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diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleAMS/index.html b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleAMS/index.html new file mode 100644 index 00000000000..0aa04db1519 --- /dev/null +++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleAMS/index.html @@ -0,0 +1,279 @@ +<!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="$\displaystyle \frac{1} {2 \pi i}\int^{c+i\infty}_{c-i\infty} +\exp \left( u \ln u + \lambda u \right ) du$"> 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 (<A HREF="sampleAMS.html#eqn:stress-sr">6</A>) or (<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>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< \sum_i M_i \mathbf{V}_i \mathbf{V}_i ++ \sum_i \sum_{j>i} \mathbf{R}_{ij} \mathbf{F}_{ij}\right>$"></TD> +<TD WIDTH=10 ALIGN="RIGHT"> +(6)</TD></TR> +<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"> </TD> +<TD WIDTH="10" ALIGN="CENTER" NOWRAP><IMG + WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" + SRC="img2.gif" + ALT="$\displaystyle =$"></TD> +<TD ALIGN="LEFT" NOWRAP><IMG + WIDTH="418" HEIGHT="63" ALIGN="MIDDLE" BORDER="0" + SRC="img20.gif" + ALT="$\displaystyle \left< \sum_i M_i \mathbf{V}_i \mathbf{V}_i ++ \sum_{i}\sum_{j>i}\... +... j\beta} +- \sum_i \sum_\alpha \mathbf{p}_{i\alpha} \mathbf{f}_{i\alpha} \right>$"></TD> +<TD WIDTH=10 ALIGN="RIGHT"> + </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 & = \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> |