summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/doc/latex/jamtimes/mathsample.tex
diff options
context:
space:
mode:
Diffstat (limited to 'Master/texmf-dist/doc/latex/jamtimes/mathsample.tex')
-rw-r--r--Master/texmf-dist/doc/latex/jamtimes/mathsample.tex953
1 files changed, 0 insertions, 953 deletions
diff --git a/Master/texmf-dist/doc/latex/jamtimes/mathsample.tex b/Master/texmf-dist/doc/latex/jamtimes/mathsample.tex
deleted file mode 100644
index 2c63fae0a12..00000000000
--- a/Master/texmf-dist/doc/latex/jamtimes/mathsample.tex
+++ /dev/null
@@ -1,953 +0,0 @@
-\documentclass{article}
-\usepackage{ifpdf}
-\ifpdf\pdfmapfile{+jtm.map}\fi
-%\usepackage[T1]{fontenc}
-\usepackage{jamtimes}
-\usepackage{lipsum,textcomp,amsmath,url,amsfonts,longtable}
-\DeclareMathSymbol{\dit}{\mathord}{letters}{`d}
-\DeclareMathSymbol{\dup}{\mathord}{operators}{`d}
-\def\test#1{#1}
-
-\def\testnums{%
- \test 0 \test 1 \test 2 \test 3 \test 4 \test 5 \test 6 \test 7
- \test 8 \test 9 }
-\def\testupperi{%
- \test A \test B \test C \test D \test E \test F \test G \test H
- \test I \test J \test K \test L \test M }
-\def\testupperii{%
- \test N \test O \test P \test Q \test R \test S \test T \test U
- \test V \test W \test X \test Y \test Z }
-\def\testupper{%
- \testupperi\testupperii}
-
-\def\testloweri{%
- \test a \test b \test c \test d \test e \test f \test g \test h
- \test i \test j \test k \test l \test m }
-\def\testlowerii{%
- \test n \test o \test p \test q \test r \test s \test t \test u
- \test v \test w \test x \test y \test z
- \test\imath \test\jmath }
-\def\testlower{%
- \testloweri\testlowerii}
-
-\def\testupgreeki{%
- \test A \test B \test\Gamma \test\Delta \test E \test Z \test H
- \test\Theta \test I \test K \test\Lambda \test M }
-\def\testupgreekii{%
- \test N \test\Xi \test O \test\Pi \test P \test\Sigma \test T
- \test\Upsilon \test\Phi \test X \test\Psi \test\Omega
-}
-\def\testupgreek{%
- \testupgreeki\testupgreekii}
-
-\def\testlowgreeki{%
- \test\alpha \test\beta \test\gamma \test\delta \test\epsilon
- \test\zeta \test\eta \test\theta \test\iota \test\kappa \test\lambda
- \test\mu }
-\def\testlowgreekii{%
- \test\nu \test\xi \test o \test\pi \test\rho \test\sigma \test\tau
- \test\upsilon \test\phi \test\chi \test\psi \test\omega }
-\def\testlowgreekiii{%
- \test\varepsilon \test\vartheta \test\varpi \test\varrho
- \test\varsigma \test\varphi \test\ell \test\wp}
-\def\testlowgreek{%
- \testlowgreeki\testlowgreekii\testlowgreekiii}
-\begin{document}
-
-\section{Sebastian's math test}
-
-
-
-The default math mode font is $Math\ Italic$. This should not be
-confused with ordinary \emph{Text Italic} -- notice the different spacing\,!
-\verb|\mathbf| produces bold roman letters: $ \mathbf{abcABC} $.
-If you wish to embolden complete formulas,
-use the \verb|\boldmath| command \emph{before} going into math mode.
-This changes the default math fonts to bold.
-
-\begin{tabular}{ll}
-\texttt{normal} & $ x = 2\pi \Rightarrow x \simeq 6.28 $\\
-\texttt{mathbf} & $\mathbf{x} = 2\pi \Rightarrow \mathbf{x} \simeq 6.28 $\\
-\texttt{boldmath} & {\boldmath $x = \mathbf{2}\pi \Rightarrow x
- \simeq{\mathbf{6.28}} $}\\
-\end{tabular}
-\smallskip
-
-Greek is available in upper and lower case:
-$\alpha,\beta \dots \Omega$, and there are special
-symbols such as $ \hbar$ (compare to $h$).
-Digits in formulas $1, 2, 3\dots$ may differ from those in text: 4, 5,
-6\dots
-
-There is Sans Serif alphabet $\mathsf{abcdeABCD}$ selected by
-\verb|\mathsf| and Typewriter math $\mathtt{abcdeABCD}$ selected by
-\verb|\mathtt|.
-
-There is a calligraphic alphabet \verb|\mathcal| for upper case letters
-$ \mathcal{ABCDE}\dots $, and there are letters for number sets: $\mathbb{A\dots Z} $,
-which are produced using \verb|\mathbb|. There are Fraktur letters
-$\mathfrak{abcdeABCDE}$ produced using \verb|\mathfrak|
-
-\begin{equation}
- \sigma(t)=\frac{1}{\sqrt{2\pi}}
- \int^t_0 e^{-x^2/2} dx
-\end{equation}
-
-\begin{equation}
- \prod_{j\geq 0}
- \left(\sum_{k\geq 0}a_{jk} z^k\right)
-= \sum_{k\geq 0} z^n
- \left( \sum_{{k_0,k_1,\ldots\geq 0}
- \atop{k_0+k_1+\ldots=n} }
- a{_0k_0}a_{1k_1}\ldots \right)
-\end{equation}
-
-\begin{equation}
-\pi(n) = \sum_{m=2}^{n}
- \left\lfloor \left(\sum_{k=1}^{m-1}
- \lfloor(m/k)/\lceil m/k\rceil
- \rfloor \right)^{-1}
- \right\rfloor
-\end{equation}
-
-\begin{equation}
-\{\underbrace{%
- \overbrace{\mathstrut a,\ldots,a}^{k\ a's},
- \overbrace{\mathstrut b,\ldots,b}^{l\ b's}}
- _{k+l\ \mathrm{elements}} \}
-\end{equation}
-
-\[
-\mbox{W}^+\
-\begin{array}{l}
-\nearrow\raise5pt\hbox{$\mu^+ + \nu_{\mu}$}\\
-\rightarrow \pi^+ +\pi^0 \\[5pt]
-\rightarrow \kappa^+ +\pi^0 \\
-\searrow\lower5pt\hbox{$\mathrm{e}^+
- +\nu_{\scriptstyle\mathrm{e}}$}
-\end{array}
-\]
-
-\[
-\frac{\pm
-\left|\begin{array}{ccc}
-x_1-x_2 & y_1-y_2 & z_1-z_2 \\
-l_1 & m_1 & n_1 \\
-l_2 & m_2 & n_2
-\end{array}\right|}{
-\sqrt{\left|\begin{array}{cc}l_1&m_1\\
-l_2&m_2\end{array}\right|^2
-+ \left|\begin{array}{cc}m_1&n_1\\
-n_1&l_1\end{array}\right|^2
-+ \left|\begin{array}{cc}m_2&n_2\\
-n_2&l_2\end{array}\right|^2}}
-\]
-
-
-
-
-\section{Math Tests}
-\label{sec:mthtests}
-
-
-
-Math test are taken from\cite{Schmidt04:PSNFSS9.2}.
-
-\parindent 0pt
-%\mathindent 1em
-
-
-\subsection{Math Alphabets}
-
-Math Italic (\texttt{\string\mathnormal})
-\def\test#1{\mathnormal{#1},}
-\begin{eqnarray*}
-% && {\testnums}\\
- && {\testupper}\\
- && {\testlower}\\
- && {\testupgreek}\\
- && {\testlowgreek}
-\end{eqnarray*}%
-
-Math Roman (\texttt{\string\mathrm})
-\def\test#1{\mathrm{#1},}
-\begin{eqnarray*}
- && {\testnums}\\
- && {\testupper}\\
- && {\testlower}\\
- && {\testupgreek}\\
- && {\testlowgreek}
-\end{eqnarray*}%
-
-%Math Italic Bold
-%\def\test#1{\mathbm{#1},}
-%\begin{eqnarray*}
-% && {\testnums}\\
-% && {\testupper}\\
-% && {\testlower}\\
-% && {\testupgreek}\\
-% && {\testlowgreek}
-%\end{eqnarray*}%
-
-Math Bold (\texttt{\string\mathbf})
-\def\test#1{\mathbf{#1},}
-\begin{eqnarray*}
- && {\testnums}\\
- && {\testupper}\\
- && {\testlower}\\
-% && {\testupgreek}
-\end{eqnarray*}%
-
-Math Sans Serif (\texttt{\string\mathsf})
-\def\test#1{\mathsf{#1},}
-\begin{eqnarray*}
- && {\testnums}\\
- && {\testupper}\\
- && {\testlower}\\
-% && {\testupgreek}
-\end{eqnarray*}%
-
-
-
-Caligraphic (\texttt{\string\mathcal})
-\def\test#1{\mathcal{#1},}
-\begin{eqnarray*}
- && {\testupper}
-\end{eqnarray*}%
-
-%Script (\texttt{\string\mathscr})
-%\def\test#1{\mathscr{#1},}
-%\begin{eqnarray*}
-% && {\testupper}
-%\end{eqnarray*}%
-
-Fraktur (\texttt{\string\mathfrak})
-\def\test#1{\mathfrak{#1},}
-\begin{eqnarray*}
- && {\testupper}\\
- && {\testlower}
-\end{eqnarray*}%
-
-Blackboard Bold (\texttt{\string\mathbb})
-\def\test#1{\mathbb{#1},}
-\begin{eqnarray*}
- && {\testupper}
-\end{eqnarray*}%
-
-
-\clearpage
-\subsection{Character Sidebearings}
-
-\def\test#1{|#1|+}
-\begin{eqnarray*}
- && {\testupperi}\\
- && {\testupperii}\\
- && {\testloweri}\\
- && {\testlowerii}\\
- && {\testupgreeki}\\
- && {\testupgreekii}\\
- && {\testlowgreeki}\\
- && {\testlowgreekii}\\
- && {\testlowgreekiii}
-\end{eqnarray*}%
-%
-\def\test#1{|\mathrm{#1}|+}%
-\begin{eqnarray*}
- && {\testupperi}\\
- && {\testupperii}\\
- && {\testloweri}\\
- && {\testlowerii}\\
- && {\testupgreeki}\\
- && {\testupgreekii}
-\end{eqnarray*}%
-%
-%\def\test#1{|\mathbm{#1}|+}%
-%\begin{eqnarray*}
-% && {\testupperi}\\
-% && {\testupperii}\\
-% && {\testloweri}\\
-% && {\testlowerii}\\
-% && {\testupgreeki}\\
-% && {\testupgreekii}\\
-% && {\testlowgreeki}\\
-% && {\testlowgreekii}\\
-% && {\testlowgreekiii}
-%\end{eqnarray*}%
-%%
-%\def\test#1{|\mathbf{#1}|+}%
-%\begin{eqnarray*}
-% && {\testupperi}\\
-% && {\testupperii}\\
-% && {\testloweri}\\
-% && {\testlowerii}\\
-% && {\testupgreeki}\\
-% && {\testupgreekii}
-%\end{eqnarray*}%
-%
-\def\test#1{|\mathcal{#1}|+}%
-\begin{eqnarray*}
- && {\testupperi}\\
- && {\testupperii}
-\end{eqnarray*}%
-
-
-\clearpage
-\subsection{Superscript positioning}
-
-\def\test#1{#1^{2}+}%
-\begin{eqnarray*}
- && {\testupperi}\\
- && {\testupperii}\\
- && {\testloweri}\\
- && {\testlowerii}\\
- && {\testupgreeki}\\
- && {\testupgreekii}\\
- && {\testlowgreeki}\\
- && {\testlowgreekii}\\
- && {\testlowgreekiii}
-\end{eqnarray*}%
-%
-\def\test#1{\mathrm{#1}^{2}+}%
-\begin{eqnarray*}
- && {\testupperi}\\
- && {\testupperii}\\
- && {\testloweri}\\
- && {\testlowerii}\\
- && {\testupgreeki}\\
- && {\testupgreekii}
-\end{eqnarray*}%
-%
-%\def\test#1{\mathbm{#1}^{2}+}%
-%\begin{eqnarray*}
-% && {\testupperi}\\
-% && {\testupperii}\\
-% && {\testloweri}\\
-% && {\testlowerii}\\
-% && {\testupgreeki}\\
-% && {\testupgreekii}\\
-% && {\testlowgreeki}\\
-% && {\testlowgreekii}\\
-% && {\testlowgreekiii}
-%\end{eqnarray*}%
-%
-%\def\test#1{\mathbf{#1}^{2}+}%
-%\begin{eqnarray*}
-% && {\testupperi}\\
-% && {\testupperii}\\
-% && {\testloweri}\\
-% && {\testlowerii}\\
-% && {\testupgreeki}\\
-% && {\testupgreekii}
-%\end{eqnarray*}
-%
-\def\test#1{\mathcal{#1}^{2}+}%
-\begin{eqnarray*}
- && {\testupperi}\\
- && {\testupperii}
-\end{eqnarray*}%
-
-
-\clearpage
-\subsection{Subscript positioning}
-
-\def\test#1{\mathnormal{#1}_{i}+}%
-\begin{eqnarray*}
- && {\testupperi}\\
- && {\testupperii}\\
- && {\testloweri}\\
- && {\testlowerii}\\
- && {\testupgreeki}\\
- && {\testupgreekii}\\
- && {\testlowgreeki}\\
- && {\testlowgreekii}\\
- && {\testlowgreekiii}
-\end{eqnarray*}%
-%
-\def\test#1{\mathrm{#1}_{i}+}%
-\begin{eqnarray*}
- && {\testupperi}\\
- && {\testupperii}\\
- && {\testloweri}\\
- && {\testlowerii}\\
- && {\testupgreeki}\\
- && {\testupgreekii}
-\end{eqnarray*}%
-%
-%\def\test#1{\mathbm{#1}_{i}+}%
-%\begin{eqnarray*}
-% && {\testupperi}\\
-% && {\testupperii}\\
-% && {\testloweri}\\
-% && {\testlowerii}\\
-% && {\testupgreeki}\\
-% && {\testupgreekii}\\
-% && {\testlowgreeki}\\
-% && {\testlowgreekii}\\
-% && {\testlowgreekiii}
-%\end{eqnarray*}
-%%
-%\def\test#1{\mathbf{#1}_{i}+}%
-%\begin{eqnarray*}
-% && {\testupperi}\\
-% && {\testupperii}\\
-% && {\testloweri}\\
-% && {\testlowerii}\\
-% && {\testupgreeki}\\
-% && {\testupgreekii}
-%\end{eqnarray*}%
-%
-\def\test#1{\mathcal{#1}_{i}+}%
-\begin{eqnarray*}
- && {\testupperi}\\
- && {\testupperii}
-\end{eqnarray*}%
-
-
-\clearpage
-\subsection{Accent positioning}
-
-\def\test#1{\hat{#1}+}%
-\begin{eqnarray*}
- && {\testupperi}\\
- && {\testupperii}\\
- && {\testloweri}\\
- && {\testlowerii}\\
- && {\testupgreeki}\\
- && {\testupgreekii}\\
- && {\testlowgreeki}\\
- && {\testlowgreekii}\\
- && {\testlowgreekiii}
-\end{eqnarray*}%
-%
-\def\test#1{\hat{\mathrm{#1}}+}%
-\begin{eqnarray*}
- && {\testupperi}\\
- && {\testupperii}\\
- && {\testloweri}\\
- && {\testlowerii}\\
-% && {\testupgreeki}\\
-% && {\testupgreekii}
-\end{eqnarray*}%
-%
-%\def\test#1{\hat{\mathbm{#1}}+}%
-%\begin{eqnarray*}
-% && {\testupperi}\\
-% && {\testupperii}\\
-% && {\testloweri}\\
-% && {\testlowerii}\\
-% && {\testupgreeki}\\
-% && {\testupgreekii}\\
-% && {\testlowgreeki}\\
-% && {\testlowgreekii}\\
-% && {\testlowgreekiii}
-%\end{eqnarray*}%
-%%
-%\def\test#1{\hat{\mathbf{#1}}+}%
-%\begin{eqnarray*}
-% && {\testupperi}\\
-% && {\testupperii}\\
-% && {\testloweri}\\
-% && {\testlowerii}\\
-% && {\testupgreeki}\\
-% && {\testupgreekii}
-%\end{eqnarray*}
-%
-\def\test#1{\hat{\mathcal{#1}}+}%
-\begin{eqnarray*}
- && {\testupperi}\\
- && {\testupperii}
-\end{eqnarray*}%
-
-
-\clearpage
-\subsection{Differentials}
-
-\begin{eqnarray*}
-\gdef\test#1{\dit #1+}%
- && {\testupperi}\\
- && {\testupperii}\\
- && {\testloweri}\\
- && {\testlowerii}\\
- && {\testupgreeki}\\
- && {\testupgreekii}\\
- && {\testlowgreeki}\\
- && {\testlowgreekii}\\
- && {\testlowgreekiii}\\
-\gdef\test#1{\dit \mathrm{#1}+}%
- && {\testupgreeki}\\
- && {\testupgreekii}
-\end{eqnarray*}%
-%
-\begin{eqnarray*}
-\gdef\test#1{\dup #1+}%
- && {\testupperi}\\
- && {\testupperii}\\
- && {\testloweri}\\
- && {\testlowerii}\\
- && {\testupgreeki}\\
- && {\testupgreekii}\\
- && {\testlowgreeki}\\
- && {\testlowgreekii}\\
- && {\testlowgreekiii}\\
-\gdef\test#1{\dup \mathrm{#1}+}%
- && {\testupgreeki}\\
- && {\testupgreekii}
-\end{eqnarray*}%
-%
-\begin{eqnarray*}
-\gdef\test#1{\partial #1+}%
- && {\testupperi}\\
- && {\testupperii}\\
- && {\testloweri}\\
- && {\testlowerii}\\
- && {\testupgreeki}\\
- && {\testupgreekii}\\
- && {\testlowgreeki}\\
- && {\testlowgreekii}\\
- && {\testlowgreekiii}\\
-\gdef\test#1{\partial \mathrm{#1}+}%
- && {\testupgreeki}\\
- && {\testupgreekii}
-\end{eqnarray*}%
-
-
-\clearpage
-\subsection{Slash kerning}
-
-\def\test#1{1/#1+}
-\begin{eqnarray*}
- && {\testupperi}\\
- && {\testupperii}\\
- && {\testloweri}\\
- && {\testlowerii}\\
- && {\testupgreeki}\\
- && {\testupgreekii}\\
- && {\testlowgreeki}\\
- && {\testlowgreekii}\\
- && {\testlowgreekiii}
-\end{eqnarray*}
-
-\def\test#1{#1/2+}
-\begin{eqnarray*}
- && {\testupperi}\\
- && {\testupperii}\\
- && {\testloweri}\\
- && {\testlowerii}\\
- && {\testupgreeki}\\
- && {\testupgreekii}\\
- && {\testlowgreeki}\\
- && {\testlowgreekii}\\
- && {\testlowgreekiii}
-\end{eqnarray*}
-
-
-\clearpage
-\subsection{Big operators}
-
-\def\testop#1{#1_{i=1}^{n} x^{n} \quad}
-\begin{displaymath}
- \testop\sum
- \testop\prod
- \testop\coprod
- \testop\int
- \testop\oint
-\end{displaymath}
-\begin{displaymath}
- \testop\bigotimes
- \testop\bigoplus
- \testop\bigodot
- \testop\bigwedge
- \testop\bigvee
- \testop\biguplus
- \testop\bigcup
- \testop\bigcap
- \testop\bigsqcup
-% \testop\bigsqcap
-\end{displaymath}
-
-
-\subsection{Radicals}
-
-\begin{displaymath}
- \sqrt{x+y} \qquad \sqrt{x^{2}+y^{2}} \qquad
- \sqrt{x_{i}^{2}+y_{j}^{2}} \qquad
- \sqrt{\left(\frac{\cos x}{2}\right)} \qquad
- \sqrt{\left(\frac{\sin x}{2}\right)}
-\end{displaymath}
-
-\begingroup
-\delimitershortfall-1pt
-\begin{displaymath}
- \sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{x+y}}}}}}}
-\end{displaymath}
-\endgroup % \delimitershortfall
-
-
-\subsection{Over- and underbraces}
-
-\begin{displaymath}
- \overbrace{x} \quad
- \overbrace{x+y} \quad
- \overbrace{x^{2}+y^{2}} \quad
- \overbrace{x_{i}^{2}+y_{j}^{2}} \quad
- \underbrace{x} \quad
- \underbrace{x+y} \quad
- \underbrace{x_{i}+y_{j}} \quad
- \underbrace{x_{i}^{2}+y_{j}^{2}} \quad
-\end{displaymath}
-
-
-\subsection{Normal and wide accents}
-
-\begin{displaymath}
- \dot{x} \quad
- \ddot{x} \quad
- \vec{x} \quad
- \bar{x} \quad
- \overline{x} \quad
- \overline{xx} \quad
- \tilde{x} \quad
- \widetilde{x} \quad
- \widetilde{xx} \quad
- \widetilde{xxx} \quad
- \hat{x} \quad
- \widehat{x} \quad
- \widehat{xx} \quad
- \widehat{xxx} \quad
-\end{displaymath}
-
-
-\subsection{Long arrows}
-
-\begin{displaymath}
- \leftarrow \mathrel{-} \rightarrow \quad
- \leftrightarrow \quad
- \longleftarrow \quad
- \longrightarrow \quad
- \longleftrightarrow \quad
- \Leftarrow = \Rightarrow \quad
- \Leftrightarrow \quad
- \Longleftarrow \quad
- \Longrightarrow \quad
- \Longleftrightarrow \quad
-\end{displaymath}
-
-
-\subsection{Left and right delimters}
-
-\def\testdelim#1#2{ - #1 f #2 - }
-\begin{displaymath}
- \testdelim()
- \testdelim[]
- \testdelim\lfloor\rfloor
- \testdelim\lceil\rceil
- \testdelim\langle\rangle
- \testdelim\{\}
-\end{displaymath}
-
-\def\testdelim#1#2{ - \left#1 f \right#2 - }
-\begin{displaymath}
- \testdelim()
- \testdelim[]
- \testdelim\lfloor\rfloor
- \testdelim\lceil\rceil
- \testdelim\langle\rangle
- \testdelim\{\}
-% \testdelim\lgroup\rgroup
-% \testdelim\lmoustache\rmoustache
-\end{displaymath}
-\begin{displaymath}
- \testdelim)(
- \testdelim][
- \testdelim//
- \testdelim\backslash\backslash
- \testdelim/\backslash
- \testdelim\backslash/
-\end{displaymath}
-
-
-\clearpage
-\subsection{Big-g-g delimters}
-
-\def\testdelim#1#2{%
- - \left#1\left#1\left#1\left#1\left#1\left#1\left#1\left#1 -
- \right#2\right#2\right#2\right#2\right#2\right#2\right#2\right#2 -}
-
-\begingroup
-\delimitershortfall-1pt
-\begin{displaymath}
- \testdelim\lfloor\rfloor
- \qquad
- \testdelim()
-\end{displaymath}
-\begin{displaymath}
- \testdelim\lceil\rceil
- \qquad
- \testdelim\{\}
-\end{displaymath}
-\begin{displaymath}
- \testdelim[]
- \qquad
- \testdelim\lgroup\rgroup
-\end{displaymath}
-\begin{displaymath}
- \testdelim\langle\rangle
- \qquad
- \testdelim\lmoustache\rmoustache
-\end{displaymath}
-\begin{displaymath}
- \testdelim\uparrow\downarrow \quad
- \testdelim\Uparrow\Downarrow \quad
-\end{displaymath}
-\endgroup % \delimitershortfall
-
-\subsection{Symbols}
-\label{sec:symbols}
-
-This is from~\cite{Eijkhout07:TeXbyTopic}
-
-\begin{longtable}{lllll}
-Symbol & Control Sequence & mathcode & Family & Hex Position \\
-$\partial$&partial& "0140&1&40\\
-$\flat$&flat& "015B&1&5B\\
-$\natural$&natural& "015C&1&5C\\
-$\sharp$&sharp& "015D&1&5D\\
-$\ell$&ell& "0160&1&60\\
-$\imath$&imath& "017B&1&7B\\
-$\jmath$&jmath& "017C&1&7C\\
-$\wp$&wp& "017D&1&7D\\
-$\prime$&prime& "0230&2&30\\
-$\infty$&infty& "0231&2&31\\
-$\triangle$&triangle& "0234&2&34\\
-$\forall$&forall& "0238&2&38\\
-$\exists$&exists& "0239&2&39\\
-$\neg$&neg& "023A&2&3A\\
-$\emptyset$&emptyset& "023B&2&3B\\
-$\Re$&Re& "023C&2&3C\\
-$\Im$&Im& "023D&2&3D\\
-$\top$&top& "023E&2&3E\\
-$\bot$&bot& "023F&2&3F\\
-$\aleph$&aleph& "0240&2&40\\
-$\nabla$&nabla& "0272&2&72\\
-$\clubsuit$&clubsuit& "027C&2&7C\\
-$\diamondsuit$&diamondsuit& "027D&2&7D\\
-$\heartsuit$&heartsuit& "027E&2&7E\\
-$\spadesuit$&spadesuit& "027F&2&7F\\
-$\smallint \displaystyle\smallint$&
- smallint& "1273&2&73\cr
-$\bigsqcup \displaystyle\bigsqcup$&
- bigsqcup& "1346&3&46\cr
-$\ointop \displaystyle\ointop$&
- ointop& "1348&3&48\cr
-$\bigodot \displaystyle\bigodot$&
- bigodot& "134A&3&4A\cr
-$\bigoplus \displaystyle\bigoplus$&
- bigoplus& "134C&3&4C\cr
-$\bigotimes \displaystyle\bigotimes$&
- bigotimes& "134E&3&4E\cr
-$\sum \displaystyle\sum$&
- sum& "1350&3&50\cr
-$\prod \displaystyle\prod$&
- prod& "1351&3&51\cr
-$\intop \displaystyle\intop$&
- intop& "1352&3&52\cr
-$\bigcup \displaystyle\bigcup$&
- bigcup& "1353&3&53\cr
-$\bigcap \displaystyle\bigcap$&
- bigcap& "1354&3&54\cr
-$\biguplus \displaystyle\biguplus$&
- biguplus& "1355&3&55\cr
-$\bigwedge \displaystyle\bigwedge$&
- bigwedge& "1356&3&56\cr
-$\bigvee \displaystyle\bigvee$&
- bigvee& "1357&3&57\cr
-$\coprod \displaystyle\coprod$&
- coprod& "1360&3&60\cr
-$\triangleright$&triangleright& "212E&1&2E\cr
-$\triangleleft$&triangleleft& "212F&1&2F\cr
-$\star$&star& "213F&1&3F\cr
-$\cdot$&cdot& "2201&2&01\cr
-$\times$&times& "2202&2&02\cr
-$\ast$&ast& "2203&2&03\cr
-$\div$&div& "2204&2&04\cr
-$\diamond$&diamond& "2205&2&05\cr
-$\pm$&pm& "2206&2&06\cr
-$\mp$&mp& "2207&2&07\cr
-$\oplus$&oplus& "2208&2&08\cr
-$\ominus$&ominus& "2209&2&09\cr
-$\otimes$&otimes& "220A&2&0A\cr
-$\oslash$&oslash& "220B&2&0B\cr
-$\odot$&odot& "220C&2&0C\cr
-$\bigcirc$&bigcirc& "220D&2&0D\cr
-$\circ$&circ& "220E&2&0E\cr
-$\bullet$&bullet& "220F&2&0F\cr
-$\bigtriangleup$&bigtriangleup& "2234&2&34\cr
-$\bigtriangledown$&bigtriangledown& "2235&2&35\cr
-$\cup$&cup& "225B&2&5B\cr
-$\cap$&cap& "225C&2&5C\cr
-$\uplus$&uplus& "225D&2&5D\cr
-$\wedge$&wedge& "225E&2&5E\cr
-$\vee$&vee& "225F&2&5F\cr
-$\setminus$&setminus& "226E&2&6E\cr
-$\wr$&wr& "226F&2&6F\cr
-$\amalg$&amalg& "2271&2&71\cr
-$\sqcup$&sqcup& "2274&2&74\cr
-$\sqcap$&sqcap& "2275&2&75\cr
-$\dagger$&dagger& "2279&2&79\cr
-$\ddagger$&ddagger& "227A&2&7A\cr
-$\leftharpoonup$&leftharpoonup& "3128&1&28\cr
-$\leftharpoondown$&leftharpoondown& "3129&1&29\cr
-$\rightharpoonup$&rightharpoonup& "312A&1&2A\cr
-$\rightharpoondown$&rightharpoondown& "312B&1&2B\cr
-$\smile$&smile& "315E&1&5E\cr
-$\frown$&frown& "315F&1&5F\cr
-$\asymp$&asymp& "3210&2&10\cr
-$\equiv$&equiv& "3211&2&11\cr
-$\subseteq$&subseteq& "3212&2&12\cr
-$\supseteq$&supseteq& "3213&2&13\cr
-$\leq$&leq& "3214&2&14\cr
-$\geq$&geq& "3215&2&15\cr
-$\preceq$&preceq& "3216&2&16\cr
-$\succeq$&succeq& "3217&2&17\cr
-$\sim$&sim& "3218&2&18\cr
-$\approx$&approx& "3219&2&19\cr
-$\subset$&subset& "321A&2&1A\cr
-$\supset$&supset& "321B&2&1B\cr
-$\ll$&ll& "321C&2&1C\cr
-$\gg$&gg& "321D&2&1D\cr
-$\prec$&prec& "321E&2&1E\cr
-$\succ$&succ& "321F&2&1F\cr
-$\leftarrow$&leftarrow& "3220&2&20\cr
-$\rightarrow$&rightarrow& "3221&2&21\cr
-$\leftrightarrow$&leftrightarrow& "3224&2&24\cr
-$\nearrow$&nearrow& "3225&2&25\cr
-$\searrow$&searrow& "3226&2&26\cr
-$\simeq$&simeq& "3227&2&27\cr
-$\Leftarrow$&Leftarrow& "3228&2&28\cr
-$\Rightarrow$&Rightarrow& "3229&2&29\cr
-$\Leftrightarrow$&Leftrightarrow& "322C&2&2C\cr
-$\nwarrow$&nwarrow& "322D&2&2D\cr
-$\swarrow$&swarrow& "322E&2&2E\cr
-$\propto$&propto& "322F&2&2F\cr
-$\in$&in& "3232&2&32\cr
-$\ni$&ni& "3233&2&33\cr
-$\not$&not& "3236&2&36\cr
-$\mapstochar$&mapstochar& "3237&2&37\cr
-$\perp$&perp& "323F&2&3F\cr
-$\vdash$&vdash& "3260&2&60\cr
-$\dashv$&dashv& "3261&2&61\cr
-$\mid$&mid& "326A&2&6A\cr
-$\parallel$&parallel& "326B&2&6B\cr
-$\sqsubseteq$&sqsubseteq& "3276&2&76\cr
-$\sqsupseteq$&sqsupseteq& "3277&2&77\cr
-\end{longtable}
-
-
-\subsection{Miscellanneous formulae}
-
-Taken from~\cite{Downes04:amsart}
-
-\label{sec:misc}
-\begin{displaymath}
- \hbar\nu=E
-\end{displaymath}
-
-Let $\mathbf{A}=(a_{ij})$ be the adjacency matrix of graph $G$. The
-corresponding Kirchhoff matrix $\mathbf{K}=(k_{ij})$ is obtained from
-$\mathbf{A}$ by replacing in $-\mathbf{A}$ each diagonal entry by the
-degree of its corresponding vertex; i.e., the $i$th diagonal entry is
-identified with the degree of the $i$th vertex. It is well known that
-\begin{equation}
-\det\mathbf{K}(i|i)=\text{ the number of spanning trees of $G$},
-\quad i=1,\dots,n
-\end{equation}
-where $\mathbf{K}(i|i)$ is the $i$th principal submatrix of
-$\mathbf{K}$.
-
-\newcommand{\abs}[1]{\left\lvert#1\right\rvert}
-\newcommand{\wh}{\widehat}
-Let $C_{i(j)}$ be the set of graphs obtained from $G$ by attaching edge
-$(v_iv_j)$ to each spanning tree of $G$. Denote by $C_i=\bigcup_j
-C_{i(j)}$. It is obvious that the collection of Hamiltonian cycles is a
-subset of $C_i$. Note that the cardinality of $C_i$ is $k_{ii}\det
-\mathbf{K}(i|i)$. Let $\wh X=\{\hat x_1,\dots,\hat x_n\}$. Define multiplication for the elements of $\wh X$ by
-\begin{equation}\label{multdef}
-\hat x_i\hat x_j=\hat x_j\hat x_i,\quad \hat x^2_i=0,\quad
-i,j=1,\dots,n.
-\end{equation}
-Let $\hat k_{ij}=k_{ij}\hat x_j$ and $\hat k_{ij}=-\sum_{j\not=i} \hat
-k_{ij}$. Then the number of Hamiltonian cycles $H_c$ is given by the
-relation
-\begin{equation}\label{H-cycles}
-\biggl(\prod^n_{\,j=1}\hat x_j\biggr)H_c=\frac{1}{2}\hat k_{ij}\det
-\wh{\mathbf{K}}(i|i),\qquad i=1,\dots,n.
-\end{equation}
-The task here is to express \eqref{H-cycles}
-in a form free of any $\hat x_i$,
-$i=1,\dots,n$. The result also leads to the resolution of enumeration of
-Hamiltonian paths in a graph.
-
-It is well known that the enumeration of Hamiltonian cycles and paths
-in a complete graph $K_n$ and in a complete bipartite graph
-$K_{n_1n_2}$ can only be found from \textit{first combinatorial
- principles}. One wonders if there exists a formula which can be used
-very efficiently to produce $K_n$ and $K_{n_1n_2}$. Recently, using
-Lagrangian methods, Goulden and Jackson have shown that $H_c$ can be
-expressed in terms of the determinant and permanent of the adjacency
-matrix. However, the formula of Goulden and
-Jackson determines neither $K_n$ nor $K_{n_1n_2}$ effectively. In this
-paper, using an algebraic method, we parametrize the adjacency matrix.
-The resulting formula also involves the determinant and permanent, but
-it can easily be applied to $K_n$ and $K_{n_1n_2}$. In addition, we
-eliminate the permanent from $H_c$ and show that $H_c$ can be
-represented by a determinantal function of multivariables, each
-variable with domain $\{0,1\}$. Furthermore, we show that $H_c$ can be
-written by number of spanning trees of subgraphs. Finally, we apply
-the formulas to a complete multigraph $K_{n_1\dots n_p}$.
-
-The conditions $a_{ij}=a_{ji}$, $i,j=1,\dots,n$, are not required in
-this paper. All formulas can be extended to a digraph simply by
-multiplying $H_c$ by 2.
-
-The boundedness, property of $\Phi_ 0$, then yields
-\[\int_{\mathcal{D}}\abs{\overline\partial u}^2e^{\alpha\abs{z}^2}\geq c_6\alpha
-\int_{\mathcal{D}}\abs{u}^2e^{\alpha\abs{z}^2}
-+c_7\delta^{-2}\int_ A\abs{u}^2e^{\alpha\abs{z}^2}.\]
-
-Let $B(X)$ be the set of blocks of $\Lambda_{X}$
-and let $b(X) = \abs{B(X)}$. If $\phi \in Q_{X}$ then
-$\phi$ is constant on the blocks of $\Lambda_{X}$.
-\begin{equation}\label{far-d}
- P_{X} = \{ \phi \in M \mid \Lambda_{\phi} = \Lambda_{X} \},
-\qquad
-Q_{X} = \{\phi \in M \mid \Lambda_{\phi} \geq \Lambda_{X} \}.
-\end{equation}
-If $\Lambda_{\phi} \geq \Lambda_{X}$ then
-$\Lambda_{\phi} = \Lambda_{Y}$ for some $Y \geq X$ so that
-\[ Q_{X} = \bigcup_{Y \geq X} P_{Y}. \]
-Thus by M\"obius inversion
-\[ \abs{P_{Y}}= \sum_{X\geq Y} \mu (Y,X)\abs{Q_{X}}.\]
-Thus there is a bijection from $Q_{X}$ to $W^{B(X)}$.
-In particular $\abs{Q_{X}} = w^{b(X)}$.
-
-
-\renewcommand{\arraystretch}{2.2}
-\[W(\Phi)= \begin{Vmatrix}
-\dfrac\varphi{(\varphi_1,\varepsilon_1)}&0&\dots&0\\
-\dfrac{\varphi k_{n2}}{(\varphi_2,\varepsilon_1)}&
-\dfrac\varphi{(\varphi_2,\varepsilon_2)}&\dots&0\\
-\hdotsfor{5}\\
-\dfrac{\varphi k_{n1}}{(\varphi_n,\varepsilon_1)}&
-\dfrac{\varphi k_{n2}}{(\varphi_n,\varepsilon_2)}&\dots&
-\dfrac{\varphi k_{n\,n-1}}{(\varphi_n,\varepsilon_{n-1})}&
-\dfrac{\varphi}{(\varphi_n,\varepsilon_n)}
-\end{Vmatrix}\]
-
-
-
-\bibliography{jamtimes}
-\bibliographystyle{unsrt}
-
-
-
-\end{document}