move english latex doc out of texmf-doc

git-svn-id: svn://tug.org/texlive/trunk@13412 c570f23f-e606-0410-a88d-b1316a301751
author: Karl Berry <karl@freefriends.org> 2009-05-23 00:23:51 +0000
committer: Karl Berry <karl@freefriends.org> 2009-05-23 00:23:51 +0000
commit: a683c3d7e9fac38ec713f23fb6b9d2c7143aea82 (patch)
tree: 424ab223921f85fd3f167a4ccd0e2d37d05c2927 /Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleAMS/index.html
parent: 5beb5368a684995153c8566797ba054f21c666af (diff)
1 files changed, 279 insertions, 0 deletions
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+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
+
+<!--Converted with LaTeX2HTML 99.1 release (March 30, 1999)
+original version by:  Nikos Drakos, CBLU, University of Leeds
+* revised and updated by:  Marcus Hennecke, Ross Moore, Herb Swan
+* with significant contributions from:
+  Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
+<HTML>
+<HEAD>
+<TITLE>sampleAMS</TITLE>
+<META NAME="description" CONTENT="sampleAMS">
+<META NAME="keywords" CONTENT="sampleAMS">
+<META NAME="resource-type" CONTENT="document">
+<META NAME="distribution" CONTENT="global">
+
+<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1">
+<META NAME="Generator" CONTENT="LaTeX2HTML v99.1 release">
+<META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css">
+
+<LINK REL="STYLESHEET" HREF="sampleAMS.css">
+
+<LINK REL="next" HREF="node1.html">
+<LINK REL="next" HREF="node1.html">
+</HEAD>
+
+<BODY >
+<!--Navigation Panel-->
+<A NAME="tex2html9"
+ HREF="node1.html">
+<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
+ SRC="/afs/cern.ch/project/tex/new/latex2html/icons.gif/next_motif.gif"></A> 
+<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
+ SRC="/afs/cern.ch/project/tex/new/latex2html/icons.gif/up_motif_gr.gif"> 
+<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
+ SRC="/afs/cern.ch/project/tex/new/latex2html/icons.gif/previous_motif_gr.gif">   
+<BR>
+<B> Next:</B> <A NAME="tex2html10"
+ HREF="node1.html">About this document ...</A>
+<BR>
+<BR>
+<!--End of Navigation Panel-->
+<P>
+<H2 ALIGN="center"><A NAME="SECTION00000000000000000000">
+Math examples</A>
+</H2>
+<BR>
+<DIV ALIGN="CENTER">
+
+<!-- MATH
+ \begin{eqnarray}
+\phi(\lambda) & = &  \frac{1} {2 \pi i}\int^{c+i\infty}_{c-i\infty}
+  \exp \left( u \ln u + \lambda u \right ) du \hspace{1cm}\mbox{for } c \geq 0 \\
+ \lambda       & = &  \frac{\epsilon  -\bar{\epsilon} }{\xi}
+                   - \gamma' - \beta^2 - \ln \frac{\xi} {E_{\rm max}}          \\
+ \gamma        & = &  0.577215\dots \mathrm{\hspace{5mm}(Euler's\ constant)}   \\
+ \gamma'       & = &  0.422784\dots = 1 - \gamma                               \\
+   \epsilon , \bar{\epsilon} & = & \mbox{actual/average energy loss}
+\end{eqnarray}
+ -->
+
+<TABLE CELLPADDING="0" ALIGN="CENTER" WIDTH="100%">
+<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><IMG
+ WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img1.gif"
+ ALT="$\displaystyle \phi(\lambda)$"></TD>
+<TD WIDTH="10" ALIGN="CENTER" NOWRAP><IMG
+ WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
+ SRC="img2.gif"
+ ALT="$\displaystyle =$"></TD>
+<TD ALIGN="LEFT" NOWRAP><IMG
+ WIDTH="220" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
+ SRC="img3.gif"
+ ALT="$\displaystyle \frac{1} {2 \pi i}\int^{c+i\infty}_{c-i\infty}
+\exp \left( u \ln u + \lambda u \right ) du$">&nbsp; &nbsp;for <IMG
+ WIDTH="40" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
+ SRC="img4.gif"
+ ALT="$\displaystyle c \geq 0$"></TD>
+<TD WIDTH=10 ALIGN="RIGHT">
+(1)</TD></TR>
+<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><IMG
+ WIDTH="13" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ SRC="img5.gif"
+ ALT="$\displaystyle \lambda$"></TD>
+<TD WIDTH="10" ALIGN="CENTER" NOWRAP><IMG
+ WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
+ SRC="img2.gif"
+ ALT="$\displaystyle =$"></TD>
+<TD ALIGN="LEFT" NOWRAP><IMG
+ WIDTH="185" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
+ SRC="img6.gif"
+ ALT="$\displaystyle \frac{\epsilon -\bar{\epsilon} }{\xi}
+- \gamma' - \beta^2 - \ln \frac{\xi} {E_{\rm max}}$"></TD>
+<TD WIDTH=10 ALIGN="RIGHT">
+(2)</TD></TR>
+<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><IMG
+ WIDTH="13" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
+ SRC="img7.gif"
+ ALT="$\displaystyle \gamma$"></TD>
+<TD WIDTH="10" ALIGN="CENTER" NOWRAP><IMG
+ WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
+ SRC="img2.gif"
+ ALT="$\displaystyle =$"></TD>
+<TD ALIGN="LEFT" NOWRAP><IMG
+ WIDTH="235" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
+ SRC="img8.gif"
+ ALT="$\displaystyle 0.577215\dots \mathrm{\hspace{5mm}(Euler's\ constant)}$"></TD>
+<TD WIDTH=10 ALIGN="RIGHT">
+(3)</TD></TR>
+<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><IMG
+ WIDTH="18" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
+ SRC="img9.gif"
+ ALT="$\displaystyle \gamma'$"></TD>
+<TD WIDTH="10" ALIGN="CENTER" NOWRAP><IMG
+ WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
+ SRC="img2.gif"
+ ALT="$\displaystyle =$"></TD>
+<TD ALIGN="LEFT" NOWRAP><IMG
+ WIDTH="143" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
+ SRC="img10.gif"
+ ALT="$\displaystyle 0.422784\dots = 1 - \gamma$"></TD>
+<TD WIDTH=10 ALIGN="RIGHT">
+(4)</TD></TR>
+<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><IMG
+ WIDTH="24" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
+ SRC="img11.gif"
+ ALT="$\displaystyle \epsilon , \bar{\epsilon}$"></TD>
+<TD WIDTH="10" ALIGN="CENTER" NOWRAP><IMG
+ WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
+ SRC="img2.gif"
+ ALT="$\displaystyle =$"></TD>
+<TD ALIGN="LEFT" NOWRAP>actual/average energy loss</TD>
+<TD WIDTH=10 ALIGN="RIGHT">
+(5)</TD></TR>
+</TABLE></DIV>
+<BR CLEAR="ALL"><P></P>
+
+<P>
+Since&nbsp;(<A HREF="sampleAMS.html#eqn:stress-sr">6</A>) or&nbsp;(<A HREF="sampleAMS.html#gdef">7d</A>) should hold for arbitrary 
+<!-- MATH
+ $\delta\mathbf{c}$
+ -->
+<IMG
+ WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
+ SRC="img12.gif"
+ ALT="$ \delta\mathbf{c}$">-vectors, it is clear that 
+<!-- MATH
+ $\mathcal{N}(A) = \mathcal{R}(B)$
+ -->
+<IMG
+ WIDTH="104" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img13.gif"
+ ALT="$ \mathcal{N}(A) = \mathcal{R}(B)$"> and that when <IMG
+ WIDTH="68" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
+ SRC="img14.gif"
+ ALT="$ y=B(x)$"> one has...
+<BR>
+...the <A NAME="tex2html4"
+ HREF="http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pythagoras.html">Pythagorians</A> knew infinitely many solutions in integers to 
+<!-- MATH
+ $a^2+b^2=c^2$
+ -->
+<IMG
+ WIDTH="88" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
+ SRC="img15.gif"
+ ALT="$ a^2+b^2=c^2$">. 
+That no non-trivial integer solutions exist for 
+<!-- MATH
+ $a^n+b^n=c^n$
+ -->
+<IMG
+ WIDTH="93" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
+ SRC="img16.gif"
+ ALT="$ a^n+b^n=c^n$"> with integers <IMG
+ WIDTH="43" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
+ SRC="img17.gif"
+ ALT="$ n&gt;2$"> has long 
+been suspected (<A NAME="tex2html5"
+ HREF="http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Fermat's_last_theorem.html">Fermat, c.1637</A>). Only during the current decade has this been proved (<A NAME="tex2html6"
+ HREF="http://www.pbs.org:80/wgbh/nova/proof">Wiles, 1995</A>).
+
+<P>
+<BR>
+<DIV ALIGN="CENTER"><A NAME="eqn:stress-sr"></A>
+<!-- MATH
+ \begin{eqnarray}
+V \mathbf{\pi}^{sr} & = & \left<  \sum_i M_i \mathbf{V}_i \mathbf{V}_i
+  + \sum_i \sum_{j>i} \mathbf{R}_{ij} \mathbf{F}_{ij}\right> \\\nonumber
+                 & = & \left< \sum_i M_i \mathbf{V}_i \mathbf{V}_i
+  + \sum_{i}\sum_{j>i}\sum_\alpha\sum_\beta \mathbf{r}_{i\alpha j\beta}\mathbf{f}_{i\alpha j\beta}
+  - \sum_i \sum_\alpha \mathbf{p}_{i\alpha} \mathbf{f}_{i\alpha}   \right>
+\end{eqnarray}
+ -->
+
+<TABLE CELLPADDING="0" ALIGN="CENTER" WIDTH="100%">
+<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><IMG
+ WIDTH="40" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
+ SRC="img18.gif"
+ ALT="$\displaystyle V \mathbf{\pi}^{sr}$"></TD>
+<TD WIDTH="10" ALIGN="CENTER" NOWRAP><IMG
+ WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
+ SRC="img2.gif"
+ ALT="$\displaystyle =$"></TD>
+<TD ALIGN="LEFT" NOWRAP><IMG
+ WIDTH="233" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
+ SRC="img19.gif"
+ ALT="$\displaystyle \left&lt; \sum_i M_i \mathbf{V}_i \mathbf{V}_i
++ \sum_i \sum_{j&gt;i} \mathbf{R}_{ij} \mathbf{F}_{ij}\right&gt;$"></TD>
+<TD WIDTH=10 ALIGN="RIGHT">
+(6)</TD></TR>
+<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT">&nbsp;</TD>
+<TD WIDTH="10" ALIGN="CENTER" NOWRAP><IMG
+ WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
+ SRC="img2.gif"
+ ALT="$\displaystyle =$"></TD>
+<TD ALIGN="LEFT" NOWRAP><IMG
+ WIDTH="418" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
+ SRC="img20.gif"
+ ALT="$\displaystyle \left&lt; \sum_i M_i \mathbf{V}_i \mathbf{V}_i
++ \sum_{i}\sum_{j&gt;i}\...
+... j\beta}
+- \sum_i \sum_\alpha \mathbf{p}_{i\alpha} \mathbf{f}_{i\alpha} \right&gt;$"></TD>
+<TD WIDTH=10 ALIGN="RIGHT">
+&nbsp;</TD></TR>
+</TABLE></DIV>
+<BR CLEAR="ALL"><P></P>
+
+<P>
+
+<DIV ALIGN="CENTER"><A NAME="bgdefs"></A><A NAME="bdef"></A><A NAME="b0def"></A><A NAME="budef"></A><A NAME="gdef"></A>
+<!-- MATH
+ \begin{subequations}
+\begin{align} B_{ij}^\alpha     & =
+\left(B_{ij}^\alpha\right)_0 + \left(B_{ij}^\alpha\right)_a\\
+  \left(B_{ij}^\alpha\right)_0  & = \frac{1}{2}\left(\frac{\d N_i^\alpha}{\d X_j}
+        + \frac{\d N_j^\alpha} {\d X_i} \right)\\
+  \left(B_{ij}^\alpha\right)_a  & = H_{ij}^{\alpha \beta} a^\beta\\
+  H_{ij}^{\alpha \beta}         & =
+    \frac{1}{2}\left( \frac{\d N_k^\alpha}{\d X_i} \frac{\d N_k^\beta}{\d X_j} 
+    + \frac{\d N_k^\beta}{\d X_i} \frac{\d N_k^\alpha}{\d X_j} \right)\end{align}
+\end{subequations}
+ -->
+<TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER">
+<TR VALIGN="MIDDLE">
+<TD NOWRAP ALIGN="CENTER"><IMG
+ WIDTH="559" HEIGHT="159" ALIGN="BOTTOM" BORDER="0"
+ SRC="img21.gif"
+ ALT="\begin{subequations}\begin{align}B_{ij}^\alpha &amp; = \left(B_{ij}^\alpha\right)_0 ...
+...\beta}{\d X_i} \frac{\d N_k^\alpha}{\d X_j} \right)\end{align}\end{subequations}"></TD></TR>
+</TABLE></DIV>
+<BR CLEAR="ALL">
+<BR><HR>
+<!--Table of Child-Links-->
+<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
+
+<UL>
+<LI><A NAME="tex2html11"
+ HREF="node1.html">About this document ...</A>
+</UL>
+<!--End of Table of Child-Links-->
+<HR>
+<!--Navigation Panel-->
+<A NAME="tex2html9"
+ HREF="node1.html">
+<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
+ SRC="/afs/cern.ch/project/tex/new/latex2html/icons.gif/next_motif.gif"></A> 
+<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
+ SRC="/afs/cern.ch/project/tex/new/latex2html/icons.gif/up_motif_gr.gif"> 
+<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
+ SRC="/afs/cern.ch/project/tex/new/latex2html/icons.gif/previous_motif_gr.gif">   
+<BR>
+<B> Next:</B> <A NAME="tex2html10"
+ HREF="node1.html">About this document ...</A>
+<!--End of Navigation Panel-->
+<ADDRESS>
+<I>Michel Goossens</I>
+<BR><I>1999-03-30</I>
+</ADDRESS>
+</BODY>
+</HTML>
author	Karl Berry <karl@freefriends.org>	2009-05-23 00:23:51 +0000
committer	Karl Berry <karl@freefriends.org>	2009-05-23 00:23:51 +0000
commit	a683c3d7e9fac38ec713f23fb6b9d2c7143aea82 (patch)
tree	424ab223921f85fd3f167a4ccd0e2d37d05c2927 /Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleAMS/index.html
parent	5beb5368a684995153c8566797ba054f21c666af (diff)