%% This document created by Scientific Notebook (R) Version 3.0


\documentclass[12pt,thmsa]{article}
\usepackage{amssymb}

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%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Fri Mar 28 19:19:20 1997}
%TCIDATA{CSTFile=Scientific Article.cst}
%TCIDATA{PageSetup=72,72,72,72,0}
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%H=36,\PARA{038<p type="texpara" tag="Body Text" >Page \thepage }
%F=36,\PARA{038<p type="texpara" tag="Body Text" >Page \thepage }
%}


\input{tcilatex}
\begin{document}


\section{A Sample Article}

\begin{quotation}
\textbf{Abstract.} This article illustrates many features of a mathematics
document created with \emph{Scientific Notebook}.
\end{quotation}

\subsection{Mathematics and Text}

Let $H$ be a Hilbert space, $C$ be a closed bounded convex subset of $H$, $T$
a nonexpansive self map of $C$. Suppose that as $n\rightarrow \infty $, $%
a_{n,k}\rightarrow 0$ for each $k$, and $\gamma _{n}=\sum_{k=0}^{\infty
}\left( a_{n,k+1}-a_{n,k}\right) ^{+}\rightarrow 0$ Then for each $x$ in $C$%
, $A_{n}x=\sum_{k=0}^{\infty }a_{n,k}T^{k}x$ converges weakly to a fixed
point of $T$ .

\subsection{In-line and Displayed Mathematics}

The equation 
\begin{equation}
u_{tt}-\Delta u+u^{5}+u\left| u\right| ^{p-2}=0\text{ in }\mathbf{R}%
^{3}\times \left[ 0,\infty \right[ .  \tag{1}  \label{wave}
\end{equation}
is numbered and it also has the label ``wave''. You can use this label to
jump to this equation using hypertext links.

\subsection{Multi-Line Displays}

\emph{Scientific Notebook} provides a range of alignment options for
multiline mathematical displays. Here is a series of multiline displays. 
\begin{eqnarray}
x &=&17y  \tag{2} \\
y &>&a+b+c+d+e+f+g+h+i+j+  \nonumber \\
&&k+l+m+n+o+p  \tag{3}
\end{eqnarray}
\begin{eqnarray*}
x &\ll &y_{1}+\cdots +y_{n} \\
&\leq &z
\end{eqnarray*}
\begin{eqnarray*}
y &=&a+b+c+d+e+f+g+h+i+j \\
&&\,+k+l+m+n+o+p
\end{eqnarray*}
\begin{eqnarray*}
w+x+y+z &=& \\
&&a+b+c+d+e+f+g+h+i+j+ \\
&&k+l+m+n+o+p
\end{eqnarray*}

If $f(x)=x+1,$ then we will have 
\[
f([x+1]/[x+2])=\{[x+1]/[x+2]\}+1=(2x+3)/(x+2) 
\]
\begin{eqnarray*}
1+2+3+4+5+6+7+8+9+10+11+12 && \\
+13+14+15+16+17+18+19+20 &=&190
\end{eqnarray*}

\begin{eqnarray}
\max (f,g) &=&\frac{f+g+\left| f-g\right| }{2}\text{,}  \tag{4} \\
\max (f,-g) &=&\frac{f-g+\left| f+g\right| }{2}\text{.}  \tag{5}
\end{eqnarray}
\begin{eqnarray}
(a+b)^{n+1} &=&(a+b)(a+b)^{n}=(a+b)\sum_{j=0}^{n}\binom{n}{j}a^{n-1}b^{j} 
\tag{6} \\
&=&\sum_{j=0}^{n}\binom{n}{j}a^{n+1-j}b^{j}+\sum_{j=1}^{n}\binom{n}{j-1}%
a^{n-1}b^{j}  \tag{7} \\
&=&\sum_{j=0}^{n}\binom{n+1}{j}a^{n+1-j}b^{j}\text{.}  \tag{8}
\end{eqnarray}

Test the overriding of automatic equation labels: 
\begin{eqnarray}
x &=&y+z  \tag{A--1} \\
&=&k+m  \tag{A--2}
\end{eqnarray}
Test the overriding of automatic equation labels, suppressing annotation: 
\begin{eqnarray}
x &=&y+z  \tag*{A--1} \\
&=&k+m  \tag*{A--2}
\end{eqnarray}

\subsection{Theorems, Lemmata, Etc.}

\begin{theorem}
\label{existence}Suppose $u_{0}\in C^{3}\left( \mathbf{R}^{3}\right)
,u_{1}\in C^{2}\left( \mathbf{R}^{3}\right) $ have finite energy 
\begin{equation}
\int_{\mathbf{R}^{3}}\left( \frac{\left| u_{1}\right| ^{2}+\left| \nabla
u_{0}\right| ^{2}}{2}+\frac{\left| u_{0}\right| ^{6}}{6}\right) dx<\infty  
\tag{9}
\end{equation}
and suppose the solution $u^{(0)}$ to the homogeneous wave equation with
initial data $u_{0},u_{1}$ is uniformly bounded. Then there exists $\epsilon
_{0}>0$ such that for $\left| \epsilon \right| <\epsilon _{0}$ the initial
value problem (\ref{wave}) with data $\epsilon u_{0},\epsilon u_{1}$ admits
a global $C^{2}$-solution.
\end{theorem}

\begin{lemma}
The plural of lemma is lemmata, so they say. Why all these lemmas?
\end{lemma}

\begin{proposition}
It is proposed that universal peace is at hand.
\end{proposition}

\begin{remark}
I don't believe it.
\end{remark}

\begin{corollary}
Unrest will continue.
\end{corollary}

\begin{example}
Rwanda was once obscure.
\end{example}

\begin{axiom}
All mathematics is fun.
\end{axiom}

\begin{conjecture}
Some people don't like mathematics.
\end{conjecture}

\begin{exercise}
Try to find one.
\end{exercise}

\begin{definition}
Hot humid days are no fun.
\end{definition}

\subsection{Heading 2}

This is body text following a Heading 2 heading. \label{sectA}

\subsubsection{Heading 3}

This is body text following a Heading 3 heading.\label{ssectA}

\paragraph{Heading 4}

This is body text following a Heading 4 heading.\label{sssectA}

\subparagraph{Heading 5}

This is body text following a Heading 5 heading.\label{ssssectA}

\subsection{Lists}

\subsubsection{Numbered Lists}

\begin{enumerate}
\item  First numbered item, level 1.\label{A}

\begin{enumerate}
\item  First numbered item, level 2.,\label{AA}

\begin{enumerate}
\item  First numbered item, level 3.\label{AAA}

\begin{enumerate}
\item  First numbered item, level 4.\label{AAAA}

\item  Second numbered item, level 4.\label{AAAB}
\end{enumerate}

\item  Second numbered item, leve1 3.\label{AAB}
\end{enumerate}

\item  Second numbered item, level 2.\label{AB}
\end{enumerate}

\item  Second numbered item, level 1.\label{B}

\begin{enumerate}
\item  First numbered item, level 2.\label{BA}

\begin{enumerate}
\item  First numbered item, level 3.\label{BAA}

\begin{enumerate}
\item  First numbered item, level 4.\label{BAAA}

\item  Second numbered item, level 4.\label{BAAB}
\end{enumerate}

\item  Second numbered item, leve1 3.\label{BAB}
\end{enumerate}

\item  Second numbered item, level 2.\label{BB}
\end{enumerate}
\end{enumerate}

Here is a list with multiple levels on one line. There should be five lines,
only. Items should not be split out on separate lines.

\begin{enumerate}
\item  First item, normal.

\item 
\begin{enumerate}
\item  Second item, both numbers.
\end{enumerate}

\item 
\begin{enumerate}
\item 
\begin{enumerate}
\item  Third item, three numbers.
\end{enumerate}
\end{enumerate}

\item 
\begin{enumerate}
\item 
\begin{enumerate}
\item 
\begin{enumerate}
\item  Fourth item, four numbers.
\end{enumerate}
\end{enumerate}

\item 
\begin{enumerate}
\item 
\begin{enumerate}
\item  Fifth item. Second, third, and fourth numbers.
\end{enumerate}
\end{enumerate}
\end{enumerate}
\end{enumerate}

Here is a list with continuation items.

\begin{enumerate}
\item  Level 1, first paragraph.

Level 1, second paragraph.

\begin{enumerate}
\item  Level 2, first paragraph.

Level 2, second paragraph.

\begin{enumerate}
\item  Level 3, first paragraph.

Level 3, second paragraph.

\begin{enumerate}
\item  Level 4, first paragraph.

Level 4, second paragraph.
\end{enumerate}
\end{enumerate}
\end{enumerate}
\end{enumerate}

\subsubsection{Bulleted Lists}

\begin{itemize}
\item  Bullet item, level 1.

\begin{itemize}
\item  Bullet item, level 2.

\begin{itemize}
\item  Bullet item, level 3.

\begin{itemize}
\item  Bullet item, level 4.
\end{itemize}
\end{itemize}
\end{itemize}

\item  Bullet item, level 1.

This is a continuation paragraph in a bullet item. The paragraph has been
made long enough to wrap, and so wrap it will. The question is, do you like
wrap? Is it your taste in music?

\begin{itemize}
\item  Bullet item, level 2.

This is a continuation paragraph in a bullet item. The paragraph has been
made long enough to wrap, and so wrap it will. The question is, do you like
wrap?

\begin{itemize}
\item  Bullet item, level 3.

This is a continuation paragraph in a bullet item. The paragraph has been
made long enough to wrap, and so wrap it will. The question is, do you like
wrap?

\begin{itemize}
\item  Bullet item, level 4.

This is a continuation paragraph in a bullet item. The paragraph has been
made long enough to wrap, and so wrap it will. The question is, do you like
wrap?
\end{itemize}
\end{itemize}
\end{itemize}
\end{itemize}

\subsubsection{Custom Lists}

\begin{description}
\item[gnat]  A small animal, found in the North Woods, that causes no end of
trouble.

\item[gnu]  A large animal, found in crossword puzzles, that causes no end
of trouble.

\item[armadillo]  A medium-sized animal, named after a medium-sized Texas
city. A medium-sized animal, named after a medium-sized Texas city.

\item[A very long custom label here]  There should be enough text following
to allow the paragraph to wrap to the next line.

Here is a continuation paragraph of the above custom item.
\end{description}

\subsection{Block Quote and Centered}

In addition to Body Text, there are paragraph tags named Block Quote and
Center. Here is a Block Quote paragraph.

\begin{quotation}
Why, there, there, there, there! A diamond gone, cost me two thousand ducats
in Frankfort! The curse never fell upon our nation till now; I never felt it
till now. Two thousand ducats in that, and other precious, precious jewels.
I would my daughter were dead at my foot, and the jewels in her ear! Would
she were hearsed at my foot, and the jewels in her coffin! No news of them?
Why, thou loss upon loss! The thief gone with so much, and so much to find
the thief, and no satisfaction, no revenge! Nor no ill luck stirring but
what lights o' my shedding.
\end{quotation}

Here is a centered paragraph:

\begin{center}
Nay, that's true, that's very true. Go, Tubal, fee me an officer; bespeak
him a fortnight before. I will have the heart of him if he forfeit, for were
he out of Venice I can make what merchandise I will. Go, Tubal, and meet me
at our synagogue; go, good Tubal; at our synagogue, Tubal.
\end{center}

\subsection{Text Tags}

Text tags are the tags you apply to text within a paragraph, to distinguish
phrases. There are tags for physical phrase markup and tags for logical
phrase markup.

The logical phrase tags are \emph{emphasized}, \textsl{strongly emphasized}, 
\textsc{keyboard input}, and \textsf{sample text}. In this style, we have
colored the logical phrases to distinguish them from the physical phrases.

The physical phrase tags are \textbf{bold}, \textit{italics}, \texttt{typed
code}, {\Large bigger}, and {\small smaller}.

\subsection{Operators}

The following is a list of operators from the \textsc{Insert, Operator}...
menu selection.

\begin{tabular}{|l|l|l|l|l|l|l|l|l|}
\hline
$\int $ & $\diint $ & $\iiint $ & $\iiiint $ & $\idotsint $ & $\oint $ & $%
\sum $ & $\prod $ & $\bigcap $ \\ \hline
$\bigwedge $ & $\bigoplus $ & $\bigodot $ & $\bigsqcup $ & $\coprod $ & $%
\bigcup $ & $\bigvee $ & $\bigotimes $ & $\biguplus $ \\ \hline
\end{tabular}
\vspace{1.0076pc}

The following is a list of operators from the \textsc{Insert, Operator}...
menu selection. In this example, all operators are set to ``Big,'' while all
limit positions are set ``at right.''

\begin{tabular}{|l|l|l|l|l|l|l|l|l|}
\hline
$\dint\nolimits_{b}^{a}$ & $\diint\nolimits_{A}^{b}$ & $\diiint\nolimits_{%
\Delta }dV$ & $\diiiint\nolimits_{?}dT$ & $\didotsint\nolimits_{\ldots
}d\cdots $ & $\doint\nolimits_{\Gamma }d\gamma $ & $\dsum\nolimits_{x=1}^{5}%
\frac{1}{x^{2}}$ & $\dprod\nolimits_{x=5}^{7}\left( 1-\sqrt{x}\right) $ & $%
\dbigcap\nolimits_{A\in \mathbf{A}}A$ \\ \hline
$\dbigwedge\nolimits_{i}x_{i}$ & $\dbigoplus\nolimits^{100}X_{i}$ & $%
\dbigodot\nolimits_{\nu \neq v}\Psi _{\nu }$ & $\dbigsqcup\nolimits_{\xi
=\left( 
\begin{array}{ll}
1 & 2 \\ 
3 & 4
\end{array}
\right) }\xi $ & $\dcoprod\nolimits^{\text{A small paragraph}}\Xi _{i}$ & $%
\dbigcup\nolimits_{x^{x^{x}}}U_{x}$ & $\dbigvee\nolimits_{\int i}y^{i}$ & $%
\dbigotimes\nolimits_{\mu \in \{1,2,5,7\}}\Phi \mu $ & $\dbiguplus%
\nolimits_{Blow}^{Joe}B$ \\ \hline
\end{tabular}
\vspace{1.0114pc}

The following is a list of operators from the \textsc{Insert, Operator}...
menu selection. In this example, all operators are set to ``Small,'' while
all limit positions are set ``at right.''

\begin{tabular}{|l|l|l|l|l|l|l|l|l|}
\hline
$\tint\nolimits_{b}^{a}xdx$ & $\tiint\nolimits_{A}\frac{dxdy}{xy}$ & $%
\tiiint\nolimits_{\Delta }dV$ & $\tiiiint\nolimits_{?}dT$ & $%
\tidotsint\nolimits_{\ldots }d\cdots $ & $\toint\nolimits_{\Gamma }d\gamma $
& $\tsum\nolimits_{x=1}^{5}\frac{1}{x^{2}}$ & $\tprod\nolimits_{x=5}^{7}%
\left( 1-\sqrt{x}\right) $ & $\tbigcap\nolimits_{A\in \mathbf{A}}A$ \\ \hline
$\tbigwedge\nolimits_{i}x_{i}$ & $\tbigoplus\nolimits^{100}X_{i}$ & $%
\tbigodot\nolimits_{\nu \neq v}\Psi _{\nu }$ & $\tbigsqcup\nolimits_{\xi
=\left( 
\begin{array}{ll}
1 & 2 \\ 
3 & 4
\end{array}
\right) }\xi $ & $\tcoprod\nolimits^{\text{A small paragraph}}\Xi _{i}$ & $%
\tbigcup\nolimits_{x^{x^{x}}}U_{x}$ & $\tbigvee\nolimits_{\int i}y^{i}$ & $%
\tbigotimes\nolimits_{\mu \in \{1,2,5,7\}}\Phi \mu $ & $\tbiguplus%
\nolimits_{Blow}^{Joe}B$ \\ \hline
\end{tabular}
\vspace{1.0114pc}

The following is a list of operators from the \textsc{Insert, Operator}...
menu selection. In this example, all operators are set to ``Big,'' while all
limit positions are set ``Above/below.''

\begin{tabular}{|l|l|l|l|l|l|l|l|l|}
\hline
$\dint\limits_{b}^{a}xdx$ & $\diint\limits_{A}\frac{dxdy}{xy}$ & $%
\diiint\limits_{\Delta }dV$ & $\diiiint\limits_{?}dT$ & $\didotsint\limits_{%
\ldots }d\cdots $ & $\doint\limits_{\Gamma }d\gamma $ & $\dsum%
\limits_{x=1}^{5}\frac{1}{x^{2}}$ & $\dprod\limits_{x=5}^{7}\left( 1-\sqrt{x}%
\right) $ & $\dbigcap\limits_{A\in \mathbf{A}}A$ \\ \hline
$\dbigwedge\limits_{i}x_{i}$ & $\dbigoplus\limits^{100}X_{i}$ & $%
\dbigodot\limits_{\nu \neq v}\Psi _{\nu }$ & $\dbigsqcup\limits_{\xi =\left( 
\begin{array}{ll}
1 & 2 \\ 
3 & 4
\end{array}
\right) }\xi $ & $\dcoprod\limits^{\text{A small paragraph}}\Xi _{i}$ & $%
\dbigcup\limits_{x^{x^{x}}}U_{x}$ & $\dbigvee\limits_{\int i}y^{i}$ & $%
\dbigotimes\limits_{\mu \in \{1,2,5,7\}}\Phi \mu $ & $\dbiguplus%
\limits_{Blow}^{Joe}B$ \\ \hline
\end{tabular}
\vspace{1.0114pc}

\subsection{Brackets}

The following is a list of the different brackets from the \textsc{Insert,
Brackets}... menu selection.

$
\begin{tabular}{|l|l|l|l|l|l|}
\hline
$\left( \frac{a}{\frac{x}{y}}\right) $ & $\left\lfloor \frac{E}{X}%
\right\rfloor $ & $\left/ \frac{\mathbf{I}}{\mathbf{J}}\right/ $ & $%
\left\Updownarrow \frac{m}{\frac{m}{m}}\right\Updownarrow $ & $%
\left\Downarrow \frac{Q}{\frac{Q}{\frac{Q}{Q}}}\right\Downarrow $ & $\left\} 
\mathsf{U}\right\{ $ \\ \hline
$\left[ \frac{b}{\frac{x}{y}}\right] $ & $\left\lceil \frac{F}{X}%
\right\rceil $ & $\left\backslash \frac{\mathbf{J}}{\mathbf{L}}%
\right\backslash $ & $\left\uparrow \frac{n}{\frac{n}{n}}\right\uparrow $ & $%
\left\rceil \frac{R}{\frac{R}{\frac{R}{R}}}\right\lceil $ & $\left] \mathsf{V%
}\right[ $ \\ \hline
$\left\{ \frac{c}{\frac{x}{y}}\right\} $ & $\left| \frac{G}{X}\right| $ & $%
\left\updownarrow \frac{\mathbf{K}}{\mathbf{L}}\right\updownarrow $ & $%
\left\Uparrow \frac{o}{\frac{o}{o}}\right\Uparrow $ & $\left\rfloor \frac{S}{%
\frac{S}{\frac{S}{S}}}\right\lfloor $ & $\left) \mathsf{W}\right( $ \\ \hline
$\left\langle \frac{d}{\frac{x}{y}}\right\rangle $ & $\left\| \frac{H}{X}%
\right\| $ & $\left. \frac{\mathbf{L}}{\mathbf{X}}\right. $ & $%
\left\downarrow \frac{p}{\frac{p}{p}}\right\downarrow $ & $\left\rangle 
\frac{T}{\frac{T}{\frac{T}{T}}}\right\langle $ &  \\ \hline
\end{tabular}
$\vspace{1.0114pc}

\subsection{Binomials}

The following is a list of operators from the \textsc{Insert, Binomials}...
menu selection.

\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|}
\hline
$\QOVERD( ) {} {}$ & $\QOVERD[ ] {} {}$ & $\QOVERD\{ \} {} {}$ & $%
\QOVERD\langle \rangle {} {}$ & $\QOVERD\lfloor \rfloor {} {}$ & $%
\QOVERD\lceil \rceil {} {}$ & $\QOVERD| | {} {}$ & $\QOVERD\| \| {} {}$ & $%
\QOVERD/ / {} {}$ & $\QOVERD\backslash \backslash {} {}$ & $%
\QOVERD\updownarrow \updownarrow {} {}$ & $\QOVERD. . {} {}$ \\ \hline
$\QOVERD\Updownarrow \Updownarrow {} {}$ & $\QOVERD\uparrow \uparrow {} {}$
& $\QOVERD\Uparrow \Uparrow {} {}$ & $\QOVERD\downarrow \downarrow {} {}$ & $%
\QOVERD\Downarrow \Downarrow {} {}$ & $\QOVERD\rceil \lceil {} {}$ & $%
\QOVERD\rfloor \lfloor {} {}$ & $\QOVERD\rangle \langle {} {}$ & $\QOVERD\}
\{ {} {}$ & $\QOVERD] [ {} {}$ & $\QOVERD) ( {} {}$ &  \\ \hline
\end{tabular}
\vspace{1.0114pc}

\subsection{Decorations}

The following is a list of decorations from the \textsc{Insert, Decorations}%
... menu selection.

$
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline
$\overline{\frac{1}{1+a^{2}}}$ & $\underleftarrow{\frac{1}{1+d^{2}}}$ & $%
\overleftrightarrow{\frac{1}{1+g^{2}}}$ & $\underbrace{\frac{1}{1+j^{2}}}$ & 
$\widetilde{\frac{1}{1+m^{2}}}$ & $\underline{\frac{1}{1+b^{2}}}$ & $%
\overrightarrow{\frac{1}{1+e^{2}}}$ \\ \hline
$\frac{1}{1+h^{2}}$ & $\widehat{\frac{1}{1+k^{2}}}$ & $\frame{$\frac{1}{%
1+n^{2}}$}$ & $\overleftarrow{\frac{1}{1+c^{2}}}$ & $\underrightarrow{\frac{1%
}{1+f^{2}}}$ & $\overbrace{\frac{1}{1+i^{2}}}$ & $\fbox{$\frac{1}{1+l^{2}}$}$
\\ \hline
\end{tabular}
$\vspace{1.0114pc}

\subsection{The Symbols}

Here are the symbols on the panels.

\subsubsection{Lowercase Greek}

\begin{tabular}{llll}
$\alpha $ & $\beta $ & $\gamma $ & $\delta $ \\ 
$\epsilon $ & $\varepsilon $ & $\zeta $ & $\eta $ \\ 
$\theta $ & $\vartheta $ & $\iota $ & $\kappa $ \\ 
$\lambda $ & $\mu $ & $\nu $ & $\xi $ \\ 
$\pi $ & $\varpi $ & $\rho $ & $\sigma $ \\ 
$\varsigma $ & $\tau $ & $\upsilon $ & $\phi $ \\ 
$\varphi $ & $\chi $ & $\psi $ & $\omega $ \\ 
$\varkappa $ & $\varrho $ &  & 
\end{tabular}

\subsubsection{Uppercase Greek}

\begin{tabular}{ll}
$\Gamma $ & $\Delta $ \\ 
$\Theta $ & $\Lambda $ \\ 
$\Xi $ & $\Pi $ \\ 
$\Sigma $ & $\Upsilon $ \\ 
$\Phi $ & $\Psi $ \\ 
$\Omega $ & $\digamma $%
\end{tabular}

\subsubsection{Binary Operations}

\begin{tabular}{lllll}
$\pm $ & $\mp $ & $\setminus $ & $\cdot $ & $\times $ \\ 
{*} & $\star $ & $\diamond $ & $\circ $ & $\bullet $ \\ 
$\div $ & $\lhd $ & $\vee $ & $\wedge $ & $\oplus $ \\ 
$\ominus $ & $\otimes $ & $\oslash $ & $\cap $ & $\cup $ \\ 
$\uplus $ & $\sqcap $ & $\sqcup $ & $\triangleleft $ & $\triangleright $ \\ 
$\wr $ & $\bigcirc $ & $\bigtriangleup $ & $\bigtriangledown $ & $\rhd $ \\ 
$\odot $ & $\dagger $ & $\ddagger $ & $\amalg $ & $\unlhd $ \\ 
$\unrhd $ & $\boxdot $ & $\boxplus $ & $\boxtimes $ & $\boxminus $ \\ 
$\veebar $ & $\barwedge $ & $\doublebarwedge $ & $\Cup $ & $\Cap $ \\ 
$\curlywedge $ & $\curlyvee $ & $\leftthreetimes $ & $\rightthreetimes $ & $%
\dotplus $ \\ 
$\intercal $ & $\circledcirc $ & $\circledast $ & $\circleddash $ & $%
\divideontimes $%
\end{tabular}

\subsubsection{Binary Relations}

\begin{tabular}{lllllll}
$\leq $ & $\prec $ & $\preceq $ & $\ll $ & $\subset $ & $\subseteq $ & $%
\sqsubset $ \\ 
$\sqsubseteq $ & $\in $ & $\vdash $ & $\smile $ & $\frown $ & $\equiv $ & $%
\sim $ \\ 
$\simeq $ & $\asymp $ & $\approx $ & $\geq $ & $\succ $ & $\succeq $ & $\gg $
\\ 
$\supset $ & $\supseteq $ & $\sqsupset $ & $\sqsupseteq $ & $\ni $ & $\dashv 
$ & $\mid $ \\ 
$\parallel $ & $\perp $ & $\cong $ & $\bowtie $ & $\propto $ & $\models $ & $%
\doteq $ \\ 
$\Join $ & $\Vdash $ & $\Vvdash $ & $\vDash $ & $\circeq $ & $\succsim $ & $%
\gtrsim $ \\ 
$\gtrapprox $ & $\therefore $ & $\because $ & $\doteqdot $ & $\triangleq $ & 
$\preccurlyeq $ & $\lesssim $ \\ 
$\lessapprox $ & $\eqslantless $ & $\eqslantgtr $ & $\curlyeqprec $ & $%
\curlyeqsucc $ & $\preccurlyeq $ & $\leqq $ \\ 
$\leqslant $ & $\lessgtr $ & $\risingdotseq $ & $\fallingdotseq $ & $%
\succcurlyeq $ & $\geqq $ & $\geqslant $ \\ 
$\gtrless $ & $\vartriangleright $ & $\vartriangleleft $ & $\trianglerighteq 
$ & $\trianglelefteq $ & $\bigstar $ & $\between $ \\ 
$\blacktriangledown $ & $\blacktriangleright $ & $\blacktriangleleft $ & $%
\vartriangle $ & $\eqcirc $ & $\lesseqgtr $ & $\gtreqless $ \\ 
$\lesseqqgtr $ & $\gtreqqless $ & $\varpropto $ & $\smallsmile $ & $%
\smallfrown $ & $\Subset $ & $\Supset $ \\ 
$\subseteqq $ & $\supseteqq $ & $\bumpeq $ & $\Bumpeq $ & $\lll $ & $\ggg $
& $\pitchfork $ \\ 
$\backsim $ & $\backsimeq $ & $\eqsim $ & $\lessdot $ & $\gtrdot $ & $%
\shortmid $ & $\shortparallel $ \\ 
$\thicksim $ & $\thickapprox $ & $\approxeq $ & $\succapprox $ & $%
\precapprox $ &  & 
\end{tabular}

\subsubsection{Negated Relations}

\begin{tabular}{lllll}
$\neq $ & $\notin $ & $\lvertneqq $ & $\gvertneqq $ & $\nleq $ \\ 
$\ngeq $ & $\nless $ & $\ngtr $ & $\nprec $ & $\nsucc $ \\ 
$\lneqq $ & $\gneqq $ & $\nleqslant $ & $\ngeqslant $ & $\lneq $ \\ 
$\gneq $ & $\npreceq $ & $\nsucceq $ & $\precnsim $ & $\succnsim $ \\ 
$\lnsim $ & $\gnsim $ & $\nleqq $ & $\ngeqq $ & $\precneqq $ \\ 
$\succneqq $ & $\precnapprox $ & $\succnapprox $ & $\lnapprox $ & $\gnapprox 
$ \\ 
$\nsim $ & $\ncong $ & $\varsubsetneq $ & $\varsupsetneq $ & $\nsubseteqq $
\\ 
$\nsupseteqq $ & $\subsetneqq $ & $\supsetneqq $ & $\varsubsetneqq $ & $%
\varsupsetneqq $ \\ 
$\subsetneq $ & $\supsetneq $ & $\nsubseteq $ & $\nsupseteq $ & $\nparallel $
\\ 
$\nmid $ & $\nshortmid $ & $\nshortparallel $ & $\nvdash $ & $\nVdash $ \\ 
$\nvDash $ & $\nVDash $ & $\ntrianglerighteq $ & $\ntrianglelefteq $ & $%
\ntriangleright $ \\ 
$\ntriangleleft $ & $\nleftarrow $ & $\nrightarrow $ & $\nLeftarrow $ & $%
\nRightarrow $ \\ 
$\nLeftrightarrow $ & $\nleftrightarrow $ & $\nexists $ &  & 
\end{tabular}

\subsubsection{Arrows}

\begin{tabular}{lllll}
$\leftarrow $ & $\Leftarrow $ & $\rightarrow $ & $\Rightarrow $ & $%
\leftrightarrow $ \\ 
$\Leftrightarrow $ & $\mapsto $ & $\hookleftarrow $ & $\leftharpoonup $ & $%
\leftharpoondown $ \\ 
$\rightleftharpoons $ & $\uparrow $ & $\Uparrow $ & $\downarrow $ & $%
\Downarrow $ \\ 
$\updownarrow $ & $\longleftarrow $ & $\Longleftarrow $ & $\longrightarrow $
& $\Longrightarrow $ \\ 
$\longleftrightarrow $ & $\Longleftrightarrow $ & $\longmapsto $ & $%
\hookrightarrow $ & $\rightharpoonup $ \\ 
$\rightharpoondown $ & $\rightsquigarrow $ & $\Updownarrow $ & $\nearrow $ & 
$\searrow $ \\ 
$\swarrow $ & $\nwarrow $ & $\circlearrowright $ & $\circlearrowleft $ & $%
\rightleftharpoons $ \\ 
$\leftrightharpoons $ & $\twoheadrightarrow $ & $\twoheadleftarrow $ & $%
\leftleftarrows $ & $\rightrightarrows $ \\ 
$\upuparrows $ & $\downdownarrows $ & $\upharpoonright $ & $%
\downharpoonright $ & $\upharpoonleft $ \\ 
$\downharpoonleft $ & $\rightarrowtail $ & $\leftarrowtail $ & $%
\leftrightarrows $ & $\rightleftarrows $ \\ 
$\Lsh $ & $\Rsh $ & $\rightsquigarrow $ & $\leftrightsquigarrow $ & $%
\looparrowleft $ \\ 
$\looparrowright $ & $\multimap $ & $\Rrightarrow $ & $\Lleftarrow $ & $%
\curvearrowleft $ \\ 
$\curvearrowright $ & $\dashrightarrow $ & $\dashleftarrow $ &  & 
\end{tabular}

\subsubsection{Miscellaneous}

\begin{tabular}{lllll}
\ldots & $\cdots $ & $\vdots $ & $\ddots $ & $\smallint $ \\ 
$\aleph $ & $\hbar $ & \i & \j & $\ell $ \\ 
$\wp $ & $\Re $ & $\Im $ & $\partial $ & $\infty $ \\ 
$\Box $ & $\forall $ & $\exists $ & $\flat $ & $\natural $ \\ 
$\mho $ & ' & $\emptyset $ & $\nabla $ & $\surd $ \\ 
$\top $ & $\bot $ & $\Vert $ & $\angle $ & $\triangle $ \\ 
$\Diamond $ & $\sharp $ & $\clubsuit $ & $\diamondsuit $ & $\heartsuit $ \\ 
$\spadesuit $ & $\square $ & $\blacksquare $ & $\blacklozenge $ & \backprime
\\ 
$\blacktriangle $ & $\triangledown $ & $\measuredangle $ & $\sphericalangle $
& $\circledS $ \\ 
$\complement $ & $\varnothing $ & $\beth $ & $\gimel $ & $\daleth $ \\ 
$\hslash $ & $\diagup $ & $\diagdown $ & $\Finv $ & $\Game $ \\ 
$\Bbbk $ & $\backepsilon $ & $\checkmark $ & $\maltese $ & 
\end{tabular}

\subsubsection{Delimiters}

\begin{tabular}{ll}
$\lfloor $ & $\rfloor $ \\ 
$\lceil $ & $\rceil $ \\ 
$\langle $ & $\rangle $ \\ 
$\ulcorner $ & $\llcorner $ \\ 
$\urcorner $ & $\lrcorner $%
\end{tabular}

\subsubsection{ASCII}

\begin{tabular}{|l|l|l|l|l|l|}
\hline
& 0 & @ & P & ` & p \\ \hline
! & 1 & A & Q & a & q \\ \hline
'' & 2 & B & R & b & r \\ \hline
\# & 3 & C & S & c & s \\ \hline
\$ & 4 & D & T & d & t \\ \hline
\% & 5 & E & U & e & u \\ \hline
\& & 6 & F & V & f & v \\ \hline
' & 7 & G & W & g & w \\ \hline
( & 8 & H & X & h & x \\ \hline
) & 9 & I & Y & i & y \\ \hline
$\ast $ & : & J & Z & j & z \\ \hline
+ & ; & K & [ & k & \{ \\ \hline
, & \TEXTsymbol{<} & L & \TEXTsymbol{\backslash} & l & \TEXTsymbol{\vert} \\ 
\hline
- & = & M & ] & m & \} \\ \hline
. & \TEXTsymbol{>} & N & \symbol{94} & n & \symbol{126} \\ \hline
/ & ? & O & \_ & o &  \\ \hline
\end{tabular}

\subsubsection{Latin1}

\begin{tabular}{|l|l|l|l|l|l|}
\hline
~ & ${{}^{\circ }}$ & \`{A} & \DH & \`{a} & \dh \\ \hline
\textexclamdown & $\pm $ & \'{A} & \~{N} & \'{a} & \~{n} \\ \hline
\cents & ${{}^2}$ & \^{A} & \`{O} & \^{a} & \`{o} \\ \hline
\pounds & ${{}^3}$ & \~{A} & \'{O} & \~{a} & \'{o} \\ \hline
\UNICODE{0xa4} & \'{} & \"{A} & \^{O} & \"{a} & \^{o} \\ \hline
\yen & $\mu $ & \AA & \~{O} & \aa & \~{o} \\ \hline
\TEXTsymbol{\vert} & \P & \AE & \"{O} & \ae & \"{o} \\ \hline
\S & $\cdot $ & \c{C} & $\times $ & \c{c} & $\div $ \\ \hline
\"{} & \c{} & \`{E} & \O & \`{e} & \o \\ \hline
\copyright & ${{}^1}$ & \'{E} & \`{U} & \'{e} & \`{u} \\ \hline
${{}^a}$ & ${{}^o}$ & \^{E} & \'{U} & \^{e} & \'{u} \\ \hline
\guillemotleft & \guillemotright & \"{E} & \^{U} & \"{e} & \^{u} \\ \hline
$\lnot $ & $\frac 14$ & \`{I} & \"{U} & \`{i} & \"{u} \\ \hline
-- & $\frac 12$ & \'{I} & \'{Y} & \'{i} & \'{y} \\ \hline
\registered & $\frac 34$ & \^{I} & \TH & \^{i} & \th \\ \hline
\={} & \textquestiondown & \"{I} & \ss & \"{i} & \"{y} \\ \hline
\end{tabular}

\subsubsection{European Latin}

\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline
\={A} & \DH & \.{G} & \.{I} & \UNICODE{0x140} & \H{O} & \v{S} & \H{U} \\ 
\hline
\={a} & \dj & \.{g} & \i & \L & \H{o} & \v{s} & \H{u} \\ \hline
\u{A} & \={E} & \c{G} & \UNICODE{0x132} & \l & \OE & \c{T} & \k{U} \\ \hline
\u{a} & \={e} & \'{g} & \UNICODE{0x133} & \'{N} & \oe & \c{t} & \k{u} \\ 
\hline
\k{A} & \v{E} & \^{H} & \^{J} & \'{n} & \'{R} & \v{T} & \^{W} \\ \hline
\k{a} & \u{e} & \^{h} & \^{j} & \c{N} & \'{r} & \v{t} & \^{w} \\ \hline
\'{C} & \.{E} & \UNICODE{0x126} & \c{K} & \c{n} & \c{R} & \UNICODE{0x166} & 
\^{Y} \\ \hline
\'{c} & \.{e} & \UNICODE{0x127} & \c{k} & \v{N} & \c{r} & \UNICODE{0x167} & 
\^{y} \\ \hline
\^{C} & \k{E} & \~{I} & \UNICODE{0x138} & \v{n} & \v{R} & \~{U} & \"{Y} \\ 
\hline
\^{c} & \k{e} & \~{\i} & \'{L} & \UNICODE{0x149} & \v{r} & \~{u} & \'{Z} \\ 
\hline
\.{C} & \v{E} & \={I} & \'{l} & \NG & \'{S} & \={U} & \'{z} \\ \hline
\.{c} & \v{e} & \={\i} & \c{L} & \ng & \'{s} & \={u} & \.{Z} \\ \hline
\v{C} & \^{G} & \u{I} & \c{l} & \={O} & \^{S} & \u{U} & \.{z} \\ \hline
\v{c} & \^{g} & \u{\i} & \v{L} & \={o} & \^{s} & \u{u} & \v{Z} \\ \hline
\v{D} & \u{G} & \k{I} & \v{l} & \u{O} & \c{S} & \r{U} & \v{z} \\ \hline
\v{d} & \u{g} & \k{i} & \UNICODE{0x13f} & \u{o} & \c{s} & \r{u} &  \\ \hline
\end{tabular}

\subsubsection{Bold Greek Letters}

Here are uppercase and lowercase greek letters, normal and bold, together
with nabla, in a variety of positions:

\[
x+\gamma +\mathbf{\alpha }+\mathbf{\Gamma }(\lambda )\Psi ^{\mathbf{\beta }%
^\delta }+\nabla (\mathbf{\kappa }_{\nu ^{\mathbf{\mu }}}\mathbf{)}+\mathbf{%
\nabla } 
\]

Here is a more comprehensive listing:

$
\begin{array}{ccccccc}
\alpha ^{\alpha ^\alpha }\mathbf{\alpha }^{\mathbf{\alpha }^{\mathbf{\alpha }%
}} & \beta ^{\beta ^\beta }\mathbf{\beta }^{\mathbf{\beta }^{\mathbf{\beta }%
}} & \gamma ^{\gamma ^\gamma }\mathbf{\gamma }^{\mathbf{\gamma }^{\mathbf{%
\gamma }}} & \delta ^{\delta ^\delta }\mathbf{\delta }^{\mathbf{\delta }^{%
\mathbf{\delta }}} & \epsilon ^{\epsilon ^\epsilon }\mathbf{\epsilon }^{%
\mathbf{\epsilon }^{\mathbf{\epsilon }}} & \varepsilon ^{\varepsilon
^\varepsilon }\mathbf{\varepsilon }^{\mathbf{\varepsilon }^{\mathbf{%
\varepsilon }}} & \zeta ^{\zeta ^\zeta }\mathbf{\zeta }^{\mathbf{\zeta }^{%
\mathbf{\zeta }}} \\ 
\eta ^{\eta ^\eta }\mathbf{\eta }^{\mathbf{\eta }^{\mathbf{\eta }}} & \theta
^{\theta ^\theta }\mathbf{\theta }^{\mathbf{\theta }^{\mathbf{\theta }}} & 
\vartheta ^{\vartheta ^\vartheta }\mathbf{\vartheta }^{\mathbf{\vartheta }^{%
\mathbf{\vartheta }}} & \iota ^{\iota ^\iota }\mathbf{\iota }^{\mathbf{\iota 
}^{\mathbf{\iota }}} & \kappa ^{\kappa ^\kappa }\mathbf{\kappa }^{\mathbf{%
\kappa }^{\mathbf{\kappa }}} & \lambda ^{\lambda ^\lambda }\mathbf{\lambda }%
^{\mathbf{\lambda }^{\mathbf{\lambda }}} & \mu ^{\mu ^\mu }\mathbf{\mu }^{%
\mathbf{\mu }^{\mathbf{\mu }}}
\end{array}
$

Here are superscript greek letters, normal and bold, following normal and
bold numbers:

$
\begin{array}{ccccccc}
1^{\alpha ^{\alpha }}1\mathbf{\alpha }^{\mathbf{\alpha }^{\mathbf{\alpha }}}
& 1^{\beta ^{\beta }}\mathbf{1}^{\mathbf{\beta }^{\mathbf{\beta }}} & 
1^{\gamma ^{\gamma }}\mathbf{1}^{\mathbf{\gamma }^{\mathbf{\gamma }}} & 
1^{\delta ^{\delta }}\mathbf{1}^{\mathbf{\delta }^{\mathbf{\delta }}} & 
1^{\epsilon ^{\epsilon }}\mathbf{1}^{\mathbf{\epsilon }^{\mathbf{\epsilon }}}
& 1^{\varepsilon ^{\varepsilon }}\mathbf{1}^{\mathbf{\varepsilon }^{\mathbf{%
\varepsilon }}} & 1^{\zeta ^{\zeta }}\mathbf{1}^{\mathbf{\zeta }^{\mathbf{%
\zeta }}} \\ 
1^{\eta ^{\eta }}\mathbf{1}^{\mathbf{\eta }^{\mathbf{\eta }}} & 1^{\theta
^{\theta }}\mathbf{1}^{\mathbf{\theta }^{\mathbf{\theta }}} & 1^{\vartheta
^{\vartheta }}\mathbf{1}^{\mathbf{\vartheta }^{\mathbf{\vartheta }}} & 
1^{\iota ^{\iota }}\mathbf{1}^{\mathbf{\iota }^{\mathbf{\iota }}} & 
1^{\kappa ^{\kappa }}\mathbf{1}^{\mathbf{\kappa }^{\mathbf{\kappa }}} & 
1^{\lambda ^{\lambda }}\mathbf{1}^{\mathbf{\lambda }^{\mathbf{\lambda }}} & 
1^{\mu ^{\mu }}\mathbf{1}^{\mathbf{\mu }^{\mathbf{\mu }}}
\end{array}
$

Here are subscript greek letters, normal and bold, following normal and bold
numbers:

$
\begin{array}{ccccccc}
1_{\alpha _{\alpha }}\mathbf{1}_{\mathbf{\alpha }_{\mathbf{\alpha }}} & 
1_{\beta _{\beta }}\mathbf{1}_{\mathbf{\beta }_{\mathbf{\beta }}} & 
1_{\gamma _{\gamma }}\mathbf{1}_{\mathbf{\gamma }_{\mathbf{\gamma }}} & 
1_{\delta _{\delta }}\mathbf{1}_{\mathbf{\delta }_{\mathbf{\delta }}} & 
1_{\epsilon _{\epsilon }}\mathbf{1}_{\mathbf{\epsilon }_{\epsilon }} & 
1_{\varepsilon _{\varepsilon }}\mathbf{1}_{\mathbf{\varepsilon }_{\mathbf{%
\varepsilon }}} & 1_{\zeta _{\zeta }}\mathbf{1}_{\mathbf{\zeta }_{\mathbf{%
\zeta }}} \\ 
1_{\eta _{\eta }}\mathbf{1}_{\mathbf{\eta }_{\mathbf{\eta }}} & 1_{\theta
_{\theta }}\mathbf{1}_{\mathbf{\theta }_{\mathbf{\theta }}} & 1_{\vartheta
_{\vartheta }}\mathbf{1}_{\mathbf{\vartheta }_{\mathbf{\vartheta }}} & 
1_{\delta _{\delta }}1_{\mathbf{\delta }_{\mathbf{\delta }}} & 1_{\kappa
_{\kappa }}\mathbf{1}_{\mathbf{\kappa }_{\mathbf{\kappa }}} & 1_{\lambda
_{\lambda }}\mathbf{1}_{\mathbf{\lambda }_{\mathbf{\lambda }}} & 1_{\mu
_{\mu }}\mathbf{1}_{\mathbf{\mu }_{\mathbf{\mu }}}
\end{array}
$

\subsection{Preformatted}

Use the Preformatted tag for computer code:
\begin{verbatim}
\long\def\@caption#1[#2]#3{%
  \par
   %\edef\@tempa{\csname #1TOCLabel\endcsname}
   \AddContentsLine
   {\csname ext@#1\endcsname}%
   {#1@toc}%
   {\csname #1toclabel\endcsname}%
   {\ignorespaces #2}%
   \begingroup
     \@parboxrestore
     \normalsize
     \csname @makecaption#1\endcsname{\ignorespaces #3}\par
   \endgroup}
\end{verbatim}

\subsection{Tables and Arrays}

\subsubsection{Tables}

There are many different tables that you can create with the table editor.
Some are included here to test

\begin{center}
\begin{tabular}{|lrrrrrr|}
\hline
&  &  &  &  &  & \% Change \\ 
Ethnicity & 1986 & 1987 & 1988 & 1989 & 1990 & 1986-1990 \\ \hline
Amer. Indian & 294 & 277 & 298 & 328 & 361 & 23.0\% \\ 
Black & 192 & 206 & 199 & 183 & 225 & 17.0\% \\ 
Hispanic & 3,108 & 3,131 & 3,433 & 3,637 & 4,038 & 30.0\% \\ 
Oriental & 67 & 65 & 71 & 77 & 96 & 30.0\% \\ 
Other & 10,057 & 10,324 & 10,283 & 10,075 & 10,089 & 0.3\% \\ \hline
\end{tabular}

\begin{tabular}{|l|rrrrr|}
\hline
Course & 1987 & 1988 & 1989 & 1990 & 1991 \\ \hline
MATH 280 & 68 & 61 & 58 & 61 & 84 \\ \hline
MATH 480 & 36 & 26 & 41 & 44 & 53 \\ \hline
\end{tabular}
\end{center}

\subsection{From the \LaTeX{} User's Guide and Reference Manual}

\begin{center}
\begin{tabular}{||l|lr||}
\hline
gnats & gram & \$13.65 \\ \cline{2-3}
& each & .01 \\ \hline
gnu & stuffed & 92.50 \\ \cline{1-1}\cline{3-3}
emur &  & 33.33 \\ \hline
armadillo & frozen & 8.99 \\ \hline
\end{tabular}

\begin{tabular}{|l|l|r|}
\hline\hline
\emph{type} & \multicolumn{2}{c|}{\emph{style}} \\ \hline
smart & red & short \\ 
rather silly & puce & tall \\ \hline\hline
\end{tabular}
\end{center}

\subsection{From Jane Hahn's \LaTeX{} for Everyone}

\begin{center}
\begin{tabular}{|l|r|c|r|}
\hline
\multicolumn{4}{|c|}{\textbf{Overall Heading of Table}} \\ \hline
\multicolumn{1}{|c|}{Left-justified} & \multicolumn{1}{c|}{Right-justified}
& Centered & \multicolumn{1}{|c|}{Right-justified} \\ \hline\hline
one & two & three & four \\ \cline{2-4}
1 & 2 & 3 & 4 \\ 
i & ii & iii & iv \\ \hline
\end{tabular}

\begin{tabular}{|l|r@{.}l|}
\hline
\multicolumn{3}{|c|}{\textbf{Household Budget}} \\ \hline\hline
& \multicolumn{2}{c|}{\textbf{\% of}} \\ 
\textbf{Item} & \multicolumn{2}{c|}{\textbf{Budget}} \\ \hline
Housing & 50 & 0 \\ 
Food & 25 & 0 \\ 
Toys & 10 & 5 \\ 
Pet Supplies & 7 & 5 \\ 
Clothes & 5 & 25 \\ 
Charity & 1 & 75 \\ \hline
\end{tabular}

\begin{tabular}{|l|cr|}
\hline
\multicolumn{3}{|c|}{\textbf{PORTABLE HOOK-ON CHAIRS}} \\ \hline\hline
\textbf{BRAND} & \textbf{Graco} & \textbf{Strolee} \\ \hline
\textbf{MODEL} & Tot Loc Chair & Meal Mate \\ \hline
\textbf{PRICE} & \$23 & \$32 \\ \hline
\textbf{OVERALL JUDGEMENT} & Satisfactory & Satisfactory \\ \hline
\textbf{WEIGHT} & 7 lb. 9 oz. & 6 lb. 8 oz. \\ \hline
\end{tabular}

\begin{tabular}{|ll|}
\hline
\multicolumn{2}{|c|}{\textbf{THE CATECHISM}} \\ \hline
Q. & What are we by nature? \\ 
A. & We are part of God's creation, made in the image of God. \\[3mm] 
Q. & What does it mean to be created in the image of God? \\ 
A. & It means that we are free to make choices: to love; to create, to
reason, and to live in harmony with creation and with God. \\[3mm] 
Q. & Why then do we live apart from God and out of harmony with creation? \\ 
A. & From the beginning, human beings have misused their freedom and made
wrong choices. \\ \hline
\end{tabular}
\end{center}

\subsection{The Economist}

Here is a table that is too wide for the page:

\begin{center}
\begin{tabular}{llllcllcl}
&  &  &  & \multicolumn{5}{c}{\textbf{\% change on}} \\ \cline{5-9}
&  & \multicolumn{2}{c}{\textbf{1993/94}} & \textbf{one} & \textbf{one} & 
\textbf{record} & \multicolumn{2}{c}{\textbf{Dec 31st 1992}} \\ \cline{3-4}
& \textbf{Feb 22nd} & \textbf{high} & \textbf{low} & \textbf{week} & \textbf{%
year} & \textbf{high} & \textbf{in local} & \textbf{in \$} \\ 
&  &  &  & \multicolumn{1}{l}{} &  &  & \textbf{currency} & \textbf{terms}
\\ \hline
\textbf{Australia} & \multicolumn{1}{r}{2,202.5} & \multicolumn{1}{r}{2,340.6
} & \multicolumn{1}{r}{1,495.0} & \multicolumn{1}{l}{$-$ 1.4} & $+$ 36.9 & $%
- $ 5.9 & \multicolumn{1}{l}{$+$42.1} & $+$48.6 \\ \hline
\textbf{Austria} & \multicolumn{1}{r}{450.7} & \multicolumn{1}{r}{460.7} & 
\multicolumn{1}{r}{300.3} & \multicolumn{1}{l}{$+$ 0.1} & $+$ 29.8 & $-$35.9
& \multicolumn{1}{l}{$+$44.0} & $+$35.0 \\ \hline
\textbf{Belgium} & \multicolumn{1}{r}{1,504.5} & \multicolumn{1}{r}{1,542.7}
& \multicolumn{1}{r}{1,125.5} & \multicolumn{1}{l}{$-$ 1.2} & $+$ 24.3 & $-$
2.5 & \multicolumn{1}{l}{$+$33.5} & $+$24.8 \\ \hline
\textbf{Britain} & \multicolumn{1}{r}{3,333.7} & \multicolumn{1}{r}{3,520.3}
& \multicolumn{1}{r}{2,737.6} & \multicolumn{1}{l}{$-$ 1.8} & $+$ 18.3 & $-$
5.3 & \multicolumn{1}{l}{$+$17.1} & $+$14.4 \\ \hline
\textbf{Canada} & \multicolumn{1}{r}{4,371.1} & \multicolumn{1}{r}{4,591.3}
& \multicolumn{1}{r}{3,275.8} & \multicolumn{1}{l}{$-$ 1.0} & $+$ 26.6 & $-$
4.8 & \multicolumn{1}{l}{$+$30.5} & $+$23.5 \\ \hline
\textbf{Denmark} & \multicolumn{1}{r}{407.4} & \multicolumn{1}{r}{415.8} & 
\multicolumn{1}{r}{261.9} & \multicolumn{1}{l}{$+$ 0.3} & $+$ 44.4 & $-$ 2.0
& \multicolumn{1}{l}{$+$55.7} & $+$45.0 \\ \hline
\textbf{France *} & \multicolumn{1}{r}{1,506.6} & \multicolumn{1}{r}{1,585.2}
& \multicolumn{1}{r}{1,114.2} & \multicolumn{1}{l}{$-$ 1.0} & $+$ 23.1 & $-$
5.0 & \multicolumn{1}{l}{$+$32.1} & $+$24.4 \\ \hline
\textbf{Germany} & \multicolumn{1}{r}{2,107.6} & \multicolumn{1}{r}{2,268.0}
& \multicolumn{1}{r}{1,516.5} & \multicolumn{1}{l}{$-$ 0.4} & $+$ 26.8 & $-$
7.1 & \multicolumn{1}{l}{$+$36.4} & $+$27.9 \\ \hline
\textbf{Holland} & \multicolumn{1}{r}{285.6} & \multicolumn{1}{r}{294.8} & 
\multicolumn{1}{r}{198.6} & \multicolumn{1}{l}{$-$ 1.4} & $+$ 35.7 & $-$ 3.1
& \multicolumn{1}{l}{$+$44.2} & $+$35.4 \\ \hline
\textbf{Italy} & \multicolumn{1}{r}{672.2} & \multicolumn{1}{r}{689.0} & 
\multicolumn{1}{r}{446.3} & \multicolumn{1}{l}{$-$ 0.6} & $+$ 33.7 & $-$26.0
& \multicolumn{1}{l}{$+$50.6} & $+$32.0 \\ \hline
\textbf{Japan} & \multicolumn{1}{r}{19,342.6} & \multicolumn{1}{r}{21,148.1}
& \multicolumn{1}{r}{16,078.7} & \multicolumn{1}{l}{$+$ 1.9} & $+$ 14.7 & $-$%
50.3 & \multicolumn{1}{l}{$+$14.3} & $+$35.3 \\ \hline
\textbf{Spain} & \multicolumn{1}{r}{339.6} & \multicolumn{1}{r}{358.3} & 
\multicolumn{1}{r}{215.6} & \multicolumn{1}{l}{$-$ 2.0} & $+$ 49.0 & $-$ 5.2
& \multicolumn{1}{l}{$+$58.5} & $+$29.2 \\ \hline
\textbf{Sweden} & \multicolumn{1}{r}{1,565.8} & \multicolumn{1}{r}{1,603.9}
& \multicolumn{1}{r}{879.1} & \multicolumn{1}{l}{$+$ 2.1} & $+$ 58.5 & $-$
2.4 & \multicolumn{1}{l}{$+$71.6} & $+$53.0 \\ \hline
\textbf{Switzerland} & \multicolumn{1}{r}{2,982.8} & \multicolumn{1}{r}{
3,178.4} & \multicolumn{1}{r}{2,049.5} & \multicolumn{1}{l}{$-$ 0.3} & $+$
45.5 & $-$ 6.2 & \multicolumn{1}{l}{$+$41.6} & $+$43.1 \\ \hline
\textbf{United States} & \multicolumn{1}{r}{3,911.7} & \multicolumn{1}{r}{
3,978.4} & \multicolumn{1}{r}{3,242.0} & \multicolumn{1}{l}{$-$ 0.4} & $+$
17.7 & $-$ 1.7 & \multicolumn{1}{l}{$+$18.5} & $+$18.5 \\ \hline
\textbf{World }$\dagger $ & \multicolumn{1}{r}{621.2} & \multicolumn{1}{r}{
641.0} & \multicolumn{1}{r}{488.6} & \multicolumn{1}{l}{$-$ 0.7} & $+$ 23.1
& $-$ 3.1 & \multicolumn{1}{l}{$+$25.0} & $+$25.0 \\ \hline
\end{tabular}
\end{center}

Here is a displayed graphic.\FRAME{dhFU}{2.3298in}{1.5489in}{0pt}{\Qcb{%
Triangle}}{\Qlb{triangle}}{triangle.wmf}{\special{language "Scientific
Word";type "GRAPHIC";maintain-aspect-ratio TRUE;display "FULL";valid_file
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In-line graphic in a centered paragraph.

\begin{center}
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\subsubsection{References}

\begin{enumerate}
\item  D. Black, \emph{The Theory of Committees and Elections}, Cambridge:
Cambridge University Press (1958).

\item  C. Blyth, \emph{Some probability paradoxes in choice from among
random alternatives}, J. Amer. Statist. Assoc. \textbf{67} (1972), 366--373.

\item  Chang Li-chien, \emph{On the maximin probability of cyclic random
inequalities}, Scientia Sinica \textbf{10} (1961), 499--504.

\item  Marquis de Condorcet, \emph{Essai sur l'application de l'analyse \`{a}
la probabilit\'{e} des d\'{e}cisions rendues \`{a} la pluralit\'{e} des voix}%
, Paris (1785).

\item  N. Dunford and J. Schwartz, \emph{Functional Analysis}, v. 2, John
Wiley and Sons, New York, 1963.

\item  W. W. Funkenbusch, \emph{A gaming wheel based on cyclic advantage in
symbol choice}, The Gambling Papers, Vol. XIII (1982), 68--83 University of
Nevada, Reno.

\item  M. Gardner, \emph{The paradox of the nontransitive dice and the
elusive principle of indifference}, Scientific American \textbf{223} (1970),
110--114.

\item  M. Gardner, \emph{On the paradoxical situations that arise from
nontransitive relations}, Scientific American \textbf{231} (1974), 120--125.

\item  W. W. Funkenbusch and Saari, D. G., \emph{Preferences among
preferences or nested cyclic stochastic inequalities}, Congr. Numer. \textbf{%
39} (1983), 419--432.

\item  M. Struwe, \emph{Semilinear wave equations}, Bull. Amer. Math. Soc. 
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\item  W.P. Thurston, \emph{Geometry and topology of three manifolds},
Lecture notes, Princeton Univ., NJ, 1979.
\end{enumerate}

\end{document}
