) future:
\begin{itemize}
\item[$\bullet$]
\textbf{correctness} \\
certainty that lemmas are correct \\
\adviwait
certainty that a paper is correct when submitted \\
(the referees won't need to judge correctness anymore,
but only originality and relevance)
\adviwait
\item[$\bullet$]
\textbf{clarity} \\
no need to ask the author of a text for clarification \\
everything is there\exclspace!
\end{itemize}
\vspace{-2em}
\vfill
\end{slide}
\begin{slide}
\slidetitle{philosophy of reliability I:
the de Bruijn principle}
worry about own mistakes $\;\to\;$ worry about bugs in the checker?
\adviwait
analogous to compiler bugs in programming: \\
software problems are hardly ever caused by compiler bugs
\medskip
\adviwait
\textbf{de Bruijn principle} \\
check mathematics using a \textbf{small} checker
\medskip
\adviwait
two approaches:
\begin{itemize}
\item[$\bullet$]
small `proof kernel' that everything has to go through \\
(many current systems)
\adviwait
\item[$\bullet$]
export in a format that can be checked by a small separate checker \\
example: the Ivy program for the Otter prover
\end{itemize}
\vfill
\end{slide}
\begin{slide}
\slidetitle{philosophy of reliability II:
are we doing what we think we are doing?}
proofs are checked, but definitions can be `wrong'
definitions often are adapted for formalization \\
how to know that they still define the intended notions?
\medskip
\adviwait
\textbf{example} \\
definition of a planar graph in the four color theorem formalization: \\
no mention of the topology of the plane\exclspace!
\medskip
\adviwait
Trybulec: \textcolor{slidegreen}{definitions are a debt, theorems pay them back} \\
trust comes from the theory that is proved about the definitions
\vfill
\end{slide}
\begin{slide}
\slidetitle{the state of the art: mathematics that already has been formalized}
examples of formalized theorems:
\begin{quote}
$\bullet$ fundamental theorem of calculus \\
$\bullet$ fundamental theorem of algebra \\
$\bullet$ Taylor's theorem \\
$\bullet$ Hahn-Banach theorem \\
$\bullet$ Urysohn's lemma \\
$\bullet$ Stone's theorem (paracompactness of metrizable spaces) \\
$\bullet$ Stone's theorem (representations of boolean algebras) \\
$\bullet$ G\"odel's first incompleteness theorem \\
$\bullet$ reducibility of the configurations for the four color theorem \\
$\bullet$ correctness of Buchberger's algorithm \\
$\bullet$ fundamental theorem of Galois theory
\end{quote}
\adviwait
full translation (half finished) of a book on continuous lattices
\vspace{-2em}
\vfill
\end{slide}
\begin{slide}
\slidetitle{how difficult is it?}
formalizing mathematics: trivial or undoable?
\medskip
\adviwait
some metrics: \\
de Bruijn factor = ratio between formalization and informal text
\begin{quote}
currently: \textbf{4 times as big}
\end{quote}
\medskip
\adviwait
time needed to formalize a page from a textbook
\begin{quote}
currently: \textbf{1 week}
\end{quote}
(estimate: `all undergraduate math' will take 140 man-year)
\vfill
\end{slide}
\begin{slide}
\slidetitle{automation $\;\leftrightarrow\;$ human control}
\hbox to 0pt{\hskip\hsize{\vbox to 0pt{\vskip-.27cm\hbox to 0pt{\hss\includegraphics[0,0][100,136]{iceberg.jpg}}\vss}}\hss}%
mathematical reasoning is like an iceberg
\vspace{.29cm}
\hspace{1.8cm} \phantom{un}conscious part of reasoning $\longrightarrow$
\vspace{.12cm}
\hspace{1.8cm} unconscious part of reasoning $\longrightarrow$
\vspace{.85cm}
\adviwait
\textcolor{slidered}{the story of the formalizations of the \\ fundamental theorem of algebra}
\medskip
\adviwait
too much automation \\
`lost in proof space':
user doesn't understand the proof anymore \\
$\to\;$ formalizing becomes much harder
\adviwait
automation should focus on the unconscious part of the reasoning \\
automation should \textbf{not} amaze the user
\vspace{-2em}
\vfill
\end{slide}
\begin{slide}
\slidetitle{can the computer prove things that human mathematicians cannot?}
EQP, 1996:
\begin{center}
\textcolor{slidegreen}{all Robbins algebras are Boolean}
\end{center}
\adviwait
the computer is:
\begin{itemize}
\item[$\bullet$]
strong in combinatorial search through many cases
\item[$\bullet$]
weak in goal oriented proof \\
surprisingly trivial steps can't be proved automatically yet
\end{itemize}
\medskip
\adviwait
Shankar: focus on decision procedures instead of proof search \\
(decision procedure $=$ algorithm to answer a specific class of questions)
\begin{itemize}
\item[$\bullet$]
general purpose proof search doesn't work well
\item[$\bullet$]
domain specific proof generation is very useful
\end{itemize}
\vspace{-2em}
\vfill
\end{slide}
\begin{slide}
\sectiontitle{three systems}
\slidetitle{\textbf{Coq}}
Huet \& Coquand, Paulin \\
INRIA, France \\
1984--today
implemented in the ocaml dialect of ML \\
advantages:
\begin{itemize}
\item[$\bullet$]
popular for mathematics
\item[$\bullet$]
powerful logic
\end{itemize}
\medskip
\adviwait
prehistoric precursor: Automath
\vfill
\end{slide}
\begin{slide}
\slidetitle{propositions as types, proofs as objects}
Coq's logic: type theory
\adviwait
types with objects $\;\leftrightarrow\;$ propositions with proofs \\
`Curry-Howard isomorphism'
proofs become first class objects \\
\adviwait
$\to\;$ proofs can be used as function arguments
\medskip
division modeled as a ternary function
$$\mbox{\it div\/}(x,y,\mbox{`proof that $y\ne 0$'})$$
\adviwait
with this kind of division it is impossible to write $1/0$ \\
(no `proof object' for the third argument)
\vfill
\end{slide}
%\begin{slide}
%\slidetitle{reflection}
%logic is the mathematics of reasoning \\
%$\to\;$ logic is mathematics too
%
%possible to formalize logic \textbf{inside} a formal system
%\medskip
%\adviwait
%
%useful `trick' to implement provers (decision procedures) for Coq \\
%possible to prove provers correct \\
%generated proofs don't need to be checked anymore
%\medskip
%\adviwait
%
%`the two level approach'
%\begin{itemize}
%\item[$\bullet$]
%expressions representing mathematical objects
%\item[$\bullet$]
%expressions representing terms representing mathematical objects
%\end{itemize}
%(possibility to distinguish between `$(x + y)^2$' and `$x^2 + 2xy + y^2$')
%\vfill
%\end{slide}
\begin{slide}
\slidetitle{\textbf{HOL Light}}
recent reimplementation of the HOL system
Gordon, Harrison \& Slind \\
Cambridge, UK \\
1985--1995--today
implemented in the ocaml dialect of ML \\
advantages:
\begin{itemize}
\item[$\bullet$]
simple and elegant
\item[$\bullet$]
strong automation
\end{itemize}
\medskip
\adviwait
prehistoric precursor: LCF
\vfill
\end{slide}
\begin{slide}
\slidetitle{the de Bruijn principle in action}
HOL Light proof kernel: \\
285 lines of ML code = 8 pages of source text \\
possible to really understand this
\medskip
\adviwait
\begin{quote}
\begin{verbatim}
type hol_type = Tyvar of string
| Tyapp of string * hol_type list;;
\end{verbatim}
\begin{verbatim}
type term = Var of string * hol_type
| Const of string * hol_type
| Comb of term * term
| Abs of term * term;;
\end{verbatim}
\begin{verbatim}
type thm = Sequent of (term list * term);;
\end{verbatim}
\end{quote}
\medskip
\adviwait
10 primitive proof rules + 3 axioms
\vfill
\end{slide}
\begin{slide}
\slidetitle{taking mathematical objects in your hands}
HOL proofs = programs in the ML programming language
variables hold `mathematical objects' and `proved theorems' \\
(really: variables hold \textbf{terms} describing mathematical objects)
\begin{quote}
\verb|#|\adviwait\textcolor{slidered}{\tt let s = `\char`{x | x * x = \&2\char`}`;;} \\
\verb/s : term = `{x | x * x = &2}`/ \\
\verb|#|\adviwait\textcolor{slidered}{\tt let t = prove(`?x. x * x = \&2`,} \\
\textcolor{slidered}{\tt\ \ EXISTS\char`_TAC `sqrt(\&2)` THEN REWRITE\char`_TAC} \\
\textcolor{slidered}{\tt\ \ [GSYM POW\char`_2; SQRT\char`_POW2] THEN ARITH\char`_TAC);;} \\
\verb/t : thm = |- ?x. x * x = &2/ \\
\verb|#|
\end{quote}
\adviwait
programming with mathematical objects instead of integers and reals
\vfill
\end{slide}
\begin{slide}
\slidetitle{\textbf{Mizar}}
Trybulec \& Bylinski \\
Bialystok, Poland \\
1973--1989--today
implemented in the Delphi dialect of Pascal \\
advantages:
\begin{itemize}
\item[$\bullet$]
mathematics oriented
\item[$\bullet$]
large library
\end{itemize}
\medskip
\adviwait
prehistoric precursor: Mizar
\vfill
\end{slide}
\begin{slide}
\slidetitle{readable proofs}
Mizar proofs can be read as text
\begin{quote}
\begin{verbatim}
per cases; suppose ex x st not P[x];
then consider a such that A1: not P[a];
take a; assume P[a]; hence thesis by A1;
suppose A2: for x holds P[x];
consider a; take a; thus thesis by A2;
\end{verbatim}
\end{quote}
\medskip
\adviwait
proofs in most other systems are unreadable `code'
\begin{quote}
\begin{verbatim}
ASM_CASES_TAC `?x:A. ~P x` THEN
RULE_ASSUM_TAC (REWRITE_RULE[NOT_EXISTS_THM]) THENL
[POP_ASSUM (X_CHOOSE_TAC `a:A`); ALL_TAC] THEN
EXISTS_TAC `a:A` THEN ASM_REWRITE_TAC[]
\end{verbatim}
\end{quote}
\vfill
\end{slide}
\begin{slide}
\slidetitle{taking ZFC seriously}
\rlap{Bourbaki:}\phantom{de Bruijn: }ZFC = foundations in theory \\
\phantom{de Bruijn: }ZFC = foundations in practice\advirecord{?}{\rlap{?}}\advirecord{!}{\exclspace!}\adviplay{?}
\medskip
de Bruijn: ZFC doesn't match mathematical practice \\
what is the meaning of the ${}\cap{}$ of a triangle and a number?
\medskip
\adviwait
\adviplay[white]{?}\adviplay{!}
Mizar shows: Bourbaki propaganda is true \\
\textbf{it is practical to formalize real mathematics on a ZFC foundation}
\adviwait
\medskip
\begin{quote}
\begin{tabular}{lcr}
Mizar axioms (ZFC + inaccessibles) &$\to$& 28 lines \\
Mizar library &$\to$& 1,400,000 lines
\end{tabular}
\end{quote}
\medskip
(everything in the Mizar library is fully proved from the axioms)
\vfill
\end{slide}
\begin{slide}
\sectiontitle{an example in Mizar}
\slidetitle{Pythagorean triples}
a solution of
$$a^2 + b^2 = c^2$$
with no common divisors always has the form
$$a = m^2 - n^2 \qquad b = 2mn \qquad c = m^2 + n^2\medskip$$
\adviwait
\textbf{examples}
$$\begin{array}{ccrcrcr}
m = 2 \qquad n = 1 & \quad\to\quad & 3^2 & + & 4^2 & = & 5^2 \\
m = 3 \qquad n = 2 & \to & 5^2 & + & 12^2 & = & 13^2 \\
m = 4 \qquad n = 1 & \to & 15^2 & + & 8^2 & = & 17^2 \\
m = 4 \qquad n = 3 & \to & 7^2 & + & 24^2 & = & 25^2
\end{array}$$
\vspace{-2em}
\vfill
\end{slide}
\begin{slide}
\slidetitle{formal proof sketch}
\begin{flushleft}
\verb|reserve a,b,c,m,n for Nat;|
\end{flushleft}
\begin{flushleft}
\verb|let a,b,c; assume a^2 + b^2 = c^2;|\\
\verb|assume a,b are_relative_prime;|\\
\adviwait
\verb|then a is odd or b is odd;|\adviwait\verb| assume a is odd;|
\adviwait
\end{flushleft}
\begin{flushleft}
\verb|ex m,n st a = m^2 - n^2 & b = 2*m*n & c = m^2 + n^2|\\
\verb|proof|\\
\adviwait
\verb| b is even; c is odd;|\\
\adviwait
\verb|X: (c + a)/2,(c - a)/2 are_relative_prime;|\\
\adviwait
\verb| ((c + a)/2)*((c - a)/2) = (c^2 - a^2)/4 .= (b/2)^2;|\\
\verb| then ((c + a)/2)*((c - a)/2) is square;|\\
\adviwait
\verb| then (c + a)/2 is square & (c - a)/2 is square by X;|\\
\verb| consider m,n such that m^2 = (c + a)/2 & n^2 = (c - a)/2;|
\verb| take m,n;|\\
\end{flushleft}
\vspace{-2em}
\vfill
\end{slide}
\begin{slide}
\slidetitle{formal proof sketch (continued)}
\begin{flushleft}
\begin{color}{slidegray}
\verb| consider m,n such that m^2 = (c + a)/2 & n^2 = (c - a)/2;|\\
\verb| take m,n;|\\
\end{color}
\verb| thus a = (c + a)/2 - (c - a)/2 .= m^2 - n^2;|\\
\verb| b^2 = (c + a)*(c - a) .= 4*m^2*n^2 .= (2*m*n)^2;|\\
\verb| hence b = 2*m*n;|\\
\verb| thus c = (c + a)/2 + (c - a)/2 .= m^2 + n^2;|\\
\verb|end;|
\end{flushleft}
\adviwait
%\medskip
syntactically correct Mizar \\
semantically correct Mizar \\
too high level: Mizar cannot check the correctness
\adviwait
\begin{itemize}
\item[$\bullet$]
steps are too big for Mizar
\item[$\bullet$]
links between steps are missing
\end{itemize}
\vspace{-2em}
\vfill
\end{slide}
\begin{slide}
\slidetitle{a fragment of the full proof}
\begin{flushleft}
\advirecord{x1}{\tt\ then}\\
\advirecord{x2}{\tt X: (c + a)/2,(c - a)/2 are\char`_relative\char`_prime}\advirecord{x3}{\tt\ by Lm3}\advirecord{x4}{;}\\
\advirecord{x5}{\tt\ ((c + a)/2)*((c - a)/2) =}\advirecord{x6}{\tt\ ((c + a)*(c - a))/(2*2)}\\
\advirecord{x7}{\ \ \ by }\advirecord{x7a}{REAL\char`_1:35}\\
\advirecord{x8}{\ \ .= }\advirecord{x9}{\tt (c\^{}2 - a\^{}2)/4}\advirecord{x10}{\tt\ by }\advirecord{x10a}{SQUARE\char`_1:67}\\
\advirecord{x11}{\tt\ \ .= (b\^{}2)/(2*2)}\advirecord{x12}{\tt\ by H1,}\advirecord{x12a}{INT\char`_1:3}\\
\advirecord{x13}{\tt\ \ .= (b\^{}2)/(2\^{}2)}\advirecord{x14}{\tt\ by }\advirecord{x14a}{SQUARE\char`_1:def 3}\\
\advirecord{x15}{\tt\ \ .= (b/2)\^{}2}\advirecord{x16}{\tt\ by }\advirecord{x16a}{SQUARE\char`_1:69}\advirecord{x17}{\tt;}\\
\advirecord{x18}{\tt\ then ((c + a)/2)*((c - a)/2) is square}\advirecord{x19}{\tt\ by A1,Def1}\advirecord{x20}{\tt ;}\\
\advirecord{x21}{\tt\ then (c + a)/2 is square \& (c - a)/2 is square by X}\advirecord{x22}{\tt ,Lm4}\advirecord{x23}{\tt ;}\\
\advirecord{x24}{\tt\ then (ex m st m\^{}2 = (c + a)/2) \&}\\
\advirecord{x25}{\tt\ \ (ex n st n\^{}2 = (c - a)/2)}\advirecord{x26}{\tt\ by Def1}\advirecord{x27}{\tt ;}\\
\advirecord{x28}{\tt\ then }\advirecord{x29}{\tt consider m,n such that}\\
\advirecord{x30}{\tt A9:}\advirecord{x31}{\tt\ m\^{}2 = (c + a)/2 \& n\^{}2 = (c - a)/2;}
\end{flushleft}
\adviplay{x2}
\adviplay{x4}
\adviplay{x5}
\adviplay{x9}
\adviplay{x15}
\adviplay{x17}
\adviplay{x18}
\adviplay{x20}
\adviplay{x21}
\adviplay{x23}
\adviplay{x29}
\adviplay{x31}
\adviwait
\adviplay[slidered]{x6}
\adviplay[slidered]{x8}
\adviplay[slidered]{x11}
\adviplay[slidered]{x13}
\adviplay[slidered]{x24}
\adviplay[slidered]{x25}
\adviplay[slidered]{x27}
\adviwait
\adviplay[slidered]{x1}
\adviplay[slidered]{x3}
\adviplay[slidered]{x7}
\adviplay[slidered]{x7a}
\adviplay[slidered]{x10}
\adviplay[slidered]{x10a}
\adviplay[slidered]{x12}
\adviplay[slidered]{x12a}
\adviplay[slidered]{x14}
\adviplay[slidered]{x14a}
\adviplay[slidered]{x16}
\adviplay[slidered]{x16a}
\adviplay[slidered]{x19}
\adviplay[slidered]{x22}
\adviplay[slidered]{x26}
\adviplay[slidered]{x28}
\adviplay[slidered]{x30}
\adviwait
\adviplay{x6}
\adviplay{x8}
\adviplay{x11}
\adviplay{x13}
\adviplay{x24}
\adviplay{x25}
\adviplay{x27}
\adviplay{x1}
\adviplay{x3}
\adviplay{x7}
\adviplay{x7a}
\adviplay{x10}
\adviplay{x10a}
\adviplay{x12}
\adviplay{x12a}
\adviplay{x14}
\adviplay{x14a}
\adviplay{x16}
\adviplay{x16a}
\adviplay{x19}
\adviplay{x22}
\adviplay{x26}
\adviplay{x28}
\adviplay{x30}
\adviwait
\adviplay[slidered]{x7a}
\adviplay[slidered]{x10a}
\adviplay[slidered]{x12a}
\adviplay[slidered]{x14a}
\adviplay[slidered]{x16a}
\vspace{-2em}
\vfill
\end{slide}
\begin{slide}
\slidetitle{formal mathematics can talk about `higher' objects}
claim: \textbf{any} mathematics can be formalized
not only about basic objects like numbers and numeric functions \\
objects can be abstract and `large'
\medskip
\adviwait
example: Yoneda lemma
\begin{quote}
\verb|definition let A be |\advirecord{y1}{\tt Category}\adviplay{y1}\verb|;|\\
\verb| func Yoneda(A) ->|\\
\verb| |\advirecord{y2}{\tt Contravariant\char`_Functor}\adviplay{y2}\verb| of A,Functors(A,EnsHom(A))|\\
\verb| means|\\
\verb| for f being Morphism of A holds|\\
\verb/ it.f = [[<|cod f,?>,<|dom f,?>],<|f,?>];/\\
\verb|end;|
\end{quote}
\medskip
\adviwait
\adviplay[slidered]{y1}\adviplay[slidered]{y2}
\adviwait
observation: abstract math is easier to formalize than basic math
\vspace{-2em}
\vfill
\end{slide}
\begin{slide}
\sectiontitle{conclusion}
\slidetitle{isn't this all just engineering?}
this talk: the user's point of view
\medskip
\adviwait
\textbf{research topics}
\begin{itemize}
\item[$\bullet$]
the theory of logical foundations
logics: paradoxes, consistency, conservativity \\
\adviwait
type systems: confluence, termination, subject reduction
\adviwait
\item[$\bullet$]
the theory of proof search
\adviwait
\item[$\bullet$]
the theory of decision procedures
interaction between decision procedures \\
\adviwait
moving the decision procedures \textbf{inside} the logic: reflection
\end{itemize}
\medskip
\adviwait
but: `just engineering' is also important to get a usable system
\vspace{-2em}
\vfill
\end{slide}
\begin{slide}
\slidetitle{it might not be for you yet, but it's serious\exclspace!}
\begin{itemize}
\item[$\bullet$]
not yet practical
\item[$\bullet$]
interesting developments
\item[$\bullet$]
it might change the (mathematical) world
\end{itemize}
\bigskip
\adviwait
\begin{itemize}
\item[$\bullet$]
ancient Greeks: invention of proof
\item[$\bullet$]
nineteenth century: invention of rigor
\item[$\bullet$]
\textbf{today?}
\end{itemize}
\vfill
\end{slide}
\end{document}
|
http://lupinia.us/personal/radio/deregulation.tex | lupinia.us | CC-MAIN-2020-34 | application/x-tex | text/x-matlab | crawl-data/CC-MAIN-2020-34/segments/1596439738380.22/warc/CC-MAIN-20200809013812-20200809043812-00273.warc.gz | 72,750,485 | 3,338 | % Django HTML to LaTeX conversion
% By Natasha L.
% www.lupinia.net | github.com/lupinia
\documentclass[11pt,letterpaper]{article}
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\usepackage[T1]{fontenc}
\usepackage[bookmarks=true,bookmarksnumbered=true,colorlinks=true,linkcolor=magenta,urlcolor=blue]{hyperref}
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\begin{document}
\title{\Huge Deregulation and Commercial Radio}
\author{By Natasha L. - \url{www.lupinia.net}}
\date{Posted: June 24, 2005}
\maketitle
In America, the commercial radio industry has undergone a major reformation in recent years. What was once a diverse mass communications medium with hundreds of small, locally-owned business is now almost exclusively controlled by just a few major corporations. Why the sudden change? The Telecommunications Act of 1996. This piece of legislation essentially removed government regulation from the equation, allowing a single company to own hundreds of radio stations across the nation, placing the interests of big business above the welfare of consumers.
When radio communications technology was first discovered, it became evident very quickly that a single regulatory body was needed to manage radio spectrum bandwidth nationwide. Early on, corporations wanted to control this increasingly important natural resource, but the government gave the scepter of regulatory power to a new agency of the bureaucracy, the Federal Communications Commission. Its mission was, and still is, to manage the spectrum of available radio frequencies, and to prevent overlaps from occurring.
Once founded, the FCC assigned blocks of frequencies for various uses, including commercial, amateur radio, government, and military. Licenses to use the commercial bands were then sold at auctions, and each license assigned the buyer a callsign for identification (four digits for commercial broadcast radio), a frequency range to operate in, an acceptable transmitter location, and a maximum power output. Using this information, a broadcast radio company could then set up shop in the location on the license they purchased, and start broadcasting to the general public.
The commercial spectrum users filled their allocated band space, and started lobbying hard to get more. The FCC recently decided to assign an unused block of government frequencies to the commercial users, and sold those licenses at a special auction that generated \$20 billion in revenue. However, the new buyers complained that due to the stringent regulations on their industry, they were having difficulty getting set up. So, the corporate lobbyists for media and communications industries drafted the TCA, and it was pushed through Congress and voted on before a single congressman had a chance to read the bill. President Clinton signed the bill into law in 1996, and with that simple flick of a pen, the consumer protection regulations that had been in place for decades were tossed out of existence.
After winning this keystone victory in Congress, the media companies started the time-tested method of buying their competitors rather than trying to compete with them. Soon, a company called Clear Channel had acquired over 1,200 radio stations nationwide, roughly 60\% of the US’s commercial broadcast radio market. Combined with the other three radio giants of the US, over 90\% of US broadcast radio is owned by major media corporations, effectively wiping out any local-level competition and creating a corporate monopoly on radio entertainment.
As proven by history, monopolies never work for the good of the consumer. And, true to form, this monopoly on content is not benefiting anyone except Clear Channel and its ilk. These companies choose the type of content to air based not on what their listeners want to hear, but instead, based solely on what they deem to be the most profitable. A perfect example of this is the radio station Y100 (WPLY), based in Philadelphia, PA. This popular station was known far beyond the Delaware Valley area for its charismatic DJs, impeccable playlist selections, and community outreach activities for over 12 years. Then, without warning, the parent company abruptly shut down the station in its current form, and replaced it with a rap/urban station. Their reasoning for this was greater profitability from their advertisers, and higher listener numbers based on the demographics of the area. There was no input from the listeners of the original 100.3MHz station, just a marketing analysis and some new contracts with advertisers. This is not the way this industry should be run.
The Telecommunications Act of 1996 has had far-reaching detrimental implications in the radio communications industry. What was once a diverse market dominated by scores of small businesses is now controlled by a small number of large corporations, and consumers are being deprived of choices in entertainment. Deregulation laws like the TCA serve no one except the corporations, and they consistently harm the consumers who are meant to be protected by organizations like the FCC. Laws like the TCA, and the monopolies created by deregulation, need to be shut down to prevent further harm to our nation’s communications media, and to protect a squandered natural resource such as the radio spectrum.
\begin{center}
\line(1,0){250}
\end{center}
\section*{About the Author, and Contact Information}
Natasha L. is a web application developer, and avid photographer and writer, living in the DC metro area. Visit \url{www.lupinia.net} to learn more. Contact information, including an email form and links to other websites, can be found at \url{www.lupinia.net/contact}.
\copyright 2005 by Natasha L., and is free for distribution, but may not be modified or used for monetary gain. Original version and further downloads available at \url{http://www.lupinia.net/personal/radio/deregulation.htm}
\end{document} |
https://melusine.eu.org/syracuse/B/BaseCollege/Quatrieme/pythagore/applications/exo64.tex?enregistrement=ok | eu.org | CC-MAIN-2022-33 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2022-33/segments/1659882572198.93/warc/CC-MAIN-20220815175725-20220815205725-00372.warc.gz | 360,851,576 | 972 | %@Dif:2
{\em L'unité de longueur est le centimètre.}
Soit $ABC$ un triangle rectangle en $B$ tel que $AB=6$ et $BC=8$.
\begin{myenumerate}
\item Quel est le nom de l'hypoténuse de ce triangle ?
\item Calcule la longueur $AC$ en détaillant la démarche.
\item Trace le triangle $ABC$.
\end{myenumerate}
%@Commentaire: Exercice détaillé d'application directe. \`A faire rapidement après la leçon. |
http://kleine.mat.uniroma3.it/e/04-150.latex.mime | uniroma3.it | CC-MAIN-2019-13 | application/x-latex | message/rfc822 | crawl-data/CC-MAIN-2019-13/segments/1552912201455.20/warc/CC-MAIN-20190318152343-20190318174343-00314.warc.gz | 121,449,347 | 45,318 | Content-Type: multipart/mixed; boundary="-------------0405122338440"
This is a multi-part message in MIME format.
---------------0405122338440
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38 pages
---------------0405122338440
Content-Type: text/plain; name="04-150.keywords"
Content-Transfer-Encoding: 7bit
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Superselection, Operator algebra, constraint, compact group action,
Hilbert system, quantum field theory, Doplicher-Roberts duality
---------------0405122338440
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\title{\bf Superselection in the presence of constraints.}
\author{
{\sc Hellmut Baumgaertel} \\
{\footnotesize
Mathematical Institute, University of Potsdam,} \\
{\footnotesize
Am Neuen Palais 10, Postfach 601~553,} \\
{\footnotesize
D--14415 Potsdam, Germany.} \\
{\footnotesize
E-mail: baumg@rz.uni-potsdam.de} \\
{\footnotesize FAX: +49-331-977-1299} \\[1mm]
\and
{\sc Hendrik Grundling} \\[1mm]
{\footnotesize Department of Mathematics,} \\
{\footnotesize University of New South Wales,} \\
{\footnotesize Sydney, NSW 2052, Australia.} \\
{\footnotesize hendrik@maths.unsw.edu.au} \\
{\footnotesize FAX: +61-2-93857123}}
\date{RUNNING TITLE: Superselection and Constraints.}
\begin{document}
\maketitle
\begin{abstract}
For systems which contain both
superselection structure and constraints, we study compatibility
between constraining and superselection. Specifically, we start with a
generalisation of Doplicher-Roberts superselection theory
to the case of nontrivial centre, and a set of Dirac quantum constraints
and find conditions under which the superselection structures will
survive constraining in some form. This involves an analysis
of the restriction and factorisation of superselection structures.
We develop an example for this theory, modelled on interacting QED.
\end{abstract}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}
In heuristic quantum field theory, there are many examples of systems
which contain global charges (hence superselection structure) as well
as a local gauge symmetry (hence constraints). Most of these systems cannot
currently be written in a consistent mathematical framework, due to
the presence of interactions. Nevertheless, the mathematical structure
of superselection by itself has been properly developed
(cf.~\cite{DR, Bg, BW}),
as well as the
mathematical structure of quantum constraints \cite{Grundling85, Lledo,
lands}, hence one can at
least abstractly consider systems which contain both.
This will be the focus of our investigations in this paper.
We will address the natural intertwining questions for the
two structures, as well as compatibility issues.
There is a choice in how the problem of superselection with
constraints is posed mathematically. We will be guided by the most
important physics example in this class, which is that of
a quantized local gauge field, acting on a fermion field.
It has a Gauss law constraint
(implementing the local gauge transformations) as well as
a set of global charges (leading to superselection).
The architecture of the paper is as follows, in Sect.~2 we give a
brief summary of the superselection theory which we intend to use here.
We include recent results concerning the case of an observable algebra
with nontrivial centre (cf.~\cite{BL}), and some new results on
the field algebra.
In Sect.~3 we give a summary of quantum constraints, and
in Sect.~4 we collect our main results. The proofs for these
are in Sect.~6, and in Sect.~5 we present an example.
\section{Fundamentals of superselection}
In this section we summarize the structures from superselection
theory which we need. For proofs, we refer to the literature
if possible.
The superselection problem in algebraic quantum field theory,
as stated by the
Doplicher--Haag--Roberts~(DHR) selection criterion,
led to a profound body of work, culminating in
the general Doplicher--Roberts~(DR) duality theory for compact groups.
The DHR criterion selects a distinguished class of ``admissible''
representations of a quasilocal algebra $\al A.$ of observables,
where the centre
is trivial, i.e.
$Z(\al A.)=\C\un,$
or even
$\al A.$
is assumed to be simple.
This
corresponds to the selection of a DR--category
$\al T.$
of ``admissible'' endomorphisms
of $\al A.\,.$
Furthermore, from this endomorphism category
$\al T.$
the
DR--analysis constructs a C*--algebra $\al F.\supset\al A.$
together with a compact group action
$\alpha:\al G.\ni g\to\alpha_{g}\in\aut\al F.$
such that
\begin{itemize}
\item{}
$\al A.$ is the fixed point algebra of this action,
\item{}
$\al T.$ coincides with the category of all ``canonical
endomorphisms" of $\al A.$ (cf. Subsection~\ref{CanEnd}).
\end{itemize}
$\al F.$
is called a Hilbert extension of $\al A.$ in \cite{BW}.
Physically, $\al F.$ is identified as a field algebra and
$\al G.$ with a global gauge group of the system.
$\{\al F.,\alpha_{\al G.}\}$
is uniquely determined by
$\al T.$
up to
$\al A.$-module isomorphisms. Conversely,
$\{\al F.,\alpha_{\al G.}\}$
determines uniquely its category of all canonical endomorphisms.
Therefore one can state the equivalence of the ``selection
principle", given by
$\al T.$
and the ``symmetry principle", given by
$\al G.\,$. This duality is one of the crucial theorems of the
Doplicher-Roberts theory.
In contrast to the original theory of Doplicher and Roberts, we allow
here a nontrivial centre for $\al A..$ The reason for this is that when there
are constraints present, the system contains nonphysical information, so
there is no physical reason why $\al A.$ should be simple.
Only after eliminating the constraints should one require the
final observable algebra to be simple, hence having trivial centre.
Now a duality theorem for a C*--algebra with nontrivial centre has been
proven recently~\cite{BL, B2}, establishing a bijection between
distinguished
categories
of endomorphisms of
$\al A.$
and Hilbert extensions of $\al A.$ satisfying some additional conditions,
of which the most important
is: ${\al A.'\cap\al F.=Z(\al A.)}$
(i.e. the relative commutant is assumed to be minimal).
This will be properly explained below. This condition has already been
used by Mack and Schomerus~\cite{MS} as a ``new principle".
\subsection{Basic properties of Hilbert systems}
Below $\al F.$ will always denote a unital C*--algebra.
A Hilbert space $\al H.\subset
\al F.$ is called {\bf algebraic} if the scalar product $\langle\cdot,\cdot
\rangle$ of $\al H.$ is given by
$\langle A,B\rangle\un := A^{\ast}B$ for $A,\; B\in\al H.\,.$ Henceforth
we consider only finite-dimensional algebraic Hilbert spaces. The
support
$\hbox{supp}\,\al H.$
of $\al H.$ is defined by
$\hbox{supp}\,\al H.:=\sum_{j=1}^{d}\Phi_j\Phi_{j}^{\ast}$
where $\{\Phi_j\,\big|\,
j=1,\ldots,\,d\}$ is any orthonormal basis of $\al H..$
{\it Unless otherwise specified, we assume below that
each algebraic Hilbert space $\al H.$ considered,
satisfies ${\rm supp}\,\al H.
=\un.$}
We also fix a compact
C*-dynamical system
$\{\al F.,\al G.,\alpha\}$,
i.e.
$\al G.$
is a compact group and
$\alpha:\al G.\ni g\to\alpha_{g}\in\aut\al F.$
is a pointwise norm-continuous morphism.
For $\gamma\in\wh{\al G.}$
(the dual of $\al G.$) its {\bf spectral projection}
$\Pi_{\gamma}\in\al L.(\al F.)$
is defined by
\begin{eqnarray*}
\Pi_\gamma(F)&:=&\int_{\al G.}\ol\chi_\gamma(g).\,\alpha_{g}(F)\,dg
\quad\hbox{for all}\quad F\in\al F., \\[1mm]
\hbox{where:}\quad\qquad
\chi_\gamma(g)&:=&\dim\gamma\cdot\tr\pi(g),\quad\pi\in\gamma\,
\end{eqnarray*}
and its {\bf spectral subspace} $\Pi_\gamma\al F.$ satisfies
$\Pi_\gamma\al F.=\csp\{\al L.\subset\al F.\}$ where $\al L.$
runs through all invariant subspaces of $\al F.$
which transform under $\alpha\s{\al G.}.$ according to $\gamma$
(cf.~\cite{ES}).
Define the {\bf spectrum} of
$\alpha_{\al G.}$ by
\[
\spec\alpha_{\al G.}:=\set \gamma\in\wh{\al G.}, \Pi_\gamma\not=0.
\]
Our central object of study is:
\begin{defi}
The C*-dynamical system
$\{\al F.,\al G.,\alpha\}$
is called a {\bf Hilbert system} if
for each $\gamma\in\wh{\al G.}$
there is an algebraic Hilbert space
$\al H._\gamma\subset\al F.,$
such that
$\alpha_{\al G.}$
acts invariantly on
$\al H._\gamma,$
and the unitary representation
$\al G.\rest\al H._\gamma$
is in the equivalence class
$\gamma\in\wh{\al G.}$.
\end{defi}
\begin{rem}
Note that for a Hilbert system $\{\al F.,\al G.,\alpha\}$
we have necessarily that the algebraic Hilbert spaces
satisfy $\al H._\gamma\subset\Pi_\gamma\al F.$ for all $\gamma,$
and hence that $\spec\alpha\s{\al G.}.=\wh{\al G.}$ i.e.
the spectrum is {\it full}.
The morphism
$\alpha:\al G.\to \hbox{Aut}\,\al F.$
is necessarily faithful. So, since
$\al G.$
is compact and
$\hbox{Aut}\,\al F.$
is Hausdorff w.r.t. the topology of pointwise norm-convergence,
$\alpha$
is a homeomorphism of
$\al G.$
onto its image. Thus
$\al G.$
and
$\alpha_{\al G.}$
are isomorphic as topological groups.
\end{rem}
We are mainly interested in Hilbert systems whose fixed point
algebras coincide such that they appear as extensions of it.
\begin{defi}
A Hilbert system
$\{\al F.,\al G.,\alpha\}$
is called a {\bf Hilbert
extension} of a C*--algebra $\al A.\subset\al F.$ if $\al A.$ is the
fixed point algebra of ${\al G.}.$
Two Hilbert extensions
$\{\al F._i,\,\al G.\,,\alpha^{i}\},\;i=1,\,2$
of $\al A.$
(w.r.t. the same group $\al G.$)
are called
$\al A.\hbox{\bf--module isomorphic}$
if there is an isomorphism
$\tau:\al F._1\to\al F._2$
such that
$\tau(A)=A$
for
$A\in\al A.,$
and
$\tau$
intertwines the group actions, i.e.
$\tau\circ\alpha^{1}_g=\alpha^{2}_g\circ\tau.$
\end{defi}
\begin{rem}
\begin{itemize}
\item[(i)]
Group automorphisms of
$\al G.$
lead to $\al A.$-module isomorphic Hilbert extensions of
$\al A.$,
i.e. if
$\{\al F.,\al G.,\alpha\}$
is a Hilbert extension of
$\al A.$
and
$\xi$
an automorphism of
$\al G.$,
then the Hilbert extensions
$\{\al F.,\al G.,\alpha\}$
and
$\{\al F.,\al G.,\alpha\circ\xi\}$
are $\al A.$-module isomorphic.
So the Hilbert system
$\{\al F.,\al G.,\alpha\}$
depends, up to $\al A.$-module isomorphisms, only on
$\alpha_{\al G.}$,
which is isomorphic to
$\al G.$.
In other words, up to $\al A.$-module isomorphism we may identify
$\al G.$
and
$\alpha_{\al G.}\subset\aut\al F.$
neglecting the action
$\alpha$
which has no relevance from this point of view. Therefore in the
following, unless it is otherwise specified, we use the notation
$\{\al F.,\al G.\}$
for a Hilbert extension of
$\al A.$,
where
$\al G.\subset\aut\al F.$.
\item[(ii)]
As mentioned above, examples of
Hilbert systems arise in DHR--superselection theory
cf.~\cite{BW, Bg}.
There are also constructions by means of
tensor products
of Cuntz algebras
(cf.~\cite{DR2}). In these examples the
relative commutant
of the fixed point algebra
$\al A.$,
hence also its center,
is trivial. Another
construction for
$\al G.=\T$,
by means of the loop group
$C^{\infty}(S^{1},\,\T)$
is in \cite{BC}, and for this
$Z(\al A.)$
is nontrivial.
\end{itemize}
\end{rem}
\begin{rem}
\label{remark1}
A Hilbert system $\{\al F.,\,\al G.\}$ is a highly structured object;-
we list some important facts and properties (for details, consult
~\cite{Bg,BW}):
\begin{itemize}
\item[(i)]
The spectral projections
satisfy:
\begin{eqnarray*}
\Pi_{\gamma_1}\Pi_{\gamma_2} &=&
\Pi_{\gamma_2}\Pi_{\gamma_1}=\delta\s\gamma_1\gamma_2.\Pi_{\gamma_1} \\[1mm]
\|\Pi_\gamma\| &\leq& d(\gamma)^{3/2}\;,
\qquad d(\gamma):=\dim(\al H._\gamma)\;, \\[1mm]
\Pi_\gamma\al F. &=& \spa(\al AH._\gamma)\;, % \\[1mm]
\quad \Pi_{\iota}\al F.=\al A.\;,
\end{eqnarray*}
where
$\iota\in\wh{\al G.}$
denotes the trivial representation of $\al G..$
\item[(ii)]
Each $F\in\al F.$ is uniquely determined by its projections
$\Pi_\gamma F,$ $\gamma\in\wh{\al G.},$ i.e. $F=0$
iff $\Pi_\gamma F =0$ for all $\gamma\in\wh{\al G.},$
cf.~Corollary~2.6 of \cite {B2}.
\item[(iii)]
A useful
*-subalgebra of
$\al F.$ is
\[
\al F._{\rm fin}:= \set F\in\al F.,\Pi_\gamma F\not=0\quad\hbox{for
only finitely many $\gamma\in\wh{\al G.}$}.
\]
which is dense in $\al F.$ w.r.t. the C*--norm (cf.~\cite{S}).
\item[(iv)]
In $\al F.$ there is an $\al A.\hbox{--scalar product}$ given by
${\langle F,\, G\rangle_{\al A.}:=\Pi_\iota FG^*},$ w.r.t. which
the spectral projections are symmetric, i.e.
$\bra\Pi_\gamma F,G.=\bra F,\Pi_\gamma G.$
for all $F,\; G\in\al F.,$ $\gamma\in\wh{\al G.}$.
Using the $\al A.$-scalar product one can define a norm on
$\al F.,$
called the $\al A.\hbox{-norm}$
\[
\vert F\vert_{\al A.}:=\Vert\langle F,F\rangle\s{\al A.}.\Vert^{1/2},\quad
F\in \al F..
\]
Note that
$\vert F\vert_{\al A.}\leq \Vert F\Vert$
and that
$\al F.$
in general is not closed w.r.t. the $\al A.$-norm.
Then
for each $F\in\al F.$ we have that
$F=\sum_{\gamma\in\wh{\al G.}}\Pi_\gamma F$
where the sum on the right hand side is convergent w.r.t. the
$\al A.\hbox{--norm}$ but not necessarily w.r.t. the C*--norm $\|\cdot\|\,.$
We also have Parseval's equation:
$\langle F,F\rangle_{\al A.}
=\sum_{\gamma\in\wh{\al G.}}\langle\Pi_\gamma F,\Pi_\gamma F\rangle_{\al A.}
\;,$ cf. Proposition~2.5 in \cite{B2}.
Moreover
$\big|\Pi_\gamma\big|_{\al A.}=1$
for all $\gamma\in\wh{\al G.}$,
where $\vert\cdot\vert_{\al A.}$
denotes the operator norm of $\Pi_\gamma$ w.r.t. the norm
$\vert\cdot\vert_{\al A.}$ in $\al F.$.
\item[(v)]
Generally for a Hilbert system, the assignment $\gamma\to\al H._\gamma$
is not unique.
If
$U\in \al A.$
is unitary then also
$U\al H._\gamma\subset\Pi_{\gamma}\al F.$
is an $\al G.$-invariant algebraic Hilbert space carrying the representation
$\gamma\in\wh{\al G.}.$ Each
$\al G.$-invariant algebraic
Hilbert space
$\al K.$
which carries the representation
$\gamma\,$
is of this form, i.e. there is a unitary
$V\in\al A.$
such that
$\al K.=V\al H._{\gamma}.$
For a general $\al G.\hbox{--invariant}$
algebraic Hilbert space $\al H.\subset\al F.,$
we may have that $\al G.\rest\al H.$ is not irreducible,
i.e. it need not be of the form $\al K.=V\al H._{\gamma}.$
Below we will consider further conditions on the Hilbert system
to control the structure of these.
\item[(vi)]
Given two $\al G.\hbox{--invariant}$
algebraic Hilbert spaces
$\al H.,\al K.\subset\al F.,$
then
$\spa(\al H.\cdot\al K.)$
is also a $\al G.\hbox{--invariant}$
algebraic Hilbert space
which we will
briefly denote by $\al H.\cdot\al K..$
It is a realization of the tensor product
$\al H.\otimes\al K.$
within
$\al F.$
and
carries the tensor product of the representations of $\al G.$
carried by $\al H.$ and $\al K.$ in the obvious way.
\item[(vii)]
Let
$\al H.,\al K.$ be two $\al G.\hbox{--invariant}$
algebraic Hilbert spaces,
but not necessarily of support 1. Then there
is a natural isometric embedding
$\al J.:\al L.(\al H.,\al K.)\to\al F.$
given by
\[
\al J.(T):=\sum_{j,k}
t_{j,k}\Psi_{j}\Phi^{\ast}_{k},\quad t_{j,k}\in \C,
\quad T\in\al L.(\al H.,\al K.)
\]
where
$\{\Phi_{k}\}_{k},\{\Psi_{j}\}_{j}$
are orthonormal bases of
$\al H.$ and $\al K.$ respectively, and where
\[
T(\Phi_{k})=\sum_{j}t_{j,k}\Psi_{j},
\]
i.e.
$(t_{j,k})$
is the matrix of $T$ w.r.t. these orthonormal bases. One has
\[
T(\Phi)=\al J.(T)\cdot\Phi,\quad \Phi\in\al H..
\]
This implies: if
$T_{j}\in\al L.(\al H._{j},\al K._{j}),j=1,2,$
hence
$T_{1}\otimes T_{2}\in\al L.(\al H._{1}\al H._{2},\al K._{1}\al K._{2}),$
then
${\al J.(T_{1}\otimes T_{2})\Phi_{1}\Phi_{2}}=\al J.(T_{1})\Phi_{1}\al J.(T_{2})\Phi_{2}$
for
$\Phi_{j}\in\al H._{j}$.
Moreover
$\al J.(T)\in\al A.$
iff
$T\in\al L._{\al G.}(\al H.,\al K.),$
where
$\al L._{\al G.}(\al H.,\al K.)$
denotes the linear subspace of
$\al L.(\al H.,\al K.)$
consisting of all intertwining operators of the representations
of
$\al G.$
on
$\al H.$ and $\al K.$ (cf. p. 222 ~\cite{BW}).
\end{itemize}
\end{rem}
\subsection{The category of $\al G.$-invariant algebraic
Hilbert spaces}
The $\al G.$-invariant algebraic Hilbert spaces
$\al H.$
of
$\{\al F.,\al G.\}$
form the objects of a category
$\al T._{\al G.}$
associated to
$\{\al F.,\al G.\}$
whose arrows are given by the elements of
$(\al H.,\,\al K.):=\al J.(\al L._{\al G.}(\al H.,\al K.))\subset\al A.$.
It is already large enough to carry all tensor products of the representations of
$\al G.$ on its objects by Remark~\ref{remark1}(vi)
(though not necessarily subrepresentations and direct sums).
First, let us state
some
of its rich structure (cf.~\cite{BW,DR2}):
\begin{pro}
\label{perm&conj}
For $\{\al F.,\al G.\}$ the category $\al T._{\al G.}$
is a {\bf tensor C*-category}, i.e. the arrow spaces $(\al H.,\,\al K.)$
are Banach spaces such that \chop
$\bullet$ w.r.t. composition of arrows $R,\, S$ we have
$\|R\circ S\|\leq\|R\|\|S\|,$\chop
$\bullet$ there is an antilinear involutive contravariant functor
$*:\al T._{\al G.}\to\al T._{\al G.}$ such that
$\|R^*\circ R\|=\|R\|^2$ for all arrows $R$ with the same range and domain
(here the functor $*$ is given by the involution in $\al F.)$\chop
$\bullet$ There is an associative product $\cdot$ on $\ob\al T._{\al G.}$
and an identity object $1\in\ob\al T._{\al G.}$ (i.e. $1\cdot\al H.=\al H.
=\al H.\cdot 1)$ and there is an associative bilinear product $\times$
of the arrows, such that if $R\in(\al H.,\al K.)$ and
$R'\in(\al H.',\al K.')$ then $R\times R'\in(\al H.\cdot\al H.',\,
\al K.\cdot\al K.').$ Moreover we require that for $R,\;R'$ as above:
\begin{equation}
1_\iota\times R=R\times 1_\iota=R\;,\quad (R\times R')^*=R^*\times R'^*\,,
\end{equation}
where $1_\iota\in(1,1)$ is the identity arrow, as well as the interchange law
\[
(S\circ R)\times (S'\circ R')=(S\times S')\circ (R\times R')\,,
\]
whenever the left hand side is defined.\chop
Here in $\al T._{\al G.},$ the product $\cdot$ is given by the product
of $\al F.,$
the identity object is
$1:=\C\un$ and the product
$\times$ is defined by
\[
R\times R':= \al J.(T\otimes T'),
\]
for
$R=\al J.(T),\,R'=\al J.(T'),$ where $T\in\al L._{\al G.}(\al H.,\al K.),\,
T'\in\al L._{\al G.}(\al H.',\al K.').$
Note that
$(1,1)=(\C\un,\C\un)=\C\un$,
i.e.
$1_{\iota}=\un.$
\end{pro}
$\al T._{\al G.}$ has additional important structures
(permutation and conjugation), which we will consider below in
Subsection~\ref{PermConj}.
We need to examine conditions to require of $\{\al F.,\,
\al G.\}$ to ensure that $\al T._{\al G.}$
carries subrepresentations and direct sums.
\begin{defi}
Let $\al H.,\,\al K.\in\ob\al T._{\al G.},$ and define
$\al H.<\al K.$
to mean that there is an orthoprojection
$E$
on
$\al K.$
such that
$E\al K.$
is invariant w.r.t.
$\al G.$
and the representation
$\al G.\rest\al H.$
is unitarily equivalent to
$\al G.\rest E\al K..$
Call $\al H.$ a {\bf subobject} of $\al K.\,.$
\end{defi}
It is easy to see that $<$ is a partial order.
Note that
$\al H.<\al K.$
iff there is an isometry
$V\in\al L._{\al G.}(\al H.,\al K.)$
such that
$VV^{\ast}=:E$
is a projection of
$\al K.$,
i.e.
$V\al H.=E\al K..$
Then
$\al J.(V)\in\al A.$
and
$E\al K.=\al J.(V)\cdot\al H..$
If
$E\in\al L._{\al G.}(\al K.)$
is an orthoprojection
$0<E<\un,$
i.e.
$E$
is a reducing projection for the representation of
$\al G.$
on
$\al K.$,
then the question arises whether there is an object
$\al H.$
such that the representations on
$\al H.$
and
$E\al K.$
are unitarily equivalent. This suggests the concept of {\it
closedness} of
$\al T._{\al G.}$
w.r.t. subobjects.
\begin{defi}
The category
$\al T._{\al G.}$
is {\bf closed w.r.t. subobjects} if to each
$\al K.\in\hbox{Ob}\,\al T._{\al G.}$
and to each nontrivial orthoprojection
$E\in\al L._{\al G.}(\al K.)$
there is an isometry
$\wh{V}\in\al A.$
with
$\wh{V}\wh{V}^{\ast}=\al J.(E).$
In this case
$\al H.:=\wh{V}^{\ast}\cdot\al K.$
is a subobject
$\al H.<\al K.$
assigned to
$E$,
where
$\wh{V}=\al J.(V)$ for some isometry $V\in\al L._{\al G.}(\al H.,\al K.)$
with $VV^*=E.$
\end{defi}
Next, we consider when an object of $\al T._{\al G.}$ carries
the direct sum of the representations of two other objects.
If
$V,W\in\al A.$
are isometries with
$VV^{\ast}+WW^{\ast}=\un$
and
$\al H.,\al K.\in\hbox{Ob}\,\al T._{\al G.}$
then
we call the algebraic Hilbert space
$V\al H.+W\al K.$
of support 1 a {\bf direct sum} of
$\al H.$ and $\al K.$.
It is $\al G.$-invariant and carries the direct sum of the
representations on
$\al H.$ and $\al K.$
but in general depends on the choice of isometries $V,\;W.$
We define
\begin{defi}
\begin{itemize}
\item[(i)]
The category
$\al T._{\al G.}$
is {\bf closed w.r.t. direct sums} if to each
$\al H._{1},\al H._{2}\in\ob\,\al T._{\al G.}$
there is an object
$\al K.\in\ob\,\al T._{\al G.}$
and there are isometries
$V_{1},V_{2}\in\al A.$
with
$V_{1}V_{1}^{\ast}+V_{2}V_{2}^{\ast}=\un$
such that
$\al K.=V_{1}\al H._{1}+V_{2}\al H._{2}$
(then
$V_{1}\in(\al H._{1},\al K.)$
and
$V_{2}\in(\al H._{2},\al K.)$
follow).
\item[(ii)]
A C*-algebra
$\al A.$
satisfies {\bf Property B} if there are isometries
$V_{1},V_{2}\in\al A.$
such that
$V_{1}V_{1}^{\ast}+V_{2}V_{2}^{\ast}=\un.$
A Hilbert system
$\{\al F.,\al G.\}$
is said to satisfy {\bf Property B} if its fixed point algebra
$\al A.:=\Pi_{\iota}\al F.$
satisfies Property B.
\end{itemize}
\end{defi}
\begin{rem}
For a Hilbert system
$\{\al F.,\al G.\}$ we have:
\begin{itemize}
\item[(i)] It
satisfies Property B iff
$\al T._{\al G.}$
is closed w.r.t. direct sums.
\item[(ii)]
For nonabelian
$\al G.,$
the category $\al T._{\al G.}$ is closed w.r.t. subobjects iff
it is closed w.r.t. direct sums iff it has Property B
cf.~Prop.~3.5 of~\cite{B2}.
\item[(iii)]
In the case that
$\al G.$
is abelian, the theory simplifies.
This is because we already have Pontryagin's duality theorem,
hence it is not necessary to consider closure under
subobjects and direct sums to obtain a duality theory.
\end{itemize}
\end{rem}
\subsection{The category of canonical endomorphisms}
\label{CanEnd}
The main aim of DR--theory is to obtain an intrinsic structure on $\al A.$
from which we can reconstruct the Hilbert system $\HS$ in an essentially unique
way. Here we want to transport the rich structure of $\al T._{\al G.}$ to $\al A.\,.$
\begin{defi}
To each $\al G.\hbox{--invariant}$ algebraic Hilbert space $\al H.\subset
\al F.$
there is assigned a corresponding
{\bf inner endomorphism} $\rho\s{\al H.}.\in\endo\al F.$ given by
\[
\rho\s{\al H.}.(F):=\sum_{j=1}^{d(\al H.)}\Phi_jF\Phi_j^*\;,
\]
where $\{\Phi_j\,\big|\,j=1,\ldots,\,d(\al H.)\}$ is any orthonormal basis of
$\al H..$ Note that $\rho\s{\al H.}.$ preserves $\al A.\,.$
A {\bf canonical endomorphism} is the restriction of an inner endomorphism
to $\al A.,$ i.e. it is of the form
$\rho_{\al H.}\rest\al A.\in\mbox{End}\,\al A.\,.$
\end{defi}
\begin{rem}
\label{remark2}
\begin{itemize}
\item[(i)]
The definition of the canonical endomorphisms
uses
$\al F.$
explicitly. The question arises whether the
canonical
endomorphisms can be
characterised by intrinsic properties
within
$\al A.$.
This interplay between the
$\rho_{\al H.}$
and the
$\rho_{\al H.}\rest\al A.$
plays an essential role in the DR-theory.
Below, we omit
the restriction symbol and regard the
$\rho_{\al H.}$
also as endomorphisms of
$\al A.$.
\item[(ii)]
If the emphasis is only on the representation
$\gamma$
and not on its corresponding algebraic Hilbert space
$\al H._{\gamma},$
we will write
$\rho_{\gamma}$
instead of
$\rho_{\al H._{\gamma}}$.
\item[(iii)]
Note that $\Phi A=\rho\s{\al H.}.(A)\Phi$ for all
$\Phi\in\al H.$ and $A\in\al A..$
\item[(iv)]
Note that the identity endomorphism $\iota$ is assigned to
$\al H.=\C\un,$
i.e. $\rho\s{\C\un}.:=\iota.$
\item[(v)]
Let
$\al H.,\al K.$
be as before, then
$\rho\s{\al H.}.\circ\rho\s{\al K.}.=\rho\s{\al H.\cdot\al K.}..$
\item[(vi)]
The map $\rho$ from $\ob\al T._{\al G.}$ to the canonical endomorphisms
is in general not injective. In fact we have:
if $\al H.,\al K.\in\ob\al T._{\al G.},$
then
$\rho_{\al H.}\rest\al A.=\rho_{\al K.}\rest\al A.$
iff
$\Psi^{\ast}\Phi\in\al A.'\cap\al F.$
for all
$\Phi\in\al H.,\Psi\in\al K.\,,$
cf. Prop.~3.9 in \cite{B2}.
\end{itemize}
\end{rem}
\begin{defi}
Define $\al T.$ to be the category with objects the
canonical endomorphisms, and arrows the intertwiner spaces, where the
{\bf intertwiner space} of canonical endomorphisms
$\sigma,\;\tau\in\endo\al A.$
is:
\[
(\sigma,\,\tau):=\set X\in\al A.,X\sigma(A)=\tau(A)X\quad\hbox{for all}
\;{A\in\al A.}.\;.
\]
and this is a complex Banach space.
For $A\in(\sigma,\sigma'),$ $B\in(\tau,\tau'),$ we define
${A\times B}:=A\sigma(B)\in{(\sigma\tau,\,\sigma'\tau')\,.}$
We will say that $\sigma,\;\tau\in\endo\al A.$ are
{\bf mutually disjoint} if ${(\sigma,\,\tau)}=\{0\}$ when
$\sigma\not=\tau.$
\end{defi}
\begin{rem}
\label{remark3}
\begin{itemize}
\item[(i)]
We have
$(\iota,\,\iota)=Z(\al A.):=$ centre of $\al A..$
\item[(ii)]
The composition of two canonical endomorphisms (which corresponds to
products of the generating Hilbert spaces, see Remark 2.13 (v), i.e. to
tensor products of representations) satisfies the correct compatibility conditions
with the product $\times$ of intertwiners
to ensure that $\al T.$ is a C*-tensor category cf. Prop.~\ref{perm&conj} and
\cite{DR}.
The identity object is $\iota.$
\item[(iii)] Recall the isometry
$\al J.:\al L.\s{\al G.}.(\al H.,\al K.)
\longrightarrow \al A.$ encountered in Remark~\ref{remark1}(vii).
We claim that
its image is in fact contained in ${\left(\rho\s{\al H.}.,\,
\rho\s{\al K.}.\right)}.$ To see this, let $\Phi\in\al H.,\;
A\in\al A.$
and
$T\in\al L._{\al G.}(\al H.,\al K.).$
Then
\[
\al J.(T)\rho\s{\al H.}.(A)\Phi=\al J.(T)\Phi\cdot A=
T(\Phi)\cdot A=\rho\s{\al K.}.(A)T(\Phi)=
\rho\s{\al K.}.(A)\al J.(T)\cdot\Phi
\]
hence
\[
\al J.(T)\rho\s{\al H.}.(A)=\rho\s{\al K.}.(A)\al J.(T)
\]
i.e. $\al J.(T)\in {\left(\rho\s{\al H.}.,\,
\rho\s{\al K.}.\right)}$
or
\begin{equation}
\label{nonful}
(\al H.,\,\al K.)=
\al J.(\al L._{\al G.}(\al H.,\al K.))\subseteq
(\rho_{\al H.},\,\rho_{\al K.}).
\end{equation}
In general, the inclusion is proper.
Note that for
$R\in(\al H.,\al K.),\; R'\in(\al H.',\al K.')$
we have
$\al J.(R\otimes R')=R\rho_{\al H.}(R'),$
i.e.
$\times$
restricted to the
$(\al H.,\al K.)'s$
coincides with the definition of
$\times$
in Proposition~\ref{perm&conj} of the category
$\al T._{\al G.}.$
\end{itemize}
\end{rem}
Next we would like to define the concepts of subobject and direct sums
on $\ob\al T.$ compatibly with those on $\ob\al T._{\al G.}$
under the morphism $\rho.$ Recall that $\al H.<\al K.$ iff we have an isometry
$V\in\al L.\s{\al G.}.(\al H.,\,\al K.)$ and a projection $E\in
\al L.\s{\al G.}.(\al K.)$
with $V\al H.=E\al K.=\al J.(E)\cdot\al K.=\al J.(V)\cdot\al H..$
Then by (\ref{nonful}) we get that
$\al J.(V)\in
(\rho_{\al H.},\rho_{\al K.})$
and
$\al J.(E)\in
(\rho_{\al K.},\rho_{\al K.}).$
Note that if $\al L.=V\al H.+W\al K.$
for isometries
$V,\,W\in\al A.$ with $VV^*+WW^*=\un,$ then
$V\in(\rho\s{\al H.}.,\rho\s{\al L.}.)$ and $W\in(\rho\s{\al K.}.,
\rho\s{\al L.}.).$
\begin{defi}
\begin{itemize}
\item[(i)]
$\tau\in\ob\al T.$ is a {\bf subobject}
of $\sigma\in\ob\al T.,$
denoted ${\tau<\sigma,}$ if
there
is an isometry
$V\in (\tau,\sigma)$.
In this case
$\tau(\cdot)=V^{\ast}\sigma(\cdot)V$
and
$VV^{\ast}=:E\in (\sigma,\sigma)$
follow.
\item[(ii)]
$\lambda\in\ob\,\al T.$
is a {\bf direct sum} of
$\sigma,\tau\in\ob\,\al T.,$
if there are isometries
$V\in(\sigma,\lambda),\,W\in(\tau,\lambda)$
with
$VV^{\ast}+WW^{\ast}=\un$
such that
\[
\lambda(\cdot)=V\sigma(\cdot)V^{\ast}+W\tau(\cdot)W^{\ast}.
\]
\end{itemize}
\end{defi}
\begin{rem}
\label{Tsubobj}
\begin{itemize}
\item[(i)]
The subobject relation
$\tau<\sigma$
is again a partial order, because
$\tau<\sigma$
and
$\sigma<\mu$
imply the existence of isometries
$V\in (\tau,\sigma),\,W\in (\sigma,\mu)$.
Then
$WV\in (\tau,\mu)$
is also an isometry, i.e.
$\tau<\mu$.
\item[(ii)]
A direct sum as defined above
is only unique up to unitary equivalence, i.e. if
$\lambda,\,\lambda'$
are direct sums of $\sigma,\tau\in\ob\,\al T.,$ then there is a unitary
$U\in(\lambda,\lambda').$
\item[(iii)]
We have
$\rho\s{V\al H.+W\al K.}.(\cdot)=V\rho_{\al H.}(\cdot)V^{\ast}+
W\rho_{\al K.}(\cdot)W^{\ast}$
where
the isometries $V,\,W\in\al A.$ satisfy $VV^*+WW^*=\un\,.$
Also, if $\al H.<\al K.,$ then
$\tau:=\rho_{\al H.}<\rho_{\al K.}=:\sigma.$
However, this does not mean that the partial order
$\tau<\sigma$
can be {\it defined} by
$\al H.<\al K.$
because
the transitivity can be violated for some choices of $\al H.,\,\al K.$
cf. Remark~\ref{remark2}(vi).
\end{itemize}
\end{rem}
The closedness of
$\al T.$
w.r.t. direct sums is defined by the closedness of
$\al T._{\al G.}$
w.r.t. direct sums.
The closedness w.r.t. subobjects for
$\al T.$
is defined by the closedness w.r.t. subobjects for
$\al T._{\al G.}$
in the following sense: If
\begin{equation}
\label{endoH}
\lambda=\rho_{\al H.}\in\ob\al T.
\end{equation}
is given then for all
$\al H.$
satisfying (\ref{endoH}) and to each nontrivial
projection
$E\in\al J.(\al L._{\al G.}(\al H.))$
there is an isometry
$V\in\al A.$
with
$VV^{\ast}=E.$
Then
\begin{pro}
If
$\{\al F.,\al G.\}$ is nonabelian and
satisfies Property B then
$\al T.$
is closed w.r.t. direct sums and subobjects.
\end{pro}
\subsection{Connection between $\al T._{\al G.}$ and $\al T.$
and further structures.}
\label{PermConj}
In the following we assume that
$\{\al F.,\al G.\}$
satisfies Property B.
There is a very important relation between the two categories $\al T._{\al G.}$
and $\al T.,$ obtained as follows. The two assignments
$\rho:\hbox{Ob}\,\al T._{\al G.}\to\al T.$
(by
$\al H.\to\rho_{\al H.})$
and
$\al J.:\al L._{\al G.}((\al H.,\al K.))\to(\rho_{\al H.},\rho_{\al K.})$
combine into a faithful categorial morphism from
$\al T._{\al G.}$
to
$\al T.$
which is compatible with direct sums and subobjects (cf. Remark~\ref{Tsubobj}(iii)) but
is not full in general, i.e. the inclusion in Equation~(\ref{nonful})
is improper for some
$\al H.$
and
$\al K.$.
If
$\al A.'\cap\al F.=\C\un,$
then this categorial morphism becomes an isomorphism, cf. Prop. 3.12 in \cite{B2}.
The category $\al T._{\al G.}$
has the following additional structures
(\cite{BW,DR2}):
\begin{pro}
\label{perm&conj2}
For $\{\al F.,\al G.\}$ the category $\al T._{\al G.}$
satisfies:
\begin{itemize}
\item[(1)] it has a {\bf permutation structure}, i.e. a map
$\epsilon$ from
$\ob\al T._{\al G.}\times\ob\al T._{\al G.}$
into the arrows such that
\begin{itemize}
\item[(i)]
$\epsilon(\al H.,\al K.)\in (\al H.\al K.,\al K.\al H.)$
is a unitary.
\item[(ii)]
$\epsilon(\al H.,\al K.)\epsilon(\al K.,\al H.)=\un$.
\item[(iii)]
$\epsilon(1,\,\al H.)=\epsilon(\al H.,1)=\un$.
\item[(iv)]
$\epsilon(\al H.\al K.,\al L.)=\epsilon(\al H.,\al L.)\rho_{\al H.}(\epsilon
(\al K.,\al L.))$.
\item[(v)]
$\epsilon(\al H.',\al K.')A\times B=B\times A\epsilon(\al H.,\al
K.)$\quad for all $A\in (\al H.,\al H.'),\,B\in (\al K.,\al K.')$.
\end{itemize}
For $\al T._{\al G.}$ the permutation structure is
given by
\[
\epsilon(\al H.,\al K.):=\al J.(\Theta(\al H.,\al K.))
=\sum_{j,k}\Psi_{j}\Phi_{k}\Psi_{j}^{\ast}\Phi_{k}^{\ast}
\]
where $\Theta$ is the flip operator
$\al H.\otimes\al K.\rightarrow\al K.\otimes\al H.,$
and where
$\{\Phi_{k}\}_{k},\,\{\Psi_{j}\}_{j}$
are orthonormal bases of
$\al H.$ and $\al K.$, respectively.
\item[(2)] It has a {\bf conjugation structure}
i.e. for each
$\al H.\in\ob\al T._{\al G.}$
there is a conjugated object
$\overline{\al H.}\in\ob\al T._{\al G.}$,
carrying the conjugated representation of
$\al G.$
and there are conjugate arrows
$R_{\al H.}\in(1,\overline{\al H.}\al H.),$
$S_{\al H.}=\epsilon(\overline{\al H.},\al H.)R_{\al H.}$
such that
\[
S_{\al H.}^{\ast}\rho\s{\al H.}.(R_{\al H.})=\un,\quad
R_{\al H.}^{\ast}\rho\s{\overline{\al H.}}.(S_{\al H.})=\un.
\]
For $\al T._{\al G.}$ we have
$R_{\al H.}:=\sum_{j}\overline{\Psi}_{j}\Psi_{j}$,
where
$\{\overline{\Psi}_{j}\}_{j}$
is an orthonormal basis of
$\overline{\al H.}$.
If
$\al H.$
carries the representation
$\oplus_{j}\gamma_{j},\,\gamma_{j}\in\wh{\al G.},$
then
$\overline{\al H.}$
is given by a direct sum of
$\al H._{\overline{\gamma_{j}}},$
where
$\overline{\gamma_{j}}\in\wh{\al G.}$
represents the conjugated representation of
$\gamma_{j}.$
\end{itemize}
\end{pro}
\begin{rem}
Using the categorial morphism from
$\al T._{\al G.}$
to
$\al T.$
we equip
$\al T.$
with the image permutation and conjugation structures of those on
$\al T._{\al G.}$.
Note that for the image permutation structure in
$\al T.,$
property (v) need not hold for {\it all} arrows (cf. Remark~\ref{remark3}(iii)).
\end{rem}
For the next definition, observe
first that from the operations defined for an abstract tensor category
(cf. Prop.~\ref{perm&conj}), we can define isometries and projections in
its arrow spaces, i.e. an arrow $V\in(\lambda,\tau)$ is an isometry if
$V^*\circ V=1_\lambda,$ and an arrow $E\in(\lambda,\lambda)$
is a projection if $E=E^*=E\circ E\,.$
\begin{defi}
An {\bf (abstract) DR-category} is an
(abstract) tensor C*-category $\al C.$
with $(1,1)=\C\un$ which has a permutation and a conjugation structure,
and has direct sums
and subobjects, i.e. to all objects $\lambda,\sigma$ there is an object $\tau$
and isometries $V\in(\lambda,\tau),\,W\in(\sigma,\tau)$
such that $VV^{\ast}+WW^{\ast}=1_{\tau}$,
and to each nontrivial projection $E\in(\lambda,\lambda)$ there is an object
$\sigma$ and an isometry $V\in(\sigma,\lambda)$
such that $E=VV^{\ast}.$
\end{defi}
If the Hilbert system $\HS$ satisfies Property B then $\al T._{\al G.}$
is an example of a DR-category, but not necessarily $\al T.$
(since property (v) in Prop.~\ref{perm&conj2} need not hold for all arrows).
However, if additionally
$\al A.'\cap\al F.=\C\un$
holds then also
$\al T.$
is a DR-category.
\subsection{Duality Theorems}
Unless otherwise specified, in the following we assume Property
B for $\HS$ when
$\al G.$
is nonabelian.
The DR-theorem
produces
a bijection between pairs
\[
\{\al A.,\al T.\} \quad\hbox{and}\quad \HS\,,
\]
where $\al T.$ is a DR-category of unital endomorphisms of the
unital C*-algebra $\al A.$ with $Z(\al A.)=\C\un,$ and
$\HS$ is a Hilbert extension of $\al A.$ having trivial relative
commutant, i.e.~$\al A.'\cap\al F.=\C\un$ (see
\cite{DR,DR5,B3}).
The DR-theorem says that in the case of
Hilbert extensions of $\al A.$
with trivial relative commutant, the category $\al T. $
of all canonical endomorphisms can indeed be characterized
intrinsically by their abstract algebraic properties
as endomorphisms of $\al A.$
and a corresponding bijection can be established.
In this subsection we want to state how to obtain such a bijection
for C*-algebras $\al A.$ with nontrivial center
$\al Z.\supset\C\un.$
A first problem is that the category $\al T._\al G.$ and
$\al T.$ {\em need not} be isomorphic anymore, cf. Remark~\ref{remark3}(iv)
and Remark~\ref{remark2}(vi), since now we have
\[
\C\un\not=\al Z.\subseteq\al A.'\cap\al F.\,.
\]
We will investigate in the following the class
of Hilbert extensions $\HS$ with compact group $\al G.$
and where the relative commutant satisfies the following
{\em minimality} condition
\begin{defi}
A Hilbert system
$\{\al F.,\al G.\}$
is called {\bf minimal} if the condition
\begin{equation}
\label{CZ}
\al A.'\cap\al F.=Z(\al A.)\;.
\end{equation}
is satisfied.
\end{defi}
Then we have cf. Prop.~4.3 of \cite{B2}:
\begin{pro}
\label{disjZ}
Let
$\HS$
be a given Hilbert system. Then
$\al A.'\cap\al F.=Z(\al A.)$ iff
$(\rho_{\gamma},\rho_{\gamma'})=\{0\}$
for
$\gamma\neq\gamma'$,
i.e. iff the set
$\{\rho_{\gamma}\;\big|\;\gamma\in\wh{\al G.}\}$
is mutually disjoint.
\end{pro}
Observe that in any Hilbert system,
for each $\tau\in
\ob\al T.$ the space ${\got h}_\tau:=
\al H._\tau Z(\al A.),$ (where $\al H._\tau $
is a $\al G.\hbox{--invariant}$ algebraic Hilbert space)
is a $\al G.\hbox{--invariant}$ right Hilbert
$Z(\al A.)\hbox{--module}$ i.e. there is a nondegenerate inner product taking
its values in $Z(\al A.)$
and it is $\langle A,B\rangle=A^*B\,.$
Now we have cf. {Prop. 3.1 \cite{BL2}}:
\begin{pro}
\label{prop0}
Let $\HS$ be a given minimal Hilbert system,
then the correspondence ${\tau\leftrightarrow{\got h}_\tau}$
is a bijection. Thus ${\got h}_\tau=
\al H._\tau Z(\al A.)$ is independent of the choice of
$\al H._\tau,$ providing that $\tau=\rho\s{\al H._\tau}..$
This bijection satisfies the conditions
\begin{eqnarray*}
\sigma\circ\tau &\longleftrightarrow&
{\got h}_\sigma\cdot{\got h}_\tau \\[1mm]
\lambda=(\Ad V)\circ\sigma+(\Ad W)\circ\tau
&\longleftrightarrow&
{\got h}\s\lambda.=V{\got h}_\sigma+W{\got h}_\tau\;.
\end{eqnarray*}
\end{pro}
Thus for minimal Hilbert systems, the
$Z(\al A.)\hbox{--modules}$ ${\got h}_\tau$
are uniquely determined by their
canonical endomorphisms $\tau,$ even though the choice of
$\al H._{\tau}$ is not unique. We are now interested in those
choices of $\al H._{\tau}$ which are compatible with products:
\begin{defi}
A Hilbert system
$\HS$
is called {\bf regular} if there is an assignment
$\sigma\rightarrow\al H._{\sigma}$
from
$\ob\,\al T.$
to
$\al G.$-invariant algebraic Hilbert spaces in
$\al F.$
such that
\begin{itemize}
\item[(i)] $\sigma=\rho\s{\al H._\sigma}.,$
i.e. $\sigma$ is the canonical endomorphism of $\al H._\sigma,$
\item[(ii)] $\sigma\circ\tau\to\al H._\sigma\cdot\al H._\tau\;.$
\end{itemize}
\end{defi}
In a minimal Hilbert system regularity means that there is a
``representing" Hilbert space
$\al H._{\tau}\subset{\got h}_{\tau}$
for each $\tau$ with
${\got h}_{\tau}=\al H._{\tau}Z(\al A.)$
such that the compatibility relation (ii) holds.
If a Hilbert system is minimal and
$Z(\al A.)=\C\un$
then it is necessarily regular.
Thus a class of examples which are trivially minimal and regular,
is provided by DHR--superselection theory.
A nontrivial example of a minimal and regular Hilbert system is constructed in \cite{B2}.
Then we obtain, cf. Theorem 4.9 of \cite{B2}:
\begin{teo}
\label{Teo1}
Let $\HS$ be a minimal and regular Hilbert system, then:
$\al T.$ contains a C*--subcategory $\al T._\C$ with
the same objects, $\ob\al T._\C=\ob\al T.,$ and arrows
$(\sigma,\,\tau)_\C:=(\al H._\sigma,\al H._\tau)=
\al J.\big(\al L.\s{\al G.}.(\al H._\sigma,\al H._\tau)\big)\subset(\sigma,\tau)$
such that:
\begin{itemize}
\item[P.1]
$\quad\al T._{\C}$ is a DR-category (in particular $(\iota,\iota)_{\C}
=\C\un)$.
\item[P.2.]
$\quad(\sigma,\tau)=(\sigma,\tau)\s\C.\sigma(Z(\al A.))
=\tau(Z(\al A.))(\sigma,\tau)\s\C.\sigma(Z(\al A.))\;.$
\end{itemize}
\end{teo}
\begin{rem}
\begin{itemize}
\item[(i)]
The conditions P.1-P.2 imply that each basis of
$(\sigma,\tau)_{\C}$
is simultaneously a module basis of
$(\sigma,\tau)$
modulo
$\sigma(\al Z.(\al A.))$
as a right module,
i.e. the module
$(\sigma,\tau)$
is free.
\item[(ii)]
We will call the DR-subcategory $\al T._\C$ in Theorem~\ref{Teo1}
{\bf admissible}.
If ``minimality" is omitted
from the hypotheses of
Theorem~\ref{Teo1}, then property P.1 remains valid, but not
P.2. In this case $\al T._\C$ is a DR-subcategory only.
A construction of an example with admissible
subcategory can be found in \cite{B2}.
\end{itemize}
\end{rem}
The converse of Theorem~\ref{Teo1} is also true, and states the main duality result
cf.~\cite{BL}:
\begin{teo}
\label{Teo2}
Let $\al T.$ be a C*--tensor category of unital endomorphisms
of $\al A.$
and let $\al T.\s\C.$
be an admissible (DR-)subcategory.
Then there is a minimal and regular Hilbert
extension $\HS$ of $\al A.$
such that $\al T.$ is isomorphic
to the category of all canonical endomorphisms of $\HS.$
Moreover, if $\al T.\s\C.,\;\al T.'_\C$ are two admissible subcategories of
$\al T.,$
then the corresponding Hilbert
extensions are $\al A.\hbox{--module}$ isomorphic iff $\al T.\s\C.$
is {\bf equivalent} to $\al T.'_\C$ i.e. iff there is a map
$V$ from $\ob\al T.$ to the arrows such that:
\begin{eqnarray*}
V_{\lambda}&\in& (\lambda,\lambda),\quad
V_{\lambda} \quad\hbox{is unitary, and}\quad V_{\lambda\circ\sigma}=V_{\lambda}\times
V_{\sigma}, \\[1mm]
(\lambda,\sigma)_{\C}'&=&V_{\sigma}(\lambda,\sigma)_{\C}V_{\lambda}^{\ast}
\subset (\lambda,\sigma)
\end{eqnarray*}
and we have the following compatibility relations for the corresponding permutators
$\epsilon,\,\epsilon'$ and conjugates $R_\lambda,\,R'_\lambda:$
\begin{eqnarray*}
\epsilon'(\lambda,\sigma)
&=&(V_\sigma\times V_{\lambda})\cdot\epsilon(\lambda,\sigma)\cdot(V_\lambda\times
V_\sigma)^{\ast} \\[1mm]
R'_\lambda&=&V_{\ol\lambda.\circ
\lambda}R_\lambda,\qquad S'_\lambda
=\epsilon'(\lambda,\ol\lambda.)R'_\lambda.
\end{eqnarray*}
\end{teo}
Thus, in minimal and regular Hilbert systems there
is an intrinsic characterization of the category of all
canonical endomorphisms in terms of
$\al A.$
only. Moreover,
up to $\al A.\hbox{--module}$ isomorphisms, there is a bijection
between minimal and regular Hilbert extensions
and C*-tensor categories $\al T.$ of unital endomorphisms of $\al A.$
with admissible subcategories.
Note that Theorem~\ref{Teo2} is a generalization of the
DR-theorem for
the case of nontrivial centre
$Z(\al A.)\supset\C\un,$ i.e. it contains the case of the DR-theorem, in that if
$Z(\al A.)=\C\un$
then $\al T.$
itself is admissible (hence a DR-category) and the corresponding
Hilbert extensions have trivial relative commutant.
\subsection{Hilbert systems with abelian groups}
\label{abelianHS}
If
$\al G.$
is abelian the preceding structure simplifies radically. Specifically,
$\wh{\al G.}$
is a discrete abelian group (the character group),
each $\al H._\gamma,\,\gamma\in\wh{\al G.}$ is one--dimensional with a generating
unitary $U_\gamma,$ hence the canonical endomorphisms
$\rho_{\al H._{\gamma}}$
(denoted by
$\rho_{\gamma},)$
are in fact automorphisms,
necessarily outer on $\al A..$
Since
$\rho_{\gamma_{1}}\circ\rho_{\gamma_{2}}=\rho_{\gamma_{1}\gamma_{2}}$
in this case the set
$\Gamma$
of all canonical endomorphisms
$\rho_{\al H._{\gamma}}$
is a group with the property
$\wh{\al G.}\cong\Gamma/\hbox{int}\,\al A..$
Hence it is not necessary to consider
direct sums, i.e. Property B for
$\al A.$
can be dropped.
In the case
$Z(\al A.)=\C\un$
the permutators $\epsilon$ (restricted to
$\wh{\al G.}\times\wh{\al G.}$)
are elements of the second cohomology group
$H^{2}(\wh{\al G.})$
and
\[
U_{\gamma_{1}}\cdot U_{\gamma_{2}}=\omega(\gamma_{1},\gamma_{2})
U_{\gamma_{1}\circ\gamma_{2}},
\]
where
\[
\epsilon(\gamma_{1},\gamma_{2})=\frac{\omega(\gamma_{1},\gamma_{2})}
{\omega(\gamma_{2},\gamma_{1})}
\]
and $\omega$ is a corresponding 2-cocycle. The field algebra $\al F.$
is just the $\omega\hbox{--twisted}$ discrete crossed product
of $\al A.$ with $\wh{\al G.}$
(see e.g. p.86 ff.~\cite{Bg} for details).
For the case
$Z(\al A.)\supset\C\un$
see ~\cite{BL3} (though the minimal case is not mentioned there).
\section{Kinematics for Quantum Constraints.}
\label{TProcedure}
In this section we give a brief summary of the method of imposing quantum
constraints, developed by Grundling and Hurst \cite{Grundling85,Grundling88b,
Lledo}. There are quite a number of diverse quantum
constraint methods available in the literature at various levels of
rigour (cf.~\cite{lands}). The one we use here is the most congenial from
the point of view of C*--algebraic methods.
Our starting point is:
\begin{defi}
A {\bf quantum system with constraints} is a
pair $(\al B.,\;\al C.)$ where the {\bf system algebra}
$\al B.$ is a unital {\rm C*}--algebra containing
the {\bf constraint set} $\al C.=\al C.^*.$ A
{\bf constraint condition} on $(\al B.,\,\al C.)$ consists of
the selection of the physical
state space by:
\[
{\got S}_D:=\Big\{ \omega\in{\got S}({\al B.})\mid\pi_\omega(C)
\Omega_\omega=0\quad {\forall}\, C\in {\al C.}\Big\}\,,
\]
where ${\got S}({\al B.})$ denotes the state space of $\al B.$,
and $(\pi_\omega,\al H._\omega,\Omega_\omega)$ denotes the
GNS--data of $\omega$. The elements of ${\got S}_D$ are called
{\bf Dirac states}.
The case of {\bf unitary constraints} means
that $\al C.=\al U.-\EINS$, $\;\al U.\subset\al B._u$, and
for this we will
also use the notation $(\al B.,\,\al U.)$.
\end{defi}
The assumption is that all physical information is contained in the
pair $(\al B.,{\got S}_D)$.
Examples of constraint theories as defined here,
have been worked out in detail
for various forms of electromagnetism~cf.~\cite{Grundling85, Grundling88c,
Lledo}.
For the case of unitary constraints we have the following equivalent
characterizations of the Dirac states
(cf.~\cite[Theorem~2.19~(ii)]{Grundling85}):
\begin{eqnarray}
\label{DiracU1}{\got S}_{{D}}&=&\Big\{ \omega\in{\got S}({\al B.})\mid
\omega(U)=1 \quad {\forall}\, U\in {\al U.}\Big\} \\[1mm]
\label{DiracU2} &=&\Big\{ \omega\in{\got S}({\al B.})\mid
\omega(FU)=\omega(F)=\omega(UF) \quad {\forall}\,
F\in\al B.,\; U\in {\al U.}\Big\}.
\end{eqnarray}
Moreover, the set $\{\alpha_U:= {\rm Ad}(U)\mid U\in\al U.\}$ of
automorphisms of $\al B.$ leaves every Dirac state invariant,
i.e.~we have $\omega\circ\alpha_U=\omega$ for all
$\omega\in {\got S}_{{D}}$, $U\in{\al U.}$.
For a general constraint set $\al C.$, observe that we have:
\begin{eqnarray*}
{\got S}_D &=& \Big\{ \omega\in{\got S}({\al B.})\mid\omega(C^*C)=0
\quad {\forall}\, C\in\al C.\Big\} \\[1mm]
&=& \Big\{ \omega\in{\got S}({\al B.})\mid \al C.\subseteq
N_\omega\Big\}\kern2mm=\kern2mm\al N.^\perp\cap{\got S}(\al B.)\;.
\end{eqnarray*}
Here $N_\omega:=\{F\in\al B.\mid\omega(F^*F)=0\}$ is the left kernel of
$\omega$ and
$\al N.:=\cap\; \{N_{\omega}\mid\omega\in{\got S}_D \}$,
and $\al N.^\perp$ denotes the annihilator of $\al N.$
in the dual of $\al B.$.
Now $\al N.=\csp(\al BC.)$
because every closed
left ideal is the intersection of the left kernels which contains it
(cf.~3.13.5 in \cite{bPedersen89}).
Thus $\al N.$ is the left ideal generated by $\al C.$.
Since $\al C.$ is selfadjoint and contained in
$\al N.$ we conclude
\[
\al C.\subset {\rm C}^*(\al C.)\subset
\al N.\cap\al N.^*=\csp(\al BC.)\,\cap\,\csp(\al CB.)\;,
\]
where ${\rm C}^*(\cdot)$
denotes the C*--algebra in $\al B.$ generated by its argument.
Then we have (cf. \cite{Lledo}):
\begin{teo}
\label{Teo.3.1}
For the Dirac states we have:
\begin{itemize}
\item[{\rm (i)}] ${\got S}_{{D}}\neq\emptyset\;$ iff
$\;\EINS\not\in {\rm C}^*(\al C.)$ iff
$\;\EINS\not\in \al N.\cap\al N.^*=:\al D.$.
\item[{\rm (ii)}] $\omega\in {\got S}_D\;$ iff
$\; \pi_{\omega}({\al D.})\Omega_{\omega}=0$.
\item[{\rm (iii)}] An extreme Dirac state is pure.
\end{itemize}
\end{teo}
We will call a constraint set $\al C.$ {\bf first class} if
$\EINS\not\in {\rm C}^*(\al C.)$, and this is the nontriviality
assumption which we henceforth make \cite[Section~3]{Grundling88a}.
Now define
\[
{\al O.} := \{ F\in {\al B.}\mid [F,\, D]:= FD-DF \in {\al D.}\quad
{\forall}\, D\in{\al D.}\}.
\]
Then ${\al O.}$ is the C$^*$--algebraic analogue of Dirac's observables
(the weak commutant of the constraints) \cite{bDirac64}.
Then (cf. \cite{Lledo}):
\begin{teo}
\label{Teo.2.2}
With the preceding notation we have:
\begin{itemize}
\item[{\rm(i)}] $\al D.=\al N.\cap \al N.^*$ is the unique maximal
{\rm C}$^*$--algebra in $\, \cap\; \{ {\rm Ker}\,\omega\mid \omega\in
{\got S}_{{D}} \}$. Moreover $\al D.$ is a hereditary
{\rm C}$^*$--subalgebra of $\al B.$.
\item[{\rm(ii)}] ${\al O.} = {M}_{\al B.}({\al D.})
:=\{ F\in{\cal B}\mid FD\in{\cal D}\ni DF\quad\forall\, D\in{\cal D}\}$,
i.e.~it is the relative multiplier algebra of ${\al D.}$ in ${\al B.}$.
\item[{\rm(iii)}] $\al O.=\{F\in\al B.\mid\; [F,\,\al C.]\subset\al D.\},$
hence $\al C.'\cap\al B.\subseteq\al O.\;.$
\item[{\rm(iv)}] $\al D.=\csp(\al OC.)=\csp(\al CO.)$.
\item[{\rm(v)}] For the case of unitary constraints, i.e.
$\al C.=\al U.-\EINS$, we have
$\al U.\subset\al O.$ and $\al O.={\{F\in\al B.\mid\alpha_U(F)-F\in\al D.
\quad\forall\; U\in\al U.\}}$
where $\alpha_U:={\rm Ad}\,U$.
\end{itemize}
\end{teo}
Thus $\al D.$ is a closed two-sided ideal of $\al O.$ and it
is proper when ${\got S}_D\not=\emptyset$ (which we assume here
by $\EINS\not\in {\rm C}^*(\al C.)$).
Since the traditional observables are $\al C.'\cap\al B.,$
by (iii) we see that these are in $\al O.\,.$ In general
$\al O.$ can be much larger than $\al C.'\cap\al B..$
Define the {\it maximal {\rm C}$^*$--algebra of physical observables} as
\[
{\al R.}:={\al O.}/{\al D.}.
\]
The factoring procedure is the actual step of imposing constraints.
This method of constructing $\al R.$ from $(\al B.,\,\al C.)$
is called the {\bf T--procedure}
in \cite{Grundling85}, and it defines a map $T$ from first class
constraint pairs $(\al B.,\,\al C.)$ to unital C*--algebras by
${T(\al B.,\,\al C.)}:=\al R.=\al O./\al D..$
We require that after the T--procedure all physical
information is contained in the pair $({\al R.}\kern.4mm ,{\got S}
({\al R.}))$, where ${\got S}({\al R.})$ denotes the set of
states on $\al R.$. Now, it is possible that $\al R.$ may not be simple
\cite[Section~2]{Grundling85}, and this would not be acceptable for a
physical algebra. So, using physical arguments, one would in practice
choose a C$^*$--subalgebra $\al O._c\subset \al O.$ containing
the traditional observables $\al C.'$ such that
\[
\al R._c :=\al O._c / (\al D.\cap\al O._c )\subset \al R.\,,
\]
is simple. The following result justifies the choice of $\al R.$ as the
algebra of physical observables (cf. Theorem 2.20 in \cite{Grundling85}):
\begin{teo}
\label{Teo.2.6}
There exists a ${\sl w}^*\hbox{--continuous}$ isometric bijection
between the Dirac states on ${\al O.}$ and the states on ${\al R.}$.
\end{teo}
Insofar as the physics is
now specified by $\al R.,$ this suggests that we
call two constraint sets equivalent if they produce the same $\al R..$
More precisely two constraint sets $\al C._1\subset\al B.\supset\al C._2$
are called {\bf equivalent}, denoted $\al C._1\sim\al C._2,$
if they select the same set of Dirac states, cf.~\cite{Lledo}.
In fact
\[
\al C._1\sim\al C._2\quad\hbox{iff}\quad
\csp(\al BC._1)=\csp(\al BC._2)\quad\hbox{iff}\quad\al D._1=\al D._2\;.
\]
The hereditary property of $\al D.$ can be further analyzed,
and we list the main points (the proofs are
in Appendix~A of \cite{Lledo}).
Denote by $\pi_u$ the universal representation of $\al B.$ on the
universal Hilbert space $\al H._u$ \cite[Section~3.7]{bPedersen89}.
$\al B.''$ is the strong closure of $\pi_u(\al B.)$ and since $\pi_u$
is faithful we make the usual identification of $\al B.$
with a subalgebra of $\al B.''$, i.e.~generally omit explicit
indication of $\pi_u$. If $\omega\in{\got S}(\al B.)$, we will
use the same symbol for the unique extension of $\omega$ from $\al B.$ to
$\al B.''$.
\begin{teo}
\label{Teo.2.7}
For a constrained system $(\al B.,\al C.)$ there exists a
projection
$P\in\al B.''$ such that
\begin{itemize}
\item[{\rm (i)}] $\al N.=\al B.''\,P\cap \al B.$,
\item[{\rm (ii)}] $\al D.=P\,\al B.''\,P \cap \al B.$
\item[{\rm (iii)}] ${\got S}_D=\{\omega\in{\got S}(\al B.)\mid\omega(P)=0\}$
\item[{\rm(iv)}] $\al O.=\{ A\in\al B. \mid PA(\EINS-P)=0=
(\EINS-P)AP \}=P'\cap \al B.\;.$
\end{itemize}
\end{teo}
A projection satisfying the conditions of Theorem~\ref{Teo.2.7}
is called {\em open} in
\cite{bPedersen89}.
What this theorem means, is that with respect to
the decomposition
\[
\al H._u=P\,\al H._u\oplus (\EINS-P)\,\al H._u
\]
we may rewrite
\begin{eqnarray*}
\al D.&=& \Big\{ F\in\al B.\;\Big|\; F=
{\left(\kern-1.5mm\begin{array}{cc}
D \kern-1.6mm & 0 \\ 0 \kern-1.6mm & 0
\end{array} \kern-1.5mm\right)},\;
D\in P\al B.P \Big\}\;\;{\rm and} \\
\al O.&=& \Big\{ F\in\al B.\;\Big|\; F=
{\left(\kern-1.5mm\begin{array}{cc}
A \kern-1.6mm & 0 \\ 0 \kern-1.6mm & B
\end{array} \kern-1.5mm\right)},\;
A\in P\al B.P,\; B\in(\EINS-P)\al B.(\EINS-P) \Big\}\,.
\end{eqnarray*}
It is clear that in general $\al O.$ can be much greater than the
traditional observables $\al C.'\cap\al B.$. Next we show how to identify the
final algebra of physical observables $\al R.$ with a subalgebra of
$\al B.''$.
\begin{teo}
\label{Teo.2.11}
For $P$ as above we have:
\[
\al R.\cong\Big\{ F\in\al B.\;\Big|\; F=
\left(\kern-1.5mm\begin{array}{cc}
0 \kern-1.6mm & 0 \\ 0 \kern-1.6mm & A
\end{array} \kern-1.5mm\right) \Big\}=
(\EINS-P)\,(P'\cap\al B.) \subset \al B.''.
\]
\end{teo}
Below we will need to consider a constraint system
contained in a larger algebra,
specifically, $\al C.\subset\al A.\subset\al F.$ where $\al C.$ is
a first--class constraint set, and $\al A.,\;\al F.$ are unital
C*--algebras.
Now there are
two constrained systems to consider;- $(\al A.,\,\al C.)$
and $(\al F.,\,\al C.).$ The first one produces the algebras
$\al D.\subset\al O.\subseteq\al A.,$ and the second produces
$\al D.\s{\al F.}.\subset\al O.\s{\al F.}.\subseteq\al F..$
where as usual,
\begin{eqnarray*}
\al N.&=& \csp(\al AC.),\qquad \al D.=\al N.\cap\al N.^*,\qquad
\al O.=M\s{\al A.}.(\al D.)
\qquad\hbox{and} \\
\al N.\s{\al F.}.&=&\csp(\al FC.),\qquad
\al D.\s{\al F.}.=\al N.\s{\al F.}.\cap
\al N.^*\s{\al F.}.,\qquad
\al O.\s{\al F.}.=M\s{\al F.}.(\al D.\s{\al F.}.).
\end{eqnarray*}
Then we have (cf. Theorem~3.2 of \cite{Grundling88b}):
\begin{teo}
\label{Teo.2.12}
Given as above $\al C.\subset\al A.\subset\al F.$
then
\[ \al N.\s{\al F.}.\cap\al A.=\al N.,\qquad
\al D.\s{\al F.}.\cap\al A.=\al D.,\qquad
\qquad\hbox{and}\qquad
\al O.\s{\al F.}.\cap\al A.=\al O.\;.
\]
Hence $\al R.=\al O./\al D.=(\al O.\s{\al F.}.\cap\al A.)\big/
(\al D.\s{\al F.}.\cap\al A.)\;.$
\end{teo}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Superselection with constraints.}
Next we would like to consider systems containing
both constraints and superselection.
There is a choice in how to define this problem mathematically,
so let us consider the physical background.
Perhaps the most important
example, is that of a local gauge theory.
It usually has a set of global charges (leading to superselection)
as well as a Gauss law constraint (implementing the local gauge symmetry),
and possibly also other constraints
associated with the field equation.
Only if the gauge group is abelian will the Gauss law constraint commute with
the global charge, since the Gauss law constraint
takes its values in the Lie algebra of the gauge group.
Thus, for nonabelian local gauge theories
we do not expect the constraints to be
in the algebra of gauge invariant
observables $\al A.$ of the superselection
theory of the global charge.
This problem is however not as serious as it looks.
The reason is that whilst the global gauge group does not preserve
the individual Gauss law constraints, it does preserve the set of these,
hence it also preserves the set of Dirac states selected by them.
Thus we can replace the original constraint set by an equivalent constraint
(i.e. selecting the same set
of Dirac states)
which is invariant under the global gauge group.
Such an equivalent constraint
is given by the projection in Theorem~\ref{Teo.2.7}.
It comes at the cost of slightly enlarging the system algebra $\al B.,$
since $P$ is in the universal Von Neumann algebra of $\al B.$.
We can avoid this cost if $\csp(\al C.)$
is separable, since then there is an equivalent constraint in
$\al B.$ itself, cf.~Theorem~3.4 of~\cite{Lledo}.
We therefore will assume below that the constraints are in
in $\al A..$
This will include the situation where
there are two or more local gauge symmetries
which mutually commute (e.g. isospin and electromagnetism),
in which case the Gauss law constraint
of one symmetry will commute with the global charges
of the other.
We can also easily find constraints which are independent of the
gauge symmetries, e.g. restriction to a submanifold,
or enforcing a dynamical law.
Let now $(\al A.,\,\al C.)$ be
a first--class constraint system, hence we have the associated
algebras $\al D.\subset\al O.\subseteq\al A.,$ and $\al R.=\al O./\al D..$
In addition, let
$\al A.$ have a superselection structure
i.e. there is a given Hilbert extension $\HS$ of $\al A..$
Thus the category
$\al T.$
of canonical endomorphisms of
$\al A.$
defines a selection criterion of unital endomorphisms of
$\al A..$
In the case that the Hilbert extension is minimal and regular,
the superselection structure of
$\al T.$
is given within
$\al A.$
without any reference to the Hilbert extension.
Then the following natural questions arise:
\begin{itemize}
\item[(1)] what compatibility conditions should be satisfied in order
to pass the superselection structure through $T,$ thus obtaining
a superselection structure on $T(\al A.,\,\al C.)=\al R.?$
\item[(2)] what is the relation between $T(\al A.,\,\al C.)$
and $T(\al F.,\,\al C.)$ where $\al F.$ is the field algebra generated from
$\al T.?$
\end{itemize}
An inverse question also arises, i.e.
\begin{itemize}
\item[(3)] if $\al R.$ has a superselection structure, what is the
weakest structure one can expect on $\al A.$ which would produce
this superselection structure on $\al R.$ via $T?$
(One should call this a {\it weak} superselection structure.)
\end{itemize}
To address (1) and (2), recall that the map $T$ consists of a restriction
(of $\al A.$ to $\al O.)$ followed by a factoring
($\al O.\to\al O./\al D.$). So, we first work out the compatibility
conditions involved with restrictions and factoring maps.
Since $\al C.\subset\al A.\subset\al F.\,,$ there are
two constrained systems to consider;- $(\al A.,\,\al C.)$
and $(\al F.,\,\al C.).$ The first one produces the algebras
$\al D.\subset\al O.\subseteq\al A.,$ and the second produces
$\al D.\s{\al F.}.\subset\al O.\s{\al F.}.\subseteq\al F.$
(cf. Theorem~\ref{Teo.2.12}).
Now since $\al C.\subset\al A.,$ the $\al G.\hbox{--invariant}$ part
of $\al F.,$ it follows that $\al G.$ preserves the set of Dirac states,
hence $\al G.$
preserves both
$\al D._{\al F.}$
and
$\al O._{\al F.}$,
i.e.
$g\al D._{\al F.}=\al D._{\al F.}$
and
$g\al O._{\al F.}=\al O._{\al F.}$
for all
$g\in\al G.$.
We denote the restriction of
$\al G.$
to
$\al O._{\al F.}$
by
$\beta_{g}:={g}\rest\al O._{\al F.}.$
The homomorphism
$\beta:\al G.\ni g\rightarrow \beta_{g}\in\aut\,\al
O._{\al F.}$
is not necessarily injective but
$\beta$
is again
pointwise norm-continuous, hence
$\al G./\al K.$
is compact where
$\al K.:=\ker\beta.$
The isomorphism
$\tilde{\beta}:\al G./\al K.\to
\beta_{\al G.}$ by
$\tilde{\beta}(g\al K.):=\beta_{g}$
is also a topological one (cf.~p.58~\cite{HR}).
Note that
$\wh{(\al G./\al K.)}=\{\gamma\in\wh{\al G.}\,\bigm|\,\gamma(k)=1\quad
\hbox{for all}\;k\in\al K.\}\supseteq\spec\,\beta_{\al G.}\,.$
The spectral projections
$\Pi^{\beta}_{\gamma}$
of
$\beta\s{\al G.}.$
are given by the restriction to
$\al O._{\al F.}$
of the spectral projections
$\Pi_{\gamma}$
of
$\al G.$,
i.e.
$\Pi^{\beta}_{\gamma}X=\Pi_{\gamma}X$
for
$X\in\al O._{\al F.}.$
We now have the:
\begin{itemize}
\item[(I)]
Restriction problem.
Find conditions to
guarantee that
the C*--dynamical system
$\{\al O._{\al F.},\al G.,\beta\}$
is a Hilbert system
$\{\al O._{\al F.},\beta_{\al G.}\}$.
Thus we have to find conditions to ensure there are algebraic
Hilbert spaces in
$\Pi^{\beta}_{\gamma}\al O._{\al F.}$
for
$\gamma\in\wh{(\al G./\al K.)}$.
(Note that this is stronger than what we need;-
we only need a Hilbert system on $\al R.\s{\al F.}.$ after factoring
out by $\al D.\s{\al F.}..)$
\item[(II)]
Factoring problem.
Find conditions to guarantee that under the map
$\al O.\s{\al F.}.\to\al R.\s{\al F.}.:={\al O.\s{\al F.}.\big/
\al D.\s{\al F.}.}$ the factoring through of the action of $\al G.$
to $\al R.\s{\al F.}.$
is a Hilbert system corresponding to a DR--category.
This is of course a special case of the general
problem for homomorphic images of Hilbert systems
under factoring by invariant ideals.
The reason why we require $Z(\al A.)=\C\un$ for $\al R.\s{\al F.}.$
is because after implementing constraints, the final physical algebra
should be simple.
\end{itemize}
Below we list our major results;- since some proofs are lengthy,
we defer these to Section~\ref{Proofs} to preserve the main flow of ideas.
\subsection{Restricting a superselection structure.}
\label{restrict}
We consider now for the system above the restriction problem (I),
i.e. we are given a Hilbert extension $\HS$ of $\al A.,$ containing
constraints $\al C.\subset\al A.,$ and we need to examine
when
$\{\al O._{\al F.},\,\beta\s{\al G.}.\}$
is a Hilbert system.
\def\of{\al O.\s{\al F.}.}
\def\df{\al D.\s{\al F.}.}
\def\rf{\al R.\s{\al F.}.}
\begin{teo}
\label{Teo.4.1}
\begin{itemize}
\item[(i)] $\{\al O._{\al F.},\al G.,\beta\}$
has fixed point algebra $\al O..$ Moreover, $Z(\al A.)\subseteq
Z(\al O.).$
\item[(ii)]
For any $\al G.$-invariant
algebraic Hilbert space $\al H._\gamma\subset\Pi_\gamma\al F.$
we have either
$\al H._\gamma\cap\of=\{0\},$
or $\al H._\gamma\subset\of\,.$
In the latter case we have
$\gamma\in
\wh{\al G./\al K.}$
where $\al K.=\ker\beta\,,$
and
\[
\al H._\gamma\subset\Pi_{\gamma}\of=\csp(\al O.\al H._{\gamma}).
\]
\item[(iii)]
Let $\sigma\in\ob\al T.,$ with $\al H._\sigma\subset\al F.$
a $\al G.$-invariant algebraic Hilbert
space such that
$\sigma=\rho\s{\al H._\sigma}..$
If $\al H._\sigma\subset\of,$
then $\sigma(\al D.)\subseteq\al D.$ and $\sigma(\al O.)\subseteq\al O..$
Thus $\sigma$ restricts to $\al O.,$ $\sigma\rest\al O.\in\endo
\al O..$
\end{itemize}
\end{teo}
The central condition for
$\{\of,\al G.,\beta\}$
to be a Hilbert system
$\{\of,\beta_{\al G.}\}$
w.r.t. the factor group
$\al G./\al K.$
is
$\al H._{\gamma}\subset\of$,
i.e.
$\al H._{\gamma}\subset\Pi_{\gamma}^{\beta}\of$
for all
$\gamma\in\wh{\al G./\al K.}$.
Next, we develop an internal criterion on $\al A.$ to guarantee that
a given
$\al H.\in\ob\al T._{\al G.}$
is contained in
$\of$.
\begin{teo}
\label{Teo.4.2}
\begin{itemize}
\item[(i)]
Given the Hilbert extension $\HS$ of the constrained system
$\al C.\subset\al A.$ assumed here, we have for
any $\al G.\hbox{--invariant}$ algebraic Hilbert space $\al H.$
that
\begin{eqnarray*}
\al H.\subset\of\qquad &\hbox{iff}&\qquad
\al D.\sim\rho\s{\al H.}.(\al D.)\\[1mm]
&\hbox{i.e.}&\qquad
\al D.=\csp\big(\al A.\rho\s{\al H.}.(\al D.)\big)\,\cap
\,\csp\big(\rho\s{\al H.}.(\al D.)\al A.\big)\,.
\end{eqnarray*}
\item[(ii)]
For all $\sigma,\;\tau\in\ob\al T.$
with $\al H._\sigma,\al H._\tau\subset\of$ we have
\[
(\sigma,\,\tau)\s{\al A.}.\subseteq\big(\sigma\rest\al O.,\,\tau
\rest\al O.\big)\s{\al O.}.\;.
\]
\end{itemize}
\end{teo}
Observe
that $\al D.\sim\rho\s{\al H.}.(\al D.)$ implies that
$\rho\s{\al H.}.(\al D.)\subseteq\al D..$
\begin{cor}
\label{cor4.1}
We have that $\{\of,\al G./\al K.,\tilde{\beta}\}$ is a Hilbert
system
$\{\of,\beta_{\al G.}\}$
w.r.t.
$\al G./\al K.$ iff
$\al D.\sim\rho_\gamma(\al D.)$
holds for all
$\gamma\in\wh{\al G./\al K.}.$
In particular, if
$\al D.\sim\rho_{\gamma}(\al D.)$
holds for all
$\gamma\in\wh{\al G.}$
then
$\al G./\al K.\cong\al G.$
i.e. $\al K.$ is trivial.
\end{cor}
Whilst the condition $\al D.\sim\rho\s\gamma.(\al D.)$
is exact for
$\al H._\gamma\subset\of,$ it may not be in practice
that easy to verify.
We therefore consider alternative conditions which will
allow the main structures involved with Hilbert extensions
to survive the restriction of
$\HS$ to $\{\of,\,\beta\s{\al G.}.\}.$
Recalling the definition of subobjects, introduce the notation
$E\simeq \un({\rm mod}\,\al A.)$
for a projection $E\in\al A.$ to mean that
there is an isometry $V\in\al A.,$ $V^*V=\un$ such that
$VV^*=E$ (i.e. Murray--Von Neumann equivalence of $E$ and $\un).$
\begin{defi}
We say the constraint set $\al C.\subset\al A.$ is an
{\bf E--constraint set} if for each projection $E\in\al O.$
such that $E\simeq \un({\rm mod}\,\al A.),$ we have
that $E\simeq \un({\rm mod}\,\al O.).$
\end{defi}
The E-constraint condition will ensure the
survival of decomposition relations of restrictable canonical
endomorphisms:
\begin{pro}
\label{pro.4.7}
Let
$\HS$ be a Hilbert system and let
$\al C.\subset\al O.$ be an E--constraint set,
$\sigma\in\ob\al T.$
and
$\al H._\sigma\subset\of$
a
$\al G.$-invariant
algebraic Hilbert space. Then
\begin{itemize}
\item[(i)] to each decomposition
\[
\sigma(\cdot)=\sum_jV_j\rho\s\gamma_j.(\cdot)
V_j^*\;,\qquad V_j\in(\rho\s\gamma_j.,\,\sigma)\s{
\al A.}.\;,
\]
where $\gamma_j\in\wh{\al G.}$ and $V_j\in\al A.$ are isometries,
there corresponds a decomposition on
$\al O.,$ i.e.
there are
$\al G.$-invariant
algebraic Hilbert spaces
$\al K._j\subset\of,$
which carry the representation $\gamma_j$ and
with canonical endomorphisms $\tau_j
:=\rho_{\al K._{j}}\rest\al O.\in\endo\al O.$
such that
on $\al O.:$
\[
\sigma(\cdot)=\sum_jW_j\tau_j(\cdot)
W_j^*\;,\qquad W_j\in(\tau_j,\,\sigma)\s{
\al O.}.\;,
\]
where $W_j\in\al O.$ are isometries.
\item[(ii)]
Let
$\{\al F.,\al G.\}$
in addition satisfies Property B and let
$\tau<\sigma\in\al T.$ in the sense of $\al A.,$
i.e. there is an isometry $V\in{(\tau,\,\sigma)\s{\al A.}.},$
and let $\al H._\sigma\subset\of.$
Then
there is a corresponding Hilbert space
$\al H._\tau\subset \of$ i.e.
$\tau\rest\al O.<\sigma\rest\al O.\in\endo\al O.$
also in the sense of $\al O..$
\end{itemize}
\end{pro}
\begin{teo}
\label{tensrep}
Let
the Hilbert system
$\HS$
satisfy Property B
where $\al G.$ is a group
with a distinguished
irreducible representation $\gamma_0\in\wh{\al G.}$
such that every irreducible representation of $\al G.$
is contained in a tensor representation of $\gamma_0.$
Let $\al C.\subset\al A.$ be an E--constraint set
then
$\al H.\s\gamma_0.\subset\of$ implies that
$\{\of,\beta\s{\al G.}.\}$ is a Hilbert system.
\end {teo}
\begin{beweis}
This follows from Proposition~\ref{pro.4.7}, by making use of the
obvious fact that $\al H._\tau\subset\of\supset\al H._\sigma$
implies that $\al H._\tau\cdot\al H._\sigma\subset\of$
for $\sigma,\;\tau\in\ob\al T.\,.$
\end{beweis}
If the group
$\al G.$
is isomorphic to $U(N)$ then it
satisfies the condition of Theorem~\ref{tensrep}.
The property of being an E--constraint set can be
characterized in terms of the open projection
$P\in\al A.''$ corresponding to the
constraints (cf. Theorem~\ref{Teo.2.7}).
Observe that if there is an $E\in\al O.$
with $E\simeq\un({\rm mod}\,\al A.),$
then the set of isometries
\[
\al V._E:=\set V\in\al A., VV^*=E,\quad V^*V=\un.
\]
is nonempty. We have:
\begin{pro}
Let $E\in\al O.$
with $E\simeq\un({\rm mod}\,\al A.),$ then $\al V._E\cap\al O.\not=
\emptyset$ iff for each $V\in\al V._E$ there is a
\[
U\in \al U._E:=\set U\in\al A., U^*U=E=UU^*.
\]
such that $VPV^*=UPU^*.$
\end{pro}
\subsection{Morphisms of general Hilbert systems.}
\label{morphsec}
Recall that the second step in the enforcement of constraints, is
the factoring $\of\to\rf:=\of/\df.$ We now consider
problem {(II)}, the factoring problem, first in a general
context. Consider a morphism of
C*--algebras $\xi:\al F.\to\al L.=\xi(\al F.).$
This specifies the subgroup of
automorphisms
\[
\autx\al F.:=\set\alpha\in\aut\al F.,\alpha(\ker\xi)\subseteq
\ker\xi.
\]
and a homomorphism $\autx\al F.\to\aut\al L.$ by
$\alpha\to\alpha^\xi$ where $\alpha^\xi(\xi(F)):=
\xi(\alpha(F))$ for all $F\in\al F..$
Henceforth let $\HS$ be a Hilbert system with Property B
and ${\al G.}\subset\autx\al F..$
Our task will be to find the best conditions to
ensure that $\{\al L.,\,\al G.^{\xi}\}$
is a Hilbert system associated with a category
described in Theorem~\ref{Teo1}.
We will denote the spectral projections
of $\al G.$ (resp. $\al G.^\xi)$ by $\Pi_\gamma$
(resp. $\Pi^\xi_\gamma).$
(Recall that in the context of the T--procedure, we have that
$\al G.$ preserves $\df$ due to the invariance of the constraints
under $\al G..$ So the current analysis applies).
\begin{teo}
\label{Teo.4.3}
Given a Hilbert system $\HS$
and a unital
morphism $\xi:\al F.\to\al L.=\xi(\al F.),$
such that ${\al G.}\subset\autx\al F.,$ then
we have:
\begin{itemize}
\item[(i)] $\{\al L.,\,\al G.^\xi\}$ is a Hilbert system
and $\al G.\cong\al G.^{\xi}.$
\item[(ii)] If $\al H._\gamma\subset\Pi_\gamma\al F.$
is an invariant algebraic Hilbert space
for $\al G.,$
then so is $\xi(\al H._\gamma)\subset\Pi^\xi_\gamma\al L.$
for $\al G.^\xi.$
\item[(iii)] Let $\al N._\gamma$ be any
orthonormal basis for $\xi(\al H._\gamma),$
then $\bigcup\set\al N._\gamma,\gamma\in\wh{\al G.}.$ is a
left module basis of $\xi(\al F._{\rm fin})$ w.r.t.
$\xi(\al A.),$ i.e. the ``essential part'' of $\xi$
is its action on $\al A..$
\item[(iv)] The fixed point algebra of $\al L.$
w.r.t.
$\al G.^{\xi}$
is exactly $\xi(\al A.),$ and
$\xi(\al F._{\rm fin})=\al L._{\rm fin}\;.$
\item[(v)] If $\HS$ has Property B, so does
$\{\al L.,\,\al G.^\xi\}.$
\end{itemize}
\end{teo}
Thus corresponding to the two Hilbert systems
$\HS$ and $\{\al L.,\al G.^{\xi}\}$
we now have the two categories $\al T.$ and
$\al T.^\xi$ respectively. Moreover:
\begin{cor}
\label{Cor.4.9}
Under the conditions of Theorem~\ref{Teo.4.3} we have that
\begin{itemize}
\item[(i)]
for any canonical endomorphism $\lambda\in\ob\al T.,$
\[
\lambda(\ker\xi\cap\al A.)\subseteq\ker\xi\cap\al A.\;.
\]
Hence there is a well--defined map
$\ob\al T.\ni\lambda\to\lambda^\xi\in\ob\al T.^\xi,$
given by $\lambda^\xi(\xi(A)):=\xi(\lambda(A))$ for all
$A\in\al A..$
\item[(ii)] the map $\ob\al T.\ni\lambda\to\lambda^\xi\in\ob\al T.^\xi$
is compatible with products, direct sums and subobjects.
It also preserves unitary equivalence.
\end{itemize}
\end{cor}
We have that $\big(\ob\al T.\big)^\xi\subseteq\ob\al T.^\xi,$
and we now claim that up to unitary equivalence, we have in fact
equality:
\begin{teo}
\label{Teo.4.4}
Under the conditions of Theorem~\ref{Teo.4.3} we have that
\begin{itemize}
\item[(i)]
if $\sigma\in\ob\al T.^\xi,$ then there is always a
$\lambda\in\ob\al T.$ such that $\lambda^\xi$ is unitarily
equivalent to $\sigma,$ i.e. each unitary equivalence class in
$\ob\al T.^\xi$ contains at least one element of the form
$\lambda^\xi.$
\item[(ii)]
the map $\ob\al T.\ni\lambda\to\lambda^\xi\in\ob\al T.^\xi$
produces an isomorphism between the sets of unitary equivalence
classes of $\ob\al T.$ and $\ob\al T.^\xi$ which
is compatible with products direct sums and subobjects.
\end{itemize}
\end{teo}
The relation between the arrows of the two categories
is however less direct:
\begin{lem}
\label{arrow1}
Under the conditions of Theorem~\ref{Teo.4.3} we have
\[
\xi\big((\sigma,\,\tau)_{\al A.}\big)\subseteq
\big(\sigma^\xi,\,\tau^\xi\big)\s{\xi(\al A.)}.\;.
\]
\end{lem}
Next we show that $\ker\xi$ is uniquely
determined by $\ker\xi\cap\al F._{\rm fin}.$
\begin{pro}
\label{Prop.4.12}
Under the conditions of Theorem~\ref{Teo.4.3} we have that
\begin{itemize}
\item[(i)]
$\ker\xi\cap\al F._{\rm fin}=
{\rm Span}\set(\ker\xi\cap\al A.)\al H._\gamma,
\gamma\in\wh{\al G.}.\;,$
\item[(ii)]
$\ker\xi=\clo\s{\vert\cdot\vert_{\al A.}}.
(\ker\xi\cap\al F._{\rm fin})
\cap\al F.\;.$
\end{itemize}
\end{pro}
Thus $\ker\xi$ is in fact uniquely determined by $\ker\xi\cap\al A.,$
as is already suggested by Theorem~\ref{Teo.4.3}(iii).
Since $\al F.$ is in general not complete w.r.t. $|\cdot|_{\al A.},$
the intersection with $\al F.$ in \ref{Prop.4.12}(ii) is necessary.
Theorem~\ref{Teo.4.3} suggests that we consider the following
subcategory
of
$\al T.^{\xi}$.
\begin{defi}
\label{CatXT}
The subcategory
$\xi(\al T.)$
of
$\al T.^{\xi}$
is defined by the objects
\[
\ob\xi(\al T.):=(\ob\al T.)^{\xi}
\]
and the arrows
\[
(\sigma^{\xi},\tau^{\xi})_{\xi(\al A.)}^{(0)}:=
\xi((\sigma,\tau)_{\al A.}).
\]
\end{defi}
By Theorem~\ref{Teo.4.4} the sets of all unitary
equivalence classes of
$\hbox{Ob}\,\xi(\al T.)$
and
$\hbox{Ob}\,\al T.^{\xi}$
coincide, each equivalence class of
$\hbox{Ob}\,\xi(\al T.)$
is a subset of the corresponding equivalence class of
$\hbox{Ob}\,\al T.^{\xi}$,
but in general these equivalence classes are much larger.
Lemma~\ref{arrow1} says that the arrow sets
$(\sigma^{\xi},\tau^{\xi})_{\xi(\al A.)}$
of the objects of
$\hbox{Ob}\,\xi(\al T.)$
considered as objects of
$\hbox{Ob}\,\al T.^{\xi}$
are in general larger than the corresponding arrow sets in
$\xi(\al T.)$.
The reason is that an element
$X=\xi(Y),\,Y\in\al A.,$
belongs to
$(\sigma^{\xi},\tau^{\xi})_{\xi(\al A.)}$
iff
$Y\sigma(A)-\tau(A)Y\in\ker\,\xi$
for all
$A\in\al A.$.
The arrow sets coincide only if this relation already implies
$Y\sigma(A)-\tau(A)Y=0.$
\subsection{Morphisms of minimal and regular Hilbert systems }
Recall now that by Theorems \ref{Teo1} and \ref{Teo2} we have an
equivalence between
minimal and regular Hilbert systems
with Property B
and the endomorphism
category $\al T.$ with an admissible
subcategory $\al T._\C.$
We called a subcategory $\al T._\C$
{\it admissible} if it satisfies conditions P.1--P.2 in Theorem~\ref{Teo1}.
As in the last subsection, we consider a unital morphism
$\xi:\al F.\to\al L.=\xi(\al F.),$ and recall by Proposition~\ref{Prop.4.12}
that $\xi$ is determined by its action on $\al A..$
Now whilst it is obvious that $\xi(Z(\al A.))\subseteq Z(\xi(\al A.)),$
we require below the stronger condition:
\begin{equation}
\label{ZZ}
\xi(Z(\al A.))=Z(\xi(\al A.))\;.
\end{equation}
When $\xi(\al A.)$ is a simple C*--algebra (as we require for
the final observables after a T--procedure), the condition~(\ref{ZZ})
will be satisfied.
\begin{teo}
\label{Teo.4.13}
Given a minimal and regular Hilbert system $\HS$
with Property B,
and a unital morphism $\xi:\al F.\to\al L.=\xi(\al F.)$
such that ${\al G.}\subset\autx\al F.$ and condition~(\ref{ZZ})
holds, then:
\begin{itemize}
\item[(i)] there is a DR- subcategory
$\al T.^\xi_\C$ of $\xi(\al T.)$,
\item[(ii)] property P.2 is satisfied for $\al T.^\xi_\C$
iff
$\xi(\al A.)'\cap\xi(\al F.)=\xi(Z(\al A.)).$
In this case the subcategory $\al T.^\xi_\C$
is admissible.
\item[(iii)] If $\xi(\al A.)'\cap\xi(\al F.)=\xi(Z(\al A.)),$
then
\[
\big(\sigma^\xi,\,\tau^\xi\big)\s{\xi(\al A.)}.
= \xi\big((\sigma,\,\tau)\s{\al A.}.\big)
\]
for all $\sigma,\;\tau\in\ob\al T.,$ where we made use of the notation
and result in Corollary~\ref{Cor.4.9}.
\item[(iv)] In this case choose
$\al H._{\gamma}\in\ob\al T._{\al G.}\,.$
Then
\[
\al M.^{\xi}:=\set{\rho\s{\xi(\al H._{\gamma})}.},{\gamma\in\wh{\al G.}}.
\subset\ob\xi(\al T.)
\]
is a complete system of (irreducible) and mutually disjoint
objects of
$\ob\xi(\al T.).$
\end{itemize}
\end{teo}
\subsection{The inverse problem.}
\begin{teo}
\label{Teo.4.14}
Let $\al A.$ be a unital C*--algebra with Property B, and let $\al T.$ be
a C*-tensor
category of
unital endomorphisms of
$\al A.$ .
Let
$\al T.$ have an
admissible subcategory
$\al T._{\C}$
whose arrow spaces are denoted by
$(\sigma,\tau)_{\C}$.
Furthermore, let $\xi$
be a unital morphism of $\al A.$ such that
\begin{itemize}
\item[(i)]
$\xi(Z(\al A.))=Z(\xi(\al A.)),$
\item[(ii)]
$\lambda(\ker\xi)\subseteq\ker\xi$ for all $\lambda\in\ob\al T..$
Thus we can define endomorphisms $\lambda^\xi\in\endo\xi(\al A.)$ by
$\lambda^\xi\big(\xi(A)\big):=\xi\big(\lambda(A)\big)$ for all $A\in\al A.$
and a category
$\xi(\al T.)$
with objects
\begin{equation}
\label{Obxi}
\ob\,\xi(\al T.):=\set{\lambda^\xi},{\lambda\in\ob\,\al T.}.
\end{equation}
and arrows
$(\sigma^{\xi},\tau^{\xi})_{\xi(\al A.)}$,
which is closed w.r.t. direct sums and products.
\item[(iii)]
$\xi\big((\sigma,\,\tau)_{\al A.}\big)=
\big(\sigma^\xi,\,\tau^\xi\big)\s{\xi(\al A.)}.$ for all
$\sigma,\;\tau\in\ob\al T..$
\end{itemize}
Then there is a subcategory
$\al T.^{\xi}_{\C}$
of
$\xi(\al T.)$
with
$\ob\al T.^{\xi}_{\C}=\ob\xi(\al T.)$
which is admissible for
$\xi(\al T.).$
Thus by Theorem \ref{Teo2} there are Hilbert
extensions $\al F.$ and $\al F.^\xi$
corresponding to $\al T.$ and $\xi(\al T.)$ repectively.
Moreover, the Hilbert extension $\al F.^\xi$ of $\xi(\al A.)$ can be chosen
in such a way that it is the homomorphic image of $\al F.$ under
a morphism which is an extension of $\xi.$
That is, $\al F.^\xi=\wt\xi(\al F.)$ where $\wt\xi$ is a morphism
of $\al F.$ such that $\wt\xi(A)=\xi(A)$ for all $A\in\al A..$
\end{teo}
\begin{rem}
A posteriori, the set of objects $\ob\xi(\al T.)$ defined in (\ref{Obxi})
could be enlarged by filling up the unitary equivalence classes of
each $\lambda^\xi$ by {\it all} $\tau$ with
$\tau=\Ad V\circ\xi(\lambda),$ where $V\in\xi(\al A.)$ is unitary.
This corresponds to the objects of the category
$\al T.^\xi$
of Definition~\ref{CatXT}
In this case we also have to add additional arrows, so if
$\tau_i=\Ad V_i\circ\xi(\lambda_i),$ $i=1,2,$ then we also need
\[
(\tau_1,\,\tau_2)\s{\xi(\al A.)}.:=
V_2\big(\tau_1^\xi,\,\tau_2^\xi\big)\s{\xi(\al A.)}.V_1^{-1}\;.
\]
However, for the application of Theorem~\ref{Teo2} this is not
necessary.
\end{rem}
\subsection{Superselection structures left after constraining.}
Recall that the enforcement of constraints by T--procedure produces a
final physical algebra $\al R..$ This algebra is usually assumed to be simple;-
if it is not, then the physics is not fully defined,
and one should extend the constraint
set $\al C.\subset\al A.$ to make $\al R.$ simple (the choice of the extension
needs to be physically motivated).
In the previous subsections we examined which conditions need to be satisfied
by a Hilbert extension ${\{\al F.,\,\al G.\}}$ of $\al A.$ for its structure
to pass through the two parts of the T--procedure.
Here we combine these to produce conditions on the initial system which will
ensure that we obtain a Hilbert extension of $\al R..$
We will also examine when this final Hilbert extension is regular
(and this produces then a DR--category via simplicity of $\al R.).$
\begin{teo}
\label{HExR}
Let ${\{\al F.,\,\al G.\}}$ be a Hilbert extension of $\al A.,$ and let
$\al C.\subset\al A.$ be a first-class constraint set such that
$\al D.\sim\rho_\gamma(\al D.)$
holds for all
$\gamma\in\wh{\al G./\al K.}.$
Then ${\{\al R.\s{\al F.}.,
\,\beta\s{\al G.}.\}}$
is a Hilbert extension of $\al R.,$ where $\al R.\s{\al F.}.
=\xi(\al O.\s{\al F.}.),$
and $\xi$ is the factor map $\al O.\s{\al F.}.
\to \al O.\s{\al F.}.\big/\al D.\s{\al F.}..$
\end{teo}
\begin{beweis}
By Corollary~\ref{cor4.1} it follows from the hypotheses that
${\{\al O.\s{\al F.}.,\,\beta\s{\al G.}.\}}$
is a Hilbert extension of $\al O..$
Since the constraint set $\al C.\subset\al A.$ is $\al G.\hbox{--invariant,}$
we have that $\alpha(\al D.\s{\al F.}.)=\al D.\s{\al F.}.$
for all $\alpha\in\beta\s{\al G.}.\subset\aut\al O.\s{\al F.}.,$
i.e. $\beta\s{\al G.}.\subset\autx\al O.\s{\al F.}..$ (Recall the discussion
in the introductory part of Section~4).
Thus by Theorem~\ref{Teo.4.3} it follows that
$(\beta\s{\al G.}.)^\xi\cong\beta\s{\al G.}.,$ and that
\[
\left\{\xi\big(\al O.\s{\al F.}.),\,(\beta\s{\al G.}.)^\xi\right\}
=\left\{\al R.\s{\al F.}.,\,\beta\s{\al G.}.\right\}
\]
is a Hilbert extension of $\al R.=\xi(\al O.).$
\end{beweis}
Next, we would like to examine when a
Hilbert extension as in Theorem~\ref{HExR}
will produce a
minimal and regular Hilbert extension of $\al R.$
(with Property B).
First recall the requirement for a Hilbert system
$\{\al F.,\,\al G.\}$ to be regular:
there is an
assignment $\sigma\to\al H._\sigma$ from $\ob\al T.$ to
$\al G.$-invariant algebraic Hilbert spaces
in $\al F.$ such that
\begin{itemize}
\item[(i)] $\sigma=\rho\s{\al H._\sigma}.,$
i.e. $\sigma$ is the canonical endomorphism of $\al H._\sigma,$
\item[(ii)] $\sigma\circ\tau\to\al H._\sigma\cdot\al H._\tau\;,$
\end{itemize}
that is, the assignment is compatible with products.
We now want to check whether this property also survives the
map $T:\{\al F.,\,\al G.\}\longrightarrow
{\{\al R.\s{\al F.}.,\,\beta\s{\al G.}.\}}. $
\begin{pro}
\label{Tsat}
Let $\al T.$
satisfy regularity. Let
$\al D.\sim\rho_\gamma(\al D.)$
for all
$\gamma\in\wh{\al G./\al K.},$ then
${\{\al R.\s{\al F.}.,\,\beta\s{\al G.}.\}}$
satisfies regularity, i.e.
there is an
assignment $\sigma\to\al H._\sigma$
such that
\begin{itemize}
\item[(i)] $\sigma=\rho\s{\al H._\sigma}.,$
i.e. $\sigma$ is the canonical endomorphism of $\al H._\sigma,$
\item[(ii)] $\sigma\circ\tau\to\al H._\sigma\cdot\al H._\tau\;.$
\end{itemize}
\end{pro}
\begin{beweis}
Given the assignment $\sigma\to\al H._\sigma$ in $\al F.,$
then whenever $\sigma=\rho_{\gamma},$ $\gamma\in\wh{\beta\s{\al G.}.}$
we have
\[
\sigma\to\al H._\sigma\subset\al O.\s{\al F.}.\longrightarrow
\al R.\s{\al F.}.
\]
where the last map is $\xi,$ so the assignment which we take for
this proposition is $\sigma\to\xi(\al H._\sigma).$
Then (i) and (ii) are automatic.
\end{beweis}
Second, we consider Property B.
\begin{pro}
Let
$\{\al F.,\al G.\}$ satisfy Property B, let $\al G.$ be nonabelian and
$\al C.\subset\al A.$
be an E-constraint set. If
$\al D.\sim\rho_{\gamma}(\al D.)$
for all
$\gamma\in \wh{(\al G./\al K.)},$
then
$\{\al O._{\al F.},\beta_{\al G.}\}$
satisfies Property B.
\end{pro}
\begin{beweis}
First
$\{\al O._{\al F.},\beta_{\al G.}\}$
is a Hilbert extension of
$\al O.$
w.r.t.
$\al G./\al K.$
because of Corollary~\ref{cor4.1}. Choose an
$\al G.\hbox{-invariant}$ Hilbert space
$\al H.\subset\al O._{\al F.}\subset\al F.$
which is not irreducible, i.e. there is
a projection
$E\in\al J.(\al L._{\al G.}(\al H.)),\,0<E<\un.$
Then one has
$E\in (\rho_{\al H.},\rho_{\al H.})_{\al A.}\subset
(\rho_{\al H.}\rest\al O.,\rho_{\al H.}\rest\al O.)_{\al O.}\subset\al O.$
by Theorem~\ref{Teo.4.2}(ii).
By Property B we get closure under subobjects, so there is a
$V\in\al A.,\,V^{\ast}V=\un,\,VV^{\ast}=E.$
In other words,
$E\cong\un(\hbox{mod}\,\al A.).$
Similarly we obtain
$\un-E\cong\un(\hbox{mod}\,\al A.).$
Since
$\al C.$
is an E-constraint set and $E\in\al O.$ we get that
$E\cong\un(\hbox{mod}\,\al O.)$
and
$\un-E\cong\un(\hbox{mod}\,\al O.)$
and this is the assertion.
\end{beweis}
Finally, we need to consider whether the requirement
\[
\al A.'\cap\al F.=Z(\al A.)
\]
passes through the T-procedure.
In full generality, this is a very hard
problem, because both stages of the T-procedure can eliminate or create
elements of $\al A.'.$
In fact, since $\al A.'\cap\al F.\subset\al D.'\cap\al F.\subset
\al O.\s{\al F.}.$ and $Z(\al A.)\subset Z(\al O.),$
we can only deduce from $\al A.'\cap\al F.=Z(\al A.)$
that $\xi(\al A.'\cap\al F.)=\xi(Z(\al A.)).$
On the other hand,
$\al R.'\cap\al R.\s{\al F.}.=Z(\al R.)$ iff
\[
A\in\al O.\s{\al F.}.\quad\hbox{and}\quad [A,\,\al O.]
\subset\al D.\s{\al F.}.\quad\hbox{implies}\quad
A\in \al O.+\al D.\s{\al F.}.\,
\]
which can be true in general for more
elements than those in $\xi(\al A.'\cap\al F.).$
We do have from Theorem~\ref{Teo.4.2} and Proposition~\ref{disjZ}
the following condition:
\begin{pro}
Let
$\HS$
be a minimal Hilbert extension of
$\al A.,$ and let $\al C.\subset\al A.$ be
a first-class constraint set such that
$\al D.\sim\rho_\gamma(\al D.)$
holds for all
$\gamma\in\wh{\al G./\al K.}.$
If the disjointness of
canonical endomorphisms survives the restriction to
$\al O.$
then the Hilbert system
$\{\of,\beta_{\al G.}\}$
is minimal, i.e.
$\al O.'\cap\of=\al Z.(\al O.)$.
\end{pro}
\section{Example}
It is difficult to produce interesting worked examples
in the current state of the theory. The problem is that in almost all
theories of physical significance, the canonical endomorphisms
$\rho_\gamma$ are not known explicitly, and so one cannot
check the compatibility conditions with the constraints
explicitly (cf. Corollary~\ref{cor4.1}).
Here we give an example which is extracted from QED, so it may have
some physical interest. It consists of a fermion in an Abelian gauge
potential. Since the global gauge group $\al G.$
is abelian, the superselection theory simplifies radically.
However, we have explicit endomorphisms $\rho_\gamma$ and can check the
compatibility conditions with the constraints.
Nevertheless, even at this simple level, it is not possible to verify all the
conditions of regularity. We will not treat the issue of dynamics.
\subsection{Constraint structure of QED}
We start with a discussion of the set--up of QED
in order to motivate our subsequent example.
The starting point for QED, is a fermion field $\psi$ in $\R^4$ satisfying
the free CARs, and a $U(1)\hbox{--gauge}$ potential $A$ in $\R^4$ satisfying
free CCRs, and initially these are assumed to commute. So the
appropriate C*-algebraic framework at this initial level is
\[
\al B.:={\rm CAR}(\al H.)\otimes{\rm CCR}(S,\,B)
\]
where $\al H.=L^2(\R^4,\,\C^4),$ $S=\al S.(\R^4,\,\R^4)\big/\ker B,$
and $B$ denotes the symplectic form for QEM, coming from the
Jordan--Wigner distribution, cf. Sect~5 of \cite{Lledo}.
(Note that the tensor product $\al B.$
is unique because ${\rm CAR}(\al H.)$ is a nuclear algebra.)
There is a global charge $Q$ acting on ${\rm CAR}(\al H.)$
and there are constraints in the heuristic theory:
\begin{eqnarray*}
{A_\mu}^{,\,\mu}(x)&:=&0 \quad\qquad\hbox{(Lorentz condition)} \\[1mm]
\hbox{and}\quad\qquad
\Box A_\mu&:=&j_\mu \quad\qquad\hbox{(Maxwell equation)}
\end{eqnarray*}
where $j_\mu:=-e\wt\psi\gamma_\mu\psi$ is the electron current,
and we denote $\wt\psi:=\psi^*\gamma_0.$
The Lorentz condition has been treated in the C*--algebra context
(cf.~\cite{Lledo}) and it needs special treatment, e.g. indefinite metric
or nonregular states, but it is not very interesting for us, since it
only affects the electromagnetic field ${\rm CCR}(S,\,B),$ hence
is independent of the charge $Q.$
The Maxwell equation is more interesting, since it involves both
factors of $\al B.$ and it expresses the interaction between the
two fields. It is however very difficult to enforce in the
C*--algebra context (and ultimately leads to the
conclusion that $\al B.$ is too
small an algebra to do this in). Naively, it seems that we can
easily realise both sides of the Maxwell equation in
the present C*--setting:
smear the left-hand side over $\al S.(\R^4,\,\R^4)$
\[
\int\Box A_\mu(x)\,f^\mu(x)\,dx=\int A_\mu\Box f^\mu dx
=A(\Box f)
\]
then this is realised in ${\rm CCR}(S,\,B)$ through the identification
of the generating Weyl unitaries $\delta_h$ with
the heuristic $\exp iA(h)$ where $h=\Box f.$
If we smear the right-hand side
of the Maxwell equation:
\[
j(f)=-e\int\wt\psi(x)\gamma_\mu\psi(x)f^\mu(x)\, dx\;,
\]
then $j(f)$ generates a Bogoliubov transformation $T_f$ on
$L^2(\R^4,\,\C^4)$ by:
\begin{eqnarray*}
\Ad\big(\exp ij(f)\big)\psi(g)&:=&\left(\exp i\ad j(f)\right)\big(\psi(g)\big)\\[1mm]
&=&\psi(T_fg)=:\alpha\s T_f.(\psi(g))
\end{eqnarray*}
where $\alpha\s T_f.$ is its associated automorphism on
${\rm CAR}(\al H.)$
(we will calculate $T_f$ explicitly in a simplified setting below).
Let $G\subset\aut\al B.$ be the discrete group generated in
$\aut\al B.$ by
\[
\set\beta_f:=\alpha\s T_f.\otimes\iota, f\in{\al S.(\R^4,\,\R^4)}.
\]
and let $\nu$ denote its action on $\al B..$ Define the crossed product
\[
\al E.:=G\cross\nu.\al B.={\rm C}^*\set{\al B.,\,U_g},
U^*_g=U_g^{-1},\; \nu_g=\Ad U_g,\; U_gU_h=U_{gh},\;g,h\in G.
\]
then we identify the heuristic objects $\exp ij(f)$ with the implementing
unitaries $U\s\beta_f..$ So each side of the Maxwell equation has a C*--realisation,
and we only need to decide how to impose the constraint equation.
Heuristically, the Maxwell equations are imposed as state conditions:
$A(\Box f)\phi = j(f)\phi$ for vectors $\phi$ in the representing
Hilbert (or Krein) space.
If we take instead the stronger condition
$A(\Box f)^n\phi = j(f)^n\phi$ for $n\in\N,$ then we can rewrite
the constraint conditions in the form ${e^{iA(\Box f)}\phi}=
{e^{ij(f)}\phi}.$ This suggests that we choose constraint
unitaries $V_f:=U\s -\beta_f.\cdot\delta\s\Box f.$ in $\al E.$
and thus select our Dirac states $\omega$ on $\al E.$
by
\[
\omega(V_f)=1\qquad\forall\; f\in {\al S.(\R^4,\,\R^4)}.
\]
As one expects from the interaction, this program encounters problems:
\begin{itemize}
\item[(1)] We always have that $\Box f\in\ker B,$ hence $\Box f$
corresponds to zero in $S$ (since we factor out by $\ker B).$
This can be remedied by changing $S$ to ${\al S.(\R^4,\,\R^4)},$
in which case $(S,\,B)$ is a degenerate symplectic space.
This problem is connected to the fact that the heuristic smearing
formula
\[
A(f)=\int_{C_+}\left(a_\mu(\b p.)\wh{f}^\mu(p)
+a_\mu^+(\b p.)\bar{\wh{f}}^\mu(p)\right){d^3p\over p_0}
\]
cannot be correct for the interacting theory, since it implies that
$A(\Box f)=0\,,$ in contradiction with the Maxwell equation.
\item[(2)]
Interaction mixes the fermions and bosons, so it is unrealistic to expect that
the interacting fermion and boson fields will commute (as in the tensor
product structure
of $\al B.).$ Even worse, perturbation theory suggests that
the interacting fields need not be canonical, so the
assumption of the CCR and CAR relations
for the interacting bosons and fermions is problematic.
\end{itemize}
\subsection{Model for the interacting Maxwell constraint}
Inspired by the observations above, we now propose an example
which is a simplified version of the Maxwell constraint.
Heuristically, we want to impose a constraint of the form
\[
a^*(x)\,a(x)=LA(x)
\]
where $a(x)$ is a fermion field on $\R^4,$ $A$ is a boson field
and $L$ is a linear differential operator on $\al S.(\R^4).$
To realise this, together with a superselection structure
in a suitable C*--algebra setting, we present our construction
in six steps.\chop\medskip
STEP 1.\chop
\medskip\noindent
For the fermion field, let $\al H.=L^2(\R^4)$ and define ${\rm CAR}(
\al H.)$ in Araki's self-dual form (cf.~\cite{Ar}) as follows.
On $\al K.:=\al H.\oplus\al H.$ define an antiunitary involution
$\Gamma$ by $\Gamma(h_1\oplus h_2):=\ol h._2\oplus\ol h._1\;.$
Then ${\rm CAR}(\al H.)$ is the unique simple C*--algebra with
generators $\set\Phi(k),k\in{\al K.}.$ such that
$k\to\Phi(k)$ is antilinear, $\Phi(k)^*=\Phi(\Gamma k)\,,$
and
\[
\left\{\Phi(k_1),\,\Phi(k_2)^*\right\}=(k_1,\,k_2)\un\;,\qquad
k_i\in\al K.\;.
\]
The correspondence with the heuristic creators and annihilators
of fermions is given by $\Phi(h_1\oplus h_2)=a(h_1)+a^*(\ol h._2)\;,$
where
\[
a(h)=\int a(x)\,\ol h(x).\,d^4x\;,\qquad
a^*(h)=\int a^*(x)\, h(x)\, d^4x\;.
\]
\noindent STEP 2.\chop\medskip\noindent
For the boson field, let $S=\al S.(\R^4,\R),$
and let $K:S\to L^2(M,\mu)$ be a linear map, where $(M,\mu)$ is
a fixed measure space. Define a symplectic form on $S$ by
$B(f,g):={\rm Im}(Kf,\,Kg),$ where $(\cdot,\cdot)$ is the
inner product of $L^2(M,\mu).$ Note that $B$ is degenerate
if $\ker K$ is nonzero.
Define then ${\rm CCR}(S,\,B)=C^*\set\delta_f,f\in S.$
where the $\delta_f$ are unitaries satisfying the Weyl relations:
\[
\delta_f\cdot\delta_g=\delta\s f+g.\exp[iB(f,g)/2]
\]
i.e. ${\rm CCR}(S,\,B)$ is the $\sigma\hbox{--twisted}$
discrete group algebra of $S$ w.r.t. the two--cocycle
$\sigma(f,g):=\exp[iB(f,g)/2]\,.$
\chop\medskip
STEP 3.\chop
\medskip\noindent
To combine the bosons and fermions in one C*--algebra, we want to
allow for the possibility that they may not commute with each other,
hence we will not take the tensor algebra
${\rm CAR}(\al H.)\otimes{\rm CCR}(S,\,B)\,.$
However, we don't know what form their commutators should take,
so we start with the free C*--algebra $\al E.$
generated by ${\rm CAR}(\al H.)$ and ${\rm CCR}(S,\,B)\,.$
The free C*--algebra $\al E.$ seems to be big enough
to allow for possible interactions, but it is also likely to contain
redundant elements.
To be explicit, let $\al L.$ be the linear space spanned by
all monomials of the form $A_0B_0A_1B_1\cdots A_nB_n$ where
$A_i\in{\rm CAR}(\al H.)$ and $B_i\in{\rm CCR}(S,\,B)\,.$
Note that $\al L.$ is an algebra w.r.t. concatenation.
Factor out by the ideal generated by $\un\s{\rm CAR}.-
\un\s{\rm CCR}.$ and replace concatenation by multiplication
for any two elements in a monomial which are in the same
algebra (either ${\rm CAR}$ or ${\rm CCR}$) after the
factorisation.
Note that this will now produce all
possible monomials of elements in ${\rm CAR}(\al H.)$ and
${\rm CCR}(S,\,B)$ - just consider those monomials
in $\al L.$ with $A_0$ or $B_n$ the identity to obtain
all other monomials.
Now the resultant algebra $\al N.$ is a *--algebra with the involution
given by
\[
(A_0B_0\cdots A_nB_n)^*=B_n^*A_n^*\cdots B_0^*A_0^*\;.
\]
Form the enveloping C*--algebra $\al E.$ of $\al N.,$ i.e.
let
\[
\al I._0:=\bigcap\set\ker\pi,\pi\in
\hbox{Hilbert space representations of $\al N.$}.
\]
and set $\al E.:=\ol{\al N.\big/\al I._0}.$ where the closure
is w.r.t. the enveloping C*--norm, i.e.
\[
\|A\|:=\sup\set\|\pi(A)\|,\pi\in
\hbox{Hilbert space representations of $\al N.$}.\;.
\]
That $\al E.$ is nontrivial, follows from the fact that any
tensor product representation of ${\rm CAR}(\al H.)\otimes{\rm CCR}(S,\,B)$
defines a Hilbert space representation of $\al N.,$ hence it
follows that $\al E.$ is nonzero and that ${\rm CAR}(\al H.)$
and ${\rm CCR}(S,\,B)$ are faithfully embedded in $\al E.$
(as the images under the factorisation maps of the original
generating algebras in the construction).
Note that we have a surjective homomorphism $\zeta:\al E.\to
{{\rm CAR}(\al H.)\otimes{\rm CCR}(S,\,B)}$
given by
\[
\zeta(A_0B_0\cdots A_n B_n):= (A_0\cdots A_n)\otimes(B_0\cdots B_n)\;,
\quad A_i\in {\rm CAR}(\al H.),\; B_i\in{\rm CCR}(S,\,B)\,.
\]
Clearly the ideal $\al I._T$ of $\al E.$ generated by
the commutators $\big[{\rm CAR}(\al H.),\,{\rm CCR}(S,\,B)\big]$
is in $\ker\zeta.$ Since $\al E.$ probably contains redundant
elements, we do not require it to be simple.
$\zeta$ will be important in proofs below.
\chop\medskip
STEP 4.\chop
\medskip\noindent
Next, we would like to model in the curent C*--setting, the
global and local heuristic charges:
\[
Q=\int a^*(x)\,a(x)\,d^4x\,,\qquad
Q(f)=\int a^*(x)\,a(x)\,f(x)\,d^4x\,,\quad
f\in\al S.(\R^4,\R)\;.
\]
Let us calculate the Bogoliubov transformations which they induce:
\begin{eqnarray*}
&&\big[Q(f),\Phi(h_1\oplus h_2)\big] \\[1mm]
&=& \int\int\left[a^*(x)a(x)f(x),\,a(y)\ol h_1(y).+
a^*(y)\ol h_2(y).\right]\,d^4x\,d^4y \\[1mm]
&=& \int\int f(x)\bigg\{\Big(a^*(x)a(x)a(y)-a(y)a^*(x)a(x)\Big)
\ol h_1(y).\\[1mm]
&&\qquad+\Big(a^*(x)a(x)a^*(y)- a^*(y)a^*(x)a(x)\Big)\ol h_2(y).
\bigg\}d^4x\,d^4y \\[1mm]
&=& \int\int f(x)\bigg\{-\big\{a^*(x),\,a(y)\big\}a(x)\,\ol h_1(y).\\[1mm]
&&\quad \left(a^*(x)\big(\delta(x-y)-a^*(y)a(x)\big)
-a^*(y)a^*(x)a(x)\right)\ol h_2(y).\bigg\}\,d^4x\,d^4y\\[1mm]
&=&\int\int f(x)\bigg\{-\delta(x-y)\ol h_1(y).a(x) +
\delta(x-y)a^*(x)\ol h_2(y).\bigg\}\,d^4x\,d^4y\\[1mm]
&=& -a(\ol f.\cdot h_1)+a^*(f\cdot\ol h_2.)\\[1mm]
&=&\Phi(-\ol f.\cdot h_1\oplus\ol f.\cdot h_2)
=\Phi\big(f(-h_1\oplus h_2)\big)
\end{eqnarray*}
since $f$ is real. For the global charge $Q,$ just put
$f=1$ in the last calculation. Thus
\begin{eqnarray*}
\big(\ad Q(f)\big)^n\big(\Phi(h_1\oplus h_2)\big)
&=&\Phi\left(f^n\cdot\big((-1)^nh_1\oplus h_2\big)\right)\qquad
\hbox{hence:}\\[1mm]
\left(\Ad\big(\exp\,iQ(f)\big)\right)\left(\Phi(h_1\oplus h_2)\right)
&=& \Big(\exp\,i\,\ad Q(f)\Big)\left(\Phi(h_1\oplus h_2)\right)\\[1mm]
&=& \sum_{n=0}^\infty{\big(i\,\ad\,Q(f)\big)^n\over n!}
\left(\Phi(h_1\oplus h_2)\right)\\[1mm]
&=& \sum_{n=0}^\infty{i^n\over n!}\,\Phi\Big(f^n\big((-1)^n
h_1\oplus h_2\big)\Big)\\[1mm]
&=& \Phi\big(e^{-if}h_1\oplus e^{if}h_2\big)=:\Phi\big(T_f(h_1\oplus h_2)
\big)\;.
\end{eqnarray*}
Now $T_f$ is unitary on $\al K.,$ and satisfies ${[T_f,\,\Gamma]}=0$
hence it is a Bogoliubov transformation (cf.~p43 in \cite{Ar}), and
so we can define automorphisms on
${\rm CAR}(\al H.)$ by
\[
\wt\gamma_f\big(\Phi(k)\big):=\Phi(T_fk)\;.
\]
It is clear that $T_fT_g=T_{f+g}\,,$ hence that
$\wt\gamma:\al S.(\R^4)+\R\to\aut({\rm CAR}(\al H.))$
is a homomorphism.
We extend these automorphisms to maps $\gamma_f$ on $\al E.$ by setting
\[
\gamma_f\restriction {\rm CAR}(\al H.) =\wt\gamma_f\;,\qquad
\hbox{and}\qquad
\gamma_f\restriction {\rm CCR}(S,B) = \iota
\]
where $\iota$ is the identity map.
The only relations between ${\rm CAR}(\al H.)$ and
${\rm CCR}(S,B)$ in the free construction of $\al E.,$ is
$\un\s{\rm CAR}.=\un\s{\rm CCR}.,$ so since the definition of
$\gamma_f$ preserves this relation, it will extend to a well-defined
map on the free *--algebra $\al N..$
In fact, since $\gamma_f$ replaces ${\rm CAR}(\al H.)$
by an isomorphic one in a free construction, it will be
an automorphism on $\al N.,$
and so will define an automorphism on the enveloping algebra $\al E..$
Let $G$ denote the Abelian group generated in
$\aut\al E.$ by $\set\gamma_f,f\in{\al S.}(\R^4)\cup\R.$
and equip it with the discrete topology.
Denote its action by $\beta:G\to\aut\al E.,$ and define the algebra
\[
\al A.:=G\cross\beta.\al E.\;,
\]
then we identify the implementing unitaries $U_{\gamma_f}\in\al A.$ of
$\gamma_f\in\aut\al E.$ with the heuristic objects
$\exp iQ(f),$ $f\in {\al S.}(\R^4)\cup\R$ (in the case that
$f=t\in\R,$ we denote $Q(t)=tQ).$
Now $\gamma$ is a surjective homomorphism $\gamma:{\al S.(\R^4)+\R}
\to G$ and from the definitions above, it is clear that its kernel
is $2\pi\Z\subset\R,$ hence the discrete group $G$ is isomorphic to
$\al S.(\R^4)\times\T.$ Of course $\T$ will be our global gauge
group below.
\chop\medskip
STEP 5.\chop
\medskip\noindent
Next, we would like to realize in $\al E.$ the heuristic constraints
\[
Q(f)^n\psi=A(Lf)^n\psi\qquad\forall\;f\in{\al S.}(\R^4),\;\;
n\in\N
\]
where $L:S\to\ker K\subseteq\ker B$ is a given linear map.
First write the heuristic constraints in bounded form:
\[
e^{iQ(f)}\psi=e^{iA(Lf)}\psi\;,\quad\hbox{i.e.}\quad
e^{-iA(Lf)}e^{iQ(f)}\psi=\psi\;.
\]
So, given the identifications with heuristic objects above,
we define our constraint unitaries to be:
\[
\al U.:=\set\delta\s-Lf.\cdot U_{\gamma_f}=:V_f,f\in{\al S.}(\R^4,\R).
\subset\al A.\;.
\]
\begin{pro}
\label{FCU}
$\al U.$ is first--class.
\end{pro}
The proof is in the next section.
The heuristic constraint conditions now correspond to the
application of the T--procedure to $\al U..$
\chop\medskip
STEP 6.\chop
\medskip\noindent
Now we will specify the superselection structure associated with
the global charge $Q$ using
the fact that $Q$ must take integer values on
the vacuum state. Recall that the global gauge transformations
$\gamma\s t.\,,$ $t\in\R$ are implemented by the unitaries
$U\s\gamma_t.\in \al A.$ which we identify with the heuristic objects
$\exp itQ$ (cf. Step 3). For the superselection sectors
we need to find cyclic representations ${(\pi,\,\Omega)}$
such that
\[
\pi(U\s\gamma_t.)\Omega=e^{itn}\Omega\qquad\forall\;t\in\R
\]
and some $n\in\Z$ (the heuristic corresponding conditions
are $Q\Omega=n\Omega).$
We recognise these as constraint conditions for Dirac states
of the constraint unitaries:
\[
\al V._n:=\set V_t^{(n)}:=e^{-itn}U\s\gamma_t.,t\in\R.\;.
\]
Denote the sets of these Dirac states by
\[
{\got S}_D^{(n)}:=\set\omega\in{\got S}(\al A.),
\omega(V_t^{(n)})=1\quad\forall\;t\in\R.\,.
\]
These folia of states will be our superselection sectors.
\begin{lem}
\label{SectDisj}
With notation as above, we have:
\begin{itemize}
\item[(i)]
${\got S}_D^{(n)}\cap{\got S}_D^{(m)}=\emptyset$ if $n\not=m\;,$
\item[(ii)]
${\got S}_D^{(0)}\not=\emptyset\;.$
\end{itemize}
\end{lem}
\begin{beweis} (i)
If there is an $\omega\in{\got S}_D^{(n)}\cap{\got S}_D^{(m)}$
for $n\not=m,$ then
\begin{eqnarray*}
\omega\big(e^{-itn}U\s\gamma_t.\big)&=& 1\; =\;\omega\big(e^{-itm}U\s\gamma_t.\big) \\[1mm]
\hbox{so:}\qquad\omega\big(U\s\gamma_t.\big) &=& e^{itn}=e^{itm}\qquad\forall\;t
\end{eqnarray*}
which contradicts $n\not=m.$\chop
(ii) In the proof of Lemma~\ref{FCU} we constructed a state
$\omega_3\in{\got S}(\al A.)$ satisfying $\omega_3(U_g)=1$
for all $g\in G.$ If we take $g=\gamma\s t.,$ then this implies
that $\omega_3\in{\got S}_D^{(0)}.$
\end{beweis}
To connect with the usual machinery for superselection used above,
we need to exhibit the canonical endomorphisms (automorphisms in
the abelian case). We construct an action $\rho:\Z\to\aut\al A.$
such that its dual action on $\al A.^*$ satisfies
$\rho^*_k({\got S}_D^{(n)})={\got S}_D^{(n+k)}.$
\begin{defi}
\label{RhDf}
For each $k\in\Z$ define a *-automorphism $\rho_k$ of $\al A.$ by:
\begin{eqnarray*}
\rho_k(A)=A\quad\forall\;A\in\al E.;\qquad
\rho_k(U\s\gamma_t.)=e^{itk}U\s\gamma_t.\quad\forall\,t\in\R;\\[1mm]
\rho_k(U\s\gamma_f.)=U\s\gamma_f.\quad\forall\;f\in\al S.(\R^4)\,.
\end{eqnarray*}
\end{defi}
\begin{lem}
\label{RkWD}
$\rho_k$ is well--defined, and $\rho_k\in\aut\al A.\,.$
\end{lem}
The proof is in the next section.
Recall that for any $\alpha\in\aut\al A.$ we define its dual
$\alpha^*:\al A.^*\to\al A.^*$ by $\alpha^*(f):=f\circ\alpha$
for all functionals $f\in\al A.^*.$
\begin{pro}
With notation as above, we have $\rho^*_k({\got S}_D^{(n)})
={\got S}_D^{(n+k)}$ and ${\got S}_D^{(n)}\not=\emptyset$
for all $n\in\Z\;.$
\end{pro}
\begin{beweis}
Let $\omega\in\rho^*_k\big({\got S}_D^{(n)}\big),$
i.e. $\omega=\omega_n\circ\rho_k$ for some $\omega_n\in{\got S}_D^{(n)}.$
Thus
\[
\omega\left(e^{-it(n+k)}U_{\gamma\s t.}\right)
=\omega_n\left(e^{-it(n+k)}\rho_k\big(U_{\gamma\s t.}\big)\right)
=\omega_n\left(e^{-itn}U_{\gamma\s t.}\right) =1
\]
i.e. $\omega\in{\got S}_D^{(n+k)}\,.$
Conversely, for any $\omega\in{\got S}_D^{(n+k)}$ there is an
$\omega_n\in{\got S}_D^{(n)}$ for which
$\omega=\omega_n\circ\rho_k$ and it is obviously
$\omega_n=\omega\circ\rho_{-k}\,.$
Thus $\rho^*_k({\got S}_D^{(n)})
={\got S}_D^{(n+k)}.$
Since we have that ${\got S}_D^{(0)}\not=\emptyset,$
it is now immediate that ${\got S}_D^{(n)}=\rho^*_k({\got S}_D^{(0)})
\not=\emptyset\;.$
\end{beweis}
Recall from our earlier discussions that the canonical automorphisms
(Abelian case) must necessarily be outer on $\al A..$
\begin{pro}
\label{RhOut}
With notation as above, $\rho_k\in\out\al A.$ if $k\not=0\;.$
\end{pro}
The proof of this is long, and is in the next section.
From the action $\rho:\Z\to{\rm Out}\,\al A.$ we construct a
Hilbert extension (cf. Subsection~\ref{abelianHS}). First set
\[
\Lambda:=\set\Ad U\circ\rho_k,{U\in\al A.\;\hbox{unitary,}\;k\in\Z}.
\]
so $\Z\cong\Lambda\big/{\rm Inn}\,\al A.\;.$
So the class of $k\in \Z$ in $\Lambda\big/{\rm Inn}\,\al A.$
is $\chi\s k.:=\set\Ad U\circ\rho_k,{U\in\al A._u}.\,.$
Take the monomorphic section $\chi\s k.\to k,$
then it has a trivial cocycle $\sigma(n,\,m)=1$ for all $n,\,m\in\Z\,.$
Define $\al F.:=\Z\cross\rho.\al A.,$ then it has the dense *--algebra
\[
\al F._0:=\set\sum_{n\in F}A_nU^n,{A_n\in\al A.\,,\;
F\subset\Z\;\hbox{finite}}.
\]
where $U\in\al F.$ is the unitary
which implements $\rho_1,$ i.e. $\rho_1=\Ad U\restriction\al A.\,.$
Fix $t\in\T=\wh\Z$ and define an action
$\alpha:\T\to\aut\al F.$ by
\[
\alpha_t\left(\sum_{n\in F}A_nU^n\right)
:=\sum_{n\in F}A_nt^nU^n\qquad\hbox{on $\al F._0\;.$}
\]
Then the fixed point algebra of $\alpha$ is $\al A.\,.$
We verify the compatibility
condition in Corollary~\ref{cor4.1}:
\begin{pro}
$\rho_k(\al D.)\sim\al D.$ for all $k\in\Z\,.$
\end{pro}
\begin{beweis}
The constraint unitaries from which we define $\al D.$ are
$V_f:=\delta\s-Lf.\cdot U_{\gamma_f}\,,$ $f\in\al S.(\R^4)\,.$
By definition~(\ref{RhDf}) we have $\rho_k\restriction\al E.
=\iota\,,$ hence $\rho_k(\delta_{-Lf})=\delta_{-Lf}\,.$
Also $\rho_k(U_{\gamma\s f.}) = U_{\gamma\s f.}$
for all $f\in\al S.(\R^4)\,,$ hence
$\rho_k(V_f)=V_f$ for all $f\in\al S.(\R^4)\,.$
Thus $\rho_k$ preserves the Dirac states ${\got S}_D$
and hence $\rho_k(\al D.)=\al D.$ for all $k\in\Z\,.$
\end{beweis}
It remains to show that this Hilbert system is regular
and minimal.
However, at this stage we do not have a proof because little is known
about the ideal $\al I._0$ factored out in Step~3.
\section{Proofs}
\label{Proofs}
\subsection*{Proof of Theorem~\ref{Teo.4.1}}
{\bf (i)}
We have that
$\beta_g:=g\rest\of.$
The pointwise norm-continuity of
$\beta_{\al G.}$
follows from the pointwise norm-convergence topology of $\al G..$
So $\{\of,\al G.,\beta\}$ is a C*--dynamical system. Since
$\al A.$
is the fixed point algebra of
$\al G.$,
the fixed point algebra of
$\beta\s{\al G.}.$ is $\of\cap\al A..$
By Theorem~\ref{Teo.2.12} we have that
$\of\cap\al A.= \al O..$\chop
If $A\in Z(\al A.),$ then ${[A,\al C.]}=0,$ hence $A\in\al O.$
by Theorem~\ref{Teo.2.2}(iii), and from this it follows that
$Z(\al A.)\subseteq Z(\al O.).$ \chop
{\bf (ii)}
Now let
$\al H._{\gamma}\subset\Pi_{\gamma}\al F.$.
If there is a unit vector $\Phi\in\al H._\gamma\cap\of,$
then by invariance of $\al H._\gamma\cap\of$ under $\al G.,$
we also have $\al H._\gamma\cap\of\supset\spa(\al G.\Phi)
=\al H._\gamma,$ where the last equality follows from
irreducibility of the action of $\al G.$ on $\al H._\gamma.$
Thus $\al H._\gamma\cap\of \not=\{0\}$ implies that
$\al H._\gamma\subset\of,$
hence
$\al H._\gamma\subset\Pi_\gamma\of.$
To prove that
$\Pi_{\gamma}\of=\hbox{clo-span}\,(\al O.\al H._{\gamma})$
we follow the proof of Lemma 10.1.3 in ~\cite{BW}. First, since
$\al O.=\Pi_\iota\of$,
it follows that
$\al O.\al H._\gamma\subseteq\Pi_\gamma\of$
by Remark~\ref{remark1}(v).
By Evans and Sund~\cite{ES},
$\Pi_\gamma\of$ is the closed span of all the $\al G.\hbox{--invariant}$
subspaces $\al E.\subset\of$ such that
$\beta_\al G.$
acts on $\al E.$ as an element of $\gamma\in\wh{\al G./\al K.}.$
So for the reverse inclusion,
$\Pi_{\gamma}\of\subseteq\csp\{\al OH._\gamma\},$
it suffices
to show that $\spa\{\al OH._\gamma\}$ contains all
$\al G.\hbox{--invariant}$
subspaces
$\al E.\subset\of$
such that $\al G.$
acts on $\al E.$ as an element of $\gamma.$
Let $\{\Psi_1,\ldots,\,\Psi_d\},$ $d={\rm dim}\,\gamma$
be a basis of such an $\al E.$ under which the matrix representation
of the action of $\al G.$ is an element of $\gamma,$ i.e.
\[
g\Psi_i=\sum_j\lambda_{ji}(g)\,\Psi_j
\]
where the matrix $(\lambda_{ji}(g))$ is a unitary matrix representation
of $\al G.$ of the type $\gamma.$
Choose an orthonormal basis $\{\Phi_1,\ldots,\,\Phi_d\}$ of $\al H._\gamma$
which also transforms under $\al G.$ according to $(\lambda_{ji}(g)).$
Consider now the element $A:=\sum\limits_j\Psi_j\Phi^*_j\in\of.$ Then
\begin{eqnarray*}
g(A)&=&\sum_jg\left(\Psi_j\Phi^*_j\right)=
\sum_{i,\,k}\Big(\sum_j\lambda_{ij}(g)\,\ol\lambda_{kj}(g).\Big)
\Psi_i\Phi^*_k \\[1mm]
&=& \sum_{i,\,k}\delta_{ik}\Psi_i\Phi^*_k =\sum_j\Psi_j\Phi^*_j=A \,.
\end{eqnarray*}
Thus $A\in\al O.,$ and hence all $\Psi_i=A\Phi_i\in\al OH._\gamma$
i.e. $\al E.\subset\spa(\al OH._\gamma).$
\chop
{\bf (iii)}
Let $\al H._\sigma$ have an orthonormal basis $\{\Phi_1,\ldots\Phi_d\}$
hence $\rho_\sigma(F)=\sum\limits_{j=1}^d\Phi_jF\Phi_j^*$ for $F\in\al F.,$
$\rho_\sigma\rest\al A.=\sigma.$
Since $\{\Phi_j\}\subset\of=M(\df)$ it is clear that $\rho_\sigma$
preserves both $\df$ and $\of.$ Since $\rho_\sigma$ also preserves $\al A.,$
it preserves $\al D.=\df\cap\al A.$ and $\al O.=\of\cap\al A.,$
where these equalities come from Theorem~\ref{Teo.2.12}.
\subsection*{Proof of Theorem~\ref{Teo.4.2}}
\def\rh{\rho\s{\al H.}.}
{\bf (i)}
Let $\al H.\subset\of$ have an orthonormal basis $\{\Phi_j\}.$
By the same proof as for Theorem~\ref{Teo.4.1}(iii) we have that
$\rh(\al D.)\subseteq\al D..$ \chop
Since $\of$ is a *--algebra and the relative multiplier algebra of
$\df\supset\al D.,$ we have that
\begin{eqnarray*}
[\Phi^*_j,\, D]&\in &\df\quad\hbox{for all}\;D\in\al D.,\;j. \\[1mm]
\hbox{Thus:}\qquad
\Phi_j[\Phi^*_j,\, D]&\in &\Phi_j\df=\rh(\df)\Phi_j
\subset\csp(\rh(\df)\al F.) \\[1mm]
\hbox{i.e.}\qquad
D-\rh(D)&=&\sum_j\left(\Phi_j\Phi^*_jD-\Phi_jD\Phi_j^*\right)
\in\csp(\rh(\df)\al F.\,.) \\[1mm]
\hbox{So}\qquad
D&\in &\csp(\rh(\df)\al F.)\quad\hbox{for all}\; D\in\al D.\,.
\end{eqnarray*}
Thus we have shown that $\al D.\subset\csp(\rh(\df)\al F.),$
and now we would like to show that
${\csp(\rh(\df)\al F.)}={\csp(\rh(\al D.)\al F.)}.$
We have that
\[
\csp(\al CF.)=\csp(\al DF.)=\csp(\df\al F.),
\]
so if we apply $\rh$ to both sides of the last equation, multiply by
$\al F.$ on the right and take closed span, we get:
\begin{eqnarray*}
\csp\big(\rh(\al D.)\rh(\al F.)\al F.\big) &=&
\csp\big(\rh(\df)\rh(\al F.)\al F.\big) \\[1mm]
\hbox{i.e.}\qquad
{\csp(\rh(\df)\al F.)} &=&
\csp(\rh(\al D.)\al F.)\;. \\[1mm]
\hbox{Thus:}\qquad\al D. \subset \csp(\rh(\al D.)\al F.) & &\quad
\hbox{and since $\al D.$ is a *--algebra in $\al A.,$} \\[1mm]
\al D.\; \subseteq \;\csp(\rh(\al D.)\al F.)\!&\cap&\!
\csp(\al F.\rh(\al D.))\cap\al A. \\[1mm]
&\subseteq &\csp(\al DF.)\cap\csp(\al FD.)\cap\al A.=\al D.
\end{eqnarray*}
where we used $\df\cap\al A.=\al D..$ Thus
\[
\al D.=\csp(\rh(\al D.)\al F.)\cap\csp(\al F.\rh(\al D.))\cap\al A.
=\csp(\rh(\al D.)\al A.)\cap\csp(\al A.\rh(\al D.))
\]
which also follows from Theorem~\ref{Teo.2.12}, treating
$\rh(\al D.)\subseteq\al D.$ as a second constraint set.
Thus $\al D.\sim\rh(\al D.)$ in $\al A..$
For the converse, let $\al D.\sim\rh(\al D.)$ and take
$\Phi\in\al H..$ From the equation $\Phi D=\rh(D)\Phi$ for all
$D\in\al D.,$ we conclude that
\[
\Phi\cdot\csp(\al DF.) \subset \csp(\rh(\al D.)\al F.)=\csp(\al DF.)
\]
using $\al D.\sim\rh(\al D.).$
Since we have trivially that
$\Phi\cdot\csp(\al FD.)\subset\csp(\al FD.),$ it follows that
\[
\Phi\df=\Phi\left(\csp(\al FD.)\cap\csp(\al DF.)\right)
\subset\df
\]
so $\Phi$ is in the left multiplier of $\df.$
We also have that
\[
\csp(\al FD.)\Phi=\csp(\al F.\rh(\al D.))\Phi=\csp(\al F.\Phi\al D.)
\subseteq\csp(\al FD.)\;.
\]
Since trivially $\csp(\al DF.)\Phi\subseteq\csp(\al DF.),$ it
follows that
\[
\df\Phi=\left(\csp(\al FD.)\cap\csp(\al DF.)\right)\Phi
\subset\df
\]
and hence $\Phi$ is in the relative multiplier algebra
of $\df,$ i.e. $\Phi\in\of$ by Theorem~\ref{Teo.2.2}(ii).\chop
{\bf (ii)}
Let $\al H._\sigma\subset\of\supset\al H._\tau,$
hence by (i) $\al D.\sim\sigma(\al D.)\sim\tau(\al D.).$
First let $X\in (\sigma,\,\tau)_{\al A.}\cap\al O.,$ i.e.
$X\in\al O.$ and $X\sigma(A)=\tau(A)X$ for all $A\in\al A..$
By letting $A$ range over only $\al O.\subset\al A.,$
we immediately get that $X\in{(\sigma\rest\al O.,\,\tau\rest\al O.)_{\al O.},}$
making use of Theorem 4.1(iii).
Therefore,
it suffices to prove that
${(\sigma,\,\tau)_{\al A.}}\subset\al O..$
Let $X\in{(\sigma,\,\tau)_{\al A.}},$ i.e.
$X\in\al A.$ and
$X\sigma(A)=\tau(A)X$ for all $A\in\al A..$ Thus
\begin{eqnarray*}
X\cdot\csp(\al DA.)&=& X\cdot\csp(\sigma(\al D.)\al A.)
=\csp(X\sigma(\al D.)\al A.) \\[1mm]
&\subseteq&
\csp(\tau(\al D.)X\al A.) \subseteq
\csp(\tau(\al D.)\al A.)=\csp(\al DA.)\;.
\end{eqnarray*}
Since we have trivially that
$X\cdot\csp(\al AD.)\subseteq\csp(\al AD.),$
it follows that
\[
X\al D.\subseteq\csp(\al AD.)\cap\csp(\al DA.)=\al D.\,,
\]
i.e. $X$ is in the left multiplier of $\al D..$
Likewise:
\begin{eqnarray*}
\csp(\al AD.)\cdot X &=& \csp(\al A.\tau(\al D.))\cdot X
=\csp(\al A.\tau(\al D.)X) \\[1mm]
&\subseteq&
\csp(\al A.X\sigma(\al D.))\subseteq\csp(\al A.\sigma(\al D.)) \\[1mm]
&=& \csp(\al AD.)\,.
\end{eqnarray*}
Since trivially $\csp(\al DA.)\cdot X\subseteq\csp(\al DA.),$
we have:
\[
\al D.\cdot X\subseteq\csp(\al AD.)\cap\csp(\al DA.)=\al D.\,,
\]
and hence $X$ is in the relative multiplier of $\al D.,$
i.e. $X\in\al O..$
\subsection*{Proof of Proposition~\ref{pro.4.7}}
(i) According to the decomposition
\[
\sigma(\cdot)=\sum_{j}V_{j}\rho_{\gamma_{j}}(\cdot)V_{j}^{\ast},\quad
V_{j}\in (\rho_{\gamma_{j}},\sigma)_{\al A.}
\]
we have
$\al H._{\sigma}=\sum_{j}V_{j}\al K.'_{j}$
where
$\rho_{\gamma_{j}}=\rho_{\al K.'_{j}}$
and
the
$\al K._{j}'$
are irreducible w.r.t.
$\al G.$
carrying the representation
$\gamma_j\in\wh{\al G.}.$
Moreover
$\hbox{supp}\,\al K.'_{j}=1.$
Put
$E_{j}:=V_{j}V_{j}^{\ast}.$
Then
$\sum_{j}E_{j}=1.$
Since
$V_{j}\al K.'_{j}\subset\al H._{\sigma}\subset\of$
it follows that
\[
E_{j}=\hbox{supp}\,V_{j}\al K.'_{j}\in\al O.
\]
for all $j$. Therefore, by assumption, there are isometries
$W_{j}\in\al O.$
with
$E_{j}=W_{j}W_{j}^{\ast}.$
Now we put
\[
\al K._{j}:=W_{j}^{\ast}V_{j}\al K.'_{j}\subset\of.
\]
Then
$\al K._{j}$
is an algebraic Hilbert space with
$\hbox{supp}\,\al K._{j}=1$,
carrying the representation
$\gamma_{j}$
and we have
$V_{j}\al K.'_{j}=W_{j}\al K._{j}$.
Hence
$\al H._{\sigma}=\sum_{j}W_{j}\al K._{j}$
and
\[
\sigma(\cdot)=\sum_{j}W_{j}\rho_{\al K._{j}}(\cdot)W_{j}^{\ast},\quad
W_{j}\in (\rho_{\al K._{j}},\sigma)_{\al O.}
\]
follows.
(ii) This follows from (i) using the existence
of subobjects.
\subsection*{Proof of Theorem~\ref{Teo.4.3}}
Let
$\al H.\subset\al F.$
be an arbitrary algebraic Hilbert space.
Then
$\xi(\al H.)\subset\al L.$
is also an algebraic Hilbert space.
with support 1.
To see this, let
$\{\Phi_{j}\}_{j}$
be an orthonormal basis of
$\al H.$,
i.e.
$\Phi_{j}^{\ast}\Phi_{k}=\delta_{j,k}1$
and
$\sum_{j}\Phi_{j}\Phi_{j}^{\ast}=1$
then the same relations are true for the system
$\{\xi(\Phi_{j})\}_{j}.$
In particular $\xi$ is
injective on $\al H..$
Moreover, if
$\al H.$
is $\al G.$-invariant and
${g}(\Phi_{j})=\sum_{k}u_{k,j}(g)\Phi_{k}$
then
${g}^{\xi}\big(\xi(\Phi_{j})\big)=\sum_{k}u_{k,j}(g)\xi(\Phi_{k}),$
i.e.
$\xi(\al H.)$
carries the same representation as
$\al H..$
In particular, if
$\al H._{\gamma}$
carries
$\gamma$,
i.e.
$\al H._{\gamma}\subset\Pi_{\gamma}\al F.$
then
$\xi(\al H._{\gamma})\subset\Pi_{\gamma}^{\xi}\al L.$.
This proves (ii) and (i).\chop
Let
$\al N._{\gamma}$ be an orthonormal basis for
$\xi(\al H._\gamma),$ then by the first part
it is the image under $\xi$ of an
orthonormal basis $\{\Phi_{\gamma,j}\}_{j}$ of $\al H._\gamma.$
Let $F=
\sum A_{\gamma,j}\Phi_{\gamma,j}\in\al F._{\rm fin}$
such that
$\xi(F)=0=\sum\xi(A_{\gamma,j})\xi(\Phi_{\gamma,j}).$
By applying $\al G.^\xi$ to this equality, and using
the relation
$g^\xi(\xi(\Phi_{\gamma,j}))=\sum\limits_{k}u_{k,j}(g)\xi(\Phi_{\gamma,k})$
we get
$\sum\limits_{\gamma,j,k}u_{k,j}^{\gamma}(g)\xi(A_{\gamma,j})\xi
(\Phi_{\gamma,k})=0$ for all $g\in\al G..$
Now the orthogonality relations for the matrix elements of the
irreducible representations of
$\al G.$
imply
$\xi(A_{\gamma,j})\xi(\Phi_{\gamma,k})=0$
for all
$\gamma\in\wh{\al G.},j,k$.
Hence
$\xi(A_{\gamma,j})=0$
follows. This proves (iii). From
$\xi\circ\Pi_{\gamma}=\Pi_{\gamma}^{\xi}\circ\xi$
(iv) follows.\chop
For (v) observe that the homomorphic images of isometries $V_i\in\al A.$
with $V_1V_1^*+V_2V_2^*=\un$ produces a pair of isometries in
$\xi(\al A.)$ satisfying the same relation. So Property B for $\al A.$
implies Property B for $\xi(\al A.)\,.$
\subsection*{Proof of Corollary~\ref{Cor.4.9}}
(i) Let $\lambda$ be generated by $\al H.$, i.e. let
$\lambda=\rho_{\al H.}$
such that
$\lambda(A)=\sum_{j}\Phi_{j}A\Phi_{j}^{\ast}$
where
$\{\Phi_{j}\}_{j}$
is an orthonormal basis of
$\al H.$.
Then
$\xi(\lambda(A))=\sum_{j}\xi(\Phi_{j})\xi(A)\xi(\Phi_{j})^{\ast}$
and
$\xi(A)=0$
implies
$\xi(\lambda(A))=0.$
Furthermore,
$\lambda^{\xi}(\xi(A))=\rho_{\xi(\al H.)}(\xi(A)).$\chop
(ii)$\lambda(\cdot)=\sum_{j}W_{j}\lambda_{j}(\cdot)W_{j}^{\ast}$
implies
$\lambda^{\xi}(\cdot)=\sum_{j}\xi(W_{j})\lambda_{j}^{\xi}(\cdot)\xi(W_{j})^{\ast}$
and
$(\lambda\circ\sigma)^{\xi}=\lambda^{\xi}\circ\sigma^{\xi}.$
Further, if
$\sigma(\cdot)=V^{\ast}\lambda(\cdot)V$
where
$V\in (\sigma,\lambda)$,
i.e.
$V\sigma(\cdot)=\lambda(\cdot)V$
then
$\xi(V)\sigma^{\xi}(\cdot)=\lambda^{\xi}(\cdot)\xi(V)$
and
$\sigma^{\xi}(\cdot)=\xi(V)^{\ast}\lambda^{\xi}(\cdot)\xi(V).$
In particular, if
$\lambda\cong\sigma$
then
$\lambda^{\xi}\cong\sigma^{\xi}.$
\subsection*{Proof of Theorem~\ref{Teo.4.4}}
(i) Let
$\sigma\in\hbox{Ob}\,\al T.^{\xi}$.
Then there is a $\al G.$-invariant algebraic Hilbert space
$\al H.\subset\al L.$
such that
$\sigma (X)=\sum_{j}\Psi_{j}X\Psi_{j}^{\ast},\;X\in\xi(\al A.),$
where
$\{\Psi_{j}\}_{j}$
denotes an orthonormal basis of
$\al H.$.
On the other hand, there is a corresponding $\al G.$-invariant
Hilbert space
$\al K.\subset\al F.$
such that
$\al H.$
and
$\al K.$
carry unitarily equivalent representations of
$\al G.$.
In
$\al K.$
we choose an orthonormal basis
$\{\Phi_{j}\}_{j}$
such that the representation matrix of
$\al G.$
in
$\al H.$
w.r.t.
$\{\Psi_{j}\}_{j}$
coincides with that in
$\al K.$
w.r.t.
$\{\Phi_{j}\}_{j}.$
Then
$\xi(\al K.)$
transforms under
$\al G.$
w.r.t.
$\{\xi(\Phi_{j})\}_{j}$
with the same representation matrix. Now we put
\[
V:=\sum_{j}\Psi_{j}\xi(\Phi_{j})^{\ast}\in\al L..
\]
Obviously, $V$ is unitary and
${g}^{\xi}(V)=V$
for all
$g\in\al G.$,
i.e.
$V\in\xi(\al A.)$.
Then
$V\xi(\Phi_{j})=\Psi_{j}$
or
$\al H.=V\xi(\al K.)$
and
$\sigma=\hbox{Ad}\,V\circ\rho_{\al K.}^{\xi}.$
(ii) According to Corollary~\ref{Cor.4.9} and
$(\hbox{Ob}\,\al T.)^{\xi}\subseteq\hbox{Ob}\,\al T.^{\xi}$
the image
$\al C.^{\xi}$
of an equivalence class
$\al C.\subset\hbox{Ob}\,\al T.$
is contained in a unique equivalence class of
$\hbox{Ob}\,\al T.^{\xi}$.
But (i) says that every equivalence class
$\al E.$
of
$\hbox{Ob}\,\al T.^{\xi}$
is an image
$\al E.=\al C.^{\xi}$.
\subsection*{Proof of Lemma~\ref{arrow1}}
Let $A\in(\sigma,\,\tau)_{\al A.},$ then
it follows immediately from
$A\sigma(B)=\tau(B)A,\;B\in\al A.$
that
$\xi(A)\sigma^{\xi}(\xi(B))=\tau^{\xi}(\xi(B))\xi(A)$
for all $B\in\al A..$ Recall that $\xi(\al A.)$
is the fixed point algebra of $\al G.^\xi.$
\subsection*{Proof of Proposition~\ref{Prop.4.12}}
(i) This is obvious because the union
$\bigcup_{\gamma}\al N._{\gamma}$
of orthonormal bases
$\al N._{\gamma}$
of
$\al H._{\gamma}$
is an $\al A.$-left module basis of
$\al F._{\rm fin}$.
\noindent
(ii)
By a straightforward calculation one obtains for all $F\in\al F.$ that:
\[
\langle\xi(F),\xi(F)\rangle_{\xi(\al A.)}=
\xi(\langle F,F\rangle_{\al A.})
\]
and
\[
\vert\xi(F)\vert_{\xi(\al A.)}=\Vert\xi(\langle F,F\rangle_{\al A.})
\Vert^{1/2}\leq\Vert\langle F,F\rangle_{\al A.}\Vert^{1/2}
=\vert F\vert_{\al A.},
\]
i.e.
$\xi$
is continuous w.r.t. the norm
$\vert\cdot\vert_{\al A.}.$
Now let
$F\in\clo\s{\vert\cdot\vert_{\al A.}}.(\ker\xi\cap
\al F._{\rm fin}),$ hence there is a sequence $\{F_n\}\subset
\ker\xi\cap\al F._{\rm fin}$ such that
$\vert F_{n}-F\vert_{\al A.}\to 0.$
Then
$\xi(F)=0$
follows. Conversely, let
$F\in\ker\xi$.
Recall
$\xi\circ\Pi_{\gamma}=\Pi_{\gamma}^{\xi}\circ\xi$
which implies
$\Pi_{\gamma}F\in\ker\xi$.
Now, according to Remark~\ref{remark1}~(iv) we have
$F=\sum_{\gamma}\Pi_{\gamma}F$
w.r.t. the
$\vert\cdot\vert_{\al A.}$-norm convergence. This implies
\[
F\in\hbox{clo}_{\vert\cdot\vert_{\al A.}}(\ker\xi\cap
\al F._{\rm fin}).
\]
\subsection*{Proof of Theorem~\ref{Teo.4.13}}
(i) Since $\HS$ is minimal and regular, there exists an
assignment
$\sigma\to\al H._{\sigma}$
such that
an admissible (DR-)subcategory
$\al T._{\C}$
can be defined by
\[
(\sigma,\tau)_{\al A.,\C}:=(\al H._{\sigma},\al H._{\tau}),
\]
cf. Theorem~\ref{Teo1}. Now we use the morphism $\xi$ to define a
corresponding subcategory
$\al T.^{\xi}_{\C}$
for
$\xi(\al T.)$.
Recall
$\hbox{Ob}\,\xi(\al T.)=(\hbox{Ob}\,\al T.)^{\xi}\subset\hbox{Ob}\,
\al T.^{\xi}.$
We put
\[
\hbox{Ob}\,\al T.^{\xi}_{\C}:=\hbox{Ob}\,\xi(\al T.).
\]
Let
$\lambda,\sigma\in\hbox{Ob}\,\al T.$.
Then
$\lambda^{\xi},\sigma^{\xi}\in\hbox{Ob}\,\xi(\al T.)$
and the arrows are defined by
\[
(\sigma^{\xi},\tau^{\xi})_{\xi(\al A.),\C}:=
\xi((\sigma,\tau)_{\al A.,\C})=(\xi(\al H._{\sigma}),\xi(\al H._{\tau})).
\]
Then
\[
(\iota^{\xi},\iota^{\xi})_{\xi(\al A.),\C}
=\xi((\iota,\iota)_{\al A.,\C})=\xi(\C\un)=\C\xi(\un).
\]
It is straightforward to show that
$\al T.^{\xi}_{\C}$
has direct sums and subobjects (in the latter case note that if
$F$ is a nontrivial projection from
$(\sigma^{\xi},\sigma^{\xi})_{\xi(\al A.),\C}$
then there is a nontrivial projection
$E\in (\sigma,\sigma)_{\al A.,\C}$
such that
$F=\xi(E)$
because the ($\al G.$-invariant) matrix
$\{p_{j,k}\}_{j,k}$
of $F$ w.r.t.
$\{\xi(\Phi_{\sigma,j})\}_{j}$,
where the
$\Phi_{\sigma,j}$
form an orthonormal basis of
$\al H._{\sigma}$,
can be used to define a corresponding $E$ in
$(\sigma,\sigma)_{\al A.,\C}$.
Furthermore, the permutation and conjugation structures of
$\al T._{\C}$
survive the morphism $\xi$.
Thus
$\al T.^{\xi}_{\C}$
is a DR-category. We use the notation
$\al T.^{\xi}_{\C}=\xi(\al T._{\C}).$
(This result means: The Hilbert system
$\{\xi(\al F.),\al G.\}$
is regular.)
(ii) First let
$\xi(\al A.)'\cap\xi(\al F.)=\xi(Z(\al A.)).$
Then, according to Theorem~\ref{Teo1}, property P.2 can be fulfilled by
an appropriate subcategory of the form described before. Second,
let property P.2 be satisfied. Then
$\xi(\al T._{\C})$
is an admissible (DR-)subcategory of
$\xi(\al T.)$.
Therefore, according to Theorem~\ref{Teo2} there is a corresponding
minimal and regular Hilbert extension
$\tilde{\al F.}$
of
$\xi(\al A.).$
The uniqueness part of Theorem~\ref{Teo2} gives that
$\tilde{\al F.}$
and
$\xi(\al F.)$
are $\al A.$-module isomorphic, hence
$\xi(\al A.)'\cap\xi(\al F.)=Z(\xi(\al A.))$
is also true.
(iii) The inclusion
$\supseteq$
is obvious (see Lemma~\ref{arrow1}). The assertion is
\begin{equation}
\label{inclusion}
(\sigma^{\xi},\tau^{\xi})_{\xi(\al A.)}\subseteq\xi((\sigma,\tau)_{\al A.}).
\end{equation}
First we prove this inclusion for the admissible subcategory, i.e. we assert
\[
(\sigma^{\xi},\tau^{\xi})_{\xi(\al A.),\C}\subseteq
\xi((\sigma,\tau)_{\al A.}).
\]
This is obvious by
\[
(\sigma^{\xi},\tau^{\xi})_{\xi(\al A.),\C}=
\xi((\sigma,\tau)_{\C})\subset\xi((\sigma,\tau)_{\al A.}).
\]
Second, recall that
$\xi((\sigma,\tau)_{\al A.
})$
is a right module w.r.t.
$\sigma^{\xi}(\xi(Z(\al A.)))$
and a left module w.r.t.
$\tau^{\xi}(\xi(Z(\al A.)))$.
On the other hand,
$(\sigma^{\xi},\tau^{\xi})_{\xi(\al A.)}$
is a right module w.r.t.
$\sigma^{\xi}(Z(\xi(\al A.)))$
and a left module w.r.t.
$\tau^{\xi}(Z(\xi(\al A.))).$
Further, according to P.2.
$(\sigma^{\xi},\tau^{\xi})_{\xi(\al A.),\C}$
is a generating subset for this module. Since, by assumption,
$Z(\xi(\al A.))$
and
$\xi(Z(\al A.))$
coincide, the inclusion~(\ref{inclusion}) follows.
(iv) This follows directly from
$\xi(\al A.)'\cap\xi(\al F.)=Z(\xi(\al A.))$
and the fact that the unitary equivalence classes of
$\al T.^{\xi}$
and
$\xi(\al T.)$
coincide.
\subsection*{Proof of Theorem~\ref{Teo.4.14}}
Since
$\al T._{\C}$
is an admissible (DR-)subcategory of
$\al T.$
we can apply Theorem\ref{Teo2}, i.e. there is a corresponding minimal
and regular Hilbert extension
$\HS$
of
$\al A.$.
Therefore the arrows of the category
$\al T._{\C}$
are given by
\begin{equation}
\label{arrowAdm}
(\sigma,\tau)_{\al A.,\C}=(\al H._{\sigma},\al H._{\tau}),
\end{equation}
where the Hilbert spaces
$\al H._{\sigma},\al H._{\tau}$
generate the endomorphisms
$\sigma,\tau$ respectively.
Now it is not hard to show that the morphism
$\xi$
can be extended to a morphism of
$\al F.$
by putting
\begin{equation}
\label{MorAdm}
\xi(\Phi_{\lambda,j}):=\Phi_{\lambda,j}
\end{equation}
where
$\lambda$
runs through a complete system of irreducible and mutually
disjoint endomorphisms and
$\{\Phi_{\lambda,j}\}$
denotes an orthonormal basis of the Hilbert space
$\al H._{\lambda}$
which generates
$\lambda$
(recall and use Proposition~\ref{Prop.4.12}). This morphism satisfies the
assumptions of Theorem~\ref{Teo.4.3}. The corresponding Hilbert system is
denoted by
$\{\al F.^{\xi},\al G.\}$
(recall that
$\al G.^{\xi}\cong\al G.$).
Equations
(\ref{arrowAdm}) and (\ref{MorAdm}) imply
\[
\sigma^{\xi}(\xi(\al A.))=\sum_{j}\Phi_{\lambda,j}\xi(A)\Phi_{\lambda,j}^{\ast}
\qquad\hbox{and}\qquad
\xi((\sigma,\tau)_{\al A.,\C})=(\sigma,\tau)_{\al A.,\C}.
\]
By assumption (iii) we have
$\xi((\sigma,\tau)_{\al A.}=(\sigma^{\xi},\tau^{\xi})_{\xi(\al A.)}$.
Since
$(\sigma,\tau)_{\al A.,\C}\subset(\sigma,\tau)_{\al A.}$
we have
$\xi((\sigma,\tau)_{\al A.,\C})\subset(\sigma^{\xi},\tau^{\xi})_
{\xi(\al A.)}.$
Therefore the subcategory
$\al T._{\C}^{\xi}$
of
$\xi(\al T.)$
defined by
\[
(\sigma^{\xi},\tau^{\xi})_{\xi(\al A.),\C}:=\xi((\sigma,\tau)_
{\al A.,\C}=(\sigma,\tau)_{\al A.,\C}
\]
is a DR-category.
Now we prove property P.2 for
$\al T._{\C}^{\xi}$.
We have to show
\[
\sigma^{\xi}(Z(\xi(\al A.)))(\lambda^{\xi},\sigma^{\xi})_{\xi(\al A.),\C}
\lambda^{\xi}(Z(\xi(\al A.)))=(\lambda^{\xi},\sigma^{\xi})_{\xi(\al A.)}.
\]
The left hand side equals
\[
\sigma^{\xi}\xi(Z(\al A.))(\lambda^{\xi},\sigma^{\xi})_{\xi(\al A.),\C}
\lambda^{\xi}(\xi(Z(\al A.)))=
\xi(\sigma(Z(\al A.)))(\lambda^{\xi},\sigma^{\xi})_{\xi(\al A.),\C}
\xi(\lambda(Z(\al A.)))=
\]
\[
\xi(\sigma(Z(\al A.)))\xi((\lambda,\sigma)_{\al A.,\C})\xi(\lambda(Z(\al A.)))=
\xi(\sigma(Z(\al A.))(\lambda,\sigma)_{\al A.,\C}\lambda(Z(\al A.)))=
\xi((\lambda,\sigma)_{\al A.})
\]
and this coincides, by assumption, with the right hand side.
Now we can apply Theorem~\ref{Teo2} to obtain a further Hilbert extension
$\{\tilde{\al F.}^{\xi},\al G.^{\xi}\}$
where again
$\al G.^{\xi}\cong\al G.$.
Using the uniqueness part of Theorem~\ref{Teo2} we obtain that both
Hilbert extensions are
$\xi(\al A.)$-module isomorphic.
\subsection*{Proof of Proposition~\ref{FCU}}
It suffices to show that there is one Dirac state,
i.e. a state $\omega\in{\got S}(\al A.)$ with
$\omega(\al U.)=1\;.$
Recall the homomorphism $\zeta:\al E.\to{\rm CAR}(\al H.)
\otimes{\rm CCR}(S,B)\;.$
Let $\omega_0\in{\got S}({\rm CAR}(\al H.))$ be that
quasi--free state which is zero on any normal--ordered
monomial of $a(f)$ and $a^*(h)$ of degree greater or equal
to 1. Then $\omega_0$ is invariant w.r.t. $\wt\gamma_f$
for all $f\in\al S.(\R^4)\cup\R.$
Moreover, since $L(S)\subset\ker B,$ there is a state
$\omega_1\in {\got S}({\rm CCR}(S,B))$ such that
$\omega_1(\delta\s Lf.)=1$ for all $f\in S.$
Then $\omega_2:=\omega_0\otimes\omega_1\in
{\got S}\big({\rm CAR}(\al H.)\otimes{\rm CCR}(S,B)\big)$
is a $\wt\gamma\s f.\otimes\iota\hbox{--invariant}$ state on
${\rm CAR}(\al H.)\otimes{\rm CCR}(S,B)$ such that
$\omega_2(\un\otimes\delta\s Lf.)=1$ for all $f\in S.$
From this we define a state on $\al E.$ by
$\wt\omega_2:=\omega_2\circ\zeta$ and since
$\zeta\circ\beta\s\gamma_f.=\wt\gamma\s f.\otimes\iota,$
it follows that $\wt\omega_2$ is
$\beta\s G.\hbox{--invariant}$ on $\al E..$
Thus $\wt\omega_2$ extends to a state $\omega_3$
on $\al A.=G\cross\beta.\al E.$ by
$\omega_3(U_g)=1$ for all $g\in G,$
where $U_g$ denotes the unitary implementer for $\beta_g.$
So $\omega_3\in{\got S}(\al A.)$ is a Dirac state w.r.t.
the unitaries $U_G\cup\delta\s LS..$
Since the maximal set of constraint unitaries for
a Dirac state is a group, it follows that for the products
$V_f=\delta\s-Lf.\cdot U_{\gamma_f}$ we have
$\omega_3(V_f)=1$ for all $f,$ i.e. $\omega_3$
is a Dirac state w.r.t. $\al U.,$ hence $\al U.$ is first--class.
\subsection*{Proof of Lemma~\ref{RkWD}}
Note that $\rho_k$ on the unitary implementers $\rho_k:U_G\to\al A.$
is a faithful group homomorphism. This is because it is the pointwise product of the
identity map $\iota$ with the character $\chi_k:U_G\to\C$ given by
$\chi\s k.\big(U\s\gamma_{f+t}.\big):=e^{itk},$ $t\in\R,$ $f\in\al S.(\R^4).$
Furthermore:
$\al A.=C^*\big(\rho_k(U_G)\cup\al E.\big).$
Thus the pair ${\{\rho_k(U_G),\;\al E.\}}$ is also a covariant system
for the action $\beta:G\to\aut\al E.$ (cf. Step~3), hence by the universal
property of cross--products (cf.~\cite{PR}) there is a *-homomorphism
$\theta:\al A.\to\al A.$ such that $\theta(A)=A$ for $A\in\al A.,$ and
$\theta(U_g)=\rho_k(U_g)\equiv\hbox{implementing unitary of the second system}.$
Then $\theta$ coincides with the definition of
$\rho_k$ on the generating elements, so it follows that $\rho_k$
extends uniquely to a homomorphism. Since it is clear that $\rho_k$
is bijective (its inverse is $\rho_{-k})$ it follows that
$\rho_k$ is an automorphism of $\al A..$
\subsection*{Proof of Proposition~\ref{RhOut}}
Proof by contradiction. Let $k\not=0$ and assume $\rho_k\in{\rm Inn}\,\al A.,$
i.e. $\rho_k=\Ad V$ for some unitary $V\in\al A.\,.$
Recall the homomorphism
\[
\zeta:\al E.\to
{\rm CAR}(\al H.)\otimes{\rm CCR}(S,\,B)
\]
encountered in Step 3. Since $(S,\,B)$ is degenerate, $\zeta(\al E.)$
is not simple which will be inconvenient in the proof below. Choose
therefore a maximal ideal $\al I.$ of ${\rm CCR}(S,\,B)$
(necessarily associated with a character of the centre
$Z\big({\rm CCR}(S,\,B)\big)),$ and let
\[
\eta:{\rm CAR}(\al H.)\otimes{\rm CCR}(S,\,B)\to
{\rm CAR}(\al H.)\otimes{\rm CCR}(S,\,B)\big/\al I.
\]
be the factorisation by the ideal $\un\otimes\al I.\,.$
Then the composition
\[
\xi:=\eta\circ\zeta :\al E.\to{\rm CAR}(\al H.)\otimes{\rm CCR}(S,\,B)\big/\al I.
\]
is a homomorphism of which the image is a simple algebra.\chop
Now the action $\beta:G\to\aut\al E.$ (Step 4) only affects
${\rm CAR}(\al H.)$ in $\al E.,$ so preserves the ideal generated
by the commutators ${[{\rm CAR}(\al H.),\,{\rm CCR}(S,\,B)]}$
in $\al E.$ as well as the ideal $\un\otimes\al I.\,.$
Thus each $\beta_g$ can be taken through the homomorphism $\xi$
to define an action
$\beta^\xi:G\to{\aut\big({\rm CAR}(\al H.)\otimes{\rm CCR}(S,\,B)\big/\al I.\big)}$
and it is just $\beta^\xi\s\gamma_f.=\wt\gamma\s f.\otimes \iota\,.$
Thus we can extend $\xi$ from $\al E.$ to $\al A.=
{G\cross\beta.\al E.}$ to get a surjective homomorphism
\[
\xi:\al A.\to G\cross\beta^\xi.\left({\rm CAR}(\al H.)\otimes{\rm CCR}(S,\,B)\big/\al I.\right)\;.
\]
Now $\rho_k\in\aut\al A.$ only affects $U_G,$ leaving $\al E.$ invariant, hence it
preserves $\ker\xi\subset\al A..$ Thus $\rho_k$ can be factored through $\xi$
to obtain the automorphisms $\rho^\xi_k\in\aut\xi(\al A.)$ by
\begin{equation}
\label{XVinn}
\rho^\xi_k\big(\xi(A)\big):= \xi\big(\rho_k(A)\big)\quad\forall\;A\in\al A.\,,\qquad
\hbox{and so}\qquad \rho^\xi_k=\Ad\xi(V)\;.
\end{equation}
Recall now that each element of the discrete crossed product
$\xi(\al A.)= {G\cross\beta^\xi.\xi(\al E.)}$
(with $\xi(\al E.)={\rm CAR}(\al H.)\otimes{\rm CCR}(S,\,B)\big/\al I.)$
can be written as a C*-norm convergent series $\sum\limits_{n=1}^\infty B_nU\s g_n.$
where $B_n\in\xi(\al E.)$ and $g_n\in G,$ (with $g_n$ distinct for different $n)$
and that the unitaries $U_G$
form a left $\xi(\al E.)\hbox{--module}$ basis.
In particular, for the implementing unitaries $\xi(V)$ of $\rho^\xi_k$ we have a
series $\xi(V)=\sum\limits_{n=1}^\infty B_nU\s g_n.\,,$ $B_n\in\xi(\al E.)\backslash 0.$
Since $\rho_k\restriction\al E.=\iota\,,$ it follows from equation~(\ref{XVinn})
that $\xi(V)A=A\xi(V)$ for all $A\in\xi(\al E.)\,,$ i.e.
\begin{eqnarray*}
A\xi(V)&=& \sum_{n=1}^\infty AB_nU\s g_n. \\[1mm]
&=&\xi(V)A=\sum_{n=1}^\infty B_nU\s g_n.A
=\sum_{n=1}^\infty B_n\beta^\xi\s g_n.(A)U\s g_n.
\end{eqnarray*}
for all $A\in\xi(\al E.)\,.$ So by the basis property of $U_G$ we have
\begin{equation}
\label{BnIntertw}
AB_n=B_n\beta^\xi\s g_n.(A)\quad\forall\;A\in\xi(\al E.)=
{\rm CAR}(\al H.)\otimes{\rm CCR}(S,\,B)\big/\al I.\,.
\end{equation}
Since $\beta^\xi\s g_n.\restriction{\rm CCR}(S,\,B)\big/\al I.
=\iota,$ this implies that
$B_n\in\left({\rm CCR}(S,\,B)\big/\al I.\right)'.$
From the fact that ${\rm CCR}(S,\,B)\big/\al I.$
is simple (hence has trivial centre)
this means that $B_n\in{\rm CAR}(\al H.)\otimes\un,$
and hence equation~(\ref{BnIntertw}) claims that $B_n$
is a nonzero intertwiner between $\iota$ and
$\beta^\xi\s g_n.$ in ${\rm CAR}(\al H.).$
We next prove that $B_n$ is invertible, in which case
$\beta^\xi\s g_n.$ becomes inner on ${\rm CAR}(\al H.).$
Let $\pi:{\rm CAR}(\al H.)\to\al B.(\al L.)$ be any faithful irreducible
representation of ${\rm CAR}(\al H.)$ on a Hilbert space $\al L.$
e.g. the Fock representation), and let $\psi\in\ker\pi(B_n)\,.$
Then by (\ref{BnIntertw})
\[
\pi(B_nA)\psi=\pi(\beta\s g_n^{-1}.(A))\,\pi(B_n)\psi=0\qquad
\forall\;A\in{\rm CAR}(\al H.)\;.
\]
Thus $\pi({\rm CAR}(\al H.))\psi\subseteq\ker\pi(B_n)\,.$
However, in an irreducible representation every nonzero vector is cyclic,
so either $\psi=0$ or $\pi(B_n)=0,$ and the latter case is excluded
by $B_n\not=0,$ $\pi$ faithful. Thus $\psi=0,$ i.e. we've shown that
$\ker\pi(B_n)=\{0\}\,.$ Moreover by equation~(\ref{BnIntertw}) we have
\[
\pi(A)\pi(B_n)\varphi=\pi(B_n)\pi(\beta\s g_n.(A))\varphi
\quad\forall\;\varphi\in\al L.\backslash 0\,,\;A\in{\rm CAR}(\al H.)
\]
hence $\pi\big({\rm CAR}(\al H.)\big)\big(\pi(B_n)\varphi\big)
\subseteq{\rm Ran}\,\pi(B_n)$ for all $\varphi\in\al L.\backslash 0\,.$
Now $\pi(B_n)\varphi\not=0$ (by $\ker\pi(B_n)=\{0\})$ and so by Dixmier
2.8.4~\cite{Di} we have that
$\pi\big({\rm CAR}(\al H.)\big)\big(\pi(B_n)\varphi\big)=\al L.$
(no closure is necessary). Thus ${\rm Ran}\,\pi(B_n)=\al L.,$
i.e. $\pi(B_n)$ is invertible, and so since $\pi$ is faithful
(hence preserves the spectrum of an element) it follows that
$B_n$ is also invertible in ${\rm CAR}(\al H.).$
Using the fact that $B_n$ is invertible, equation~(\ref{BnIntertw})
becomes $\beta\s g_n.(A)=B_n^{-1}AB_n$ for all $A\in{\rm CAR}(\al H.)\,.$
Since $\beta\s g_n.$ is a *-homomorphism, this implies that
$B_n^{-1}A^*B_n=B_n^*A^*(B_n^{-1})^*,$ i.e.
$B_nB_n^*A^*=A^*B_nB_n^*$ for all $A\in{\rm CAR}(\al H.)\,,$
and since ${\rm CAR}(\al H.)$ has trivial centre, this means
$B_nB_n^*\in\C\un\,.$
Put $B_nB_n^*=:t_n$ (necessarily $t_n>0)$ then
$U_n:=B_n\big/\sqrt{t_n}$ satisfies
$U_nU_n^*=\un.$ By substituting $A$ by $\beta\s g_n^{-1}.(A)$
in (\ref{BnIntertw}) we also obtain $B_n^*B_n\in\C\un$ by the above
argument, then using $t_n=\|B_nB_n^*\|=\|B_n\|^2=\|B_n^*B_n\|=B_n^*B_n$
we get also $U_n^*U_n=\un\,.$
Thus
\[
\beta\s g_n.(A) =B_n^{-1}AB_n=\left({B_n\over\sqrt{t_n}}\right)^{-1}
A\left({B_n\over\sqrt{t_n}}\right)=U_n^*AU_n
\]
for $A\in {\rm CAR}(\al H.)\,,$ i.e. $\beta\s g_n.$ is inner on
${\rm CAR}(\al H.)\,.$
Recall however, that on ${\rm CAR}(\al H.)$ $\beta\s g_n.$ is just
an automorphism $\wt\gamma\s f_n.$ for some $f_n\in\al S.(\R^4)+\R,$
coming from a Bogoliubov transformation:
$\wt\gamma\s f_n.\big(\Phi(k)\big):=\Phi(T_{f_n}k)$ (cf. Step 4).
So for $\beta\s g_n.$ to be inner on ${\rm CAR}(\al H.),$
this means that either of $I\pm T_{f_n}$ must be trace--class
(cf. Theorem~4.1, p48 of Araki~\cite{Ar} or Theorem~4.1.4 in
\cite{PlR}).
However
\[
T_{f_n}(h_1\oplus h_2):=e^{-if_n}h_1\oplus e^{if_n}h_2\quad\forall\;
h_i\in\al H.=L^2(\R^4)\,.
\]
Now for any $f_n$ such that $T_{f_n}\not=I\,,$ it is clear
that the multiplication operators on $L^2(\R^4)$ by
$(I\pm e^{\pm if_n})$ cannot be trace--class.
This contradicts our finding that $\beta\s g_n.$ is inner
if $g_n\not=e,$ hence only $g_n=e$ is possible in the series
$\xi(V)=\sum\limits_{n=1}^\infty B_nU\s g_n.$ i.e.
$\xi(V)= B\cdot U_e\,,$ $B\in\xi(\al E.)\backslash 0\,.$
But in this case equation~(\ref{BnIntertw}) becomes $AB=BA$
for all $A\in\xi(\al E.)$ and so since $\xi(\al E.)$ is simple,
$B\in\C\un\,.$ This however implies that
$\iota=\Ad\xi(V)=\rho^\xi_k$ which cannot be because
$\rho_k(U\s\gamma_t.)=e^{ikt}U\s\gamma_t.$ factors unchanged through $\xi.$
From this contradiction, it follows that our initial assumption
$\rho_k\in {\rm Inn}\,\al A.$ is false.
\providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace}
\begin{thebibliography}{10}
\bibitem{Ar}
Araki, H.: Bogoliubov automorphisms and Fock representations of
canonical anticommutation relations. Contemp. Math. {\bf 62}, 23--141 (1987)
\bibitem{Bg}
Baumgaertel, H.: Operatoralgebraic methods in quantum field theory.
Akademie Verlag, Berlin 1995.
\bibitem{BL} Baumgaertel, H., Lled\'o, F.:
An application of the DR-duality theory for compact groups to endomorphism
categories of C*-algebras with nontrivial center.
Mathematical physics in mathematics and physics (Siena, 2000), 1--10,
Fields Inst. Commun., {\bf 30}, Amer. Math. Soc., Providence, RI, 2001
\chop Also at http://lanl.arXiv.org/abs/math/?0012037
\bibitem{BL2} Baumgaertel, H., Lled\'o, F.:
Superselection structures for C*--algebras with nontrivial centre.
Rev. Math. Phys. {\bf 9}, 785--819 (1997)
\bibitem{BW}
Baumgaertel, H., Wollenberg: Causal nets of operator algebras, Akademie Verlag,
Berlin 1992
\bibitem{DR}
Doplicher, S., Roberts, J.: A new duality of compact groups, Invent. Math.
{\bf 98}, 157--218 (1989)\chop
Doplicher, S., Roberts, J.: Why there is a field algebra
with a compact gauge group describing the superselection
structure in particle physics.
Comm. Math. Phys. {\bf 131}, no. 1, 51--107 (1990)
\bibitem{DR2}
Doplicher, S., Roberts, J.: Compact group actions on C*--algebras. J. Op. Th.
{\bf 19}, 283--305 (1988)
\bibitem{ES}
Evans, D., Sund, T.: Spectral subspaces for compact actions. Rep. Math. Phys.
{\bf 17}, 299-308 (1980)
\bibitem{PR}
Packer, J., Raeburn, I:
Twisted crossed products of C*-algebras.
Math. Proc. Cambridge Philos. Soc. {\bf 106},
293--311 (1989)
\bibitem{Grundling88b}
Grundling, H.: Systems with outer constraints. Gupta--Bleuler
electromagnetism as an algebraic field theory. Commun. Math. Phys.
\textbf{114}, 69--91 (1988)
\bibitem{Grundling97}
\bysame: A group algebra for inductive limit groups. Continuity problems
of the canonical commutation relations. Acta Applicandae Mathematicae
\textbf{46}, 107--145 (1997)
\bibitem{Grundling85}
Grundling, H., Hurst, C.A.: Algebraic quantization of systems with a
gauge degeneracy. Commun. Math. Phys. \textbf{98}, 369--390 (1985)
\bibitem{Grundling88c}
\bysame: A note on regular states and supplementary conditions. Lett.
Math. Phys. \textbf{15}, 205--212 (1988) [Errata: ibid. {\bf 17},
173--174 (1989)]
\bibitem{Grundling88a}
\bysame: The quantum theory of second class constraints: Kinematics.
Commun. Math. Phys. \textbf{119}, 75--93 (1988) [Erratum: ibid. {\bf
122}, 527--529 (1989)]
\bibitem{Lledo}
Grundling, H., Lled\'o, F.: Local quantum constraints.
Rev. Math. Phys.\textbf{12}, 1159--1218 (2000)
\bibitem{bDirac64}
Dirac, P.A.M.: Lectures on Quantum Mechanics. Belfer Graduate School of
Science: Yeshiva University 1964
\bibitem{bPedersen89}
Pedersen, G.K.: {\rm C}$^*$--Algebras and their Automorphism Groups.
London: Academic Press 1989
\bibitem{lands}
Landsman, N.P.: Rieffel induction as generalised quantum Marsden--Weinstein
reduction. J. Geom. Phys. \textbf{15}, 285--319 (1995)\chop
Grundling, H., Hurst, C.A.: Constrained dynamics for quantum mechanics I.
J. Math. Phys. \textbf{39}, 3091--3119 (1998)\chop
M. Henneaux, C. Teitelboim: Quantization of Gauge Systems.
Princeton University Press, Princeton 1992\chop
Giulini, D., Marolf, D.: On the generality of refined algebraic
quantization. Class. Quant. Grav. \textbf{16}, 2479--2488 (1999)\chop
Klauder, J., Ann. Physics \textbf{254}, 419--453 (1997)\chop
Faddeev, L., Jackiw, R.: Hamiltonian reduction of unconstrained and constrained systems.
Phys. Rev. Lett. \textbf{60}, 1692 (1988)\chop
Landsman, N.P., Wiedemann, U.: Massless particles, electromagnetism and
Rieffel induction. Rev. Math. Phys. \textbf{7}, 923--958 (1995)
\bibitem{MS}
Mack, G., Schomerus, V.: Conformal Field Algebras with Quantum Symmetry
from the Theory of Superselection Sectors,
Commun. Math. Phys. \textbf{134}, 139-196 (1990)
\bibitem{S}
Shiga, K.: Representations of a compact group on a Banach space,
J. Math. Soc. Japan \textbf{7}, 224-248 (1955)
\bibitem{BC}
Baumgaertel, H., Carey, A.: Hilbert C*-systems for actions of
the circle group,
Rep. on Math. Phys. \textbf{47}, 349-361 (2001)
\bibitem{BL3}
Baumgaertel, H., Lled\'o, F.: Dual group actions on C*-algebras
and their description by Hilbert extensions,
Math. Nachr. \textbf{239-240}, 11-47 (2002)
\bibitem{HR}
Hewitt, E., Ross, A.K.: Abstract Harmonic Analysis I,
Springer Verlag Berlin 1963
\bibitem{HR2}
Hewitt, E., Ross, A.K.: Abstract Harmonic Analysis II,
Springer Verlag Berlin 1970
\bibitem{B2}
Baumgaertel, H., Lled\'o, F.: Duality of compact groups and
Hilbert C*-systems for C*-algebras
with a nontrivial center. (To be published)\chop
http://xxx.lanl.gov/abs/math.OA/0311170
\bibitem{Cu}
Cuntz, J.: Simple C*-algebras generated by isometries,
Commun. Math. Phys. \textbf{57}, 173-185 (1977)
\bibitem{DR5}
Doplicher, S., Roberts, J.: Endomorphisms of C*-algebras,
tensor products and duality for compact groups,
Ann.Math. \textbf{130}, 75-119 (1989)
\bibitem{B3}
Baumgaertel, H.: A modified approach to the Doplicher/Roberts
theorem on the construction of the field algebra and the
symmetry group in superselection theory,
Rev.Math.Phys. \textbf{9}, 279-313 (1997)
\bibitem{PlR}
Plymen, R.J., Robinson, P.L.: Spinors in Hilbert space,
Cambridge University Press (1994)
\bibitem{Di}
Dixmier, J.: C*-algebras,
North Holland Publishing Company, Amsterdam - New York - Oxford 1977
\bibitem{LR}
Longo, R. and Roberts, J.E.: A theory of dimension,
K-theory \textbf{11}, 103-159 (1997)
\end{thebibliography}
\end{document}
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\begin{thebibliography}{1}
\bibitem{CaroValverde2004} Caro Valverde, M. T. (2004). \textit{Teor{\'\i}a de la pasi{\'o}n literaria: {\textquotedblleft}al hilo{\textquotedblright} de {\textquotedblleft}La Celestina{\textquotedblright}}. Murcia: Universidad de Murcia.
\end{thebibliography}
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http://porocila.imfm.si/2006/mat/clani/turnsek.tex | imfm.si | CC-MAIN-2023-14 | text/x-tex | application/x-tex | crawl-data/CC-MAIN-2023-14/segments/1679296943695.23/warc/CC-MAIN-20230321095704-20230321125704-00667.warc.gz | 37,722,955 | 2,385 | \clan {Aleksej Turn\v{s}ek}
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\begin{skupina}{B}
\sprejetoRevija
{A.~Blanco, \crta}
{On the converse of Anderson's theorem}
{Linear Algebra Appl.}
\sprejetoRevija
{}
{On mappings approximately preserving orthogonality}
{J.\ Math.\ Anal.\ Appl.}
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% 1.01: {\bf 1}. BLANCO, Ariel, TURN\v{S}EK, Aleksej. On maps that preserve orthogonality in
%normed spaces. {\it Proc. R. Soc. Edinb., Sect. A, Math.}, 2006, vol. 136, no. 4,
%str. 709-716. http://www.ingentaconnect.com/content/rse/proca/2006/00000136/00000004.
%$[$COBISS.SI-ID 14182745$]$\\
{A.~Blanco, \crta}
{On maps that preserve orthogonality in normed spaces}
{Proc.\ Roy.\ Soc.\ Edinburgh Sect.\ A} {136} {2006} {4} {709--716}
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%\razno
% 1.19: {\bf 2}. TURN\v{S}EK, Aleksej. Duggal, B.P.; Harte, Robin E.: Range-kernel orthogonality and range closure of an elementary operator. (English). - $[$J$]$ Monatsh. Math. 143, No.3, 179-187 (2004). $[$ISSN 0026-9255; ISSN 1436-5081$]$. {\it Zentralblatt MATH database}. $[$Online ed.$]$, 2006, zbl 1083.47029. http://www.emis.de/ZMATH/. $[$COBISS.SI-ID 13980505$]$\\
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% 1.19: %list {\bf 3}. TURN\v{S}EK, Aleksej. Furuta, Takayuki; Giga, Mariko: Order preserving inequalities and related operator functions. (English). - $[$J$]$ Arch. Inequal. Appl. 2, No.1, 113-122 (2004). $[$ISSN 1542-6149$]$. {\it Zentralblatt MATH database}. $[$Online ed.$]$, 2006, zbl 1083.47508. http://www.emis.de/ZMATH/. $[$COBISS.SI-ID 13980761$]$\\
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% 1.19: %list {\bf 4}. TURN\v{S}EK, Aleksej. Arlinskij, Yury; Tsekanovskij, Eduard: Constant J-unitary factor and operator-valued transfer functions. (English). - $[$J$]$ Discrete Contin. Dyn. Syst. 2003, Suppl. Vol., 48-56 (2003). $[$ISSN 1078-0947; ISSN 1553-5231$]$. {\it Zentralblatt MATH database}. $[$Online ed.$]$, 2006, zbl pre02046166. http://www.emis.de/ZMATH/. $[$COBISS.SI-ID 13979737$]$\\
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% 1.19: %list {\bf 5}. TURN\v{S}EK, Aleksej. Bourin, Jean-Christophe: Convexity or concavity inequalities for Hermitian operators. (English). - $[$J$]$ Math. Inequal. Appl. 7, No.4, 607-620 (2004). $[$ISSN 1331-4343$]$. {\it Zentralblatt MATH database}. $[$Online ed.$]$, 2006, zbl pre02152410. http://www.emis.de/ZMATH/. $[$COBISS.SI-ID 13979993$]$\\
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% 1.19: %list {\bf 6}. TURN\v{S}EK, Aleksej. Stochel, Jan: Logarithmic concavity, unitarity and selfadjointness. (English). - $[$CA$]$ Jarosz, Krzysztof (ed.) et al., Topological algebras, their applications,and related topics. Proceedings of the conference to celebrate the 70th birthday of Professor Wieslaw Zelazko, Bedlewo, Poland, May 11-17, 2003. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 67, 335-348 (2005). {\it Zentralblatt MATH database}. $[$Online ed.$]$, 2006, zbl pre02176448. http://www.emis.de/ZMATH/. $[$COBISS.SI-ID 13981273$]$\\
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% 1.19: %list {\bf 7}. TURN\v{S}EK, Aleksej. Petersson, Henrik: PDE-preserving properties. (English). - $[$J$]$ J. Korean Math. Soc. 42, No.3, 573-597 (2005). $[$ISSN 0304-9914$]$. {\it Zentralblatt MATH database}. $[$Online ed.$]$, 2006, zbl pre02186590. http://www.emis.de/ZMATH/. $[$COBISS.SI-ID 13981017$]$\\
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% 2.03: {\bf 8}. TURN\v{S}EK, Aleksej{\it . Tehni\v{s}ka matematika}. $[$1. izd.$]$. Ljubljana: Fakulteta za strojni\v{s}tvo, 2006. 255 str., graf. prikazi. ISBN 961-6536-02-8. $[$COBISS.SI-ID 224253440$]$\\
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%\gostovanje {Aleksej Turnšek} {1 mesec} {Quenn's University} {Belfast} {Sev. Irska} {januar} {2006}
%\end{seznam}
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https://share.cocalc.com/share/d3562b16810a1d032909c07a70235ff58809b992/latex-tests/test-concordance.tex?viewer=download | cocalc.com | CC-MAIN-2020-10 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2020-10/segments/1581875146809.98/warc/CC-MAIN-20200227191150-20200227221150-00462.warc.gz | 537,276,427 | 1,006 | \Sconcordance{concordance:test.tex:test.rnw:%
1 16 1 50 0 4 1 4 0 4 1 21 0 5 1 7 0 8 1 8 0 7 1 7 0 6 1 4 0 5 1 8 %
0 4 1 6 0 80 1 6 0 24 1 6 0 24 1 6 0 8 1}
|
https://smlnj-gforge.cs.uchicago.edu/scm/viewvc.php/*checkout*/trunk/doc/report/grammar-defs.tex?revision=97&root=diderot&pathrev=105 | uchicago.edu | CC-MAIN-2021-25 | text/x-tex | application/postscript | crawl-data/CC-MAIN-2021-25/segments/1623487610841.7/warc/CC-MAIN-20210613192529-20210613222529-00285.warc.gz | 469,755,106 | 2,100 | %!TEX root = report.tex
%
% Macros for the various rules of the Diderot grammar. We collect the
% grammer into these macros to ensure consistency between the collected
% syntax and the body of the text.
%
\newcommand{\ProgramRULES}{
\begin{Rules}{Program}
\RHS{\LISTONE{\nt{Declaration}}}
\end{Rules}}
\newcommand{\DeclarationRULES}{
\begin{Rules}{Declaration}
\RHS{\nt{InputDecl}}
\RHS{\nt{VarDecl}}
\RHS{\nt{ActorDecl}}
\RHS{\nt{CoordinationDecl}}
\end{Rules}}
\newcommand{\InputDeclRULES}{
\begin{Rules}{InputDecl}
\RHS{\kw{input} \nt{Type} \term{Id} \OPTGRP{\kw{=} \nt{Expr}} \kw{;}}
\end{Rules}}
\newcommand{\ActorDeclRULES}{
\begin{Rules}{ActorDecl}
\RHS{\kw{actor} \term{Id} \kw{(} \nt{Params} \kw{)} \kw{\{} \LISTGRP{\nt{VarDecl}} \LISTONEGRP{\nt{ActorMethod}} \kw{\}}}
\end{Rules}}
\newcommand{\ParamsRULES}{
\begin{Rules}{Params}
\RHS{\OPTGRP{\nt{Param} \LISTGRP{\kw{,} \nt{Param}}}}
\end{Rules}}
\newcommand{\ParamRULES}{
\begin{Rules}{Param}
\RHS{\nt{Type} \term{Id}}
\end{Rules}}
\newcommand{\ActorMethodRULES}{
\begin{Rules}{ActorMethod}
\RHS{\term{Id} \nt{Block}}
\end{Rules}}
\newcommand{\BlockRULES}{
\begin{Rules}{Block}
\RHS{\kw{\{} \LISTGRP{\nt{Stmt}} \kw{\}}}
\end{Rules}}
\newcommand{\StmtRULES}{
\begin{Rules}{Stmt}
\RHS{\nt{Block}}
\RHS{\nt{VarDecl}}
\RHS{\kw{stabilize} \kw{;}}
\RHS{\kw{die} \kw{;}}
\RHS{\kw{new} \term{Id} \kw{(} \nt{Arguments} \kw{)} \kw{;}}
\RHS{\term{Id} \kw{=} \nt{Expr} \kw{;}}
\RHS{\kw{if} \kw{(} \nt{Expr} \kw{)} \nt{Stmt} \kw{else} \nt{Stmt}}
\RHS{\kw{if} \kw{(} \nt{Expr} \kw{)} \nt{Stmt}}
\end{Rules}}
\newcommand{\VarDeclRULES}{
\begin{Rules}{VarDecl}
\RHS{\nt{Type} \term{Id} \kw{=} \nt{Expr} \kw{;}}
\end{Rules}}
\newcommand{\TypeRULES}{
\begin{Rules}{Type}
\RHS{\kw{image} \kw{(} \nt{Dimension} \kw{)} \nt{Dimensions}}
\RHS{\kw{field} \kw{\#} \nt{Dimension} \kw{(} \nt{Dimension} \kw{)} \nt{Dimensions}}
\RHS{\kw{kernel} \kw{\#} \nt{Dimension}}
\RHS{\nt{ValueType} \LISTGRP{\kw{[} \nt{Dimension} \kw{]}}}
\end{Rules}}
\newcommand{\CoordinationDeclRULES}{
\begin{Rules}{CoordinationDecl}
\RHS{\kw{initially} \nt{\GRP{\nt{Array} $\;|\;$ \nt{Collection}}} \kw{;}}
\end{Rules}}
\newcommand{\ArrayRULES}{
\begin{Rules}{Array}
\RHS{\kw{[} \nt{Create} \kw{|} \nt{Iterations} \kw{]}}
\end{Rules}}
\newcommand{\CollectionRULES}{
\begin{Rules}{Collection}
\RHS{\kw{\{} \nt{Create} \kw{|} \nt{Iterations} \kw{]}}
\end{Rules}}
\newcommand{\CreateRULES}{
\begin{Rules}{Create}
\RHS{\term{Id} \kw{(} \nt{Arguments} \kw{)}}
\end{Rules}}
\newcommand{\IterationsRULES}{
\begin{Rules}{Iterations}
\RHS{\nt{Iteration} \LISTONEGRP{\kw{,} \nt{Iteration}}}
\end{Rules}}
\newcommand{\IterationRULES}{
\begin{Rules}{Iteration}
\RHS{\term{Id} \kw{in} \nt{Expr} \kw{..} \nt{Expr}}
\end{Rules}}
\newcommand{\ExprRULES}{
\begin{Rules}{Expr}
\RHS{\nt{AndExpr} \LISTGRP{\kw{||} \nt{AndExpr}}}
\end{Rules}}
\newcommand{\AndExprRULES}{
\begin{Rules}{AndExpr}
\RHS{\nt{CmpExpr} \LISTGRP{\kw{\&\&} \nt{CmpExpr}}}
\end{Rules}}
\newcommand{\CmpExprRULES}{
\begin{Rules}{AddExprCmpExpr}
\RHS{\nt{AddExpr} \LISTGRP{\nt{CmpOp} \nt{AddExpr}}}
\end{Rules}}
\newcommand{\AddExprRULES}{
\begin{Rules}{AddExpr}
\RHS{\nt{MulExpr} \LISTGRP{\nt{AddOp} \nt{MulExpr}}}
\end{Rules}}
\newcommand{\MulExprRULES}{
\begin{Rules}{MulExpr}
\RHS{\nt{PrefixExpr} \LISTGRP{\nt{MulOp} \nt{PrefixExpr}}}
\end{Rules}}
\newcommand{\PrefixExprRULES}{
\begin{Rules}{PrefixExpr}
\RHS{\nt{SelExpr}}
\RHS{\kw{-} \nt{PrefixExpr}}
\RHS{\kw{!} \nt{PrefixExpr}}
\RHS{\kw{D} \nt{PrefixExpr}}
\end{Rules}}
\newcommand{\SelExprRULES}{
\begin{Rules}{SelExpr}
\RHS{\nt{AtomExp} \LISTGRP{\kw{@} \nt{AtomExp} $\;|\;$ \kw{[} \nt{Expr} \kw{]}}}
\end{Rules}}
\newcommand{\AtomExpRULES}{
\begin{Rules}{AtomExp}
\RHS{\term{Id} \OPTGRP{\kw{(} \nt{Arguments} \kw{)}}}
\RHS{\nt{ValueType} \kw{(} \nt{Arguments} \kw{)}}
\RHS{\term{Int}}
\RHS{\term{Float}}
\RHS{\term{String}}
\RHS{\kw{(} \nt{Expr} \LISTGRP{\kw{,} \nt{Expr}} \kw{)}}
\RHS{\kw{$|$} \nt{Expr} \kw{$|$}}
\end{Rules}}
\newcommand{\ArgumentsRULES}{
\begin{Rules}{Arguments}
\RHS{\OPTGRP{\nt{Expr} \LISTGRP{\kw{,} \nt{Expr}}}}
\end{Rules}}
\newcommand{\CmpOpRULES}{
\begin{Rules}{CmpOp}
\RHS{\kw{<}}
\RHS{\kw{<=}}
\RHS{\kw{==}}
\RHS{\kw{!=}}
\RHS{\kw{>=}}
\RHS{\kw{>}}
\end{Rules}}
\newcommand{\AddOpRULES}{
\begin{Rules}{AddOp}
\RHS{\kw{+}}
\RHS{\kw{-}}
\end{Rules}}
\newcommand{\MulOpRULES}{
\begin{Rules}{MulOp}
\RHS{\kw{*}}
\RHS{\kw{/}}
\end{Rules}}
\newcommand{\ValueTypeRULES}{
\begin{Rules}{ValueType}
\RHS{\kw{tensor} \nt{Dimensions}}
\RHS{\kw{vec2}}
\RHS{\kw{vec3}}
\RHS{\kw{vec4}}
\RHS{\kw{bool}}
\RHS{\kw{int}}
\RHS{\kw{real}}
\RHS{\kw{string}}
\end{Rules}}
\newcommand{\DimensionsRULES}{
\begin{Rules}{Dimensions}
\RHS{\kw{[} \OPTGRP{\nt{Dimension} \LISTGRP{\kw{,} \nt{Dimension}}} \kw{]}}
\end{Rules}}
\newcommand{\DimensionRULES}{
\begin{Rules}{Dimension}
\RHS{\term{Int}}
\end{Rules}}
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|
http://porocila.imfm.si/2019/mat/clani/orel.tex | imfm.si | CC-MAIN-2020-29 | text/x-tex | application/x-tex | crawl-data/CC-MAIN-2020-29/segments/1593655880665.3/warc/CC-MAIN-20200714114524-20200714144524-00547.warc.gz | 87,591,855 | 2,063 | \clan {Marko Orel}
%--------------------------------------------------------
% A. objavljene znanstvene monografije
%--------------------------------------------------------
%\begin{skupina}{A}
%\disertacija
% {NASLOV}
% {UNIVERZA}
% {FAKULTETA}
% {ODDELEK}
% {KRAJ} {DRZAVA} {LETO}
%\magisterij
% {NASLOV}
% {UNIVERZA}
% {FAKULTETA}
% {ODDELEK}
% {KRAJ} {DRZAVA} {LETO}
%\monografija
% {AVTORJI}
% {NASLOV}
% {ZALOZBA}
% {KRAJ} {DRZAVA} {LETO}
%\end{skupina}
% Ni podatkov za to sekcijo
%--------------------------------------------------------
% B. raziskovalni clanki sprejeti v objavo v znanstvenih
% revijah in v zbornikih konferenc
%--------------------------------------------------------
%\begin{skupina}{B}
%\sprejetoRevija
% {AVTORJI}
% {NASLOV}
% {REVIJA}
%\sprejetoZbornik
% {AVTORJI}
% {NASLOV}
% {KONFERENCA}
% {KRAJ} {DRZAVA} {MESEC} {LETO}
%\end{skupina}
% Ni podatkov za to sekcijo
%--------------------------------------------------------
% C. raziskovalni clanki objavljeni v znanstvenih revijah
% in v zbornikih konferenc
%--------------------------------------------------------
%\begin{skupina}{C}
%\objavljenoRevija
% {AVTORJI}
% {NASLOV}
% {REVIJA} {LETNIK} {LETO} {STEVILKA} {STRANI}
%\objavljenoZbornik
% {AVTORJI}
% {NASLOV}
% {KONFERENCA}
% {KRAJ} {DRZAVA} {MESEC} {LETO}
% {ZBORNIK} {STRANI}
%\end{skupina}
\begin{skupina}{C}
\objavljenoRevija
% 1. M.~Orel. Nonstandard rank-one nonincreasing maps on symmetric matrices. Linear Multilinear Algebra. 2019, vol. 67, iss. 2, str. 391-432. ISSN 0308-1087. https://doi.org/10.1080/03081087.2017.1419456, DOI: 10.1080/03081087.2017.1419456. [COBISS.SI-ID 1540253892]
{}
{Nonstandard rank-one nonincreasing maps on symmetric matrices}
{Linear Multilinear Algebra} {67} {2019} {} {391--432}
\end{skupina}
% Ni podatkov za to sekcijo
%--------------------------------------------------------
% D. urednistvo v znanstvenih revijah in zbornikih
% znanstvenih konferenc
%--------------------------------------------------------
%\begin{skupina}{D}
%\urednikRevija
% {OPIS}
% {REVIJA}
%\urednikZbornik
% {OPIS}
% {KONFERENCA}
% {KRAJ} {DRZAVA} {MESEC} {LETO}
%\end{skupina}
% Ni podatkov za to sekcijo
%--------------------------------------------------------
% E. organizacija mednarodnih in domacih znanstvenih
% srecanj
%--------------------------------------------------------
%\begin{skupina}{E}
%\organizacija
% {OPIS}
% {KONFERENCA}
% {KRAJ} {DRZAVA} {MESEC} {LETO}
%\end{skupina}
% Ni podatkov za to sekcijo
%--------------------------------------------------------
% F. vabljena predavanja na tujih ustanovah in
% mednarodnih konferencah
%--------------------------------------------------------
%\begin{skupina}{F}
%\predavanjeUstanova
% {NASLOV}
% {OPIS}
% {USTANOVA}
% {KRAJ} {DRZAVA} {MESEC} {LETO}
%\predavanjeKonferenca
% {NASLOV}
% {OPIS}
% {KONFERENCA}
% {KRAJ} {DRZAVA} {MESEC} {LETO}
%\end{skupina}
% Ni podatkov za to sekcijo
%--------------------------------------------------------
% G. aktivne udelezbe na mednarodnih in domacih
% konferencah
%--------------------------------------------------------
%\begin{skupina}{G}
%\konferenca
% {NASLOV}
% {KONFERENCA}
% {KRAJ} {DRZAVA} {MESEC} {LETO}
%\end{skupina}
\begin{skupina}{G}
\konferenca
% 3. M.~Orel. On some connections between finite geometry, graph theory, and matrix theory. V: Finite geometry workshop 2019 : January 31 - February 3, 2019 University of Szeged, Szeged, Hungary. Szeged: University of Szeged, 2019. Str. 29. [COBISS.SI-ID 1541257924]
{On some connections between finite geometry, graph theory, and matrix theory}
{Finite geometry workshop}
{Szeged} {Madžarska} {februar} {2019}
\konferenca
% 2. M.~Orel. Rank-one nonincreasing maps on symmetric matrices over small fields. V: Book of Abstracts. Preserver Weekend in Szeged, 12-14 April 2019 - Bolyai Institute, University of Szeged. Szeged: Bolyai Institute, 2019. Str. 12. https://users.renyi.hu/~titkos/Abstracts.pdf. [COBISS.SI-ID 1541247428]
{Rank-one nonincreasing maps on symmetric matrices over small fields}
{Preserver Weekend in Szeged}
{} {Madžarska} {april} {2019}
\end{skupina}
% Ni podatkov za to sekcijo
%--------------------------------------------------------
% H. strokovni clanki
%--------------------------------------------------------
%\begin{skupina}{H}
%\clanekRevija
% {AVTORJI}
% {NASLOV}
% {REVIJA} {LETNIK} {LETO} {STEVILKA} {STRANI}
%\clanekZbornik
% {AVTORJI}
% {NASLOV}
% {KONFERENCA}
% {KRAJ} {DRZAVA} {MESEC} {LETO}
% {ZBORNIK} {STRANI}
%\end{skupina}
% Ni podatkov za to sekcijo
%--------------------------------------------------------
% I. razno
%--------------------------------------------------------
%\begin{skupina}{I}
%\razno
% {OPIS}
% \end{skupina}
\begin{skupina}{I}
\razno
% 1.19 Recenzija, prikaz knjige, kritika
% 4. M.~Orel. Ahmia, Moussa(DZ-UJ-M); Belbachir, Hac\`{e}ne(DZ-BOUMM-RCL) p,q-analogue of a linear transformation preserving log-convexity. (English summary) Indian J. Pure Appl. Math. 49 (2018), no. 3, 549-557. MathSciNet. mr3854452. ISSN 2167-5163. http://www.ams.org/mathscinet. [COBISS.SI-ID 1541309124]
{Ena recenzija za MathSciNet}
\end{skupina}
% Ni podatkov za to sekcijo
%--------------------------------------------------------
% tuji gosti
%--------------------------------------------------------
%\begin{seznam}
%\gost {IME} {TRAJANJE} {USTANOVA} {KRAJ} {DRZAVA} {MESEC} {LETO} {POVABILO}
%\end{seznam}
%--------------------------------------------------------
% gostovanja
%--------------------------------------------------------
%\begin{seznam}
%\gostovanje {IME} {TRAJANJE} {USTANOVA} {KRAJ} {DRZAVA} {MESEC} {LETO}
%\end{seznam}
|
https://www.coaps.fsu.edu/bibliography/search.php?sqlQuery=SELECT%20author%2C%20title%2C%20type%2C%20year%2C%20publication%2C%20abbrev_journal%2C%20volume%2C%20issue%2C%20pages%2C%20keywords%2C%20abstract%2C%20thesis%2C%20editor%2C%20publisher%2C%20place%2C%20abbrev_series_title%2C%20series_title%2C%20series_editor%2C%20series_volume%2C%20series_issue%2C%20edition%2C%20language%2C%20author_count%2C%20online_publication%2C%20online_citation%2C%20doi%2C%20serial%2C%20area%20FROM%20refs%20WHERE%20serial%20%3D%20526%20ORDER%20BY%20first_author%2C%20author_count%2C%20author%2C%20year%2C%20title&client=&formType=sqlSearch&submit=Cite&viewType=&showQuery=0&showLinks=1&showRows=10&rowOffset=&wrapResults=1&citeOrder=&citeStyle=APA&exportFormat=RIS&exportType=html&exportStylesheet=&citeType=LaTeX&headerMsg= | fsu.edu | CC-MAIN-2022-40 | application/x-latex | application/x-latex | crawl-data/CC-MAIN-2022-40/segments/1664030337404.30/warc/CC-MAIN-20221003070342-20221003100342-00599.warc.gz | 717,355,281 | 1,419 | %&LaTeX
\documentclass{article}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{textcomp}
\begin{document}
\begin{thebibliography}{1}
\bibitem{Meyers+Basu1999} Meyers, S. D., \& Basu, S. (1999). Eddies in the eastern Gulf of Alaska from TOPEX/POSEIDON altimetry. \textit{J. Geophys. Res.}, \textit{104}(C6), 13333--13343.
\end{thebibliography}
\end{document}
|
http://www.jp.netbsd.org/gallery/advocacy/sschumacher/netbsd-a5-flyer-en.tex | netbsd.org | CC-MAIN-2020-24 | application/x-tex | text/x-matlab | crawl-data/CC-MAIN-2020-24/segments/1590347409337.38/warc/CC-MAIN-20200530133926-20200530163926-00353.warc.gz | 182,434,308 | 3,730 | % $Id: netbsd-a5-flyer-en.tex,v 1.3 2016/01/27 12:52:03 sevan Exp $
% written by Stefan Schumacher, <stefan [at] net-tex.de>, 2006-01-08
% Do not remove my copyright notice!
\documentclass[9pt,a5paper]{article}
\usepackage[pdftex]{graphicx}
\usepackage{multicol}
\usepackage[UKenglish]{babel}
\usepackage[nofancy]{rcsinfo}
\usepackage{kopf}
% set the margins
\usepackage{geometry}
\geometry{margin=10mm}
% pretty-print CVS tags for footer
\setlength{\parindent}{0pt}
% mySection
\newcommand{\mySection}[1]{\begin{center}\large{\sffamily\bfseries #1}\end{center}}
% begin
\begin{document}
\pagestyle{empty}
\KopfAFuenf[13]{Introducing NetBSD}
%
% Body
\begin{multicols}{2}
\mySection{What is the NetBSD Project?}
The NetBSD Project gives you a complete Unix-like operating
system that is up to today's Open Source and security
standards, supporting industry-standard APIs, communication protocols,
and a huge variety of hardware platforms. NetBSD is suited to a wide
range of applications, from servers and workstations to PDAs and
embedded systems.
NetBSD is often chosen to control newly developed hardware and to
drive such products as network computers, single-board computers,
internet appliances, firewalls, printers, copiers and even web-cams.
NetBSD is used in network development all over the
world. ISPs use NetBSD because of the wide spectrum of network
possibilities, and enthusiasts choose NetBSD for its excellent hardware
support.
\mySection{Why is NetBSD so special?}
Since NetBSD was founded in 1993 as a successor of the BSD-line, it has always been at the forefront
of Open Source operating system development. NetBSD has been the
complete foundation or reference for other projects. Many of NetBSD's
advantages are not found in any other open source operating system.
\begin{itemize}\itemsep-1ex
\item NetBSD offers support for 55 different hardware platforms and 17 CPU
architectures. And even more will follow.
\item POSIX threads implementation based on Scheduler Activations
\item Cross compiling of the kernel and userland supported by the
standard toolchain - build NetBSD almost anywhere, out of the box!
\item Kernel events notification framework provides a stateful and efficient
event notification, including socket, file, directory, fifo, pipe, tty
and device changes
\item Many security-specific features, including Verified Exec and the
systrace framework are implemented in the base system.
\item Complete source, including the history of the development,
available via anonymous CVS, rsync and CVSweb
\item Support for various network technologies including ATM, HIPPI, FDDI,
HSSI, IEEE 802.11, Token-Ring, ARCnet and Ethernet (up to 10Gbps!)
\item NetBSD was the first open source operating system to support USB, USB2,
and PCMCIA audio.
% \item Many subsystems are described in detail in published articles.
\end{itemize}
\mySection{Use Your Favorite Tools and Applications}
NetBSD contains all the features you would expect in an open source
operating system today, including X11, tools for firewalls, and software
RAID. With NetBSD's package tools you can install more than 5500 freely
available software packages easily.
% NetBSD's {\it binary compatibility} feature lets you run applications
% compiled for other operating systems (for the same CPU architecture). This
% includes most applications for Linux, Solaris, SCO, FreeBSD, BSD/OS,
% OSF/1, and Ultrix; and some for Darwin and IRIX. In fact, testing has
% shown NetBSD runs the Sun JDK/JRE for Linux as well as Linux itself does.
\mySection{Ideal for Embedded Environments}
NetBSD is designed to minimize the effort needed to make it run on new
hardware. As a result, you are able to concentrate on the development of
the hardware.
NetBSD is particularly well suited to embedded environments. It supports
many lower-power CPUs, such as ARM, MIPS, PowerPC, Xscale, and Hitachi SH
3/4/5. By removing optional components, NetBSD can be trimmed down to fit
comfortably on very small systems. And of course tools are available to do
cross-development. Both the toolchain and compilers support
cross-compiling. Cross-compiling the kernel and the whole operating system
is easily possible, as is cross-building whole distribution sets.
Make the decision---joining many Fortune 100 and Fortune 500 companies---to
use NetBSD, the world's most portable operating system, for your
product.
\mySection{Security for Paranoids}
With integrated firewall tools and tools that can be easily installed from
our software archives---including IPsec, Kerberos 5, SSH, SSL, and
encryption tools such as PGP---you have access to a modern security system.
NetBSD enforces non-executable mappings on many platforms. Stack and heap
mappings are non-executable by default, making exploitation of potential
buffer overflows harder. NetBSD also supports PROT\_EXEC permission via
mmap(2) for all platforms where the hardware differentiates execute access
from data access.
In the public forums related to Security issues, such as the Bugtraq
mailing list, NetBSD has always had fewer known security problems than the
alternative solutions. One more reason security consultants
choose NetBSD!
\mySection{Help is only an e-mail away!}
In case of trouble you can find fast and unbureaucratic help through
our mailing lists and the bug-tracking system. For more professional help,
you'll find many consultants listed at our website.
There is no phone support but your questions will be answered
without wasting time listening to music while on hold.
\mySection{Don't miss the connection}
NetBSD has been growing since March 1993, longer than any other
alternative solutions in the field of open source, and is today stronger
than ever. We won't disappear and leave you alone or stop supporting
your platform. You can put your mind at ease knowing that the future
development of your OS is in the hands of capable experts.
\end{multicols}
\mySection{Where do I get NetBSD?}
\begin{itemize}\itemsep-1ex
\item WWW: {\tt http://www.NetBSD.org/}
\item FTP: {\tt ftp://ftp.NetBSD.org/pub/NetBSD/}
\item CVS: {\tt anoncvs@anoncvs.NetBSD.org:/cvsroot}
\item CD/DVD: {\tt http://www.NetBSD.org/Sites/cdroms.html}
\end{itemize}
%
% Footer
%
\rcsInfo $Id: netbsd-a5-flyer-en.tex,v 1.3 2016/01/27 12:52:03 sevan Exp $
\scriptsize
\rcsInfoRevision\ \rcsInfoYear-\rcsInfoMonth-\rcsInfoDay. All rights
reserved.
Created by Stefan Schumacher \texttt{<stefan@net-tex.de>}
% Do not remove my copyright notice!
%
\end{document}
|
http://hendrikmaryns.name/Wiskunde/Funksileer/bronbestanden/toets%202%20havo%20a%202013.tex | hendrikmaryns.name | CC-MAIN-2018-51 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2018-51/segments/1544376831334.97/warc/CC-MAIN-20181219045716-20181219071716-00605.warc.gz | 136,784,906 | 2,062 | \documentclass[dutch,headinclude=false,footinclude=false,headsepline]{scrartcl}
% schreefloze lettertiepes voor tekst en wiskunde, moet voor fontspec, of hoe
% anders oproepen?
\usepackage{cmbright}
\usepackage{fontspec}
% oplossing voor °. Deze beter niet als superskript gebruiken volgens Context
% gurus, bovendien bevat cmbright het Unicode-symbool niet.
\DeclareMathSymbol{°}{\mathbin}{symbols}{"0E}
% standaartpakketten
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\ihead{Klas 11 havo EM}
\chead{\textbf{\Large Toets functieleer}}
\ohead{2013-03-12}
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\noindent Deze toets bestaat uit 15 opgaven. Voor elk onderdeel is
aangegeven hoeveel punten kunnen worden behaald. Er zijn maximaal 46 punten te
behalen. Antwoorden moeten altijd zijn voorzien van een \emph{berekening,
toelichting of argumentatie}.
\vspace{1ex}
\hrule
\section*{Felicitatiekaarten}
Een fabrikant van felicitatiekaarten weet uit ervaring dat het aantal per week verkochte kaarten $q$ omgekeerd evenredig is met de prijs $p$ in euro’s.
Bij een prijs van € 1,90 verkoopt hij wekelijks 8500 kaarten.
\begin{enumerate}[resume]
\item \preitem{3} Stel de formule op van de weekverkoop $q$ bij een prijs van $p$ euro.
\item \preitem{1} Bereken de weekverkoop bij een prijs van € 2,50.
\item \preitem{2} Bereken welke prijs bij een weekverkoop van 4750 kaarten hoort.
\item \preitem{3} Onderzoek bij welke prijs per kaart de fabrikant wekelijks meer dan 12000 kaarten verkoopt.
\end{enumerate}
\section*{Verbindingsteller}
Het aantal verbindingen die gemaakt zijn met een internetsite waarop allerlei goederen te koop worden aangeboden is voor een doordeweekse dag te benaderen door het model \[N=0,02t^5-1,225t^4+22,5t^3-84t^2-646t+5000.\]
Hierin is $t$ het tijdstip van de dag in uren met $t = 0$ om 0.00 uur en $N$ het aantal verbindingen.
\begin{enumerate}[resume]
\item \preitem{5} Schets de grafiek van $N$. Welke \texttt{Xmin}, \texttt{Xmax}, \texttt{Ymin} en \texttt{Ymax} heb je genomen?
\item \preitem{2} Hoeveel verbindingen zijn er om half een ’s middags?
\item \preitem{2} Bereken het differentiequotiënt op $[1, 3]$.
\item \preitem{2} Bereken de gemiddelde toename van $N$ tussen 8 uur en 12 uur.
\item \preitem{4} Hoe laat is het aantal verbindingen het grootst? Hoeveel verbindingen zijn er dan?
\item \preitem{4} Er zijn 6000 verbindingen. Hoe laat kan het zijn?
\end{enumerate}
\section*{Supersize me}
\begin{enumerate}[resume]
\item \preitem{18} Maak de examenopgave ‘Supersize me’ van 2012, eerste tijdvak.\label{laatste}
\end{enumerate}
\end{document}
|
https://www.zentralblatt-math.org/matheduc/en/?id=134482&type=tex | zentralblatt-math.org | CC-MAIN-2019-47 | text/plain | application/x-tex | crawl-data/CC-MAIN-2019-47/segments/1573496671053.31/warc/CC-MAIN-20191121231600-20191122015600-00537.warc.gz | 1,044,506,150 | 1,108 | \input zb-basic
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\iteman{ZMATH 1987a.02821}
\itemau{Steinberg, G.}
\itemti{Curvature of a graph - a teaching proposal for the upper secondary. Die Kruemmung von Funktionsgraphen - Unterrichtsvorschlaege fuer Leistungs- und Grundkurse.}
\itemso{Didakt. Math. (1985) v. 13(3) p. 222-236. [ISSN 0343-5334]}
\itemab
\itemrv{~}
\itemcc{I54}
\itemut{Graph of A Function; Curve Sketching; Upper Secondary (Gymnasium); Curve Theory; Lesson Plans; Kruemmung; ; Schaubild; Kurvendiskussion; Gymnasiale Oberstufe; Kurventheorie; Unterrichtsentwurf; Kruemmung}
\itemli{}
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\def\RunningAuthor{Abilasha R}
\firstPage{526}
\articleType{Original Article}
\receivedDate{20 Jun 2020}
\acceptedDate{05 Aug 2020}
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\title{General awareness about Covid-19 and the role of Convalescent plasma therapy in the treatment of Covid -19 among post graduate dental students - A KAP Survey}
\author{Deepa~Viswasini~R,
Abilasha~R\textsuperscript{*}~\\[5pt]{Department of Oral Pathology, Saveetha Dental College and Hospitals, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai-600077 Tamil Nadu, India}}
\begin{abstract}
COVID-19, caused by SARS Cov2 virus is a global pandemic and a threat to the world population and economy. It can manifest with a broad spectrum of clinical symptoms ranging from asymptomatic cases to pneumonia or even fatality. One of the treatments suggested is convalescent plasma therapy. The study aims at assessing the general awareness about Covid-19 and knowledge about the role of Convalescent plasma therapy for treatment of Covid -19 among post graduate dental students. The survey was conducted among postgraduate dental students through an online survey tool using google forms. The survey was conducted online among postgraduate dental students on the go with 19 and convalescent plasma therapy.A total of 103 participant were included in the study. The responses were collected, tabulated and analysed using SPSS software. The knowledge regarding covid -19 and the awareness about the usefulness of convalescent plasma was variable. Around 90\% of the participants were aware of the effectiveness of convalescent plasma therapy. Advance training, proper PPE and training on handling the patients with any infectious disease should be dealt with in detail for reducing the spread from dental clinics and dentists.
\end{abstract}\def\keywordstitle{Keywords}
\begin{keywords}COVID 19,\newline pathogenesis,\newline convalescent plasma therapy,\newline undergraduate dental students
\end{keywords}
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\makeatletter\textsuperscript{*}Corresponding Author\par Name:\ Abilasha~R~\\ Phone:\ ~\\ Email:\ abilasha@saveetha.com
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\section{Introduction}
COVID-19 has been caused by the novel coronavirus SARS-CoV 2. The ICTV (international committee of the taxonomy of virus) has labelled SARS CoV 2, which has an outbreak from Wuhan, China, from January 2020 \unskip~\citep{843100:19919524}. It was similar to a different pathogen named SARS Cov (2003) and MERS CoV (Middle East Respiratory Syndrome corona virus 2015) \unskip~\citep{843100:19919523}, \unskip~\citep{843100:19919526}. Corona virus belongs to the corona family beta Corona virus family with a size of 65 to 125 nm in diameter. This has led to severe respiratory problems and is at high risk of spreading to the common public; the scenario in India on COVID-19 is better than other tablet affected countries due to the precautionary measures \unskip~\citep{843100:19919524}, \unskip~\citep{843100:19919507}. Medical researchers have done a lot of studies to attend vaccination for this single-stranded RNA containing virus \unskip~\citep{843100:19919530}. Passive immunisation therapy has been used since 1890 to treat infectious disease \unskip~\citep{843100:19919506}, \unskip~\citep{843100:19919530}. Plasma transfusion is a way to administer neutralising antibodies in patients with the specified clinical disease to reduce symptoms and mortality \unskip~\citep{843100:19919515}. This has increased attention to reduce large-scale epidemic disease. In SARS and severe influenza, convalescent plasma therapy was recommended as the production of endogenous IgM and IgG Antibodies peaks at 2 to 4 weeks after transfusion respectively \unskip~\citep{843100:19919521}, \unskip~\citep{843100:19919532}. This led to a recommendation of convalescent plasma therapy for Covid 19 but has to be administered as early as possible. Convalescent plasma therapy as a classic adaptive Therapy which was used for the treatment of SARS, MERS, H1 N1 pandemic, which gave a satisfactory and efficient result. There has been little evidence of the contribution of viral disease in the pathogenesis of pulp stones.\unskip~\citep{843100:19919505} The main aim of
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\caption{\boldmath {Percentage of participants who agree that COVID 19 is caused by SARS- CoV-2 virus. }}
\label{f-738b2702b8a1}
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\caption{\boldmath {Percentage of responses of various symptoms of COVID 19. }}
\label{f-044308f6fb42}
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\caption{\boldmath {The association of symptoms of COVID 19 and the participants aware of COVID 19. }}
\label{f-eedc83bd1336}
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\caption{\boldmath {The response of participants on the incubation period of coronavirus. }}
\label{f-137ed389a9be}
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\caption{\boldmath {Distribution of responses for groups who are highly prone to COVID 19. }}
\label{f-0fd243c62b6c}
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\caption{\boldmath {The percentage of participants who were aware about convalescent plasma therapy. }}
\label{f-4a1e3e1bc46f}
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\caption{\boldmath {Frequency distribution of responses for the various pandemic diseases that are treated by convalescent plasma therapy. }}
\label{f-a011464f30ca}
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\caption{\boldmath {The response of participants who agree that convalescent plasma therapy could be a vaccine for covid19. }}
\label{f-eb72dc309959}
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\egroup
\bgroup
\fixFloatSize{images/51f5ef4e-54b3-4521-8550-dfcd0d8924e6-upicture9.png}
\begin{figure}[!htbp]
\centering \makeatletter\IfFileExists{images/51f5ef4e-54b3-4521-8550-dfcd0d8924e6-upicture9.png}{\includegraphics{images/51f5ef4e-54b3-4521-8550-dfcd0d8924e6-upicture9.png}}{}
\makeatother
\caption{\boldmath {The responses for the various groups who are ideal for convalescent plasma therapy. }}
\label{f-29cbf1dc6e81}
\end{figure}
\egroup
\bgroup
\fixFloatSize{images/8fc446dd-30d7-41c5-adec-329368212141-upicture10.png}
\begin{figure}[!htbp]
\centering \makeatletter\IfFileExists{images/8fc446dd-30d7-41c5-adec-329368212141-upicture10.png}{\includegraphics{images/8fc446dd-30d7-41c5-adec-329368212141-upicture10.png}}{}
\makeatother
\caption{\boldmath {The responses for the suitable group of patients to donate blood for convalescent plasmatherapy. }}
\label{f-de1804593788}
\end{figure}
\egroup
\bgroup
\fixFloatSize{images/538dfb0b-7d6c-421e-b1c9-41cd2b278e07-upicture11.png}
\begin{figure}[!htbp]
\centering \makeatletter\IfFileExists{images/538dfb0b-7d6c-421e-b1c9-41cd2b278e07-upicture11.png}{\includegraphics{images/538dfb0b-7d6c-421e-b1c9-41cd2b278e07-upicture11.png}}{}
\makeatother
\caption{\boldmath {The responses X axis represents the participants aware of convalescent plasma therapy and Y axis represents the response of the suitable people to donate blood for convalescent plasma therapy. }}
\label{f-74e427c59d19}
\end{figure}
\egroup
\bgroup
\fixFloatSize{images/d4c9d8ba-afc8-48e7-9268-cec8878fa90e-upicture12.png}
\begin{figure}[!htbp]
\centering \makeatletter\IfFileExists{images/d4c9d8ba-afc8-48e7-9268-cec8878fa90e-upicture12.png}{\includegraphics{images/d4c9d8ba-afc8-48e7-9268-cec8878fa90e-upicture12.png}}{}
\makeatother
\caption{\boldmath {The percentage of participants who are willing to treat the patients with history of Covid-19. }}
\label{f-f76f57b6000c}
\end{figure}
\egroup
\bgroup
\fixFloatSize{images/c5f1d842-c0e8-4926-9a65-8f7cd33ac80c-upicture13.png}
\begin{figure}[!htbp]
\centering \makeatletter\IfFileExists{images/c5f1d842-c0e8-4926-9a65-8f7cd33ac80c-upicture13.png}{\includegraphics{images/c5f1d842-c0e8-4926-9a65-8f7cd33ac80c-upicture13.png}}{}
\makeatother
\caption{\boldmath {Frequency distribution of willingness of post kinds of treatment for patients with the history of COVID 19. }}
\label{f-76adbcbc91f6}
\end{figure}
\egroup
\bgroup
\fixFloatSize{images/896fb625-0983-42c0-be73-3fbd2d63966a-upicture14.png}
\begin{figure}[!htbp]
\centering \makeatletter\IfFileExists{images/896fb625-0983-42c0-be73-3fbd2d63966a-upicture14.png}{\includegraphics{images/896fb625-0983-42c0-be73-3fbd2d63966a-upicture14.png}}{}
\makeatother
\caption{\boldmath {X axis represents the participants willing to treat and Y axis represents the type of treatment done. }}
\label{f-a43dcf98703f}
\end{figure}
\egroup
Figure~\ref{f-738b2702b8a1}, X axis represents whether the respondents agreed or disagreed, Y axis represents the number of responses. 98.1\% of the participants accepted that COVID-19 was caused by SARS-COV to virus and 1.9\% disagreed.
Figure~\ref{f-044308f6fb42}, 67.0\% of the participants felt that the symptoms of COVID was a combination of fever, Cough and shortness of breath.
Figure~\ref{f-eedc83bd1336}, X axis represents the symptoms of Covid 19 and y axis represents the participants aware that COVID 19 were caused by SARS-CoV-2virus. The Pearson Chi Square test shows p value is 0.730. (p value{\textgreater}0.05). Hence, it is statistically not significant.
Figure~\ref{f-137ed389a9be} shows, 1-14 days- 55.3 \% and 1 to 12.5 days 35.9 \%
Figure~\ref{f-0fd243c62b6c} shows, 61.2\% agreed that elderly individuals, immuno-compromised individuals, people with systemic illness are at high risk, 19.4 \% strongly felt that only elderly individuals are at higher risk.
Figure~\ref{f-4a1e3e1bc46f} represents, 90.3\% of participants are aware of convalescent plasma therapy.
Figure~\ref{f-a011464f30ca} depicts, CP therapy was suggested that treatment of SARS be 49.5\%, MERS by 14.6 \% and SARS, MERS and H1 N1 by 34\%
Figure~\ref{f-eb72dc309959} shows, 94.2\% of the participants suggested convalescent plasma therapy to be used as a vaccine prior to the incidence COVID 19.
Figure~\ref{f-29cbf1dc6e81} shows, 78.6\% of participants accepted that severe cases of COVID-19 are the ideal people to receive convalescent plasma therapy whereas only 20.4 \% accepted it to be in the initial face of COVID-19
Figure~\ref{f-de1804593788} shows, 74.8\% by those recovered from COVID-19, 22.3\% by healthy person withno viral history and 2.9 \% by healthy persons with viral history.
Figure~\ref{f-74e427c59d19} depicts, The Pearson Chi Square test shows p value is 0.491 (p value{\textgreater}0.05). Hence, it is statistically not significant.
Figure~\ref{f-f76f57b6000c} shows, 95.1\% are willing to treat the patients with Covid or history of Covid 19 when provided with PPE.
Figure~\ref{f-76adbcbc91f6} represents, 47.6\% of postgraduate were willing to provide only palliative treatment, 13.6 \% were ready to do emergency treatment.
Figure~\ref{f-a43dcf98703f} shows, The Pearson Chi Square test shows p value is 0.212 (p value{\textgreater}0.05). Hence, it is statistically not significant.
The study aims at assessing the general awareness about Covid-19 and the effective role of Convalescent plasma therapy in Covid-19 treatment among post graduate dental students.
\section{Materials and Methods}
A KAP survey was conducted online among Postgraduate dental students on the pathogenesis and convalescent plasma therapy for COVID-19. A total of 15 questions were included in the study. All the questions framed were close-ended, and the question was conducted online. The survey was conducted to analyse the cause of COVID-19, symptoms, incubation time, recovery time and The people at higher risk.10 questions were based on the above mentioned. The rest ten questions were based on convalescent plasma therapy, its application, suitable people to receive and donate blood and the attitude and practice towards the patients with a history of COVID-19 for dental treatment. The dependent variables used in the study are awareness knowledge attitude and perception and convalescent plasma therapy and COVID-19, and the independent variables are pathogenesis, convalescent plasma therapy. The data were analysed using SPSS software. The statistical test used to be percentage analysis, mean and standard deviation.
\section{Results and Discussion}
Pneumonia associated with severe acute respiratory syndrome Coronavirus 2SARS-COV-two named coronavirus disease 2019 (covid19) By WHO emerged in December 2019 from Wuhan, China. As this epidemic spread within three months WHO categorised it as a pandemic in March 2020. Even though the positive cases and the mortality are being increased day by day, no approved specific anti-viral agent is targeting the novel virus such as remdesivir, lopinavir, and ritonavir is an understudy for determining the efficacy and safety \unskip~\citep{843100:19919521}, \unskip~\citep{843100:19919517}, \unskip~\citep{843100:19919533},\unskip~\citep{843100:19919529}.\textit{\space }
Convalescent plasma therapy as a standard adaptive immune therapy that has been applied for the prevention and treatment of other infectious diseases for more than one century. [for the past decade's CP therapy has been successfully used for the treatment of say RS, MARS, H1 N1 2009 pandemic with satisfactory efficacy and safety \unskip~\citep{843100:19919516}, \unskip~\citep{843100:19919513}. Since the virology and clinical characteristics shared similarly among SARS, MERS, H1N1 and COVID-19, CP has been proposed as a treatment option for COVID-19 \unskip~\citep{843100:19919525}. Kai Duan et al. has suggested that the first endpoint for COVID-19 as safety for convalescent plasma transfusion and the second endpoint being the improvement of clinical symptoms and laboratory parameters within three days after CP transfusion. The exact pathogenesis of COVID-19 is under study, and there are several kinds of research on it. Other parameters like increased lymphocyte count, decrease C-reactive protein has been proved due to convalescent plasma therapy, thereby increasing the likelihood of individuals to recover. There was a radiological examination done which revealed that there are varying degrees of absorption in lesions within seven days \unskip~\citep{843100:19919525}.
A survey was conducted among postgraduate dental students, where 103 Participated in the study. The survey was conducted online, and 15 questions were included. In the study, 98.1\% of the participants accepted that SARS-COV caused COVID-19 to the virus and 1.9\% disagreed with that(Figure~\ref{f-738b2702b8a1}). There are several studies on the symptoms of COVID- 19 \unskip~\citep{843100:19919517} describing the primary symptoms be cough and fever \unskip~\citep{843100:19919518}, \unskip~\citep{843100:19919525}, other symptoms of SARS, MERS, Covid 19 being myalgia, fatigue, dyspnea and anorexia \unskip~\citep{843100:19919717}, \unskip~\citep{843100:19919522}, \unskip~\citep{843100:19919524}. In our study, we observed that 67.0\% of the participants felt that the symptoms of COVID were a combination of fever, cough and shortness of breath. (Figure~\ref{f-044308f6fb42}). Association of symptoms of COVID 19 and the participants aware of COVID 19 where the p-value is 0.730. (p value{\textgreater}0.05) which is statistically not significant (Figure~\ref{f-eedc83bd1336}).
The incubation period of COVID-19 was suggested to be 1-14 days by 55.3 \%and 1 to 12.5 days by 35.9 \%(Figure~\ref{f-137ed389a9be}).In the study, 61.2 percentage agreed that elderly individuals, immuno compromised individuals, people with the systemic illness are at high risk, 19.4\% strongly felt that only elderly individuals are at higher risk(Figure~\ref{f-0fd243c62b6c} ). The recovery period suggested by 51.6 \% with 3 to 6 weeks, whereas 38.8\% agreed that the recovery period was two weeks. We observe that 90.3\% of the participants were aware of convalescent plasma therapy, and correlation was done. (Figure~\ref{f-4a1e3e1bc46f}).
In the present study, 90.3 \% of participants are aware of convalescent plasma therapy. There are several studies on convalescent plasma therapy on SARS, MERS, H1N1. In our research, CP was suggested that treatment of SARS by 49.5\%, MERS by 14.6 \% and SARS, MERS and H1 N1 by 34\%(Figure~\ref{f-a011464f30ca}). This revealed that dentists are aware of the management of pandemic disease with the help of convalescent plasma therapy.
In the present study, 94.2\% of the participants suggested convalescent plasma therapy be used as a vaccine before the incidence COVID 19(Figure~\ref{f-eb72dc309959}). Few authors conducted a study on convalescent plasma therapy and found that early stage of the disease is the ideal time for convalescent plasma therapy for most effective results \unskip~\citep{843100:19919521}. In our study, we observed that 78.6 \%of participants accepted that severe cases of COVID-19 are the ideal people to receive convalescent plasma therapy. In contrast, only 20.4 \% accepted it to be in the first face of COVID-19(Figure~\ref{f-29cbf1dc6e81}). The suitable people to donate blood for convalescent plasma therapy according to our responses were - 74.8\% by those recovered from COVID 19, 22.3\% by a healthy person with no viral history and 2.9 \% by healthy persons with viral history(Figure~\ref{f-de1804593788}). Association between participants who were aware of convalescent plasma therapy and the ideal people to donate blood for convalescent plasma therapy shows p-value is 0.491 (p value{\textgreater}0.05)which is statistically not significant(Figure~\ref{f-74e427c59d19}).
The mean time for the onset of symptoms to receive convalescent plasma therapy was reported to be 16.5 days by \unskip~\citep{843100:19919513}. In our study, we observe that the mean time was agreed to be 16.5 days by 52.4 \% and ten days by 36.9\%. 95.1\% of, the participants were willing to treat the patients during Covid 19 pandemic even though they were aware that dentists are the most vulnerable and are at higher risk of covid 19.
Among the 103 participants, 95.1 \% are willing to treat the patients with Covid or history of Covid 19 when provided with PPE(Figure~\ref{f-f76f57b6000c}), and 96.1\% do agree that dentists are at higher risk of transmission of COVID-19. In the study 47.6\% of postgraduate were willing to provide only palliative treatment, 13.6 \% were ready to do an emergency treatment like surgical or endodontic treatment, 11.7 \% were prepared for providing oral prophylaxis including scaling and curettage and 27.2\% were prepared to do all the dental procedures(Figure~\ref{f-76adbcbc91f6}). Association of responses of the dentist willing to treat patients with a history of COVID 19 and various treatments are done where the p-value is 0.212 (p value{\textgreater}0.05) which is statistically not significant(Figure~\ref{f-a43dcf98703f}). Previously, different research was done by our team on awareness \unskip~\citep{843100:19919520}, molecular diagnostic studies \unskip~\citep{843100:19919512}, \unskip~\citep{843100:19919510}, \unskip~\citep{843100:19919509}, \unskip~\citep{843100:19919527}, \unskip~\citep{843100:19919528}, immunohistochemical studies \unskip~\citep{843100:19919514}, \unskip~\citep{843100:19919533}, histological assessment \unskip~\citep{843100:19919531}, \unskip~\citep{843100:19919508}, \unskip~\citep{843100:19919519}, case report \unskip~\citep{843100:19919505}, \unskip~\citep{843100:19919511}, \unskip~\citep{843100:19919516} and systematic review \unskip~\citep{843100:19919512}, on advances in pathology to know the pathogenesis and the prognosis. Advance training, proper PPE and training on handling the patients with any infectious disease should be dealt with in detail for reducing the spread from dental clinics and dentists.
\section{Conclusions}
In this study, we found that postgraduate dental students have a varied knowledge of COVID-19, and most of them suggested that plasmatherapy is beneficial. Despite the spread and severity of COVID-19, most of them are willing to treat patients by providing palliative treatment by limiting the spread from dental clinics or hospitals.
\section*{Acknowledgement}We thank the management and students of Saveetha Dental college for their timely support.
\textbf{Conflict of Interest}
Nil.
\textbf{Funding Support}
Nil.
\bibliographystyle{pharmascope_apa-custom}
\bibliography{\jobname}
\end{document}
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https://www2.math.upenn.edu/~kazdan/425S15/hw/hw4.tex | upenn.edu | CC-MAIN-2022-21 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2022-21/segments/1652662647086.91/warc/CC-MAIN-20220527112418-20220527142418-00233.warc.gz | 1,238,752,079 | 3,687 | \documentclass[11pt]{article}
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{\bf Math 425, Spring 2015\hfill Jerry L. Kazdan}
\medskip
\begin{center}
{\large\bf Problem Set 4}
\end{center}
{\sc Due:} Thurs. Feb.~12 in class. [Late papers will be accepted until 1:00 PM Friday.]
\bigskip
{\bf \large This week}. Please read all of Chapter 3 and Chapter 4 in the Strauss text.
\bigskip
\begin{problems}
\item{} [One goal of this problem is to understand ``periodic boundary conditions''. See Part (e) below.]\\
Say a function $u(t)$ satisfies the differential equation
\begin{equation}\label{odeH}
u'' +b(t)u' +c(t)u=0
\end{equation}
on the interval $[0,\,A]$ and that the coefficients
$b(t)$ and $c(t)$ are both bounded, say $\abs{b(t)}\le M$ and
$\abs{c(t)}\le M$ (if the coefficients are continuous, this is always
true for some $M$).
\begin{parts}
\item Define $E(t):=\frac{1}{2}(u'^2 +u^2)$. Show that for some constant
$\gamma$ (depending on $M$) we have $E'(t)\le \gamma E(t)$. [{\sc
Suggestion:} use the simple inequality $2xy\le x^2+y^2$.]
\item Show that $E(t)\le e^{\gamma t}E(0)$ for all $t\in[0,\,A]$.
[{\sc Hint: } First use the previous part to show that
$(e^{-\gamma t}E(t))' \le 0$].
\item In particular, if $u(0)=0$ and $u'(0)=0$, show that
$E(t)=0$ and hence $u(t)=0$ for all $t\in [0,\,A]$. In other words, if
$u'' +b(t)u' +c(t)u=0$ on the interval $[0,\,A]$ and that the functions
$b(t)$ and $c(t)$ are both bounded, and if $u(0)=0$ and $u'(0)=0$,
then the only possibility is that $u(t)\equiv 0$ for all $t\ge 0$.
\item Use this to prove the {\it uniqueness theorem\,}: if $v(t)$ and
$w(t)$ both satisfy equation
\begin{equation}\label{odeI}
u'' +b(t)u' +c(t)u=f(t)
\end{equation}
and have the same initial conditions, $v(0)=w(0)$ and $v'(0)=w'(0)$,
then $v(t)\equiv w(t)$ in the interval $[0,\,A]$.
\item Assume the coefficients $b(t)$, $c(t)$, and $f(t)$ in equation
\eqref{odeI} are periodic with period $P$, that is, $b(t+P)=b(t)$
etc.\ for all real $t$. If $\phi(t)$ is a solution of equation
\eqref{odeI} that satisfies the \emph{periodic boundary conditions}
\begin{equation}\label{periodic}
\phi(P)=\phi(0)\quad \text{and}\quad \phi'(P)=\phi'(0),
\end{equation}
show that $\phi(t)$ is periodic with period $P$: $\phi(t+P)=\phi(t)$
for all $t\ge 0$. Thus, the periodic boundary conditions
\eqref{periodic} do imply the desired periodicity of the solution
\end{parts}
\item Let $C$ be a circle of radius $1$ and let $u(\theta,t)$ be the
temperature at a point $\theta,$ at time $t$. To make this
well-defined, we need that $u(\theta + 2\pi)=u(\theta)$. Say
$u(\theta,t)$ satisfies the heat equation $u_t=u_{\theta\theta}$. Let
$$
E(t) = \frac{1}{2}\int_{-\pi}^\pi u^2(\theta,t)\,d\theta.
$$
\begin{parts}
\item Show that $E'(t)\le 0$.
\item If the initial temperature $u(\theta, 0)=0$, show that
$u(\theta,t)=0$ for all $t\ge 0$.
\end{parts}
\item Let $u(x,t)$ be the temperature at time $t$ at the point $x$, $-L\le x \le L$. Assume it satisfies the heat equation $u_t =u_{xx}$ for $ 0<t<\infty$
with the boundary condition $u(-L,t)=u(L,t)=0$ and initial condition
$u(x, 0) = f(x)$.
\begin{parts}
\item Show that \ $\displaystyle E(t):=\frac{1}{2}\int_{-L}^L u^2(x,t)
\,dx$ \ is a decreasing function of $t$.
\item Use this to prove uniqueness for the heat equation with these
specified initial and boundary conditions $u(-L,t)=f(t)$,
$u(L,t)=g(t)$.
\item If $u(x, 0) = \varphi(x)$ is an even function of $x$, and
$u(-L,t)=u(L,t)$ show that the temperature $u(x,t)$ at later times is
also an even function of $x$.
\end{parts}
\item Find a formula for the solution of
$$
u_{xx} + u_{xt} - 20u_{tt} = 0\qquad\text{with}\qquad
u(x,0)=\varphi(x) \text{\ \ and\ \ } u_t(x,0)=\psi(x).
$$
Your result should be something like equation (8) on page 36 of the
text.
\item {}[{\sc The dulcimer}, P.\ 38 \#5] Solve the wave equation
$u_{tt} = c^2 u_{xx}$ with initial conditions $u(x, 0) = 0$ and
$u_t(x,0) = g(x)$, where $g(x) = 1$ if $|x| < a$ and $g(x) = 0$ for
$|x| \ge a$. This corresponds to hitting the string with a hammer of
width $2a$. Draw sketches of snapshots of the string (i.e., plot $u$
versus $x$) for $t = \frac{1}{2} a/c$, $t = a/c$, $t = \frac{3}{2}
a/c$, $t = 2a/c$ and $t = \frac{5}{2} a/c$. [{\sc Remark: } This is
very similar to p.\ 38 \#3].
\item Solve the wave equation $u_{tt}=c^2u_{xx}$ for the semi-infinite string $x\ge 0$ with the initial and boundary conditions
$$
u(x,0) = 3 - \sin x,\quad u_t(x,0) = 0,\quad
u(0,t) = 3-t^2.
$$
\item p.\ 60 \#1
\item p.\ 60 \#4
\item {} [p.\ 66 \#1] Find an explicit formula for the solution of the
wave equation \ $u_{tt} = u_{xx}$ \ on the half-line $0<x<\infty$ with
initial conditions $u(x,0)=\varphi(x)$, \ $u_t(x,0)=\psi(x)$ and the
homogeneous Neumann boundary condition $u_x(0,t)=0$.
\item p.\ 66 \#3
\comments{
\item Let $u(x,t)$ be a solution of the inhomogeneous wave equation
$u_{tt} - c^2u_{xx} = \sin\pi x$ for $0<x<1$, $t>0$ with the boundary
$conditions $u(0,t)=0$ and $u(1,t)=0$.
\begin{parts}
\item Find the solution if $u(x,0)=0$ and $u_t(x,0)=0$.
\item Find the solution if $u(x,0)=x(1-x)$ and $u_t(x,0)=0$.
\end{parts}
\item p.\ 71 \#2
}
\end{problems}
\comments{
\vskip 20pt
\begin{center}{\large \bf Bonus Problem}
[Please give this directly to Professor Kazdan]
\end{center}
\begin{problems}
\item [B-1] Strauss P. 41 \#6
\end{problems}
}
\medskip
[Last revised: \today]
\end{document}
|
https://gapil.gnulinux.it/gitweb/?p=gapil.git;a=blob_plain;f=fileadv.tex;hb=81ff87c3e2a6ecd3e33867798cba0d27576f44d0 | gnulinux.it | CC-MAIN-2022-27 | text/x-tex | application/x-tex | crawl-data/CC-MAIN-2022-27/segments/1656104692018.96/warc/CC-MAIN-20220707124050-20220707154050-00534.warc.gz | 322,913,768 | 4,579 | \chapter{La gestione avanzata dei file}
\label{cha:file_advanced}
In questo capitolo affronteremo le tematiche relative alla gestione avanzata
dei file, che non sono state trattate in \capref{cha:file_unix_interface},
dove ci si è limitati ad una panoramica delle funzioni base. In particolare
tratteremo delle funzioni di input/output avanzato e del \textit{file
locking}.
\section{Le funzioni di I/O avanzato}
\label{sec:file_advanced_io}
In questa sezione esamineremo le funzioni che permettono una gestione più
sofisticata dell'I/O su file, a partire da quelle che permettono di gestire
l'accesso contemporaneo a più file, per concludere con la gestione dell'I/O
mappato in memoria.
\subsection{La modalità di I/O \textsl{non-bloccante}}
\label{sec:file_noblocking}
Abbiamo visto in \secref{sec:sig_gen_beha}, affrontando la suddivisione fra
\textit{fast} e \textit{slow} system call, che in certi casi le funzioni di
I/O possono bloccarsi indefinitamente.\footnote{si ricordi però che questo può
accadere solo per le pipe, i socket ed alcuni file di dispositivo; sui file
normali le funzioni di lettura e scrittura ritornano sempre subito.} Ad
esempio le operazioni di lettura possono bloccarsi quando non ci sono dati
disponibili sul descrittore su cui si sta operando.
Questo comportamento causa uno dei problemi più comuni che ci si trova ad
affrontare nelle operazioni di I/O, che è quello che si verifica quando si
devono eseguire operazioni che possono bloccarsi su più file descriptor:
mentre si è bloccati su uno di questi file su di un'altro potrebbero essere
presenti dei dati, così che nel migliore dei casi si avrebbe una lettura
ritardata inutilmente, e nel peggiore si potrebbe addirittura arrivare ad un
deadlock.
Abbiamo già accennato in \secref{sec:file_open} che però è possibile prevenire
questo tipo di comportamento aprendo un file in modalità
\textsl{non-bloccante}, attraverso l'uso del flag \macro{O\_NONBLOCK} nella
chiamata di \func{open}. In questo caso le funzioni di input/output che
altrimenti si sarebbero bloccate ritornano immediatamente, restituendo
l'errore \macro{EAGAIN}.
L'utilizzo di questa modalità di I/O permette di risolvere il problema
controllando a turno i vari file descriptor, in un ciclo in cui si ripete
l'accesso fintanto che esso non viene garantito. Ovviamente questa tecnica,
detta \textit{polling}, è estremamente inefficiente: si tiene costantemente
impiegata la CPU solo per eseguire in continuazione delle system call che
nella gran parte dei casi falliranno. Per evitare questo, come vedremo in
\secref{sec:file_multiplexing}, è stata introdotta una nuova interfaccia di
programmazione, che comporta comunque l'uso della modalità di I/O non
bloccante.
\subsection{Le funzioni \func{poll} e \func{select}}
\label{sec:file_multiplexing}
Per superare il problema di dover usare il \textit{polling} controllare la
disponibilità di accesso ad un file aperto in modalità non bloccante, sia BSD
che SysV hanno introdotto delle nuove funzioni in grado di sospendere
l'esecuzione di un processo fino a che l'accesso diventi possibile; il primo
ad introdurre questa nuova interfaccia, chiamata usualmente \textit{I/O
multiplexing}, è stato BSD, con l'introduzione della funzione \func{select},
il cui prototipo è:
\begin{prototype}{sys/select.h}
{int select(int n, fd\_set *readfds, fd\_set *writefds, fd\_set *exceptfds,
struct timeval *timeout)}
Attende che un certo insieme di file descriptor cambi stato.
\bodydesc{La funzione restituisce il numero di file descriptor, anche nullo,
che hanno cambiato stato in caso di successo e -1 in caso di errore, nel
qual caso \var{errno} viene settata ai valori:
\begin{errlist}
\item[\macro{EBADF}] Si è specificato un file descriptor sbagliato in uno
degeli insiemi.
\item[\macro{EINTR}] La funzione è stata interrotta da un segnale.
\item[\macro{EINVAL}] Si è specificato per \param{n} un valore negativo.
\end{errlist}
ed inoltre \macro{ENOMEM}.
}
\end{prototype}
La funzione mette il processo in stato di \textit{sleep} (vedi
\tabref{tab:proc_proc_states}) fintanto che non viene rilevate dell'attività
sull'insieme dei file descriptor specificati (\param{readfds},
\param{writefds} e \param{exceptfds}), per un tempo massimo specificato da
\param{timeout}.
Per specificare quali file descriptor si intende selezionare, la funzione usa
un particolare oggetto, il \textit{file descriptor set}, identificato dal tipo
\type{fd\_set}, che serve ad identificare un insieme di file descriptor, in
maniera analoga a come un \textit{signal set} (vedi \secref{sec:sig_sigset})
identifica un insieme di segnali. Per la manipolazione di questi \textit{file
descriptor set} si possono usare delle opportune macro di preprocessore:
\begin{functions}
\headdecl{sys/select.h}
\funcdecl{FD\_ZERO(fd\_set *set)}
Inizializza l'insieme (vuoto).
\funcdecl{FD\_SET(int fd, fd\_set *set)}
Inserisce il file descriptor \param{fd} nell'insieme.
\funcdecl{FD\_CLR(int fd, fd\_set *set)}
Rimuove il file descriptor \param{fd} nell'insieme.
\funcdecl{FD\_ISSET(int fd, fd\_set *set)}
Controlla se il file descriptor \param{fd} è nell'insieme.
\end{functions}
In genere un \textit{file descriptor set} può contenere fino ad un massimo di
\macro{FD\_SETSIZE} file descriptor. Questo a seconda del sistema può essere
il limite del numero massimo di file aperti\footnote{ad esempio in Linux, fino
alla serie 2.0.x, c'era un limite di 256 file per processo.}, ma quando,
come nelle versioni più recenti del kernel, questo limite non c'è un massimo,
esso indica le dimensioni in munero di bit utilizzabili per l'insieme.
La funzione richiede di specificare tre insiemi distinti di file descriptor;
il primo, \param{readfds}, verrà osservato per rilevare la disponibilità di
input in lettura, il secondo, \param{writefds} per verificare la possibilità
di scrivere ed il terzo, \param{exceptfds}, per verificare l'esistenza di
eccezioni. I corrispondenti valori dei \textit{file descriptor set} saranno
modificati di conseguenza per mostrare quale dei file descriptor ha cambiato
stato.
Come accennato l'interfaccia di \func{select} è una estensione aggiunta BSD, e
poi entrata a far parte di POSIX; allo stesso tempo System V aveva introdotto
una interfaccia alternativa, basata sulla funzione \func{poll}, il cui
prototipo è:
\begin{prototype}{sys/poll.h}
{int poll(struct pollfd *ufds, unsigned int nfds, int timeout)}
La funzione attente un cambiamento di stato per uno dei file descriptor
specificati da \param{ufds}.
\bodydesc{La funzione restituisce il numero di file descriptor con attività in
caso di successo, o 0 se c'è stato un timeout; in caso di errore viene
restituito -1 ed \var{errno} viene settata ai valori:
.}
\end{prototype}
\subsection{L'I/O asincrono}
\label{sec:file_asyncronous_io}
Una modalità alternativa all'uso dell'I/O non bloccante è quella di fare
ricorso all'I/O asincrono. Abbiamo accennato in \secref{sec:file_open} che è
possibile, attraverso l'uso del flag \macro{O\_ASYNC}, aprire un file in
modalità asincrona, così come è possibile settare questo flag attraverso l'uso
di \func{fcntl}.
In tal caso il sistema genera un segnale \macro{SIGIO} tutte le volte che sono
presenti dei dati in input su un file aperto in questa modalità. Uno dei
problemi che si presentavano con le prime implementazioni di questa modalità
di I/O è che essa poteva essere usata in maniera semplice aprendo un solo file
per processo, dato che altrimenti si sarebbe dovuto provvedere ad effettuare
una serie di controlli su tutti i file aperti per distinguere a quale fosse
dovuto l'emissione del segnale.
Tutto questo adesso può essere evitato facendo ricorso alle informazioni
restituite al manipolatore del segnale attraverso la struttura
\var{siginfo\_t} (vedi \figref{fig:sig_siginfo_t}), il cui campo \var{si\_fd}
riporta il file descriptor che ha generato il segnale.
\subsection{File mappati in memoria}
\label{sec:file_memory_map}
\subsection{I/O multiplo}
\label{sec:file_multiple_io}
\section{Il file locking}
\label{sec:file_locking}
In \secref{sec:file_sharing} abbiamo preso in esame le mosalità in cui un
sistema unix-like gestisce la condivisione dei file da parte di processi
diversi. In quell'occasione si è visto come, con l'eccezione dei file aperti
in \textit{append mode}, quando più processi scrivono contemporaneamente sullo
stesso file non è possibile determinare la sequenza in cui essi opereranno.
Questo causa la possibilità di race condition\index{race condition}; in
generale le situazioni più comuni sono due: l'interazione fra un processo che
scrive e altri che leggono, in cui questi ultimi possono leggere informazioni
scritte solo in maniera parziale o incompleta; o quella in cui diversi
processi scrivono, mescolando in maniera imprevedebile il loro output sul
file.
In tutti questi casi il \textit{file locking} è la tecnica che permette di
evitare le race condition, attraverso una serie di funzioni che permettono di
bloccare l'accesso al file da parte di altri processi, così da evitare le
sovrapposizioni, e garantire la atomicità delle operazioni di scrittura.
\subsection{L'\textit{advisory locking}}
\label{sec:file_record_locking}
La prima modalità di file locking che è stata implementata nei sistemi
unix-like è quella che viene usualmente chiamata \textit{advisory locking}, in
quanto è il processo, e non il sistema, che si incarica di verificare se
esiste una condizione di blocco per l'accesso ai file.
\subsection{Il \textit{mandatory locking}}
\label{sec:file_mand_locking}
Il \textit{mandatory locking} è una opzione introdotta inizialmente in SVr4,
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https://git.lysator.liu.se/ceder/ceder-1616-generations-topgit/-/raw/187743c492201f0919ab24d765798de58b1e6118/doc/lyskomd.texi | liu.se | CC-MAIN-2021-49 | text/plain | application/x-tex | crawl-data/CC-MAIN-2021-49/segments/1637964358323.91/warc/CC-MAIN-20211127223710-20211128013710-00193.warc.gz | 360,789,636 | 32,852 | \input texinfo
@c $Id: lyskomd.texi,v 1.70 2003/08/14 23:06:43 ceder Exp $
@c %**start of header
@setfilename lyskomd.info
@include version.texi
@settitle lyskomd @value{VERSION} Reference Manual
@setchapternewpage odd
@c %**end of header
@iftex
@parindent 0pt
@begin tex
\global\def\BB#1{\b{#1}}
\global\def\II#1{\i{#1}}
@end tex
@end iftex
@ifinfo
@macro BB {text}
'\text\'
@end macro
@macro II {text}
/\text\/
@end macro
@end ifinfo
@ifinfo
This is the reference manual for the lyskomd LysKOM server version
@value{VERSION}.
Copyright @copyright{} 1995-2002 Lysator ACS.
Permission is granted to make and distribute verbatim copies of this
specification provided the copyright notice and this permission notice
are preserved on all copies.
@end ifinfo
@dircategory LysKOM
@direntry
* lyskomd: (lyskomd). lyskomd reference manual.
@end direntry
@titlepage
@sp 10
@title lyskomd Reference Manual
@sp 2
@subtitle Server version @value{VERSION}
@sp 2
@author by the lyskomd developers
@page
@vskip 0pt plus 1filll
Copyright @copyright{} 1995-2002 Lysator ACS
Permission is granted to make and distribute verbatim copies of this document
provided the copyright notice and this permission notice are preserved on all
copies.
Modified versions of this document may be redistributed with the added
condition that all modifications not cleared with the LysKOM development group
are clearly marked and that the entire modified work be redistributed under the
same conditions as the original.
Permission is granted to copy and distribute translations of this manual into
another language under the same conditions as for modified versions.
@end titlepage
@ifinfo
@node Top
@top lyskomd
lyskomd is a server for the LysKOM conferencing system. This info file
documents version @value{VERSION} of lyskomd.
@menu
* Copying:: lyskomd is free software.
* Overview:: Overview of LysKOM.
* Installation:: How to install lyskomd.
* Configuration:: How to configure lyskomd.
* Running lyskomd:: How to run lyskomd.
* Invoking updateLysKOM:: How to run updateLysKOM.
* Invoking komrunning:: How to run komrunning.
* Administration:: Administering a LysKOM server.
* Bugs:: Known bugs in lyskomd.
* DBCK Reference:: Checking and repairing the database.
* splitkomdb:: How to backup the database.
* Hacking:: Notes for server developers.
* lyskomd Database Specification::
@end menu
@end ifinfo
@node Copying
@chapter Copying
lyskomd is free software. It is distributed under the Gnu General Public
License version 2. The file COPYING in the top level of the distribution
contains the text of the license.
@node Overview
@chapter Overview
LysKOM is a conferencing system@footnote{Or in modern terms, enabling
technology for Computer-Supported Cooperative Work (CSCW).}. Similar
systems were QZ-KOM and PortaCOM@footnote{Also known as ``PottaKOM'' and
``BortaKOM''.}. The LysKOM system is copyrighted by Lysator Academic
Computing Society and distributed under conditions of the GNU General Public
License version 2. LysKOM and its documentation is provided ``as is'' without
warranty of any kind.
This reference manual documents version @value{VERSION} of the lyskomd
LysKOM server. The lyskomd server is the work of several people. The main
contributors have been
Per Cederqvist @email{ceder@@lysator.liu.se},
Inge Wallin @email{inge@@lysator.liu.se},
Thomas Bellman @email{bellman@@lysator.liu.se},
David Byers @email{byers@@lysator.liu.se} and
Peter Eriksson @email{pen@@lysator.liu.se}.
@section History
In 1990, Per Cederqvist @email{ceder@@lysator.liu.se} and Peter Eriksson
@email{pen@@lysator.liu.se} and a few other persons started to write the
server. It was operational in the summer of 1990, even though the
members of Lysator discovered a thing called MUD. We started using RCS
on 20 May 1991. The first release was made on 16 Sept 1991. Around that
time we switched from RCS to CVS to handle our source code.
@node Installation
@chapter Installation
Instructions for compiling and installing lyskomd are in the files
@file{README} and @file{INSTALL}, located in the top level of the
lyskomd distribution. Installation should be straightforward on most
platforms.
@node Configuration
@chapter Configuration
There are two configuration files for lyskomd. One defines the server
options and the other defines aux-item types @ref{(protocol-a)The
Aux-Item List,The Aux-Item List}.
@menu
* Server Configuration File:: The server configuration file.
* Aux-Item Definition File:: The aux-item definition file.
@end menu
@node Server Configuration File
@section Server Configuration File
The server reads its configuration from a configuration file. The
default configuration file is @file{/usr/lyskom/etc/config}. The
location of the configuration file can be changed at run-time by
supplying an argument to lyskomd.
The configuration file is line oriented. Each line consists of a
parameter name followed by a colon, and the value of the parameter.
Empty lines and lines whose first non-blank character is a @samp{#} are
ignored.
@menu
* Parameter Types:: Types of configuration parameters.
* Parameters:: Valid configuration parameters.
@end menu
@node Parameter Types
@subsection Parameter Types
Every parameter has a type. The standard types are:
@table @code
@item bool
The parameter can be true or false. Legal values are @code{on},
@code{true}, @code{yes} and @code{1} for true and @code{off},
@code{false}, @code{no} and @code{0} for false.
@item locale-name
The parameter is a locale name. The value must be a legal locale name of
the system where lyskomd is running.
@item path
The parameter is a path name. The value must be a legal path on the
system where lyskomd is running. Most paths you can specify can be
either absolute paths (if they begin with a @samp{/}) or paths relative
to the installation prefix which is specified at compile time and can
be overridden by the @code{Prefix:} parameter in the configuration file.
@item portname
The parameter is a TCP/IP port. It can be a symbolic port name
(traditionally looked up in @file{/etc/services}) or a port number.
@item int
The parameter is a number of some sort. It can be a conference number,
text number or perhaps something else.
@item double
The parameter is a floating point number. Any syntax that the C
function @code{strtod} accepts is OK. Examples of truly portable
values: @samp{1} or @samp{1.3}.
@item timeval
The parameter is a time period. It consists of a floating point
number (in the same format as for parameters of type @code{double}),
optionally followed by optional whitespace and a suffix. If no suffix
is specified, it defaults to the suffix mentioned in the description
of the parameter.
Valid suffixes includes:
@itemize
@item seconds
@item second
@item sec
@item s
@item minutes
@item minute
@item min
@item hours
@item hour
@item h
@item days
@item day
@item d
@item milliseconds
@item millisecond
@item m
@item microseconds
@item microsecond
@item u
@end itemize
@end table
A few parameters have ad-hoc types, that are used for a single
parameter. They are documented in the description of that parameter.
@node Parameters
@subsection Parameters
@table @code
@item Max conferences: @var{int}
The maximum number of conferences possible in the server. This number
must be larger than the number of conferences in the database. This
parameter is required. There is no default.
@item Max texts: @var{int}
The maximum number of texts possible in the server. This number
must be larger than the number of texts in the database. This
parameter is required. There is no default.
@item Locale: @var{string}
Use @var{string} as the locale to run in. This parameter is only
available om systems which support the @code{setlocale} call. If this
parameter is not set, no call to @code{setlocale} will be made. The
default is unset.
@item Force ISO 8859-1: @var{bool}
This option is provided for those with dysfunctional computers that
cannot handle @code{setlocale} properly. If this is set, lyskomd will
handle texts according to the ISO 8859-1 (latin1) alphabet. Default
is off.
@item Prefix: @var{path}
Specify the installation prefix. All relative filenames that the
server uses are interpreted relative to this directory. The default
value of this parameter is set at compile time. The default at
compile time is @file{/usr/lyskom}.
@item Send async: @var{bool}
Do not send any non-requested messages. This disables the sending of
messages about events in the server to all connections. Use of this
parameter is not recommended. Default is on.
@item Client host: @var{hostname}
Specify which IP number the server should use when listening for new
clients. @var{hostname} may be a FQDN (such as
@samp{kom.lysator.liu.se}) or an IP number (such as @samp{10.0.0.1}).
Default is to bind @code{INADDR_ANY}, which means that the server will
listen to all IP numbers of the computer it is running on.
@item Client port: @var{portname}
Listen for new clients on port @var{portname}. The default is 4894, which
is what all clients expect. Do not change this parameter without really
good reason.
@item Presentation of conferences: @var{int}
The number of the conference where presentations should be sent.
Defaults to 1. This option is ignored in lyskomd 1.9 and later. Set this
using dbck or the @ref{(protocol-a)set-info,set-info}.
@item Presentation of persons: @var{int}
The number of the conference where presentations should be sent.
Defaults to 2. This option is ignored in lyskomd 1.9 and later. Set this
using dbck or the @ref{(protocol-a)set-info,set-info}.
@item Motd-conference: @var{int}
The number of the conference where "message-of-the-day" messages should
be sent. Defaults to 3. This option is ignored in lyskomd 1.9 and later.
Set this using dbck or the @ref{(protocol-a)set-info,set-info}.
@item News-conference: @var{int}
The number of the conference where news of interest to the readers of
this LysKOM server should be written. This is typically a conference
with very low traffic which everyone shoule be a member of. Clients
should offer new users to join it. Defaults to 4. This option is ignored
in lyskomd 1.9 and later. Set this using dbck or the
@ref{(protocol-a)set-info,set-info}.
@item Message of the day: @var{int}
Default message-of-the-day of this server. The text will be shown
automatically by conforming LysKOM clients when a user logs on. This
option is ignored in lyskomd 1.9 and later. Set this using dbck or the
@ref{(protocol-a)set-info,set-info}.
@item Garb: @var{bool}
Should the database be automatically purged of old texts? The default
is on.
@item Never save: @var{bool}
Completely disables saving the database. Do not set this to @code{true}
unless you really know what you're doing. The default is @code{false}.
@item Log accesses: @var{path}
This parameter can only be set if the server has been compiled with
@code{LOGACCESSES} defined. It will save a trace of all activity in the
database to a file, for later use in simulations et c. Compiling with
@code{LOGACCESSES} slows the server down quite a lot, so it is normally
not defined.
@item Data file: @var{path}
The path relative to the installation prefix@footnote{The installation
prefix can be specified at compile time, and overridden by the
@code{Prefix:} parameter.} where part of the database is kept. The
default is @file{db/lyskomd-data}.
@item Backup file: @var{path}
The path relative to the installation prefix where a backup of the
database is kept. This file will always contain a complete database, but
it may be a little out-of-date. Default is @file{db/lyskomd-backup}.
@item Backup file 2: @var{path}
The path relative to the installation prefix where a previous generation
of the backup of the database is kept. This file may be needed if an
error in the backup file is detected during the creation of the data
file. Default is @file{db/lyskomd-backup-prev}.
@item Lock file: @var{path}
Name of the lock file that ensures that @code{dbck} and @code{lyskomd}
never attempt to modify the database at the same time. It should always
reside in the same directory as the @samp{Data file}. Default is
@file{db/lyskomd-lock}.
@item Text file: @var{path}
The path relative to the installation prefix where the actual texts in
the database are kept. Default is @file{db/lyskomd-texts}.
@item Text backup file: @var{path}
When @code{dbck} is run with the @samp{-g} option (@ref{Invoking
dbck}, it will store the previous contents of the text file in the
file specified by this option. The path is relative to the
installation prefix. This file is never used by @code{lyskomd}
itself. Default is @file{db/lyskomd-texts-backup}.
@item Backup export directory: @var{path}
When @code{splitkomdb} is run, it will create a copy of the database
in this directory. The copy will be split in a way that helps to keep
incremental backups of that directory small. @xref{splitkomdb}. The
path is relative to the directory specified by @code{Prefix:}. This
directory is never used by @code{lyskomd} itself. Default is
@file{exportdb}.
@item Number file: @var{path}
@itemx Number temp file: @var{path}
Name of the file where the first unused conference and text numbers
are stored. This file contains a single line. It is rewritten each
time a new conference or text is created, to ensure that numbers are
never reused even if the server later crashes before it has time to
save the database. The information is first written to @code{Number
temp file:}, and then renamed to @code{Number file:}. The path is
relative to the installation prefix. Default is @file{db/number.txt}
and @file{db/number.tmp}, respectively. Both files must reside on the
same partition.
@item Log file: @var{path}
The path relative to the installation prefix where log messages from
lyskomd are written. Default is @file{etc/server-log}.
@item Log statistics: @var{path}
Whenever lyskomd receives a SIGUSR1 it will append a timestamp and
a count of how many different atomic calls have been made in this file.
The path is relative to the installation prefix. Default is
@file{etc/lyskomd-log}.
@item Pid file: @var{path}
When lyskomd is up and running it will write its pid in this file. The
path is relative to the installation prefix. This file is used so the
@code{updateLysKOM} script can easily find out what pid the LysKOM
server has. Default is @file{etc/pid}.
This file should be removed when the computer reboots, before
@code{komrunning} or @code{updateLysKOM} is run.
@item Memory usage file: @var{path}
When lyskomd exits normally it appends some info on its usage of memory
to this file. The path is relative to the installation prefix. Almost
any memory leak bugs should be detectable by looking in this file.
Default is @file{etc/memory-usage}.
@item Aux-item definition file: @var{path}
This file defines which aux-items the server should support and how it
should handle them. You will find the details in
@xref{Aux-Item Definition File}.
The path is relative to the installation prefix. Default is
@file{etc/aux-items.conf}.
This file is re-read if a @samp{SIGWINCH} singal is sent to the server.
@item Core directory: @var{path}
The Directory where core dumps are written. This path is relative to the
installation prefix. Default is @file{cores}.
@item Connection status file: @var{path}
@itemx Connection status temp file: @var{path}
Where to store a status file that contains information about all
connections. The status is written to the temp file and atomically
renamed to the status file.
The path is relative to the installation prefix. Defaults are
@file{etc/connections.txt} and @file{etc/connections.tmp}. Both files
must reside on the same file system. @xref{Files}, for information
about the file format.
@item Status file: @var{path}
This file is created by @code{komrunning} to indicate that lyskomd
should currently not be running. When this file exists
@code{updateLysKOM} will send it a @samp{SIGTERM} signal, so that it
saves the database and dies. Default is @file{etc/status}.
@item Nologin file: @var{path}
If this file exists, the server will not allow any connections at all.
Default is @file{/etc/nologin}.
@item Garb busy postponement: @var{timeval}
The garb only runs while the server is idle. This determines how
often the garb will check if the server is idle. Default is @code{20
milliseconds}.
@item Garb timeout: @var{timeval}
How long to sleep when the server is garbage-collecting texts, but has
nothing else important to do. Default is @code{100 milliseconds}.
@item Sync timeout: @var{timeval}
How long to sleep when lyskomd is saving its database.
Defaults to @code{0 milliseconds}.
@item Permissive sync: @var{bool}
Turning this option on lets any session sync the LysKOM database.
Turning it off restricts the operation to LysKOM administrators. Default
is off.
@item Garb interval: @var{timeval}
How long to wait between each garb sweep. Defaults to @code{1440
minutes}, which means that 24 hours will pass between each garb sweep.
@item Sync interval: @var{timeval}
How long to wait between syncs. The current version of lyskomd keeps
changes to the database in memory until they are synced to disk. This
parameter specifies how long the server waits before attempting to
dump the database. The default is @code{5 minutes}.
@item Sync retry interval: @var{timeval}
If anything goes wrong while trying to dump the data base (such as if
the disk is full), lyskomd will wait for this long before trying
again. Default is @code{1 minute}.
@item Saved items per call: @var{int}
When the server is saving the database, it does so in the background.
It serves one call from a client, saves a few items to the new database
file, serves another call, et c. This parameter sets the number of
items (texts, conferences, persons) that are saved after each call.
Default is @code{5}.
@item Penalty per call: @var{int}
Penalty points given to a client once a call is completed. This
affects the scheduling. Default is @code{10}.
@item Penalty per read: @var{int}
Penalty points given to a client each time a @code{read(2)} is
performed on the socket connected to the client. This affects the
scheduling. Default is @code{1}.
@item Max penalty: @var{int}
Once a client receives this many penalty points, the server will stop
reading from the socket connected to the client. (Once the server
becomes idle, all penalty points will be aged, so the server will soon
start reading from it again.) Default is @code{100}.
@item Low penalty: @var{int}
Once the penalty points for a client is reduced below this setting,
the server will start reading from the client again. This should be
lower than @code{Max penalty}. Default is @code{20}.
@item Default priority: @var{int}
@itemx Max priority: @var{int}
The default and max scheduling priority of a client. Both values must
currently be set to @code{0}, which is the default.
@item Default weight: @var{int}
@itemx Max weight: @var{int}
The default and max scheduling weight for a client. Defaults to
@code{20} and @code{100}.
@item Connect timeout: @var{timeval}
If the client doesn't send the initial handshake (such as
@samp{A27Hceder@@stanly.lysator.liu.se}) within this time period, the
client will be disconnected.
Default is @code{30 seconds}.
@item Login timeout: @var{timeval}
@itemx Active timeout: @var{timeval}
If nothing is sent to the client for this long, the client will be
disconnected. Both asynchronous messages and replies to requests from
the clients will reset the timer. The @samp{Login timout:} value is
used while nobody is logged in on the session.
Default is @code{30 minutes} and @code{11.5 days}, respectively.
@item Max client data length: @var{int}
The maxiumum allowed length for client name and version data. The
default is @code{60}.
@item Max conference name length: @var{int}
The maximum length of conference names. The default is @code{60}.
@item Max password length: @var{int}
Only the first eight characters of the password are currently
significant, even if this number is much larger. The default is
@code{128}.
@item Max what am I doing length: @var{int}
The maximum length of the string permitted in the protocol A call
@ref{(protocol-a)change-what-i-am-doing, change-what-i-am-doing}. The
default is 60.
@item Max username length: @var{int}
The maximum length permitted for user names. Default is 128.
@item Max text length: @var{int}
The maximum length allowed for a text. The default is 131072 characters.
@item Max aux_item length: @var{int}
The maximum length allowed for a single aux-item. The default is 16384
characters.
@item Max broadcast length: @var{int}
The maximum length allowed for broadcast messges. The default is 1024
characters.
@item Max regexp length: @var{int}
The maximum length allowed for regexps in various calls. The default is
1024 characters.
@item Statistic name length: @var{int}
The maximum lenght allowed for the name of a measured statistics. The
default is 64 characters.
@item Max marks per person: @var{int}
The maximum number of marks a person is allowed to have. The default is
2048.
@item Max marks per text: @var{int}
The maximum number of marks a text can have. The default is 1024.
@item Max recipients per text: @var{int}
The maximum number of recipients of a text. The default is 512.
@item Max comments per text: @var{int}
The maximum number of comments a text can have. The default is 128.
@item Max footnotes per text: @var{int}
The maximum number of footnotes a text can have. The default is 32.
@item Max links per text: @var{int}
The maximum number of misc info items that can be added to a text.
@item Max mark_as_read chunks: @var{int}
@c FIXME: What is this?
@item Max super_conf loop: @var{int}
@c FIXME: What is this?
@item Max accept_async len: @var{int}
Maximum length of list accepted in the accept_async call. Default is
128.
@item Max aux_items deleted per call: @var{int}
Maximum number of aux_items that can be deleted in one call. Default is
128.
@item Max aux_items added per call: @var{int}
Maximum number of aux_items that can be added at once. Default is 128.
@item Max read_ranges per call: @var{int}
Maximum number of read_ranges that can sent in a single request.
Default is 512.
@item Default garb nice: @var{int}
Each conference has a lifetime for texts written in it. The lifetime is
counted in days, and can be set for each conference by the administrator
of the conference. This is the default value assigned to new
conferences. Default is 77 days.
@item Default keep commented nice: @var{int}
A text will not be removed if it has comments newer than a certain
number of days. This number can be set for each conference. This
parameter specifies the default value for that number of days. The
default is 77.
@item Max client message size
The maximum number of bytes that is read or written in a single system
call. Defaults to 8176. (Attempts to set it to a larger value will
currently only affect the input.)
@item Max client transmit queue messages: @var{int}
@itemx Max client transmit queue bytes: @var{int}
Max number of pending data blocks (or total number of bytes) in the
reply queue to a client. If there is ever more than this many data
blocks in the queue the client will be disconnected. Each atomic
question typically generates two data blocks. Default is 50 and
100000, respectively.
@item Stale timeout: @var{timeval}
If the transmit queue of a client is full for this long, without the
server being able to send anything to the client, the client will be
disconnected. Default is 60 minutes.
@item Max simultaneous client replies: @var{int}
This is a performance tuning parameter of little real interest. Default
is 10.
@item Open files: @var{int}
Try to persuade the operating system to allow lyskomd to have this many
open file descriptors simultaneously. Each client that is connected to
the server occupies one file descriptor, and lyskomd needs several file
descriptors for internal purposes. Default is to not use this parameter.
@item Use DNS: @var{bool}
The IP address of a client is looked up using DNS when it connects.
Unfortunately, this lookup blocks the entire server, and it can take
several minutes. You can disable DNS lookup with this parameter.
Default is on.
@item DNS log threshold: @var{double}
If the @samp{Use DNS:} parameter is true, the server will measure the
time each DNS lookup takes. If the time exceeds the specified
threshold, an entry will be made in the log. The value is specified
in seconds. The default value is 1.5 seconds. If your libc supports
it, you can enter @code{+inf} to disable logging.
@item Anyone can create new persons: @var{bool}
If this is set, anyone can create a new person, even if he lacks
special bits for doing so. Default is on.
@item Anyone can create new conferences: @var{bool}
If this is set, anyone can create a new conferences, even if he lacks
special bits for doing so. Default is on.
@item Allow creation of persons before login: @var{bool}
If this is set, persons can connect the the server and create a new
person without logging in. This is how new users register in open
environments. If this option is off, then new persons can only be
created by existing users. The default is on.
@item Default change name capability: @var{bool}
If this is set, new users are created with the ability to change their
own name. Default is on.
@item Ident-authentication: @var{policy}
Decide how strictly the server should use the IDENT protocol.
The policy can take any of three values:
@table @asis
@item @code{off} or @code{never}
Do not use the IDENT protocol.
@item @code{on} or @code{try}
Use it, but allow logins even if the lookup fails.
@item @code{require} or @code{required}
Disallow connections if the server cannot find a IDENT login name.
@end table
@item Log login: @var{bool}
Should logins be logged to the log file? Default value is off.
@item Cache conference limit: @var{int}
How many conference statuses the server cache should hold in main
memory. Default is 20. This parameter should be set to at least the
number of expected simultaneous logins.
@item Cache person limit: @var{int}
How many person statuses the server cache should hold in main
memory. Default is 20. This parameter should be set to at least the
number of expected simultaneous logins.
@item Cache text_stat limit: @var{int}
How many text statuses the server cache should hold in main
memory. The default is 20. This parameter should be increased on busy
servers.
@item Echo: @var{string}
Write @var{string} in the log when the config file is read.
@item Jubel: @var{pers_no} @var{text_no}
@itemx Jubel: public @var{pers_no} @var{text_no}
States that @var{pers_no} is not allowed to create text number
@var{text_no}. Default is unset. This parameter may be used multiple
times. The form with the string @code{public} means that the text must
have a public conference as recipient.
@item Jubel: @var{pers_no} @var{dividend} @var{remainder}
@item Jubel: public @var{pers_no} @var{dividend} @var{remainder}
States that @var{pers_no} is not allowed to create any text number
@var{T} which meets the condition @var{T} % @var{dividend} == @var{remainder}.
Default is unset. This parameter may be used multiple
times. The form with the string @code{public} means that the text must
have a public conference as recipient.
@item Add members by invitation: @var{bool}
If this is set, then adding others as members to a conference sets the
invitation bit of the membership. If this is off, the membership bit is
set to whatever the caller specifies. The default is on.
@item Allow secret memberships: @var{bool}
If this is set, then memberships may be secret. Otherwise any attempt
to create a secret membership or change an existing membership to a
secret membership will fail. The default is on.
@item Allow reinvitations: @var{bool}
If this is set, then it is possible to set the invitation bit of a
membership even after it has been cleared. If it is not set, then the
invitation bit of a conference type can only be set when the
membership is created. It can be cleared at any time. The default is
off.
@item lyskomd path: @var{path}
Path to the @code{lyskomd} binary. This is used by @code{updateLysKOM}
to find the right program to run. Defaults to @file{bin/lyskomd}.
@item savecore path: @var{path}
Path to the @code{savecore} program. If a file named @file{core} exists
in the directory specified with @code{Core directory} when
@code{updateLysKOM} is about to start @code{lyskomd}, this program will
be called first. It could, for instance, move the core file so that it
is available for later debugging.
@item Normal shutdown time: @var{int}
In a normal setup, @code{updateLysKOM} will be run from @code{cron} once
every ten minutes or so. If it detects that it has taken @code{lyskomd}
more than @var{int} minutes to shut down it will print a warning
message.
@item Mail after downtime: @var{int}
@itemx Mail until downtime: @var{int}
If @code{lyskomd} has been down for X minutes, where @code{Mail after
downtime} <= X < @code{Mail until downtime}, @code{updateLysKOM} will
send a mail message to the mail address found on the first line of the
status file. Actually, it is the age of the status file (named with
@code{Status file}) that is measured.
@end table
@node Aux-Item Definition File
@section Aux-Item Definition File
The default aux-item definition file should not be changed unless it is
really necessary. The need to change the definitions will probably only
arise at installations used for client or server development.
The location of the aux-item definition file is specified by the
@code{Aux-item definition file} option in the server configuration
file. The default location is @file{/usr/lyskom/etc/aux-items.conf}.
@subsection Syntax of the Aux-Item Definition File
The aux-item definition file contains a sequence of aux-item
definitions. Each definition specifies one type of predefined aux-item:
its number, name, and properties. Empty lines and all characters from a
# character to the end of the line are ignored.
Each entry has the following format:
@example
tag : name (target, target, ... )
@{
field = value;
field = value;
...
@}
@end example
@var{tag} is an integer, the aux-item's tag. If a tag is defined more than
once, the last definition is used.
The @var{target}s specify what kind of objects aux-items with tag @var{tag}
can be added to. Valid targets are:
@table @code
@item any
Aux-items with the specified tag can be added to any object in the
database. This is shorthand for @code{text,conference,letterbox,server}.
@item text
Aux-items with the specified tag can be added to texts.
@item conference
Aux-items with the specified tag can be added to conferences that are
@emph{not} letterboxes.
@item letterbox
Aux-items with the specified tag can be added to conferences that are
letterboxes.
@item server
Aux-items with the specified tag can be added to the server itself.
@end table
It is legal to add one of the keywords @code{create} or @code{modify}
before any target except @code{server}. If @code{create} is specified,
aux-items with the specified tag can only be added when an object is
being created. They cannot be added later. If @code{modify} is
specified, aux-items with the specified tag can only be added after an
object has been created. They cannot be added when the object is being
created.
Each @var{field}/@var{value} pair specifies a property of aux-items with the
specified tag. Most values are boolean or trillian. Legal values for
either type are @code{true} and @code{false}. Boolean values have
reasonable defaults; trillian values can be unset.
@table @code
@item author-only
Boolean, default false. When true, only the author of a text or
supervisor of a conference can create items with this tag.
@item supervisor-only
Boolean, default false. When true, only the supervisors of the author or
letterbox can create items with this tag. In all likelihood, the
implementation of this flag is screwed up in version 2.0 of lyskomd.
@item system-only
Boolean, default false. When true, only the server can initiate creation
of items with this tag. This is normally used for items that are created
automatically in response to events in the system.
@item permanent
Boolean, default false. When true, aux-items with this tag cannot be
deleted once they have been created. (They will be deleted
automatically when the object they are assigned to is deleted.)
@item unique
Boolean, default false. When true, there can only be one non-deleted
item with this tag per creator.
@item unique-data
Boolean, default false. When true, there can only be one non-deleted
item with this tag that contains the same data (regardless of who
creates the item).
@item owner-delete
Boolean, default false. When true, the owner of the object that this
aux-item is attached to can always delete the aux-item. For a text,
the owner is defined as the supervisor(s) of the author of the text.
For a conference, the owner is defined as the supervisor(s) of the
conference.
@item inherit-limit
Integer, default 0. The maximum number of times items with this tag can
be inherited, plus one. Zero means an unlimited number of times, one
means no times, 2 means once and so forth. This number overrides the
inherit-limit set by the client only if that number is higher than this
one.
@item inherit
Trillian. When set, the inherit bit on new items with this tag is forced
to the specified value.
@item secret
Trillian. When set, the secret bit on new items with this tag is forced
to the specified value.
@item hide-creator
Trillian. When set, the hide-creator bit on new items with this tag is
forced to the specified value.
@item dont-garb
Trillian. When set, the dont-garb bit on new items will be forced to the
specified value.
@item reserved-2
@item reserved-3
@item reserved-4
Trillian. When set, these flags force the values of the three reserved
bits in the aux-item flags field. These should only be used by lyskomd
developers, and then only very carefully.
@item validate
String or function, default none. When set to a string, this specifies a
regexp that must match the data field in newly created items with this
tag. If the regexp fails to match, then the item will not be created.
The syntax for strings is essentially the same as the syntax used in C
files. When set to a function, this specified a built-in validation
function to call.
The following validator functions are currently implemented:
@table @code
@item existing-readable-text
Creation is only allowed if the item contains the number of an existing
text that the item creator has permission to read.
@end table
@end table
There are a few fields which specify actions the server is to take when
something happens to aux-items with the specified tag. Each of these
values is a function specification, the name of a trigger function
defined in lyskomd. The syntax for functions is the name followed by
an empty pair of parens. It is not possible to pass arguments to the
functions yet.
@table @code
@item add-trigger
Function to call when an item with the specified tag is added to an
object.
@item delete-trigger
Function to call when an item with the specified tag is scheduled for
deletion.
@item undelete-trigger
Function to call when an item with the specified tag scheduled for
deletion is unscheduled. It should undo the effects of the delete
trigger.
@end table
The following trigger functions are currently defined:
@table @code
@item mark-text
Increase the mark count for the text the item refers to. The item must
contain the number of a text. This trigger should be combined with the
existing-readable-text validation function.
@item unmark-text
Decrease the mark count for the text the item refers to. The item must
contain the number of a text. This trigger should be combined with the
existing-readable-text validation function.
@item link-faq
Create a faq-for-conf item linked to a faq-text item. This trigger is
used exclusively for faq-text items. The item must contain the number of
a text. This trigger must be combined with the existing-readable-text
validation function.
@end table
@node Running lyskomd
@chapter Running lyskomd
This section explains how to run lyskomd, the files it uses and how it
can be controlled while running.
@menu
* Invoking lyskomd:: How to run lyskomd.
* Signals:: How to control lyskomd with Unix signals.
* Files:: Files used by lyskomd.
@end menu
@node Invoking lyskomd
@section Invoking lyskomd
@example
lyskomd [-f] [-d] [@var{config-file}]
@end example
The option @samp{-d} adds one to the debug level. The amount of output
on stderr/to the log file is increased for each time the option is
specified on the command line.
Using one @samp{-d} makes the process print a `>' for every timeout, a
message for every person that is connecting or disconnecting and a
message for every successful or unsuccessful communication to the
process.
The option @samp{-f} tells lyskomd to stay in forground mode, and not
run in the background as a daemon. The output that is normally
written to the log file is instead sent to stderr.
The optional @var{config-file} argument can be used to specify the server
configuration file. @xref{Server Configuration File}.
@node Signals
@section Signals
It is possible to control some aspects of lyskomd using Unix signals.
The following signals have special meaning to the server:
@table @samp
@item SIGTERM
@itemx SIGHUP
@itemx SIGINT
Logs out all sessions, saves the database and exits normally. Use
@samp{SIGTERM}; the other signals currently have the same
functionality, but that may be changed in the future.
@item SIGQUIT
Saves the database and dump core. (This should only be used for
debugging purposes.)
@item SIGUSR1
Print statistics about how often different commands have been used
since the process started.
@item SIGUSR2
Forks a child that immediately dumps core. The main process just waits
until the child is done and then continues.
@item SIGWINCH
Re-read the aux-item definition file.
@end table
@node Files
@section Files Used by lyskomd
All file names can be changed in the server configuration file.
@xref{Parameters}.
@table @file
@item /usr/lyskom
Default value of the @code{Prefix} parameter. The default of this value
is set at compile time, but it can be changed in the server
configuration file. @xref{Parameters}.
@item @var{prefix}/db/lyskomd-data
Half of the database: all status information.
@item @var{prefix}/db/lyskomd-texts
The other half of the database: the actual texts.
@item @var{prefix}/db/lyskomd-backup
A backup copy of @file{lyskomd-data}. Never, ever delete this file
unless you know what you are doing, or you may lose the entire data
base. Most of the time this is the only complete database file!
@item @var{prefix}/db/number.txt
Information about the highest used text- and conference numbers. In
case of a crash, some objects may be lost. This file ensures that
even if that happens, their numbers will not be reused.
@item @var{prefix}/etc/pid
File with the pid of the lyskom-process.
@item @var{prefix}/etc/memory-usage
On normal exit, @code{lyskomd} will append some statistics to this file.
It can be used for detecting memory leaks.
@item @var{prefix}/etc/aux-items.conf
This file contains definitions of the aux-items that the server should
support. It is read by @code{lyskomd} at startup.
@item @var{prefix}/etc/connections.txt
A list of all currently connected clients, maintained by the server.
The data about each client is collected on a single line:
@itemize @bullet
@item The file descriptor
@item The session number
@item @samp{1} if the handshake is OK, the reverse DNS has completed,
and the IDENT lookup has completed. @samp{0} otherwise.
@item The IP address of the client
@item The port number of the client
@end itemize
In the following example, we see that file descriptor 437 is used by
session 330978, and the connection is from 130.236.254.83:3156.
@example
437 330978 130.236.254.83 3156
@end example
@item /etc/nologin
If this file exists, lyskomd will not allow anyone to connect to the
server. This path can be set with the @code{Nologin file} parameter in
the server configuration file.
@end table
@node Invoking updateLysKOM
@chapter Invoking updateLysKOM
@example
updateLysKOM [-c @var{config-file}] [ -v ] [ -V ]
@end example
@code{updateLysKOM} determines if @code{lyskomd} should be running. It
can start or stop @code{lyskomd} if needed. It uses the same
configuration file as @code{lyskomd} (@pxref{Server Configuration
File}). You can use @samp{-c @var{config-file}} to override the
compiled-in default. Note, however, that this option is not passed
along to @code{lyskomd} if @code{updateLysKOM} starts it, so the option
should be used with extreme caution.
@samp{-v} and @samp{-V} causes @code{updateLysKOM} to report its version
number and exit.
@code{updateLysKOM} is normally run from @code{cron};
@pxref{Administration}.
@node Invoking komrunning
@chapter Invoking komrunning
@example
komrunning [-c config-file] [start | stop]
komrunning -v | -V
@end example
@code{komrunning}, when invoked with no arguments, reports whether
@code{lyskomd} is currently running or not, and whether it should be
running or not. @samp{komrunning start} attempts to start
@code{lyskomd}. @samp{komrunning stop} attempts to stop @code{lyskomd},
and it will not return until the server has saved its database and
exited.
@code{komrunning} uses the same configuration file as @code{lyskomd}
(@pxref{Server Configuration File}). You can use @samp{-c
@var{config-file}} to override the compiled-in default. Note, however,
that this option is not passed along to @code{updateLysKOM} if
@code{komrunning} invokes it, so the option should be used with extreme
caution.
The @code{komrunning} can be installed in @file{/etc/init.d/}. Be
careful, however, to ensure that the pid file is removed earlier during
the boot sequence.
@samp{-v} and @samp{-V} causes @code{komrunning} to report its version
number and exit.
@node Administration
@chapter Administration
The first thing you will have to do is to follow the instructions in the
files @file{INSTALL} and @file{README}. This will set up the LysKOM
system with a database containing a few necessary conferences and one
person - the administrator.
Once the LysKOM system is running, there is not much you will have to do
to keep it that way. One thing to remember is that the current release
of the server has an incomplete handling of garbage collection of the
database. The database is split into two files, the information file and
the text file. Newly written texts are concatenated to the text file and
old texts are never removed. The information file contains information
about conferences, users and where in the text file the texts are. This
file is properly garbage collected, but not the text file.
There is a program called @code{dbck} (Data Base Check) which is used
to check the consistency of the LysKOM database. This program can also
be used to shrink the text file. To do this, just type @samp{dbck
-g}. @xref{DBCK Reference}. When @code{dbck} is to be run on the
database, the LysKOM server @emph{must} be stopped, or unrepairable
damage may result. See below for a description on how to stop the
server.
There is a program called @code{updateLysKOM} which is used to ensure
continuous operation. This program should be run with certain intervals,
for instance from @code{cron}. If the LysKOM server has died for some
reason, @code{updateLysKOM} restarts it. If the server is still running
properly, @code{updateLysKOM} sends a signal (@samp{SIGUSR1}) to it,
which causes the server to write some statistics to a file named
@file{etc/lyskomd-log} in the lyskom directory.
Taking the server down cleanly can be done in two ways: through the use
of the LysKOM protocol on a socket, preferably through the use of a
suitable client, or by sending the signal @samp{SIGTERM} to it. This will
cause the server to save the database and close all client
connections. It will also create a file named @file{etc/memory-usage} in
which the memory usage of the server is reported.
To prevent @code{updateLysKOM} from restarting a server, create a file
named @file{/usr/lyskom/etc/status}. The file should contain a valid
mail address on the first line. @code{updateLysKOM} will not restart the
server as long as that file exists. In addition, if the file is between
1 and 2 hours old (configurable) an email will be sent to the mail
address found in the file. If the file is older than that, an error
message will be printed on stderr and @code{updateLysKOM} will exit with
a non-zero exit status. cron is expected to deliver the error message to
an operator.
The shell script @code{komrunning} can be used to start and stop the
LysKOM server. With no arguments, it will report the status.
@example
komrunning stop
@end example
will (attempt to) shut down the server, creating the file
@file{/usr/lyskom/etc/status}. If the user running @code{komrunning}
doesn't have permission to send signals to @code{lyskomd} the actual
shutdown will be delayed until the next time that @code{updateLysKOM} is
run.
@example
komrunning start
@end example
will restart the server. The actual starting of the server will be done
by @code{updateLysKOM} the next time it is run. @code{komrunning} only
removes the @file{/usr/lyskom/etc/status} file.
@node Bugs
@chapter Known Bugs
@itemize @bullet
@item lyskomd should re-read the config file when a @samp{SIGHUP} is
received.
@item The security policy is vague and the implementation is frayed at
the edges.
@item The choice of asynchronous messages is not very good.
@item The server uses too much memory.
@end itemize
@c ======================================================================
@c ======================================================================
@c == ==
@c == DBCK REFERENCE ==
@c == ==
@c ======================================================================
@c ======================================================================
@node DBCK Reference
@chapter DBCK Reference
dbck is a program that can is used for minor database maintenance tasks
and for repairing a corrupt lyskomd database.
@menu
* DBCK Overview:: Overview of dbck.
* Invoking dbck:: How to run dbck.
* DBCK Notes:: Notes about running dbck.
* DBCK Files:: Files used by dbck.
* DBCK Bugs:: Known bugs in dbck.
@end menu
@node DBCK Overview
@section Overview
The dbck program is used for minor maintenance of the LysKOM database
and for repairing corrupt databases. In brief it performs the following
functions:
@itemize @bullet
@item Compact the text file to remove deleted texts.
@item Repair inconsistent membership information.
@item Repair invalid recipients
@item Repair inconsistent comment links
@item Correct invalid local text numbers
@item Correct invalid text maps
@item Set special conferences
@item Convert between database formats
@end itemize
@node Invoking dbck
@section Invoking dbck
The functionality of dbck is controlled through command-line switches.
These are documented below.
If @code{dbck} is invoked without any options it will read the database
and report on its integrity. No files will be modified.
@menu
* General Options:: Controlling the overall behavior of dbck.
* Database Repair Options:: Repairing errors in the LysKOM database.
* Format Conversion Options:: Converting the database file to a new format.
* Database Maintenance Options:: Options for database maintenance.
* Reporting Options:: Options controlling status reports.
@end menu
@node General Options
@subsection General Options
These options control the general behavior of lyskomd.
@table @asis
@item @samp{-h} or @samp{--help}
Give a usage message (which includes the version number and the
compiled-in default location of the config file) and exit immediately.
@item @samp{-v} or @samp{--verbose}
Verbose mode. Report not only errors but the status of the database.
@item @samp{-F} or @samp{--force-output}
This option forces dbck to write the database file. Normally @code{dbck}
will only write a new database file if changes have been made for some
other reason. If you want to simply convert a database from one version
to another, you will probably have to give this option.
@end table
@node Database Repair Options
@subsection Database Repair Options
The following options control database repair.
@table @asis
@item @samp{-i} or @samp{--interactive}
Run interactively. If any inconsistency is found, a remedial cure will
be suggested and the user must confirm the correction.
@item @samp{-r} or @samp{--auto-repair}
Repair simple errors without asking.
@item @samp{-c} or @samp{--set-change-name}
Consider it an error if the @code{change-name} capability of a person is
not set. Due to a bug that capability was never set for newly created
persons in release 1.6.1 of lyskomd. This option can be used to repair
the damage.
@end table
@node Format Conversion Options
@subsection Format Conversion Options
dbck can be used to conver the LysKOM database from one storage format
to another. This is necessary only when moving the database to a new
server version.
@table @asis
@item @samp{-F} or @samp{--force-output}
This option forces dbck to write the database file. Normally @code{dbck}
will only write a new database file if changes have been made for some
other reason. If you want to simply convert a database from one version
to another, you will probably have to give this option.
@item @samp{-o} or @samp{--output-version}
This option is used to set the output version of the database. This
option will normally be used in conjunction with the @samp{-F} option.
Version 1.9 of @code{lyskomd} requires database version 1; version 2.0
requires database version 2. Versions of @code{lyskomd} prior to 1.9
requires database version 0. Note that information is irrevocably lost
when converting from a higher to a lower database version. This options
requires an argument: the output format version.
@end table
@node Database Maintenance Options
@subsection Database Update Options
dbck can be used to update certain aspects of the database that either
were impossible to update in early versions of protocol A or that are
inconvenient in all protocol versions.
@table @asis
@item @samp{-g} or @samp{--compact-text-mass}
Do garbage collection on the texts part of the database. This removes
all unreferenced texts from the database.
@item @samp{-P} or @samp{--clear-password}
Clear the password of a specified user. This option is silently ignored
if the user does not exist. This option requires an argument: the ID of
the person whose password is to be cleared.
@item @samp{-G} or @samp{--grant-all}
Grant all privileges to the specified user. This option is silently
ignored if the user does not exist. This option requires an argument:
the ID of the person who is to be granted all privileges.
@item @samp{--pers-pres-conf}
Set the person presentation conference of the server to the specified
conference. Since version 1.9 of lyskomd the @code{set-info} call can be
used to do this.
@item @samp{--conf-pres-conf}
Set the conference presentation conference of the server to the specified
conference. Since version 1.9 of lyskomd the @code{set-info} call can be
used to do this.
@item @samp{--motd-conf}
Set the message-of-the-day conference of the server to the specified
conference. Since version 1.9 of lyskomd the @code{set-info} call can be
used to do this.
@item @samp{--kom-news-conf}
Set the news-about-lyskom conference of the server to the specified
conference. Since version 1.9 of lyskomd the @code{set-info} call can be
used to do this.
@item @samp{--motd-of-kom}
Set the message of the day of the server to the specified text. Since
version 1.9 of lyskomd the @code{set-info} call can be used to do this.
@end table
@node Reporting Options
@subsection Reporting Options
These options control reporting of information about the database.
@table @asis
@item @samp{-s} or @samp{--print-statistics}
Gather statistics about the lengths of texts. A table containing the
frequence of all lengths that are currently present is printed.
@item @samp{-t} or @samp{--list-text-no}
Print ``Checking @var{text-no}'' for every text that examined.
@b{Warning:} This produces lots of output.
@end table
@node DBCK Notes
@section Notes for DBCK
The messages ``Conference @var{conf-no} has a bad Text-list. Starts with
0'' and ``Person @var{pers-no} has created @var{num} conferences, not
@var{num} (as said in person-stat).'' are normal. If you get them when
you specify the @samp{-g} option, let @code{dbck} repair them and run
@samp{dbck -g} again.
@node DBCK Files
@section Files Used by dbck
dbck uses the same files as @code{lyskomd} (@xref{(lyskomd)}.)
All file names can be changed in the server configuration file.
@xref{(lyskomd)Parameters}.
@table @file
@item /usr/lyskom
Default value of @code{Prefix:}. The default of this value is set at compile
time, but it can be changed in the server configuration file.
@xref{(lyskomd)Parameters}.
@item @var{prefix}/db/lyskomd-data
Half of the database: all status information.
@item @var{prefix}/db/lyskomd-texts
The other half of the database: the actual texts.
@item @var{prefix}/db/lyskomd-backup
A backup copy of @file{lyskomd-data}. Never, ever delete this file
unless you know what you are doing, or you may lose the entire data
base. Most of the time this is the only complete database file!
@end table
@node DBCK Bugs
@section Known Bugs
@itemize @bullet
@item Should have an unlock database option.
@item Does not check that the data file and text file are consistent.
@end itemize
@c ======================================================================
@c ======================================================================
@c == ==
@c == SPLITKOMDB REFERENCE ==
@c == ==
@c ======================================================================
@c ======================================================================
@node splitkomdb
@chapter Backups with splitkomdb
The files created by @code{lyskomd} can become huge. They are more
or less constantly modified, so if you do incremental backups the
entire @code{lyskomd} database will be saved each time you perform a
backup. The @code{splitkomdb} program improves the situation.
@menu
* splitkomdb basics:: How splitkomdb works.
* Invoking splitkomdb:: splitkomdb reference.
* splitkomdb example:: A typical setup of splitkomdb.
* splitkomdb restore:: How to restore the database.
@end menu
@ifnottex
@node splitkomdb basics
@section splitkomdb theory of operation
@end ifnottex
The @code{splitkomdb} program attempts to split the current database
in several files, some of which will not be modified the next time you
run @code{splitkomdb}. An incremental backup will thus only have to
save some of the files created by @code{splitkomdb}.
@code{splitkomdb} can be run while @code{lyskomd} is running. It will
use the last completely saved snapshot, and make a copy of it in the
directory specified by the @code{Backup export directory:} parameter
(default: @file{/usr/lyskom/exportdb/}).
There are two recommended ways to make backups of a @code{lyskomd}
database:
@itemize @bullet
@item Run @code{splitkomdb} before each backup, and instruct the backup
program to backup @file{/usr/lyskom/exportdb}, but ignore
@file{/usr/lyskom/db}. Run @samp{splitkomdb -f} before each full
backup.
@item Backup all the files in @file{/usr/lyskom/db}.
@end itemize
The first alternative needs more disk for the copy in
@file{/usr/lyskom/exportdb} and is slightly more complex to set up;
the second alternative saves the entire database each time you make a
backup.
@node Invoking splitkomdb
@section Invoking splitkomdb
@example
splitkomdb [-c config-file] [-f]
splitkomdb -v | -V
@end example
@code{splitkomdb} creates a splitted copy of the most recent database
snapshot in the directory specified by the @code{Backup export
directory:} parameter.
If @samp{-v} or @samp{-V} is specified, @code{splitkomdb} prints its
version number and exits.
The @samp{-f} option is a hint to @code{splitkomdb} that the next
backup will be a full backup. When this option is used,
@code{splitkomdb} might rewrite all the output files in a way so that
future invocations of @code{splitkomdb} will create a little
incremental data as possible.
The optional @var{config-file} argument can be used to specify the server
configuration file. @xref{Server Configuration File}.
@node splitkomdb example
@section Typical splitkomdb setup
A typical way to run @code{splitkomdb} is from @code{cron}. A
@file{crontab} entry might look like this:
@example
50 2 26 * * /sw/lyskom/bin/splitkomdb -f
10 3 * * * /sw/lyskom/bin/splitkomdb
@end example
This entry assumes that backups are started at 03:30. It gives
@code{splitkomdb} 20 minutes to run. (That should be enough for most
sites, but please check what is appropriate for your site.)
Full backups are run on the 26th of each month. On those days, at
02:50, @samp{splitkomdb -f} is run.
@node splitkomdb restore
@section Restoring the database from splitkomdb
The splitted format of the database is currently very simple:
@table @file
@item exportdb/lyskomd-texts-base.backup
This file contains the first part of @code{Text file:} (default:
@file{db/lyskomd-texts}). This file is created when the @samp{-f}
option is given to @code{splitkomdb}.
@item lyskomd-texts-tail.backup
This file contains the rest of @code{Text file:}. It is always
recreated when @code{splitkomdb} is run.
@item lyskomd-data.backup
This file contains a copy of @code{Data file:} (default:
@file{db/lyskomd-data}). If @code{Data file:} file wasn't clean
when @code{splitkomdb} was run, @code{Backup file:} (default:
@file{db/lyskomd-backup}) will be copied instead.
@end table
This means that it is easy to restore the database from the splitted
database. If you use the default paths, all you have to do is run
these commands:
@example
$ cd /usr/lyskom/exportdb
$ cat lyskomd-texts-base.backup \
> lyskomd-texts-tail.backup \
> > ../db/lyskomd-texts
$ cp lyskomd-data.backup ../db/lyskomd-data
@end example
Future versions of @code{splitkomdb} may use a different format. It
may even evolve into something so complex that you need a program to
recreate the database. Always check the current documentation for
information on how to restore the database.
@c ======================================================================
@c ======================================================================
@c == ==
@c == LYSKOMD HACKING GUIDE ==
@c == ==
@c ======================================================================
@c ======================================================================
@node Hacking
@chapter Hacking lyskomd
@menu
* The Database::
* Adding Configuration Parameters:: How to add configuration options.
* Adding Asynchronous Messages:: Adding protocol A messages.
* Adding a New Protocol Request:: Adding protocol A calls.
* Adding New Input Types::
* Adding New Result Types::
* Modifying Output Types::
* Adding Aux-Item Types:: Adding predefined aux item types.
* Modifying Stored Types:: Modifying types stored in the DB.
* Notes:: Mixed notes.
* Debugging and Testing:: How to test and debug the server.
* local-to-global:: The Local_to_global structure.
@end menu
@node The Database
@section The Database
@c FIXME: ramkomd är död! Länge leve LysKOM!
@c FIXME:
@c FIXME: Jag har tillsammans med Inge kommit på ett sätt att dels få ner
@c FIXME: väntetiden i samband med syncningar till <1 sekund, dels få ner
@c FIXME: storleken på serverprocessen till mer rimliga nivåer. Denna lösning
@c FIXME: lider dock av det stora problemet att den kräver dubbelt så mycket
@c FIXME: diskutrymme som den egentligen behöver. Det gör även ramkomd, så det
@c FIXME: är ingen försämring i det avseendet. Dock är detta bara en temporär
@c FIXME: lösning i väntan på ldb.
@c FIXME:
@c FIXME: Varför spara allt på en gång? Varför inte spara en liten del av filen
@c FIXME: i taget, och utföra några atomiska anrop mellan varje liten
@c FIXME: delsynkning? Ungefär så tänkte jag när jag kom på följande schema för
@c FIXME: hur man kan göra det hela bättre än det är nu.
@c FIXME:
@c FIXME: Den databas som ligger på fil är en ögonblickbild (snapshot) av det
@c FIXME: som finns i LysKOM. Så är det i ramkomd; så blir det i diskomd.
@c FIXME: (Bättre namn, någon? lyskomd tycker jag är reserverat för den version
@c FIXME: som har en riktig cache&ldb.) I ramkomd skrivs allt ut på disk
@c FIXME: samtidigt. I diskomd minns man bara vad som skall sparas, och sparar
@c FIXME: bara en bit i taget.
@c FIXME:
@c FIXME: I ramkomd finns allt inne i ram-minnet (i teorin. I praktiken är det
@c FIXME: mesta utswappat - något som märks varje gång det är dags att synca!).
@c FIXME: I diskomd ligger det mesta på disk. I minnet finns dels det som har
@c FIXME: använts nyligen, dels det som är ändrat och ännu ej syncat. Diskomd
@c FIXME: har alltid minst en, ofta två, databasfiler öppna:
@c FIXME:
@c FIXME: Fil A Senaste kompletta fil.
@c FIXME: Fil B Fil under uppbyggnad.
@c FIXME FIXME: Fil Z Näst senast kompletta fil
@c FIXME FIXME: (den här gick att kopiera en gång i
@c FIXME FIXME: tiden, även om A inte går att kopiera
@c FIXME FIXME: just nu.)
@c FIXME:
@c FIXME: (Dessutom textmassefilen, precis som ramkomd nuförtiden.)
@c FIXME:
@c FIXME: Så till detaljerna:
@c FIXME:
@c FIXME: Det finns tre typer av objekt som berörs av den här ändringen:
@c FIXME: Text_stat, Person och Conference. Jag använder Person som ett exempel
@c FIXME: nedan.
@c FIXME:
@c FIXME: I ram-cache.c finns en array
@c FIXME:
@c FIXME: Person *pers_arr[ MAX_CONF ];
@c FIXME:
@c FIXME: Den byts mot
@c FIXME:
@c FIXME: Cache_node *pers_arr[ MAX_CONF ];
@c FIXME:
@c FIXME: typedef struct cache_node @{
@c FIXME: Bool exists;
@c FIXME: Bool exists_b;
@c FIXME: Bool dirty; /* Är *ptr modifierad? */
@c FIXME: void *snap_shot;
@c FIXME: void *ptr;
@c FIXME: off_t pos;
@c FIXME: off_t pos_b;
@c FIXME: struct cache_node *lru_link;
@c FIXME: int lock_cnt;
@c FIXME: @} Cache_node;
@c FIXME:
@c FIXME:
@c FIXME:
@c FIXME: UPPSTART
@c FIXME:
@c FIXME: När servern startas scannar den igenom datafilen (fil A) och fyller i
@c FIXME: fältet exists till TRUE/FALSE och pos till att peka på början av det
@c FIXME: ställe i filen där data ligger. Övriga fält sätts till FALSE/NULL/0.
@c FIXME:
@c FIXME:
@c FIXME:
@c FIXME: CACHE_GET_PERSON
@c FIXME:
@c FIXME: När ovanliggande rutiner vill läsa en person händer följande:
@c FIXME:
@c FIXME: !exists Returnera NULL
@c FIXME: ptr != NULL Lägg noden först i lru_link. Returnera ptr.
@c FIXME: snap_shot != NULL Kopiera snap_shot till ptr. Lägg noden först i
@c FIXME: lru_link. Returnera ptr.
@c FIXME: annars Läs in från fil A, sätt ptr till den inlästa
@c FIXME: structen, lägg noden först i lru_link,
@c FIXME: returnera ptr.
@c FIXME:
@c FIXME:
@c FIXME: MARK_PERSON_AS_CHANGED
@c FIXME:
@c FIXME: När något har ändrats sätts dirty-flaggan till TRUE.
@c FIXME:
@c FIXME:
@c FIXME: CREATE_PERSON
@c FIXME:
@c FIXME: Sätt exists=TRUE, dirty=TRUE, ptr och lru.
@c FIXME:
@c FIXME:
@c FIXME: DELETE_PERSON
@c FIXME:
@c FIXME: Sätt exists=FALSE. ptr=NULL. Troligtvis error om lock_cnt != 0.
@c FIXME:
@c FIXME:
@c FIXME:
@c FIXME: THROW-OUT
@c FIXME:
@c FIXME: För att inte diskomd ska bli för stor slängs saker ut ur cachen.
@c FIXME: Algoritm: tag första elementet i lru_list. Om dirty==FALSE och
@c FIXME: ptr!=NULL och lock_cnt==0 så frigör ptr. Upprepa tills antalet noder
@c FIXME: med ptr!=NULL och dirty==FALSE är mindre än antalet "rena"
@c FIXME: element man vill ha inne i minnet. (Smutsiga element slängs
@c FIXME: aldrig ut.)
@c FIXME:
@c FIXME:
@c FIXME: LOCK_PERSON
@c FIXME:
@c FIXME: Öka lock_cnt.
@c FIXME:
@c FIXME:
@c FIXME: UNLOCK_PERSON
@c FIXME:
@c FIXME: Minska lock_cnt.
@c FIXME:
@c FIXME:
@c FIXME: PRE-SYNC
@c FIXME:
@c FIXME: Utsparningen till fil sker i tre steg. Först sveper man över alla
@c FIXME: Cache_noder. För alla som har dirty=TRUE gör man följande:
@c FIXME:
@c FIXME: if ( lock_cnt == 0 ) @{
@c FIXME: snap_shot = ptr; (Pekartilldelning, ej kopiering.)
@c FIXME: ptr = NULL;
@c FIXME: Ta bort ptr ur lru-kedjan.
@c FIXME: @} else @{
@c FIXME: snap_shot = copy(ptr);
@c FIXME: @}
@c FIXME:
@c FIXME: dirty = FALSE;
@c FIXME:
@c FIXME: För _alla_ noder görs dessutom följande:
@c FIXME:
@c FIXME: b_exists==exists;
@c FIXME:
@c FIXME:
@c FIXME: SYNC
@c FIXME:
@c FIXME: Steg två utförs en liten bit i taget. Till exempel så skulle
@c FIXME: man kunna spara en person efter varje atomiskt anrop, eller så.
@c FIXME:
@c FIXME: b_exists==FALSE? Sätt pos_b. Skriv "@@\n" till fil B.
@c FIXME: Är snap_shot != NULL? Sätt pos_b. Skriv ut innehållet i snap_shot
@c FIXME: till fil B.
@c FIXME: dirty==FALSE && ptr!=NULL Skriv ut innehållet i ptr till fil B.
@c FIXME: annars: Kopiera från fil A till fil B. (Eftersom man
@c FIXME: vet både var blocket börjar och slutar kan
@c FIXME: man kopiera blocket utan att bry sig om vad
@c FIXME: som står i det -> väldigt lite CPU går åt).
@c FIXME:
@c FIXME:
@c FIXME:
@c FIXME:
@c FIXME: POST-SYNC
@c FIXME:
@c FIXME: När alla Person:er har hanterats som i SYNC ovan är det dags för det
@c FIXME: tredje steget. Då går man igenom alla Cache_node:er och gör följande:
@c FIXME:
@c FIXME: pos = pos_b;
@c FIXME: file_b = FALSE;
@c FIXME: free(snap_shot);
@c FIXME: snap_shot = NULL;
@c FIXME:
@c FIXME: Fil B som man förut hade öppen för skrivning öppnar man i stället för
@c FIXME: läsning som fil A.
@c FIXME:
@c FIXME:
@c FIXME:
@c FIXME:
@c FIXME: ANMÄRKNINGAR
@c FIXME:
@c FIXME: Innehållet i snap_shot är alltid "smutsigt" jämfört med innehållet i
@c FIXME: fil A. Det som snap_shot pekar på finns aldrig med i lru-kedjan.
@c FIXME:
@node Adding Configuration Parameters
@section Adding Configuration Parameters
Make sure that you really understand what you want to configure. Think
it over again. Find a good, descriptive name for it.
Decide what values the parameter can be set to. Integers? Booleans?
Document the parameter in @file{lyskomd.texi}.
Add a field to @code{struct kom_par} in @file{param.h}.
Add it to @code{parameters[]} in @file{server-config.c}. See
@file{conf-file.h} and maybe @file{conf-file.c} for information on this
structure.
Make sure that the parameter is used instead of any previous hard-coded
value. Make sure that @code{dbck} can cope with it.
@node Adding Asynchronous Messages
@section Adding Asynchronous Messages
@table @asis
@item @file{async.h}
Add the message in @code{enum async @{ @}}. Make sure that
@code{ay_dummy_last} is one more than any other message. If the message
is to be sent by default, which is @emph{not} recommended, place its number
into @code{ASYNC_DEFAULT_MESSAGES}.
@item @file{prot-a-send-async.c}
@itemx @file{prot-a-send-async.h}
Write a function that sends the message. This function is responsible
for writing the message to a particular connection and for ensuring that
the message is not sent to clients who do not want it. Make sure that
the second argument to @code{async_header} really is the number of
elements being sent. Arrays count as two elements: the item count and
the elements.
@item @file{send-async.c}
@itemx @file{send-async.h}
Write a function that sends the message to appropriate clients. This
function is responsible for checking that async messages should be sent
at all, for each client check if it allowed to see the message and
ensure that the protocol specified by the connection is appropriate. The
send function should either take a @code{struct connection *} as an
argument and send the message to that connection, or loop over all
connections. Most send functions take a connection pointer; the looping
is dealt with elsewhere.
@item @file{session.c}
Add a case label for the @code{enum} in the large @code{switch}
statement.
@item Make sure that the message is sent in appropriate places.
@item @file{testsuite/lyskomd.0/03.exp}
A few tests will fail. Fix them.
@item Document the message type in @file{Protocol-A.texi}.
@item Write test cases for the new async message.
@end table
@menu
* Function Templates for prot-a-send-async.c::
* Function Templates for send-async.c::
@end menu
@node Function Templates for prot-a-send-async.c
@subsection Function Templates for prot-a-send-async.c
This is what a typical function in @file{prot-a-send-async.c} should
look like. This function is responsible for checking that the client is
accepting the message and writing the message itself to the connection.
@example
void
prot_a_async_@var{something}(Connection *cptr,
@var{parameters})
@{
ASYNC_CHECK_ACCEPT(cptr, ay_@var{something});
async_header(cptr, @var{num_tokens}, ay_@var{something});
/* Output the body of the message */
async_trailer(cptr);
@}
@end example
@node Function Templates for send-async.c
@subsection Function Templates for send-async.h
This is what a typical function in @file{send-async.c} should look like.
This function is responsible for sending the message to all connections
that are appropriate, not sending it if the server is not supposed to
send messages at all, and for checking that the protocol specified by
the client is one the server knows.
@example
void async_@var{something}( @var{parameters} )
@{
Connection *cptr;
Session_no i = 0;
if (!param.send_async_messages)
return;
while ((i = traverse_connections(i)) != 0)
@{
cptr = get_conn_by_number(i);
switch(cptr->protocol)
@{
case 0:
/* No protocol specified yet */
break;
case 'A':
/* Check that connection is logged on. We might
want to check other things here too, such as
if the connection is allowed to see the message */
if (handshake_ok(cptr, 0))
prot_a_async_@var{something}(cptr, @var{parameters});
break;
default:
restart_kom("async_@var{something}(): bad protocol.\n");
break;
@}
@}
@}
@end example
Template for a function that sends to a single connection:
@example
void async_@var{something}(struct connection *cptr,
@var{parameters})
@{
if (!param.send_async_messages)
return;
switch(cptr->protocol)
@{
case 0:
/* No protocol specified yet */
break;
case 'A':
/* Check that connection is logged on. We might
want to check other things here too, such as
if the connection is allowed to see the message */
if (handshake_ok(cptr))
prot_a_async_@var{something}(cptr, @var{parameters});
break;
default:
restart_kom("async_@var{something}(): bad protocol.\n");
break;
@}
@}
@end example
@node Adding a New Protocol Request
@section Adding a New Protocol Request
Before doing anything, think again. Make sure that the protocol request
is needed, is in line with the rest of the protocol, behaves the way
people want it to, and that everyone involved agrees that it is a good
idea.
@enumerate
@item Document the request in @file{Protocol-A.texi}
@item Declare the function in @file{include/services.h}
@item Declare the function @emph{last} in @file{server/fncdef.txt}. It
should be given a call number one higher than the currently existing
highest contiguous call number.
@item If the function takes an input parameter of a new type, changes
need to be made in several places. @xref{Adding New Input Types}.
@item If the function takes too many parameters of type @code{num},
@code{string} or @code{c_string}, the definition of @code{Connection} in
@file{server/connection.h} has to be changed.
@item If the function has an output parameter of a new type, changes
need to be made in several plaves. @xref{Adding New Result Types}.
@item Write the function in a suitable place in the server directory.
@item Write tests for the new function in
@file{server/testsuite/lyskomd.0}. Write one file for testing the
functionality. Write tests in @file{01.exp} (behavior when the client is
not logged on) and @file{03.exp} (normal behavior.)
@item Run the testsuite to make sure nothing old has been broken.
@end enumerate
Every request handler should call the @code{CHK_CONNECTION} macro before
doing anything else. This ensures that the @code{active_connection}
variable is non-NULL. The only time when this might not be the case is
if the request handler is not called in response to a client request.
This should never happen, but might if someone gets careless.
If your function should not be available before the user is logged in,
call the CHK_LOGIN macro after doing @code{CHK_CONNECTION}.
Take care returning errors to the client. Previous versions of
@samp{lyskomd} leaked secret information through error returns. For
example, the following code leaks information:
@example
Success service(Conf_no conf_no, Text_no text_no)
@{
Conference *conf_stat;
Text_stat *text_stat;
CHK_CONNECTION(FAILURE);
CHK_LOGIN(FAILURE);
GET_C_STAT(conf_stat, conf_no, FAILURE);
GET_T_STAT(text_stat, text_no, FAILURE);
if (!has_access(conf_no, active_connection, read_protected))
@{
err_stat = conf_no;
kom_errno = KOM_UNDEF_CONF;
return FAILURE;
@}
if (!text_read_access(active_connection, text_no, text_stat))
@{
err_stat = text_no;
kom_errno = KOM_NO_SUCH_TEXT;
return FAILURE;
@}
/* Permissions checked. Do the deed. */
return OK;
@}
@end example
This request can be used to gain precise information on which
conferences and texts exist in the system. If an unprivileged user makes
a request for any conference and readable text, and the user receives a
@samp{KOM_NO_SUCH_TEXT} error, the user can deduce that the conference
exists, but is secret. If the user makes a request for a conference
known to be secret and a text known not to be readable (either secret or
deleted), and the user receives a @samp{KOM_UNDEF_CONF} error, the user
can deduce that the text does exist.
To avoid traps like these, do permission checks for objects immediately
after attempting to get them from the database.
See also:
@itemize @bullet
@item @ref{Adding New Input Types}
@item @ref{Adding New Result Types}
@item @ref{Modifying Output Types}
@end itemize
@node Adding New Input Types
@section Adding New Input Types
Changes need to be made in the following files:
@table @file
@item Protocol-A.texi
Document the new type.
@item server/call-switch.awk
The new type has to be added to the cascaded ifs that translate the type
name to code that points to the appropriate field in a
@code{Connection} structure.
@item server/prot-a-parse-arg-c.awk
The new type has to be added to the cascaded ifs that create the
argument list parser.
@item server/connections.h
The definition of @code{Connection} must be extended with a field where
the parse value can be stored. Don't even think about trying to reuse an
existing field. It's more trouble than it's worth.
@item server/connection.c
Free the contents of the field in @code{free_parsed}.
@item server/prot-a.c
Free the contents of the field in @code{prot_a_destruct}.
@item server/internal-connections.c
Initialize the contents of the field in @code{init_connection}.
@item server/testsuite/lyskomd.0/29.exp
Add test cases for disconnecting in the middle of the data type. This
is important both for singletons and lists.
@end table
@node Adding New Result Types
@section Adding New Result Types
Changes need to be made in the following files:
@table @file
@item Protocol-A.texi
Document the new type.
@item server/prot-a.c
Add a line in the @code{prot_a_reply} switch that calls the correct
output function.
@item server/connections.h
Add the type in @code{enum res_type} and @code{union result_holder}.
@item server/prot-a-output.c
@itemx server/prot-a-output.h
Write a function that outputs the new type
to a connection. Use the existing functions as templates.
@end table
@node Modifying Output Types
@section Modifying Output Types
When you modify an existing type you have to rename the old version of
the type since it will still be used in existing calls. The convention
has previously been to rename @var{Something} to
@var{Something}@samp{_old}, but the preferred method is to append an
underscore and the protocol version in which the current version of the
type was introduced. For example, if the type @samp{Gazonk} was
introduced in protocol version 11, and a new version is to be introduced
in protocol version 15, the current @samp{Gazonk} structure is renamed
to @samp{Gazonk_11}.
This is to avoid names like @samp{Something_older},
@samp{Something_oldest} and @samp{Something_Truly_Ancient}.
Changes need to be made to the following files:
@table @file
@item Protocol-A.texi
Document the new type in the appropriate section. Rename the existing
type in the type documentation and in all calls that return it. Be
thorough!
@item fncdef.txt
Rewrite all calls that use the modified type so they use the old version
of the type.
@item prot-a.c
Modify the current line in @code{prot_a_reply} for the existing version
of the type, and add a new line for the new version of the type.
@item connections.h
Modify the existing entry in @code{enum res_type} and @code{union
result_holder}, if necessary. This should only be necessary if the
server uses both a new and old type internally, which is not
recommended. Add new entries for the new version of the type.
@item prot-a-output.h
@itemx prot-a-output.c
Rename the existing output routing according to the new name of the
type. Write a new output routine for the new version of the type.
@item memory.c
If there are functions for the type in @code{memory.c}, make sure that
your new type is initialized, cleared and copied in an appropriate
manner.
@end table
If the type you modify is stored in the database, make sure it gets
saved properly. @xref{Modifying Stored Types}.
@node Adding Aux-Item Types
@section Adding Aux-Item Types
@enumerate
@item Document the new type in Protocol-A.texi
@item Write a definition of the new type in
@file{run-support/aux-items.conf}.
@item Some tests in at least
@file{server/testsuite/lyskomd.0/01.exp},
@file{server/testsuite/lyskomd.0/03.exp} and
@file{server/testsuite/lyskomd.0/18.exp} will fail when new predefined
aux-items are added. Fix the tests.
@item Write test cases for the new aux-item. If the aux item can be
set on a letterbox, do so in @file{server/testsuite/lyskomd.0/03.exp}
where the comment containing @samp{AUXITEM} says to do so. More
complex aux-items should have more tests written for them.
@file{server/testsuite/lyskomd.0/20.exp} might provide some
inspiration.
@item If the new type requires add, delete or undelete triggers that do
not already exist, declare the trigger functions in @file{aux-items.c}
and add them to the @code{aux_item_triggers} array in the same file.
@item If the new type is so complex that is cannot be fully defined in
@file{aux-items.conf}, then add it to the @code{compiled_aux_items}
array in @file{aux-items.c}. Note that this functionality has not been
tested until someone actually adds one of these beasts, so watch your
step.
@end enumerate
@node Modifying Stored Types
@section Modifying Stored Types
If you want to modify an existing type that is stored in the database,
think again. Can the job be done with aux-items instead? Is it really
necessary?
Be very, very careful when doing this. You have to make sure that the
type as sent in old calls and async messages is not changed in any way.
You have to make sure that the type can be stored to and read from the
database.
@enumerate
@item Document the changes in Protocol-A.texi if the change is visible
in the protocol.
@item Bump the database version number by one for the next release of
the server.
@item Write a function in @file{ram-output.c} to output the new format.
Update all old functions in @file{ram-output.c} that are database
version dependent so that they can deal with the new database format.
@item Write a function in @file{ram-parse.c} to read the new format.
Update all old functions in @file{ram-parse.c} that are database version
dependent so that they can deal with the new database format.
@item Set the default database format in @file{ram-parse.c} and
@file{ram-output.c}. The variables to change are @code{input_format} and
@file{output_format}, respectively.
@item Don't forget to update the functions in @file{memory.c}
@end enumerate
@menu
* Template for ram-output.c::
* Template for ram-parse.c::
@end menu
@node Template for ram-output.c
@subsection Template for ram-output.c
For types that can be output in several different formats, use the
following templates for them. You have to be able to output in all
formats, or @code{dbck} will be unable to convert between formats.
@example
static void
foutput_@var{something}_0(FILE *fp, @var{something} *o)
@{
/* Output version 0 of @var{something} */
@}
static void
foutput_@var{something}_1(FILE *fp, @var{something} *o)
@{
/* Output version 1 of @var{something} */
@}
static void
foutput_@var{something}_2(FILE *fp, @var{something} *o)
@{
/* Output version 2 of @var{something} */
@}
void foutput_@var{something}(FILE *fp, @var{something} *o)
@{
switch(output_format)
@{
case 0:
foutput_@var{something}_0(fp, info);
break;
case 1:
foutput_@var{something}_1(fp, info);
break;
case 2:
foutput_@var{something}_2(fp, info);
break;
default:
restart_kom("unknown database format: %d", output_format);
break;
@}
@}
@end example
Note that if two versions are the same, only write one function. For
example, if version 0 and version 1 are the same, only write an
@code{foutput_@var{something}_0} function and call it from both case 0
and case 1.
@node Template for ram-parse.c
@subsection Template for ram-parse.c
@example
static Success
fparse_@var{something}_0(FILE *fp, @var{something} *o)
@{
/* Parse version 0 */
return OK;
@}
static Success
fparse_@var{something}_1(FILE *fp, @var{something} *o)
@{
/* Parse verson 1 */
return OK;
@}
static Success
fparse_@var{something}_2(FILE *fp, @var{something} *o)
@{
/* Parse verson 2 */
return OK;
@}
extern Success
fparse_@var{something}(FILE *fp, @var{something} *o)
@{
if ( fparse_long_errors != 0 )
@{
log("fparse_@var{something}(): fparse_long_errors == %d on entry."
" Reset.\n",
fparse_long_errors);
fparse_long_errors = 0;
@}
switch (input_format)
@{
case 0:
return fparse_@var{something}_0(fp, o);
break;
case 1:
return fparse_@var{something}_1(fp, o);
break;
case 2:
return fparse_@var{something}_2(fp, o);
break;
default:
restart_kom("unknown input format: %d\n", input_format);
return FAILURE;
break;
@}
@}
@end example
Note that if two versions are the same, only write one function. For
example, if version 0 and version 1 are the same, only write an
@code{fparse_@var{something}_0} function and call it from both case 0
and case 1.
@node Notes
@section Hacking Notes
@menu
* Parsing Bit Fields:: How to parse bit fields properly.
* Membership Notes:: How members and memberships are handled.
* Linking Pairs of Aux Items:: How to link pairs of aux items.
* Notes for fncdef.txt:: Format of the fncdef.txt file.
* Traversing Connections:: How to traverse connections in lyskomd.
@end menu
@node Parsing Bit Fields
@subsection Parsing Bit Fields
The parser for a bit field parameter type should be very tolerant of the
length of the token. Anything from a single bit and up should be
permitted. The parser should use default values for bits that are not
provided and ignore extra bits.
Here is a model function:
@example
void
prot_a_parse_bitfield(Connection *client,
Bitfield *res)
@{
String token;
String_size len;
token = prot_a_get_token(client);
len = s_strlen(token);
if (len <= 0)
longjmp(parse_env, ISC_PROTOCOL_ERR);
init_bitfield(res);
switch (len = s_strlen(token))
@{
default:
case 8: res->bit_8 = token.string[7];
case 7: res->bit_7 = token.string[6];
case 6: res->bit_6 = token.string[5];
case 5: res->bit_5 = token.string[4];
case 4: res->bit_4 = token.string[3];
case 3: res->bit_3 = token.string[2];
case 2: res->bit_2 = token.string[1];
case 1: res->bit_1 = token.string[0];
@}
@}
@end example
The function gets the token, checks the sanity of the length, then
initialized the result to its default values. Then it does a switch on
all token lengths that are equal to or smaller than the number of bits
the server knows about. The fall-through ensures that all bits in the
token are read.
@node Membership Notes
@subsection Membership Notes
The @code{position} field in the membership is @emph{not} stored. It has
to be set every time a membership is requested for transmission to the
client.
@node Linking Pairs of Aux Items
@subsection Linking Pairs of Aux Items
Sometimes two aux items need to work in tandem. The first instance of
this was the FAQ and FAQ-for-conference items. The FAQ item contains the
text number of a text that is a FAQ for a conference. The
FAQ-for-conference item contains the conference for which a text is a
FAQ. This is needed so that deletion of the text properly removes the
aux-item on the conf (plus, it's nice to be able to see that a text is a
FAQ.)
The @code{linked_item} field in the Aux_item structure is for linking
items. The linking must be managed through the use of triggers. This
field is not visible in the protocol. It is saved in the database. It is
not possible to have more than one link per item.
Please remember the following points.
@itemize @bullet
@item The target of a link should have a link back. All links need to go
both ways.
@item In the add trigger for one end, create the other end of the link
and set the @code{linked_item} field in both items. Don't forget to mark
the objects at both ends as changed.
@item Deletion and undeletion of the other side of the link will be
managed automatically. You don't need delete and undelete triggers
simply to destroy the other side of a link.
@item Don't kill the server because one end is missing. It is possible
for the administrator to remove an item manually. Log a message and
continue working.
@end itemize
@node Notes for fncdef.txt
@subsection Notes for fncdef.txt
The fncdef.txt file is used to define the RPC functions. Each line
consists of the call number, the return type of the call, the parameters
and the output types of the call.
Some examples:
@example
10 number create_conf_old c_string (param.conf_name_len) conf_type
12 success lookup_name c_string (param.conf_name_len) : conf_list
@end example
The first line defines a call named @code{create_conf_old} that takes
two arguments, a string that can only be as long as
@code{param.conf_name_len} and a @code{conf_type}. It returns a number
to the client. If the service call returns -1, the server will return an
error. The @code{create_conf_old} call has RPC number 10.
The second line defines a call named @code{lookup_name} that takes a
string argument that can be no longer than @code{param.conf_name_len},
and returns a @code{conf_list}. The service call returns a
@code{Success}. If it does not return @code{OK}, the server will return
an error. The @code{lookup_name} call has RPC number 12.
@subsubsection Scripts That Use fncdef.txt
The following scripts operate on @file{fncdef.txt}. If you make
modifications to the format of @file{fncdef.txt}, you have to update
these scripts.
@table @file
@item call-switch.awk
Generates @file{call-switch.incl}, which is included by
@file{connections.c}
@item com-h.awk
Generates @file{com.h}, which is included by several files.
@item fnc-def-init.awk
Generates @file{fnc-def-init.incl}, which is included by
@file{connections.c}.
@item prot-a-is-legal-fnc.awk
Generates @file{prot-a-is-legal-fnc.incl}, which is included by
@file{prot-a.c}
@item prot-a-parse-arg-c.awk
@itemx prot-a-parse-arg-h.awk
Generates @file{prot-a-parse-arg.c} and @file{prot-a-parse-arg.h}.
@end table
@node Traversing Connections
@subsection Traversing Connections
Since session 0 is interpreted as the currently active session by
get_conn_by_number it is important to be careful when traversing
sessions. Code like this does not work since it will do one iteration
through the loop with @code{sess} set to zero. This formerly caused
@code{get_conn_by_number} to return @code{NULL}, but now causes it to
return the session pointer for the current session.
@example
for (sess = 0; (sess = traverse_connections(sess)) != 0; )
@{
cptr = get_conn_by_number(sess);
...
@}
@end example
The canonical traversal code looks like this:
@example
Session_no session = 0;
while ((session = traverse_connections(session)) != 0)
@{
cptr = get_conn_by_number(session);
if (handshake_ok(cptr, 0)) /* can sometimes be skipped */
@{
...
@}
@}
@end example
This code has @code{session} set to a session number before ever
entering the loop.
@node Debugging and Testing
@section Debugging and Testing
We're slowly adding support for debugging and testing lyskomd properly.
@menu
* The Test Suite:: The lyskomd regression test suite.
* Configuration Options:: Debugging options for the configure script.
* Coverage Testing:: How to do coverage testing with gcov.
* Debug Calls:: Special protocol A calls for testing.
@end menu
@node The Test Suite
@subsection The Test Suite
The lyskomd test suite is in src/server/testsuite. Please extend this
with additional test cases every time you make modifications to the
server. Run the test suite often to make sure that your changes did not
break anything.
The file config/prot-a.exp contains some support for protocol A. Don't
use these functions in test cases. Use them to set up the inital
database and for things that have to be done, such as logins and enabling
privileges, but that don't need to be tested. Also, don't count on all
the code in prot-a.exp to be fully functional. Add new functions to this
file as you see fit.
The basic structure of a test case is the following:
@example
source "config/prot-a.exp"
read_versions
lyskomd_start
client_start 0
talk_to client 0
kom_connect "DejaGnu test suite"
@i{The test cases}
talk_to client 0
kom_logout
kom_login 5 [holl "gazonk"] 0
kom_enable 255
send "9999 44 0\n"
simple_expect "=9999"
client_death 0
lyskomd_death
@end example
Use the existing test cases as templates.
@node Configuration Options
@subsection Configuration Options
There are several testing and debugging-related configuration options
for lyskomd. Some of them also apply to libisc.
@table @samp
@item --with-purify
Build lyskomd with Purify. This currently does not work.
@item --with-efence
Build lyskomd with Electric Fence for checking buffer overruns. This
option does work.
@item --with-checker
Build lyskomd with Gnu Checker for checking memory accesses, leaks, file
descriptors and all kinds of stuff. As of Checker version 0.99.6, Gnu
Checker cannot deal with lyskomd. Once built, and this requires
modifications to Checker (at least on Linux) it reports spurious errors.
Still, the option is here for those who want to try it out.
@item --with-gcov
Build lyskomd with instrumentation for @code{gcov}. You have to use this
option if you want to run @code{gcov} on lyskomd. For @code{gcov} to be
effective, you should turn off optimization as well.
@item --with-traced-allocations
There is some builtin support for detecting memory leaks in lyskomd.
Whenever the server exits normally it reports how much memory it still
uses to @file{etc/memory-usage}. The count should always be 0.
If there is a leak you can use this option to trace it down. See
@file{src/server/ram-smalloc.c} for more information. You need gdb and
a lot of time to use this option.
@item --with-optimization=@var{value}
Build lyskomd with the specified level of optimization. Use either
numeric values to select the level of optimization, or say
@samp{--with-optimization=no} or @samp{--without-optimization} to turn
optimization off.
@end table
@node Coverage Testing
@subsection Coverage Testing
When you write new code, make sure that it is completely covered by the
test suite. Run the lyskomd configure script with the
@samp{--with-gcov}, @samp{--with-debug-calls} and
@samp{--without-optimization} flags to instrument the server for
coverage testing with gcov.
If you run configure without the @samp{--without-optimization} option,
the server will be compiled with optimizations on. This is fine, but the
coverage data from gcov isn't completely reliable since parts of the
program may have been optimized out of existance.
Recompile everything, then run the test suite. Next do @samp{gcov -f
@var{filename}} to compute coverage information for the file @var{filename}.
The resulting file @var{filename}@samp{.gcov} shows which lines have been
executed, and which haven't been run. Try to get 100% coverage.
@node Debug Calls
@subsection Debug Calls
Run the configure script with @samp{--with-debug-calls} to compile in
support for debugging calls in the server. These calls are strictly for
making testing easier (or possible.) They are not official, and they may
change at any time.
@menu
* memory-info:: Get information from malloc (1000)
* set-marks:: Set the number of marks on a text (1001)
* backdate-text:: Change the creation date of a text (1002)
@end menu
@node memory-info
@subsubsection memory-info (DEBUG) Experimential
@findex memory-info
@example
memory-info [1000] ( )
-> (( arena : INT32;
ordblks : INT32;
smblks : INT32;
hblks : INT32;
hblkhd : INT32;
usmblks : INT32;
fsmblks : INT32;
uordblks : INT32;
fordblks : INT32;
keepcost : INT32; ));
@end example
This call returns the data returned by @code{mallinfo} in the server.
See the man page for @code{mallinfo} for explanations of the fields.
@node set-marks
@subsubsection set-marks (DEBUG) Experimental
@findex set-marks
@example
set-marks [1001] (( text-no : Text_no;
no-of-marks : INT32; ))
-> ( );
@end example
Set the number of marks on text @code{text-no} to @code{no-of-marks},
regardless of how many marks it really has. This call is useful for
forcing the database into a state where the number of marks is incorrect
in some way.
@node backdate-text
@subsubsection backdate-text (DEBUG) Experimental
@findex backdate-text
@example
backdate-text [1002] (( text-no : Text_no;
seconds : INT32; ))
-> ( );
@end example
Backdate a text in the server. Change the creation date of text
@code{text-no} so it appears to have been created @code{seconds} earlier
than it was actually created. This can be used to test the garbage
collector.
@node local-to-global
@section The local-to-global structure
The data structure that stores the mapping from local to global text
numbers is currently one of the more advanced structures used by
lyskomd.
@ignore
@c FIXME: Translate this
@subsection Background
The
Det sätt som textnummer läggs till har ett antal egenskaper:
- Texter läggs hela tiden på bakifrån, aldrig i mitten eller i
början.
- Numren på de lokala textnumren är konsekutiva, dvs inga hål
finns. Sådana hål kan dock uppstå (och uppstår!) när texter tas
bort.
Lösning
=======
Det första man ser när man analyserar innehållet i en mapp, är att det
finns långa avsnitt av idel nollor, och långa avsnitt där det inte
finns några nollor alls, eller åtminstone väldigt få. Detta antyder
alltså att man bör ha en adaptiv datastruktur som anpassar sig till
det lokala förhållanden. Vi föreslår alltså följande.
Mappen lagras i block (små arrayer). Det finns två sorters block:
1. Glesa block. Glesa block består egentligen av två block. I det
ena blocket ligger nycklar (Local_text_no) och i det andra blocket
ligger data (Text_no). Inom ett block använder man binärsökning i det
ena blocket för att hitta just den Local_text_no man är ute efter.
2. Täta block. Täta block består av ett enda block som innehåller
data (Text_no). Man vet vilket lokalt textnummer det första entryt
svarar mot. Det kan finnas enstaka lokala nummer i ett tätt block som
inte finns -- då innehåller data 0.
Blockstorleken är fixerad till t ex 100 entries. (Det verkar som om
man tjänar nästan exakt samma antal bytes oavsett om man väljer
blockstorlek 50 eller 1000). Ett fullt tätt block innehåller alltid
exakt 100 lokala textnummer. Ett fullt glest block innehåller alltid
100 existerande globala textnummer. (Ett glest block tar dubbelt så
mycket plats som ett tätt block, eftersom ett glest block ju
egentligen består av både ett nyckelblock och ett värdeblock).
För att hålla reda på sina block har man en array av block_info:
typedef struct block_info {
int first_free;
int zeroes;
Local_text_no start;
Local_text_no * key_block;
Text_no * value_block;
} L2g_block_info;
Om key_block == NULL så är det ett tätt block.
first_free
Fältet first_free visar var i blocket som man kan fylla på med
fler värden. Det är 100 för fulla block. För block som inte är
fulla pekar det ut det entry i value_block som nästa värde ska
hamna i. Det gäller t ex det sista blocket, som fylls på allt
eftersom nya inlägg skickas till mötet eller block där texter har
tagits bort.
zeroes
Fältet zeroes används bara för täta block, och räknar antalet
nollor i blocket. Om zeroes blir större än 50% av blockstorleken
gör man om blocket till ett glest block. Fältet zeroes är en
optimering som troligtvis underlättar ihopslagning av block. Det
är möjligt att den inte behövs.
start
Fältet start innehåller numret på det första lokala textnumret i
blocket.
key_block
Fältet key_block är en pekare till blocket med Local_text_no, dvs
nycklarna i blocket. Detta fält är NULL om detta är ett tätt
block.
value_block
Fältet value_block är en pekare till blocket med Text_no, dvs
värdena i blocket.
Förutom detta behövs en struct per möte som håller reda på arrayen med
block:
typedef struct local_to_global {
int num_blocks;
int block_size;
L2g_block_info * blocks;
} Local_to_global;
@end ignore
@c ======================================================================
@c ======================================================================
@c == ==
@c == LYSKOMD DATABASE FORMAT ==
@c == ==
@c ======================================================================
@c ======================================================================
@ifinfo
@node lyskomd Database Specification
@chapter lyskomd Database Specification
This document specifies the format of the lyskomd database files. The
specification is currently incomplete. Only the structure, not the
actual data records are documented.
@menu
* Version 0:: Database used with early versions of lyskomd.
* Version 1:: Database used with lyskomd 1.9.0.
* Version 2:: Database used with lyskomd 2.0.0.
@end menu
@end ifinfo
@node Version 0
@section Data File Version 0
Version 0 was used by lyskomd versions up to 1.8.
@example
database : header @II{NL}
next-free-num @II{NL}
confs
persons
next-text-num @II{NL}
texts
;
header : @BB{CLEAN}
| @BB{DIRTY}
;
next-free-num : @II{INTEGER}
;
confs : confs conf
| @II{empty}
;
conf : empty-record
| @BB{+} conf-record @II{NL}
;
persons : persons person
| @II{empty}
;
person : empty-record
| @BB{+} person-record @II{NL}
;
next-text-num : @II{INTEGER}
;
texts : texts text
| @II{empty}
;
text : empty-record
| @BB{+} text-record @BB{NL}
;
empty-record : @BB{@@} @BB{NL}
;
@end example
The number of person and conference records is exactly one less than
@II{next-free-num}. The number of text records is exactly one less than
@II{next-text-num}.
Records are stored sequentially. Conference number 18 is the 18th
conference record in the file. This implies that deleted records must be
stored as @II{empty-record} records.
@II{next-text-num} is the number of the highest text. There are exactly
one less than
this number of text records in the database.
@II{next-free-num} is the number of the highest conference. There are
exactly one less than this number of both person and conference
records. This implies that if conference N is not a letterbox, then
person record N will be an @II{empty-record}.
If the header says ``CLEAN'', the database file is complete. If the
header says ``DIRTY'', the server has not finished writing it
completely.
@node Version 1
@section Data File Version 1
Version 1 was used by lyskomd version 1.9.
@example
database : header @BB{NL} @BB{records}
;
header : @BB{CLEAN:00001}
| @BB{DIRTY:00001}
;
records : records record
| @II{empty}
;
record : next-free-num
| next-text-num
| conference
| person
| info
| text
| deleted
;
next-free-num : @BB{#C} @II{INTEGER}
;
next-text-num : @BB{#P} @II{INTEGER}
;
conference : @BB{C} @II{integer} conf-record @BB{NL}
| @BB{P} @II{integer} person-record @BB{NL}
| @BB{T} @II{integer} text-record @BB{NL}
| @BB{I} info-record @BB{NL}
;
deleted : @BB{-C} @II{integer} @BB{NL}
| @BB{-P} @II{integer} @BB{NL}
| @BB{-T} @II{integer} @BB{NL}
;
@end example
The integer in the conference, text and person records is the ID of the
record. This implies that records can be in any order.
The @II{next-free-num} record is used to store the next available ID for
conferences in the system. There may be several of these records in the
database.
The @II{next-text-num} record is used to store the next available ID for
texts in the system. There may be several of these records in the
database.
A conference or text must have a number lower than the closest
@II{next-free-num} or @II{next-text-num} preceding it.
The deletion records are used to indicate that an object found earlier
in the database has been deleted. The implementation of these in lyskomd
1.9 does not work, and they are not used. The @II{-C} record indicates
deletion of a conference. The @II{-P} record indicates deletion of a
person. The @II{-T} record indicates deletion of a text. The integer
in the deletion record is the ID of the object being deleted.
@node Version 2
@section Data File Version 2
Version 2 is used by lyskomd version 2.0.
The structure of the data file is similar to version 1. The header has
been extended with a timestamp contaning the time when the database file
was saved. This timestamp consists of twenty characters, the number of
seconds since 00:00:00 GMT January 1, 1970 (a Unix @code{time_t}.)
@example
database : header @BB{NL} @BB{records}
;
header : @BB{CLEAN:00001} @BB{NL} timestamp @BB{NL}
| @BB{DIRTY:00001} @BB{NL} timestamp @BB{NL}
;
timestamp : digit digit digit digit digit
digit digit digit digit digit
digit digit digit digit digit
digit digit digit digit digit
;
;
digit : @BB{0} | @BB{1} | @BB{2} | @BB{3} | @BB{4}
| @BB{5} | @BB{6} | @BB{7} | @BB{8} | @BB{9}
;
@end example
Furthermore several data types have been changed to accommodate
additions introduced in version 10 of protocol A. The @II{server-info},
@II{conf-record} and @II{text-record} include information about
aux-items (highest-aux-no and aux-item-list.) The @II{conf-record}
contains the expire field added to the conf-stat structure. The
@II{conf-record} and @II{person-record} records use the new
local-to-global structure for storing maps.
@contents
@bye
|
https://authorea.com/users/300596/articles/430295/download_latex | authorea.com | CC-MAIN-2021-17 | application/x-tex | application/x-tex | crawl-data/CC-MAIN-2021-17/segments/1618038879305.68/warc/CC-MAIN-20210419080654-20210419110654-00575.warc.gz | 232,821,685 | 2,457 | \documentclass[10pt]{article}
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\begin{document}
\title{The functions of Spirulina powder on the enhanced anaerobic degradation
of quinoline and indole}
\author[1]{Jingxin Shi}%
\author[2]{Chunyan Xu}%
\author[2]{ Hongjun Han}%
\affil[1]{Harbin Institute of Technology}%
\affil[2]{Harbin Institute of Technology State Key Laboratory of Urban Water Resource and Environment}%
\vspace{-1em}
\date{\today}
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\begin{abstract}
Large amount of algae has been significantly increased due to
eutrophication of water bodies. However, algae is rich in bio-active
compounds, such as vitamins, proteins, polysaccharides, unsaturated
fatty acids, nucleic acids, minerals and pigments. In the study,
spirulina was proved to be an novel and appropriate co-metabolic
substance in enhancing the anaerobic degradation of quinoline and
indole. When the dosage of Spirulina powder was 1.0 mg/L, reactor showed
the highest degradation efficiency, with ratios of 99.77\% and 99.57\%,
respectively. Further, the addition of Spirulina powder led to the
increase of MLSS, MLVSS, proteins, and polysaccharides concentration of
sludge. Finally, the addition of Spirulina powder resulted in the
decrease of Acinetobacter and the enrichment of Aminicenantes,
Levilinea, and Longilinea. The reactor with Spirulina powder had richer
and more diverse archaea community.%
\end{abstract}%
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|
https://is.jabok.cz/zivotopisy/cv?lang=cs;uco=4050;zjazyk=cze;varianta=8;tiskproh=latex_rich | jabok.cz | CC-MAIN-2022-33 | application/x-text | application/x-tex | crawl-data/CC-MAIN-2022-33/segments/1659882572908.71/warc/CC-MAIN-20220817122626-20220817152626-00409.warc.gz | 309,143,242 | 5,596 | \documentclass[12pt,a4paper]{artikel1}
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\begin{document}
\begin{vitae}{\czech}{Michal Pařízek
narozen v roce 1979}
\nadpis{Profesní životopis}
\vspace{0.8cm}
\podnadpis{\textbf{Osobní údaje} }
\begin{ul}
\item Michal Pařízek\\
narozen v roce 1979, původem z Dobrušky, nyní z Prahy\\
manžel a otec\\
ORCID ID: 0000--0001--6959--8416
\end{ul}
\podnadpis{\textbf{Současné pracoviště} }
\begin{ul}
\item Jabok -- Vyšší odborná škola sociálně pedagogická a teologická\\
Salmovská 8\\
120 00 Praha 2\\
Katedra pedagogiky a psychologie (vedoucí katedry)\\
\item Vyučované předměty: Zážitková pedagogika, Volnočasová pedagogika, Metody pohybových a herních aktivit, Metody práce s pohybem a tělesností, Kurz plavání, Seznamovací kurz, Lyžařský kurz, vybraná témata v předmětu Sociální pedagogika, The World Around Us -- Understanding the Context, Current Social Issues from the Global Perspective, Zkušenostně reflektivní přístupy v pedagogice\\
\end{ul}
\podnadpis{\textbf{Vzdělání} }
\begin{ul}
\item 2014 -- 2022 \quad Pedagogická fakulta MU v Brně\\
Doktorské kombinované studium Pedagogiky se zaměřením na Sociální pedagogiku\\
Výzkumné téma: Celostní vzdělávání sociálních pedagogů na terciární úrovni\\
https://is.muni.cz/th/sjuv2/Celostni\_vzdelavani\_socialnich\_pedagogu\_na\_terciarni\_urovni\_--\_Michal\_Parizek.pdf \\
\item 2002 \quad ? 2008 Evangelická teologická fakulta UK v Praze -- Institut ekumenických studií\\
Bakalářský obor Teologie křesťanských tradic\\
Bakalářská práce na téma: Tělo a tělesnost u Oliviera Clémenta, Louis--Marie Chauveta a Jürgena Moltmanna\\
https://dspace.cuni.cz/bitstream/handle/20.500.11956/16719/130093957.pdf?sequence=1\&isAllowed=y \\
\item 1999 \quad ? 2005 Fakulta tělesné výchovy a sportu UK v Praze\\
Magisterský obor Učitelství pro SŠ, obor Tělesná výchova ? Anglický jazyk (na PedF UK)\\
Diplomová práce na téma: Sport a prožitek skrze sport ve vztahu ke křesťanství\\
https://knihovna.jabok.cuni.cz/eg/opac/record/12304?locg=102;detail\_record\_view=0;facet=author%7Cpersonal%5BPa%C5%99%C3%ADzek%2C%20Michal%5D;query=author%3AMichal%20Pa%C5%99%C3%ADzek\\
\item 1998 \quad ? 1999 Midkent College, Maidstone, Anglie\\
Studium anglického jazyka zakončené zkouškou Cambridge Proficiency (CPE)\\
\item 1997 \quad ? 1998 Falkirk College, Stirling Centre, Stirling, Skotsko (nyní Forth Valley College)\\
Studium anglického jazyka zakončené zkouškami Cambridge First Certificate (FCE) a Scottish Qualification Authority SQA ? ESOL 3\\
\item 1993 \quad ? 1997 Střední průmyslová škola elektrotechnická v Dobrušce\\
obor Automatizace (Maturita v červnu 1997)\\
\end{ul}
\podnadpis{\textbf{Přednáškové a studijní pobyty} }
\begin{ul}
\item Kratší přenáškové pobyty:
\item 2015, 2017, 2019, 2021 VIVES University of Applied Sciences, Kortrijk, Belgie
\item 2014 \quad Complutense University, Madrid, Španělsko\\
\item 2013 \quad Thomas More University of Applied Sciences, Antverpy, Belgie
\item 2012 \quad Artevelde University of Applied Sciences, Gent, Belgie \\
\\
\item Kratší studijní pobyty:
\item 2018 \quad Studijní cesta do Švýcarska (Lucern, Curych, Biel/Bienne) v rámci projektu \duv{Škola jako místo, kde se vzdělává i žije} -- zaměřeno na práci s mladými lidmi a místními komunitami metodou sociálně kulturní animace\\
\item 2015 \quad Spiritualita -- Zážitková vědecká škola 2015, organizováno FTK UP (projekt VIPPA2)\\
\item 2012 \quad Grangemockler Camphill, Irsko -- Projekt \duv{Metody sociální práce s multiproblémovými rodinami}\\
\item 2011 \quad Sofie, Bulharsko -- \duv{Global Education in non--formal youth work} \\
\item 2011 \quad Benediktbeuern, Německo -- Projekt \duv{Využití zážitkové pedagogiky v sociální práci} \\
\item 2010 \quad Berlín, Německo -- Projekt \duv{Metody sociální práce s mládeží ohroženou sociálním vyloučením}\\
\item 2006 \quad Durham, Anglie -- \duv{Living Theology}\\
\item 2002 \quad Londýn + Oxford, Anglie -- University of Surrey, Roehampton a Oxford University v rámci International Youth Trust of Saint Pierre de Thaon (za KAJL, PedF UK)\\
\item
\end{ul}
\podnadpis{\textbf{Vzdělávání v kurzech a seminářích} }
\begin{ul}
\item 2021 \quad MOOC -- LEARNx: Deep Learning through Transformative Pedagogy (edX -- The University of Queensland -- UQx \& microsoftedu)
\item 2021 \quad Konference místně zakotveného učení (SEVER)\\
\item 2020 \quad MOOC -- Social Pedagogy Across Europe (Coursera -- Universitat Aut?noma de Barcelona)\\
\item 2020 \quad MOOC -- The Science of Well--Being (Coursera -- Yale University)\\
\item 2019 \quad Formativní hodnocení + Formative Assessment (IVOV)\\
\item 2018 \quad Principy nezraňující komunikace ve škole (Varianty)\\
\item 2016 \quad Svět v otázkách: Globální rozvojové vzdělávání prostřednictvím Filosofie pro děti a Velké otázky o světě prostřednictvím Filosofie pro děti 2 (Varianty)\\
\item 2016 \quad Cílená zpětná vazba aneb Jak pracovat se zážitkem ve skupině (Varianty)
\item 2014 \quad Rekvalifikační kurz Metoda zážitkové pedagogiky (Prázdninová škola Lipnice, akreditováno MŠMT)\\
\item 2010 \quad MEKKA -- metodický kurz zážitkové pedagogiky (Prázdninová škola Lipnice)\\
\item
\end{ul}
\podnadpis{\textbf{Publikační a přednášková činnost} }
\begin{ul}
\item 2021 \quad PAŘÍZEK, Michal. Principles of holistic education applied to the Teacher Education Model for the 21st Century in Singapore. Sociální pedagogika / Social Education. 2021, 9(2), 9--22. ISSN 18058825. Dostupné z: doi:10.7441/soced.2021.09.02.01\\
\item 2019 \quad Martin Buber \& Holistic Education in Relation to Wellbeing (SDG 3) -- přednáška a Setting the right goals in everyday routine of a social worker/social pedagogue -- workshop\\
Předneseno k zastřešujícímu tématu Sustainable Development Goals v průběhu International and Intercultural Week na VIVES University of Applied Sciences v Kortrijku, Belgie -- staff mobility, Erasmus+
\item 2019 \quad SoFarEDU -- základní informace o projektu\\
Předneseno na: Malá konference o využití zahrady v terapeutickém kontextu (Jabok)\\
\item 2018 \quad Holistic Approaches towards Physical Movement and Sport Education\\
Předneseno na 7th Czech Philosophy of Sport Conference v Olomouci (FTK UP)\\
\item 2018 \quad Principy celostního vzdělávání v procesu odborné i osobnostní přípravy pedagogů volného času\\
Předneseno na konferenci ČPdS v Opavě -- Profesní rozvoj pedagogických pracovníků a pracovníků ve školství\\
\item 2017 \quad Being a Good Steward (přednáška) a The World, Our Responsibility (návazný workshop, založený na principech zážitkové pedagogiky)\\
Předneseno k zastřešujícímu tématu Human Rights v průběhu International--Intercultural Week na VIVES University College v Kortijku, Belgie
\item 2016 \quad Experience and Holistic Education\\
Předneseno na 5th Czech Philosophy of Sport Conference v Olomouci (FTK UP)
\item 2016 \quad Výkon a--nebo radost z pohybu?\\
Předneseno na 12. konferenci o výchově a volném čase se zaměřením na zájmové činnosti v Českých Budějovicích (organizace: PdF JU, ČPdS, AVPVČ)
\item 2016 \quad Holistic Education -- A Gateway to Full and Responsible Citizenship?\\
Předneseno k zastřešujícímu tématu Migration v průběhu International--Intercultural Week na VIVES University of Applied Sciences v Kortijku, Belgie
\item 2016 \quad Vybrané aspekty celostního vzdělávání ve světě -- Podněty pro vzdělávání a osobnostní růst pedagogů v České republice \\
Předneseno na konferenci ČPdS v Ostravě -- Perspektivy výchovy a vzdělávání v podmínkách současného světa
\item 2015 \quad Možnosti přesahů a setkání s nevyslovitelným na adaptačních kurzech\\
Předneseno na 11. konferenci AVPVČ O výchově a volném čase v Hradci Králové\\
\item 2014 \quad English for Social Services\\
Učebnice anglického jazyka především pro potřeby studentů VOŠ Jabok a ETF UK, ISBN 978--80--904681--2--2\\
člen editorského týmu\\
\item 2013 \quad Význam prožívání vlastního těla při utváření identity mladých lidí\\
Publikováno: Teologie a sociální práce -- dvacet let dialogu (ISBN:978--80--904681--1--5)\\
\item 2010 \quad Tělo jako symbol dneška\\
Publikováno ve sborníku z konference (ISBN: 78--80--7290--428--0) Symbol ve výchově, umění a sportu (na PedF UK)\\
\item 2007 \quad Hodnoty ve sportu (Olympijské, filosofické, křesťanské nebo konzumní?)\\
Publikováno ve sborníku z konference (ISBN 80--7290--272--5) Hodnoty ve výchově, umění a sportu (na PedF UK)\\
\item 2005 \quad Křesťanské denominace a sport\\
Předneseno v rámci mezinárodní konference Mladí evropané ve vědě (na FTVS UK, publikováno ve sborníku z konference ISBN 80--86317--41--2)\\
\item 2005 \quad Křesťanství a prožitek ve sportu\\
Předneseno v rámci mezinárodní konference Prožitek a dobrodružství prožívání (na FTVS UK)\\
\end{ul}
\podnadpis{\textbf{Zapojení v projektech} }
\begin{ul}
\item SoFarTEAM -- Social Work in Farming ? Teaching material about client groups and their involvement in social farming -- ERASMUS+\\
\item Inovace VOV -- tvorba kurzů v Moodle\\
Sociální pedagogika III\\
Metody práce s pohybem a tělesností\\
\item Inovace VOV -- tvorba MOOC\\
Zážitková pedagogika -- po registraci do Moodle Jabok (zdarma) dostupné zde: https://moodle.jabok.cuni.cz/course/view.php?id=183\\
Metody herních a pohybových aktivit -- po registraci do Moodle Jabok (zdarma) dostupné zde: https://moodle.jabok.cuni.cz/course/view.php?id=184\\
\item SoFarEDU -- Social Farming in Higher Education https://sofaredu.eu/\\
Aktivní participace v mezinárodním projektu -- ERASMUS+ grantový program Evropské Unie, grant no. 2017--1--DE01--KA203--003583\\
Společně s E. Hudcovou editor \duv{Pedagogical Guide} -- dostupné zde:https://sofaredu.eu/wp--content/uploads/2020/02/Pedagogical--guide--1.pdf\\
Společně s R. Evans, M. Nobelmann, C. Schneider a S. Wagner \duv{Online Guide} Tips and tricks for teaching social farming online -- dostupné zde: https://sofaredu.eu/wp--content/uploads/2020/08/Tips--and--tricks--for--teaching--social--farming--online.pdf
\item
\end{ul}
\podnadpis{\textbf{Členství v (akademických) organizacích} }
\begin{ul}
\item Asociace vzdělavatelů pedagogů volného času\\
Od 1.1.2016 člen výkonného výboru\\
\item Česká pedagogická společnost\\
člen sekce zaměřené na pedagogiku volného času\\
\item Člen redakční rady časopisu Gymnasion -- https://gymnasion.org/\\
\item
\end{ul}
\podnadpis{\textbf{Licence a další aktivity} }
\begin{ul}
\item Instruktor lyžování\\
\item Instruktor snowboardingu\\
\item Dobrovolník v organizaci Statek Vlčkovice o.p.s. a dříve i Bodaj o.s.
\end{ul}
\vspace{0.5cm} 11. 7. 2022
\vspace{0.5cm} \end{vitae}
\end{document}
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http://porocila.imfm.si/2005/mat/clani/saksida.tex | imfm.si | CC-MAIN-2023-14 | text/x-tex | application/x-tex | crawl-data/CC-MAIN-2023-14/segments/1679296945183.40/warc/CC-MAIN-20230323194025-20230323224025-00206.warc.gz | 48,510,922 | 1,277 | \clan {Pavle Saksida} % 7.5.
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% 1.01: {\bf 1}. SAKSIDA, Pavle. Maxwell-Bloch equations, C Neumann system and
% Kaluza-Klein theory. {\it J. phys. A}, 2005, vol. 38, no. 48, str. 10321-10344.
% http://www.iop.org/EJ/toc/0305-4470/38/48. $[$COBISS.SI-ID 13802073$]$\\
{}
{Maxwell-Bloch equations, C Neumann system and Kaluza-Klein theory}
{J.\ Phys.\ A} {38} {2005} {48} {10321--1034{4}}
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% Ured: {\bf 2}. {\it Obzornik za matematiko in fiziko}. Saksida, Pavle (podro\v{c}ni urednik 2004-). Ljubljana: Dru\v{s}tvo matematikov, fizikov in astronomov Slovenije, 1951-. ISSN 0473-7466. $[$COBISS.SI-ID 753412$]$\\
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% Ment: {\bf 3}. KOMLANC, Tanja{\it . Hiperboli\v{c}na ravnina : diplomsko delo}. Ljubljana: $[$T. Komlanc$]$, 2005. 44 f., graf. prikazi. http://www.matknjiz.si/diplome/uni/p/2005/11000-591.pdf. $[$COBISS.SI-ID 13638233$]$\\
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