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-\documentclass[a4paper,twoside]{article}
-\usepackage{html}
-\usepackage{amsmath}
-
-\renewcommand{\d}{\partial}\providecommand{\bm}[1]{\mathbf{#1}}
-\providecommand{\Range}{\mathcal{R}}\providecommand{\Ker}{\mathcal{N}}
-\providecommand{\Quat}{\vec{\mathbf{Q}}}
-
-\newcommand{\StAndrews}{\url{http://www-groups.dcs.st-and.ac.uk/~history}}%
-\newcommand{\Pythagorians}{\htmladdnormallink
- {Pythagorians}{\StAndrews/Mathematicians/Pythagoras.html}}
-\newcommand{\Fermat}{\htmladdnormallink
- {Fermat, c.1637}{\StAndrews/HistTopics/Fermat's_last_theorem.html}}
-\newcommand{\Wiles}{\htmladdnormallink
- {Wiles, 1995}{http://www.pbs.org:80/wgbh/nova/proof}}
-
-\begin{document}
-\htmlhead[center]{section}{Math examples}
-\begin{flushright}
-\begin{makeimage}
-\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}
-\end{makeimage}
-\end{flushright}
-
-Since~\eqref{eqn:stress-sr} or~\eqref{gdef} should hold for arbitrary $\delta\bm{c}$%
--vectors, it is clear that $\Ker(A) = \Range(B)$ and that when $y=B(x)$ one has...\\
-...the \Pythagorians{} knew infinitely many solutions in integers to $a^2+b^2=c^2$.
-That no non-trivial integer solutions exist for $a^n+b^n=c^n$ with integers $n>2$ has long
-been suspected (\Fermat). Only during the current decade has this been proved (\Wiles).
-
-\begin{flushright}
-\begin{eqnarray}\htmlimage{}
-\label{eqn:stress-sr}
- V \bm{\pi}^{sr} & = & \left< \sum_i M_i \bm{V}_i \bm{V}_i
- + \sum_i \sum_{j>i} \bm{R}_{ij} \bm{F}_{ij}\right> \\ \nonumber
- & = & \left< \sum_i M_i \bm{V}_i \bm{V}_i
- + \sum_{i}\sum_{j>i}\sum_\alpha\sum_\beta \bm{r}_{i\alpha j\beta}\bm{f}_{i\alpha j\beta}
- - \sum_i \sum_\alpha \bm{p}_{i\alpha} \bm{f}_{i\alpha} \right>
-\end{eqnarray}
-\end{flushright}
-
-\begin{flushright}
-\begin{subequations}\htmlimage{}
-\label{bgdefs}
-\begin{align} B_{ij}^\alpha & =
- \left(B_{ij}^\alpha\right)_0 + \left(B_{ij}^\alpha\right)_a \label{bdef} \\
- \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) \label{b0def} \\
- \left(B_{ij}^\alpha\right)_a & = H_{ij}^{\alpha \beta} a^\beta \label{budef} \\
- 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) \label{gdef}
-\end{align}
-\end{subequations}
-\end{flushright}
-\end{document}