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diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMathThumb/index.html b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMathThumb/index.html new file mode 100644 index 00000000000..b8c1d4fd048 --- /dev/null +++ b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMathThumb/index.html @@ -0,0 +1,171 @@ +<!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>sampleMathThumb</TITLE> +<META NAME="description" CONTENT="sampleMathThumb"> +<META NAME="keywords" CONTENT="sampleMathThumb"> +<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="sampleMathThumb.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> +<DIV ALIGN="RIGHT"> +<IMG + WIDTH="474" HEIGHT="160" ALIGN="BOTTOM" BORDER="0" + SRC="img1.gif" + ALT="\begin{eqnarray} +\phi(\lambda) & = & \frac{1} {2 \pi i}\int^{c+i\infty}_{c-i\in... +...\epsilon , \bar{\epsilon} & = & \mbox{actual/average energy loss} +\end{eqnarray}"> +<BR> + +</DIV> + +<P> +Since (<A HREF="sampleMathThumb.html#eqn:stress-sr">6</A>) or (<A HREF="sampleMathThumb.html#gdef">7d</A>) should hold for arbitrary +<!-- MATH + $\delta\mathbf{c}$ + --> +<IMG + WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img2.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="img3.gif" + ALT="$ \mathcal{N}(A) = \mathcal{R}(B)$"> and that when <IMG + WIDTH="68" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" + SRC="img4.gif" + ALT="$ y=B(x)$"> one has... +<BR> +...the <A NAME="tex2html3" + 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="img5.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="img6.gif" + ALT="$ a^n+b^n=c^n$"> with integers <IMG + WIDTH="43" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" + SRC="img7.gif" + ALT="$ n>2$"> has long +been suspected (<A NAME="tex2html4" + 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="tex2html5" + HREF="http://www.pbs.org:80/wgbh/nova/proof">Wiles, 1995</A>). + +<P> +<DIV ALIGN="RIGHT"> +</DIV> +<BR> +<DIV ALIGN="RIGHT"> +<P ALIGN="RIGHT"><A NAME="eqn:stress-sr"></A> +<!-- MATH + \begin{eqnarray} +\htmlimage{thumbnail=.4} 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} + --> +<A NAME="eqn:stress-sr"></A><A NAME="eqnarray52" + HREF="img8.gif"><IMG + WIDTH="140" HEIGHT="29" ALIGN="LEFT" + SRC="Timg8.gif" + ALT="\begin{eqnarray}V \mathbf{\pi}^{sr} & = & \left< \sum_i M_i \mathbf{V}_i \mathbf... +...m_i \sum_\alpha \mathbf{p}_{i\alpha} \mathbf{f}_{i\alpha} \right> +\end{eqnarray}"></A> +<BR CLEAR="ALL"> +<P> +<BR CLEAR="ALL"></DIV><P></P> +<DIV ALIGN="RIGHT"> +</DIV> + +<P> +<DIV ALIGN="RIGHT"> +</DIV><A NAME="bgdefs"></A><A NAME="bdef"></A><A NAME="b0def"></A><A NAME="budef"></A><A NAME="gdef"></A> +<!-- MATH + \begin{subequations} +\htmlimage{thumbnail=.3}\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"><A NAME="tex2html_wrap_indisplay268" + HREF="img9.gif"><IMG + WIDTH="1" HEIGHT="6" ALIGN="MIDDLE" BORDER="0" + SRC="Timg9.gif" + ALT="$\displaystyle \begin{align}B_{ij}^\alpha & = \left(B_{ij}^\alpha\right)_0 + \le... +...} + \frac{\d N_k^\beta}{\d X_i} \frac{\d N_k^\alpha}{\d X_j} \right)\end{align}$"></A></TD></TR> +</TABLE> +<DIV ALIGN="RIGHT"> +</DIV> +<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--> +<BR><HR> +<ADDRESS> +<I>Michel Goossens</I> +<BR><I>1999-03-30</I> +</ADDRESS> +</BODY> +</HTML> |