diff options
author | Karl Berry <karl@freefriends.org> | 2012-08-26 23:07:28 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2012-08-26 23:07:28 +0000 |
commit | d3535e838cefea309221187bb9e62698c0df8c51 (patch) | |
tree | dbee8197e1bfecefe547d53e843f0acff729a3fe /Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath | |
parent | 33353453d22fc5877a8ced58c673c7008ce8c00a (diff) |
latex-web-companion non-update
git-svn-id: svn://tug.org/texlive/trunk@27531 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath')
29 files changed, 0 insertions, 1004 deletions
diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/WARNINGS b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/WARNINGS deleted file mode 100644 index 9d1d9f764ee..00000000000 --- a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/WARNINGS +++ /dev/null @@ -1,2 +0,0 @@ - -redefining command \d diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/images.pl b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/images.pl deleted file mode 100644 index a319f5c597b..00000000000 --- a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/images.pl +++ /dev/null @@ -1,132 +0,0 @@ -# LaTeX2HTML 99.1 release (March 30, 1999) -# Associate images original text with physical files. - - -$key = q/displaystylefrac{epsilon-bar{epsilon}}{xi}-gamma'-beta^2-lnfrac{xi}{E_{{rm{max}};MSF=1.6;AAT/; -$cached_env_img{$key} = q|<IMG - WIDTH="185" HEIGHT="51" ALIGN="MIDDLE" BORDER="0" - SRC="img5.gif" - ALT="$\displaystyle \frac{\epsilon -\bar{\epsilon} }{\xi} -- \gamma' - \beta^2 - \ln \frac{\xi} {E_{\rm max}}$">|; - -$key = q/a^2+b^2=c^2;MSF=1.6;AAT/; -$cached_env_img{$key} = q|<IMG - WIDTH="88" HEIGHT="33" ALIGN="MIDDLE" BORDER="0" - SRC="img15.gif" - ALT="$a^2+b^2=c^2$">|; - -$key = q/n>2;MSF=1.6;AAT/; -$cached_env_img{$key} = q|<IMG - WIDTH="43" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img17.gif" - ALT="$n>2$">|; - -$key = q/y=B(x);MSF=1.6;AAT/; -$cached_env_img{$key} = q|<IMG - WIDTH="68" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" - SRC="img14.gif" - ALT="$y=B(x)$">|; - -$key = q/mathcal{N}(A)=mathcal{R}(B);MSF=1.6;AAT/; -$cached_env_img{$key} = q|<IMG - WIDTH="104" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" - SRC="img13.gif" - ALT="$\mathcal{N}(A) = \mathcal{R}(B)$">|; - -$key = q/displaystylelambda;MSF=1.6;AAT/; -$cached_env_img{$key} = q|<IMG - WIDTH="13" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" - SRC="img4.gif" - ALT="$\displaystyle \lambda$">|; - -$key = q/displaystyle0.577215dotsmathrm{hspace{5mm}(Euler'sconstant)};MSF=1.6;AAT/; -$cached_env_img{$key} = q|<IMG - WIDTH="235" HEIGHT="33" ALIGN="MIDDLE" BORDER="0" - SRC="img7.gif" - ALT="$\displaystyle 0.577215\dots \mathrm{\hspace{5mm}(Euler's\ constant)}$">|; - -$key = q/displaystylegamma;MSF=1.6;AAT/; -$cached_env_img{$key} = q|<IMG - WIDTH="13" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img6.gif" - ALT="$\displaystyle \gamma$">|; - -$key = q/displaystylefrac{1}{2pii}int^{c+iinfty}_{c-iinfty}expleft(ulnu+lambdauright)duhspace{1cm}mbox{for}cgeq0;MSF=1.6;AAT/; -$cached_env_img{$key} = q|<IMG - WIDTH="325" HEIGHT="58" ALIGN="MIDDLE" BORDER="0" - SRC="img3.gif" - ALT="$\displaystyle \frac{1} {2 \pi i}\int^{c+i\infty}_{c-i\infty} -\exp \left( u \ln u + \lambda u \right ) du \hspace{1cm}\mbox{for } c \geq 0$">|; - -$key = q/displaystylembox{actualslashaverageenergyloss};MSF=1.6;AAT/; -$cached_env_img{$key} = q|<IMG - WIDTH="187" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" - SRC="img11.gif" - ALT="$\displaystyle \mbox{actual/average energy loss}$">|; - -$key = q/displaystyleleft<sum_iM_imathbf{V}_imathbf{V}_i+sum_isum_{j>i}mathbf{R}_{ij}mathbf{F}_{ij}right>;MSF=1.6;AAT/; -$cached_env_img{$key} = q|<IMG - WIDTH="233" HEIGHT="63" ALIGN="MIDDLE" BORDER="0" - SRC="img19.gif" - ALT="$\displaystyle \left< \sum_i M_i \mathbf{V}_i \mathbf{V}_i -+ \sum_i \sum_{j>i} \mathbf{R}_{ij} \mathbf{F}_{ij}\right>$">|; - -$key = q/displaystylegamma';MSF=1.6;AAT/; -$cached_env_img{$key} = q|<IMG - WIDTH="18" HEIGHT="33" ALIGN="MIDDLE" BORDER="0" - SRC="img8.gif" - ALT="$\displaystyle \gamma'$">|; - -$key = q/a^n+b^n=c^n;MSF=1.6;AAT/; -$cached_env_img{$key} = q|<IMG - WIDTH="93" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" - SRC="img16.gif" - ALT="$a^n+b^n=c^n$">|; - -$key = q/textstyle=;MSF=1.6;AAT/; -$cached_env_img{$key} = q|<IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$">|; - -$key = q/displaystyleepsilon,bar{epsilon};MSF=1.6;AAT/; -$cached_env_img{$key} = q|<IMG - WIDTH="24" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img10.gif" - ALT="$\displaystyle \epsilon , \bar{\epsilon}$">|; - -$key = q/displaystyleleft<sum_iM_imathbf{V}_imathbf{V}_i+sum_{i}sum_{j>i}sum_alphasum_betalphajbeta}-sum_isum_alphamathbf{p}_{ialpha}mathbf{f}_{ialpha}right>;MSF=1.6;AAT/; -$cached_env_img{$key} = q|<IMG - WIDTH="418" HEIGHT="63" ALIGN="MIDDLE" BORDER="0" - SRC="img20.gif" - ALT="$\displaystyle \left< \sum_i M_i \mathbf{V}_i \mathbf{V}_i -+ \sum_{i}\sum_{j>i}\... -... j\beta} -- \sum_i \sum_\alpha \mathbf{p}_{i\alpha} \mathbf{f}_{i\alpha} \right>$">|; - -$key = q/deltamathbf{c};MSF=1.6;AAT/; -$cached_env_img{$key} = q|<IMG - WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" - SRC="img12.gif" - ALT="$\delta\mathbf{c}$">|; - -$key = q/displaystyle0.422784dots=1-gamma;MSF=1.6;AAT/; -$cached_env_img{$key} = q|<IMG - WIDTH="143" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img9.gif" - ALT="$\displaystyle 0.422784\dots = 1 - \gamma$">|; - -$key = q/displaystylephi(lambda);MSF=1.6;AAT/; -$cached_env_img{$key} = q|<IMG - WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" - SRC="img1.gif" - ALT="$\displaystyle \phi(\lambda)$">|; - -$key = q/displaystyleVmathbf{pi}^{sr};MSF=1.6;AAT/; -$cached_env_img{$key} = q|<IMG - WIDTH="40" HEIGHT="30" ALIGN="MIDDLE" BORDER="0" - SRC="img18.gif" - ALT="$\displaystyle V \mathbf{\pi}^{sr}$">|; - -1; - diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/images.tex b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/images.tex deleted file mode 100644 index 9b738e34b59..00000000000 --- a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/images.tex +++ /dev/null @@ -1,254 +0,0 @@ -\batchmode -\documentclass[a4paper,twoside]{article} - -\usepackage{html} - -% -\renewcommand{\d}{\partial}% -\providecommand{\bm}[1]{\mathbf{#1}}% -\providecommand{\Range}{\mathcal{R}}% -\providecommand{\Ker}{\mathcal{N}}% -\providecommand{\Quat}{\vec{\mathbf{Q}}} -% -\providecommand{\StAndrews}{\htmlurl{http://www-groups.dcs.st-and.ac.uk/~history}}%% -\providecommand{\Pythagorians}{\htmladdnormallink - {Pythagorians}{\htmlurl{http://www-groups.dcs.st-and.ac.uk/~history}/Mathematicians/Pythagoras.html}}% -\providecommand{\Fermat}{\htmladdnormallink - {Fermat, c.1637}{\htmlurl{http://www-groups.dcs.st-and.ac.uk/~history}/HistTopics/Fermat's_last_theorem.html}}% -\providecommand{\Wiles}{\htmladdnormallink - {Wiles, 1995}{\htmlurl{http://www.pbs.org:80/wgbh/nova/proof}}} - -\usepackage[dvips]{color} -\pagecolor[gray]{.7} - - - -\makeatletter - -\makeatletter -\count@=\the\catcode`\_ \catcode`\_=8 -\newenvironment{tex2html_wrap}{}{} \catcode`\_=\count@ -\newcommand{\renewedcommand}[1]{\expandafter\renewcommand\csname #1\endcsname}% -\makeatother -\let\mathon=$ -\let\mathoff=$ -\ifx\AtBeginDocument\undefined \newcommand{\AtBeginDocument}[1]{}\fi -\newbox\sizebox -\setlength{\hoffset}{0pt}\setlength{\voffset}{0pt} -\addtolength{\textheight}{\footskip}\setlength{\footskip}{0pt} -\addtolength{\textheight}{\topmargin}\setlength{\topmargin}{0pt} -\addtolength{\textheight}{\headheight}\setlength{\headheight}{0pt} -\addtolength{\textheight}{\headsep}\setlength{\headsep}{0pt} -\setlength{\textwidth}{349pt} -\newwrite\lthtmlwrite -\makeatletter -\let\realnormalsize=\normalsize -\global\topskip=2sp -\def\preveqno{}\let\real@float=\@float \let\realend@float=\end@float -\def\@float{\let\@savefreelist\@freelist\real@float} -\def\end@float{\realend@float\global\let\@freelist\@savefreelist} -\let\real@dbflt=\@dbflt \let\end@dblfloat=\end@float -\let\@largefloatcheck=\relax -\let\if@boxedmulticols=\iftrue -\def\@dbflt{\let\@savefreelist\@freelist\real@dbflt} -\def\adjustnormalsize{\def\normalsize{\mathsurround=0pt \realnormalsize - \parindent=0pt\abovedisplayskip=0pt\belowdisplayskip=0pt}% - \def\phantompar{\csname par\endcsname}\normalsize}% -\def\lthtmltypeout#1{{\let\protect\string\immediate\write\lthtmlwrite{#1}}}% -\newcommand\lthtmlhboxmathA{\adjustnormalsize\setbox\sizebox=\hbox\bgroup\kern.05em }% -\newcommand\lthtmlhboxmathB{\adjustnormalsize\setbox\sizebox=\hbox to\hsize\bgroup\hfill }% -\newcommand\lthtmlvboxmathA{\adjustnormalsize\setbox\sizebox=\vbox\bgroup % - \let\ifinner=\iffalse }% -\newcommand\lthtmlboxmathZ{\@next\next\@currlist{}{\def\next{\voidb@x}}% - \expandafter\box\next\egroup}% -\newcommand\lthtmlmathtype[1]{\def\lthtmlmathenv{#1}}% -\newcommand\lthtmllogmath{\lthtmltypeout{l2hSize % -:\lthtmlmathenv:\the\ht\sizebox::\the\dp\sizebox::\the\wd\sizebox.\preveqno}}% -\newcommand\lthtmlfigureA[1]{\let\@savefreelist\@freelist - \lthtmlmathtype{#1}\lthtmlvboxmathA}% -\newcommand\lthtmlpictureA[1]{\let\@savefreelist\@freelist - \lthtmlmathtype{#1}\lthtmlhboxmathB}% -\newcommand\lthtmlpictureZ[1]{\hfill\lthtmlfigureZ}% -\newcommand\lthtmlfigureZ{\lthtmlboxmathZ\lthtmllogmath\copy\sizebox - \global\let\@freelist\@savefreelist}% -\newcommand\lthtmldisplayA[1]{\lthtmlmathtype{#1}\lthtmlvboxmathA}% -\newcommand\lthtmldisplayB[1]{\edef\preveqno{(\theequation)}% - \lthtmldisplayA{#1}\let\@eqnnum\relax}% -\newcommand\lthtmldisplayZ{\lthtmlboxmathZ\lthtmllogmath\lthtmlsetmath}% -\newcommand\lthtmlinlinemathA[1]{\lthtmlmathtype{#1}\lthtmlhboxmathA - \vrule height1.5ex width0pt }% -\newcommand\lthtmlinlineA[1]{\lthtmlmathtype{#1}\lthtmlhboxmathA}% -\newcommand\lthtmlinlineZ{\egroup\expandafter\ifdim\dp\sizebox>0pt % - \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetinline} -\newcommand\lthtmlinlinemathZ{\egroup\expandafter\ifdim\dp\sizebox>0pt % - \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetmath} -\newcommand\lthtmlindisplaymathZ{\egroup % - \centerinlinemath\lthtmllogmath\lthtmlsetmath} -\def\lthtmlsetinline{\hbox{\vrule width.1em\kern-.05em\vtop{\vbox{% - \kern.1em\copy\sizebox}\ifdim\dp\sizebox>0pt\kern.1em\else\kern.3pt\fi - \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}} -\def\lthtmlsetmath{\hbox{\vrule width.1em\kern-.05em\vtop{\vbox{% - \kern.1em\kern0.8 pt\hbox{\hglue.17em\copy\sizebox\hglue0.8 pt}}\kern.3pt% - \ifdim\dp\sizebox>0pt\kern.1em\fi \kern0.8 pt% - \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}} -\def\centerinlinemath{% - \dimen1=\ifdim\ht\sizebox<\dp\sizebox \dp\sizebox\else\ht\sizebox\fi - \advance\dimen1by.5pt \vrule width0pt height\dimen1 depth\dimen1 - \dp\sizebox=\dimen1\ht\sizebox=\dimen1\relax} - -\def\lthtmlcheckvsize{\ifdim\ht\sizebox<\vsize - \ifdim\wd\sizebox<\hsize\expandafter\hfill\fi \expandafter\vfill - \else\expandafter\vss\fi}% -\providecommand{\selectlanguage}[1]{}% -\makeatletter \tracingstats = 1 - - -\begin{document} -\pagestyle{empty}\thispagestyle{empty}\lthtmltypeout{}% -\lthtmltypeout{latex2htmlLength hsize=\the\hsize}\lthtmltypeout{}% -\lthtmltypeout{latex2htmlLength vsize=\the\vsize}\lthtmltypeout{}% -\lthtmltypeout{latex2htmlLength hoffset=\the\hoffset}\lthtmltypeout{}% -\lthtmltypeout{latex2htmlLength voffset=\the\voffset}\lthtmltypeout{}% -\lthtmltypeout{latex2htmlLength topmargin=\the\topmargin}\lthtmltypeout{}% -\lthtmltypeout{latex2htmlLength topskip=\the\topskip}\lthtmltypeout{}% -\lthtmltypeout{latex2htmlLength headheight=\the\headheight}\lthtmltypeout{}% -\lthtmltypeout{latex2htmlLength headsep=\the\headsep}\lthtmltypeout{}% -\lthtmltypeout{latex2htmlLength parskip=\the\parskip}\lthtmltypeout{}% -\lthtmltypeout{latex2htmlLength oddsidemargin=\the\oddsidemargin}\lthtmltypeout{}% -\makeatletter -\if@twoside\lthtmltypeout{latex2htmlLength evensidemargin=\the\evensidemargin}% -\else\lthtmltypeout{latex2htmlLength evensidemargin=\the\oddsidemargin}\fi% -\lthtmltypeout{}% -\makeatother -\setcounter{page}{1} -\onecolumn - -% !!! IMAGES START HERE !!! - -{\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay173}% -$\displaystyle \phi(\lambda)$% -\lthtmlindisplaymathZ -\lthtmlcheckvsize\clearpage} - -{\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay174}% -$\textstyle =$% -\lthtmlindisplaymathZ -\lthtmlcheckvsize\clearpage} - -{\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay175}% -$\displaystyle \frac{1} {2 \pi i}\int^{c+i\infty}_{c-i\infty} -\exp \left( u \ln u + \lambda u \right ) du \hspace{1cm}\mbox{for } c \geq 0$% -\lthtmlindisplaymathZ -\lthtmlcheckvsize\clearpage} - -{\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay176}% -$\displaystyle \lambda$% -\lthtmlindisplaymathZ -\lthtmlcheckvsize\clearpage} - -{\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay178}% -$\displaystyle \frac{\epsilon -\bar{\epsilon} }{\xi} -- \gamma' - \beta^2 - \ln \frac{\xi} {E_{\rm max}}$% -\lthtmlindisplaymathZ -\lthtmlcheckvsize\clearpage} - -{\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay179}% -$\displaystyle \gamma$% -\lthtmlindisplaymathZ -\lthtmlcheckvsize\clearpage} - -{\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay181}% -$\displaystyle 0.577215\dots \mathrm{\hspace{5mm}(Euler's\ constant)}$% -\lthtmlindisplaymathZ -\lthtmlcheckvsize\clearpage} - -{\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay182}% -$\displaystyle \gamma'$% -\lthtmlindisplaymathZ -\lthtmlcheckvsize\clearpage} - -{\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay184}% -$\displaystyle 0.422784\dots = 1 - \gamma$% -\lthtmlindisplaymathZ -\lthtmlcheckvsize\clearpage} - -{\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay185}% -$\displaystyle \epsilon , \bar{\epsilon}$% -\lthtmlindisplaymathZ -\lthtmlcheckvsize\clearpage} - -{\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay187}% -$\displaystyle \mbox{actual/average energy loss}$% -\lthtmlindisplaymathZ -\lthtmlcheckvsize\clearpage} - -{\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline112}% -$\delta\mathbf{c}$% -\lthtmlinlinemathZ -\lthtmlcheckvsize\clearpage} - -{\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline114}% -$\mathcal{N}(A) = \mathcal{R}(B)$% -\lthtmlinlinemathZ -\lthtmlcheckvsize\clearpage} - -{\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline116}% -$y=B(x)$% -\lthtmlinlinemathZ -\lthtmlcheckvsize\clearpage} - -{\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline118}% -$a^2+b^2=c^2$% -\lthtmlinlinemathZ -\lthtmlcheckvsize\clearpage} - -{\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline120}% -$a^n+b^n=c^n$% -\lthtmlinlinemathZ -\lthtmlcheckvsize\clearpage} - -{\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_inline122}% -$n>2$% -\lthtmlinlinemathZ -\lthtmlcheckvsize\clearpage} - -{\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay195}% -$\displaystyle V \mathbf{\pi}^{sr}$% -\lthtmlindisplaymathZ -\lthtmlcheckvsize\clearpage} - -{\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay197}% -$\displaystyle \left< \sum_i M_i \mathbf{V}_i \mathbf{V}_i -+ \sum_i \sum_{j>i} \mathbf{R}_{ij} \mathbf{F}_{ij}\right>$% -\lthtmlindisplaymathZ -\lthtmlcheckvsize\clearpage} - -{\newpage\clearpage -\lthtmlinlinemathA{tex2html_wrap_indisplay199}% -$\displaystyle \left< \sum_i M_i \mathbf{V}_i \mathbf{V}_i -+ \sum_{i}\sum_{j>i}\sum_\alpha\sum_\beta \mathbf{r}_{i\alpha j\beta}\mathbf{f}_{i\alpha j\beta} -- \sum_i \sum_\alpha \mathbf{p}_{i\alpha} \mathbf{f}_{i\alpha} \right>$% -\lthtmlindisplaymathZ -\lthtmlcheckvsize\clearpage} - - -\end{document} diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/img1.gif b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/img1.gif Binary files differdeleted file mode 100644 index 5916d47b1f4..00000000000 --- a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/img1.gif +++ /dev/null diff --git 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-* 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>sampleMath</TITLE> -<META NAME="description" CONTENT="sampleMath"> -<META NAME="keywords" CONTENT="sampleMath"> -<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="sampleMath.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"><A NAME="xiEmax"></A> - -<!-- 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 ALIGN="CENTER" CELLPADDING="0" 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 ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></TD> -<TD ALIGN="LEFT" NOWRAP><IMG - WIDTH="325" HEIGHT="58" ALIGN="MIDDLE" BORDER="0" - SRC="img3.gif" - ALT="$\displaystyle \frac{1} {2 \pi i}\int^{c+i\infty}_{c-i\infty} -\exp \left( u \ln u + \lambda u \right ) du \hspace{1cm}\mbox{for } c \geq 0$"></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="img4.gif" - ALT="$\displaystyle \lambda$"></TD> -<TD ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></TD> -<TD ALIGN="LEFT" NOWRAP><IMG - WIDTH="185" HEIGHT="51" ALIGN="MIDDLE" BORDER="0" - SRC="img5.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="img6.gif" - ALT="$\displaystyle \gamma$"></TD> -<TD ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></TD> -<TD ALIGN="LEFT" NOWRAP><IMG - WIDTH="235" HEIGHT="33" ALIGN="MIDDLE" BORDER="0" - SRC="img7.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="img8.gif" - ALT="$\displaystyle \gamma'$"></TD> -<TD ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></TD> -<TD ALIGN="LEFT" NOWRAP><IMG - WIDTH="143" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img9.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="img10.gif" - ALT="$\displaystyle \epsilon , \bar{\epsilon}$"></TD> -<TD ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></TD> -<TD ALIGN="LEFT" NOWRAP><IMG - WIDTH="187" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" - SRC="img11.gif" - ALT="$\displaystyle \mbox{actual/average energy loss}$"></TD> -<TD WIDTH=10 ALIGN="RIGHT"> -(5)</TD></TR> -</TABLE></DIV> -<BR CLEAR="ALL"><P></P> - -<P> -Since <A HREF="sampleMath.html#xiEmax">2</A> and <A HREF="sampleMath.html#eqn:stress-sr">6</A> 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 <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 <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 ALIGN="CENTER" CELLPADDING="0" 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 ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></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 ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></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> -<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> diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/internals.pl b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/internals.pl deleted file mode 100644 index 129a18c5241..00000000000 --- a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/internals.pl +++ /dev/null @@ -1,14 +0,0 @@ -# LaTeX2HTML 99.1 release (March 30, 1999) -# Associate internals original text with physical files. - - -$key = q/xiEmax/; -$ref_files{$key} = "$dir".q|sampleMath.html|; -$noresave{$key} = "$nosave"; - -$key = q/eqn:stress-sr/; -$ref_files{$key} = "$dir".q|sampleMath.html|; -$noresave{$key} = "$nosave"; - -1; - diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/labels.pl b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/labels.pl deleted file mode 100644 index 47f50cc587b..00000000000 --- a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/labels.pl +++ /dev/null @@ -1,29 +0,0 @@ -# LaTeX2HTML 99.1 release (March 30, 1999) -# Associate labels original text with physical files. - - -$key = q/xiEmax/; -$external_labels{$key} = "$URL/" . q|sampleMath.html|; -$noresave{$key} = "$nosave"; - -$key = q/eqn:stress-sr/; -$external_labels{$key} = "$URL/" . q|sampleMath.html|; -$noresave{$key} = "$nosave"; - -1; - - -# LaTeX2HTML 99.1 release (March 30, 1999) -# labels from external_latex_labels array. - - -$key = q/xiEmax/; -$external_latex_labels{$key} = q|2|; -$noresave{$key} = "$nosave"; - -$key = q/eqn:stress-sr/; -$external_latex_labels{$key} = q|6|; -$noresave{$key} = "$nosave"; - -1; - diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/node1.html b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/node1.html deleted file mode 100644 index 35ab2f29258..00000000000 --- a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/node1.html +++ /dev/null @@ -1,72 +0,0 @@ -<!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>About this document ...</TITLE> -<META NAME="description" CONTENT="About this document ..."> -<META NAME="keywords" CONTENT="sampleMath"> -<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="sampleMath.css"> - -<LINK REL="previous" HREF="sampleMath.html"> -<LINK REL="up" HREF="sampleMath.html"> -</HEAD> - -<BODY > -<!--Navigation Panel--> -<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" - SRC="/afs/cern.ch/project/tex/new/latex2html/icons.gif/next_motif_gr.gif"> -<A NAME="tex2html16" - HREF="sampleMath.html"> -<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" - SRC="/afs/cern.ch/project/tex/new/latex2html/icons.gif/up_motif.gif"></A> -<A NAME="tex2html12" - HREF="sampleMath.html"> -<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" - SRC="/afs/cern.ch/project/tex/new/latex2html/icons.gif/previous_motif.gif"></A> -<BR> -<B> Up:</B> <A NAME="tex2html17" - HREF="sampleMath.html">sampleMath</A> -<B> Previous:</B> <A NAME="tex2html13" - HREF="sampleMath.html">sampleMath</A> -<BR> -<BR> -<!--End of Navigation Panel--> - -<H1><A NAME="SECTION00010000000000000000"> -About this document ...</A> -</H1> - <P> -This document was generated using the -<A HREF="http://www-dsed.llnl.gov/files/programs/unix/latex2html/manual/"><STRONG>LaTeX</STRONG>2<tt>HTML</tt></A> translator Version 99.1 release (March 30, 1999) -<P> -Copyright © 1993, 1994, 1995, 1996, -<A HREF="http://cbl.leeds.ac.uk/nikos/personal.html">Nikos Drakos</A>, -Computer Based Learning Unit, University of Leeds. -<BR> -Copyright © 1997, 1998, 1999, -<A HREF="http://www.maths.mq.edu.au/~ross/">Ross Moore</A>, -Mathematics Department, Macquarie University, Sydney. -<P> -The command line arguments were: <BR> - <STRONG>latex2html</STRONG> <TT>sampleMath</TT> -<P> -The translation was initiated by Michel Goossens on 1999-03-30 -<BR><HR> -<ADDRESS> -<I>Michel Goossens</I> -<BR><I>1999-03-30</I> -</ADDRESS> -</BODY> -</HTML> diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/sampleMath.css b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/sampleMath.css deleted file mode 100644 index 1993b851311..00000000000 --- a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/sampleMath.css +++ /dev/null @@ -1,31 +0,0 @@ - -/* Century Schoolbook font is very similar to Computer Modern Math: cmmi */ -.MATH { font-family: "Century Schoolbook", serif; } -.MATH I { font-family: "Century Schoolbook", serif; font-shape: italic } -.BOLDMATH { font-family: "Century Schoolbook", serif; font-weight: bold } - -/* implement both fixed-size and relative sizes */ -SMALL.XTINY { font-size : xx-small } -SMALL.TINY { font-size : x-small } -SMALL.SCRIPTSIZE { font-size : smaller } -SMALL.FOOTNOTESIZE { font-size : small } -SMALL.SMALL { } -BIG.LARGE { } -BIG.XLARGE { font-size : large } -BIG.XXLARGE { font-size : x-large } -BIG.HUGE { font-size : larger } -BIG.XHUGE { font-size : xx-large } - -/* heading styles */ -H1 { } -H2 { } -H3 { } -H4 { } -H5 { } - -/* mathematics styles */ -DIV.displaymath { } /* math displays */ -TD.eqno { } /* equation-number cells */ - - -/* document-specific styles come next */ diff --git a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/sampleMath.html b/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/sampleMath.html deleted file mode 100644 index 47104a5ce76..00000000000 --- a/Master/texmf-dist/doc/latex/latex-web-companion/ch3bis/sampleMath/sampleMath.html +++ /dev/null @@ -1,235 +0,0 @@ -<!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>sampleMath</TITLE> -<META NAME="description" CONTENT="sampleMath"> -<META NAME="keywords" CONTENT="sampleMath"> -<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="sampleMath.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"><A NAME="xiEmax"></A> - -<!-- 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 ALIGN="CENTER" CELLPADDING="0" 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 ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></TD> -<TD ALIGN="LEFT" NOWRAP><IMG - WIDTH="325" HEIGHT="58" ALIGN="MIDDLE" BORDER="0" - SRC="img3.gif" - ALT="$\displaystyle \frac{1} {2 \pi i}\int^{c+i\infty}_{c-i\infty} -\exp \left( u \ln u + \lambda u \right ) du \hspace{1cm}\mbox{for } c \geq 0$"></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="img4.gif" - ALT="$\displaystyle \lambda$"></TD> -<TD ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></TD> -<TD ALIGN="LEFT" NOWRAP><IMG - WIDTH="185" HEIGHT="51" ALIGN="MIDDLE" BORDER="0" - SRC="img5.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="img6.gif" - ALT="$\displaystyle \gamma$"></TD> -<TD ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></TD> -<TD ALIGN="LEFT" NOWRAP><IMG - WIDTH="235" HEIGHT="33" ALIGN="MIDDLE" BORDER="0" - SRC="img7.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="img8.gif" - ALT="$\displaystyle \gamma'$"></TD> -<TD ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></TD> -<TD ALIGN="LEFT" NOWRAP><IMG - WIDTH="143" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img9.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="img10.gif" - ALT="$\displaystyle \epsilon , \bar{\epsilon}$"></TD> -<TD ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></TD> -<TD ALIGN="LEFT" NOWRAP><IMG - WIDTH="187" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" - SRC="img11.gif" - ALT="$\displaystyle \mbox{actual/average energy loss}$"></TD> -<TD WIDTH=10 ALIGN="RIGHT"> -(5)</TD></TR> -</TABLE></DIV> -<BR CLEAR="ALL"><P></P> - -<P> -Since <A HREF="sampleMath.html#xiEmax">2</A> and <A HREF="sampleMath.html#eqn:stress-sr">6</A> 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 <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 <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 ALIGN="CENTER" CELLPADDING="0" 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 ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></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 ALIGN="CENTER" NOWRAP><IMG - WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0" - SRC="img2.gif" - ALT="$\textstyle =$"></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> -<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> |