<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">%   charset.tex January 11 1993
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%   Version 3.0 of REVTeX, November 10, 1992.
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\documentstyle[aps]{revtex}

\def\btt#1{{\tt$\backslash$\string#1}}%

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\begin{document}

%\appendix
%\twocolumn
\narrowtext

\def\xxx{4pt}


\subsubsection[Standard \protect\LaTeX{} symbols]{Standard LaTeX symbols}
The following tables show the standard symbols for \LaTeX{} users.

\begin{table}
\caption{Text accents with letter a.}
\begin{tabular}{c@{\hspace{\xxx}}lc@{\hspace{\xxx}}lc@{\hspace{\xxx}}%
                lc@{\hspace{\xxx}}l}
\`{a} &amp; \verb+\`{a}+&amp;
\'{a} &amp; \verb+\'{a}+&amp;
\^{a} &amp; \verb+\^{a}+&amp;
\"{a} &amp; \verb+\"{a}+\\
\~{a} &amp; \verb+\~{a}+&amp;
\={a} &amp; \verb+\={a}+&amp;
\.{a} &amp; \verb+\.{a}+&amp;
\u{a} &amp; \verb+\u{a}+\\
\v{a} &amp; \verb+\v{a}+&amp;
\H{a} &amp; \verb+\H{a}+&amp;
\t{aa} &amp; \verb+\t{aa}+&amp;
\c{a} &amp; \verb+\c{a}+\\
\d{a} &amp; \verb+\d{a}+&amp;
\b{a} &amp; \verb+\b{a}+
\end{tabular}
\end{table}


\begin{table}
\caption{Math accents with letter a.}
\begin{tabular}%
  {c@{\hspace{\xxx}}lc@{\hspace{\xxx}}lc@{\hspace{\xxx}}lc@{\hspace{\xxx}}l}
$\hat{a}$ &amp; \verb+\hat{a}+ &amp;
$\check{a}$ &amp; \verb+\check{a}+ &amp;
 $\dot{a}$ &amp; \verb+\dot{a}+ &amp;
 $\ddot{a}$ &amp; \verb+\ddot{a}+ \\
$\breve{a}$ &amp; \verb+\breve{a}+ &amp;
 $\tilde{a}$ &amp; \verb+\tilde{a}+ &amp;
 $\grave{a}$ &amp; \verb+\grave{a}+ &amp;
 $\acute{a}$ &amp; \verb+\acute{a}+ \\
  $\bar{a}$ &amp; \verb+\bar{a}+ &amp;
  $\vec{a}$ &amp; \verb+\vec{a}+ &amp;
\end{tabular}
\end{table}

\newpage

\begin{table}
\caption{Special symbols; any mode.}
\begin{tabular}{c@{\hspace{\xxx}}lc@{\hspace{\xxx}}lc@{\hspace{\xxx}}l}
\dag &amp; \verb+\dag+&amp; \S &amp; \verb+\S+&amp; \copyright &amp; \verb+\copyright+\\
\ddag &amp; \verb+\ddag+&amp; \P &amp; \verb+\P+&amp; \pounds &amp; \verb+\pounds+\\
\end{tabular}
\end{table}




\begin{table}
\caption{Other special (foreign) symbols; text mode.}
\begin{tabular}%
  {c@{\hspace{\xxx}}lc@{\hspace{\xxx}}lc@{\hspace{\xxx}}lc@{\hspace{\xxx}}l}
 \aa &amp; \verb+\aa+&amp;
 \AA &amp; \verb+\AA+&amp;
\ae &amp; \verb+\ae+&amp;
\AE &amp; \verb+\AE+\\
 \o &amp; \verb+\o+&amp;
 \O &amp; \verb+\O+&amp;
\oe &amp; \verb+\oe+&amp;
\OE &amp; \verb+\OE+\\
 \l &amp; \verb+\l+&amp;
 \L &amp; \verb+\L+&amp;
 ?` &amp; \verb+?`+&amp;
 !` &amp; \verb+!`+\\
 \ss &amp; \verb+\ss+
\end{tabular}
\end{table}


\newpage

\begin{table}
\caption{Greek letters; used in math mode.}
\begin{tabular}%
  {c@{\hspace{\xxx}}lc@{\hspace{\xxx}}lc@{\hspace{\xxx}}lc@{\hspace{\xxx}}l}
\multicolumn{8}{c}{\it Lowercase}\\
$\alpha$ &amp; \verb+\alpha+ &amp;
$\beta$ &amp; \verb+\beta+ &amp;
$\gamma$ &amp; \verb+\gamma+ &amp;
$\delta$ &amp; \verb+\delta+\\
$\epsilon$ &amp; \verb+\epsilon+ &amp;
$\varepsilon$ &amp; \verb+\varepsilon+ &amp;
$\zeta$ &amp; \verb+\zeta+ &amp;
$\eta$ &amp; \verb+\eta+ \\
 $\theta$ &amp; \verb+\theta+ &amp;
 $\vartheta$ &amp; \verb+\vartheta+ &amp;
 $\iota$ &amp; \verb+\iota+ &amp;
 $\kappa$ &amp; \verb+\kappa+ \\
 $\lambda$ &amp; \verb+\lambda+ &amp;
 $\mu$ &amp; \verb+\mu+ &amp;
 $\nu$ &amp; \verb+\nu+ &amp;
 $\xi$ &amp; \verb+\xi+\\
 $o$ &amp; \verb+o+ &amp;
 $\pi$ &amp; \verb+\pi+ &amp;
 $\varpi$ &amp; \verb+\varpi+ &amp;
 $\rho$ &amp; \verb+\rho+ \\
   $\varrho$ &amp; \verb+\varrho+ &amp;
   $\sigma$ &amp; \verb+\sigma+ &amp;
 $\varsigma$ &amp; \verb+\varsigma+ &amp;
    $\tau$ &amp; \verb+\tau+ \\
   $\upsilon$ &amp; \verb+\upsilon+ &amp;
   $\phi$ &amp; \verb+\phi+ &amp;
   $\varphi$ &amp; \verb+\varphi+ &amp;
 $\chi$ &amp; \verb+\chi+ \\
 $\psi$ &amp; \verb+\psi+ &amp;
  $\omega$ &amp; \verb+\omega+ &amp;
 \\[\baselineskip]
\multicolumn{8}{c}{\it Uppercase}\\
$\Gamma$ &amp; \verb+\Gamma+ &amp;
$\Delta$ &amp; \verb+\Delta+ &amp;
$\Theta$ &amp; \verb+\Theta+ &amp;
 $\Lambda$ &amp; \verb+\Lambda+\\
 $\Xi$ &amp; \verb+\Xi+ &amp;
 $\Pi$ &amp; \verb+\Pi+ &amp;
   $\Sigma$ &amp; \verb+\Sigma+ &amp;
    $\Upsilon$ &amp; \verb+\Upsilon+ \\
 $\Phi$ &amp; \verb+\Phi+ &amp;
 $\Psi$ &amp; \verb+\Psi+ &amp;
 $\Omega$ &amp; \verb+\Omega+ &amp;
\end{tabular}
\end{table}

\newpage

\begin{table}
\caption{Binary operation symbols; used in math mode.}
\def\xxx{3.2pt}
\begin{tabular}%
  {c@{\hspace{\xxx}}lc@{\hspace{\xxx}}lc@{\hspace{\xxx}}lc@{\hspace{\xxx}}l}
$\pm$ &amp; \verb+\pm+ &amp;
$\mp$ &amp; \verb+\mp+ &amp;
$\times$ &amp; \verb+\times+ &amp;
$\div$ &amp; \verb+\div+ \\
$\ast$ &amp; \verb+\ast+ &amp;
$\star$ &amp; \verb+\star+ &amp;
$\circ$ &amp; \verb+\circ+ &amp;
$\bullet$ &amp; \verb+\bullet+\\
 $\cap$ &amp; \verb+\cap+ &amp;
 $\cup$ &amp; \verb+\cup+ &amp;
 $\uplus$ &amp; \verb+\uplus+ &amp;
$\cdot$ &amp; \verb+\cdot+ \\
 $\sqcap$ &amp; \verb+\sqcap+  &amp;
 $\sqcup$ &amp; \verb+\sqcup+ &amp;
 $\vee$ &amp; \verb+\vee+ &amp;
 $\wedge$ &amp; \verb+\wedge+\\
   $\oplus$ &amp; \verb+\oplus+ &amp;
 $\ominus$ &amp; \verb+\ominus+ &amp;
 $\otimes$ &amp; \verb+\otimes+ &amp;
 $\oslash$ &amp; \verb+\oslash+ \\
$\bigtriangleup$ &amp; \verb+\bigtriangleup+ &amp;
 $\odot$ &amp; \verb+\odot+ &amp;
  $\lhd$ &amp; \verb+\lhd+ &amp;
 $\dagger$ &amp; \verb+\dagger+ \\
$\bigtriangledown$ &amp; \verb+\bigtriangledown+ &amp;
 $\bigcirc$ &amp; \verb+\bigcirc+ &amp;
  $\rhd$ &amp; \verb+\rhd+ &amp;
 $\ddagger$ &amp; \verb+\ddagger+\\
$\triangleleft$ &amp; \verb+\triangleleft+ &amp;
 $\diamond$ &amp; \verb+\diamond+ &amp;
  $\unlhd$ &amp; \verb+\unlhd+ &amp;
 $\setminus$ &amp; \verb+\setminus+\\
$\triangleright$ &amp; \verb+\triangleright+ &amp;
 $\wr$ &amp; \verb+\wr+  &amp;
 $\unrhd$ &amp; \verb+\unrhd+  &amp;
  $\amalg$ &amp; \verb+\amalg+
\end{tabular}
\end{table}


\newpage

\begin{table}
\caption{Relation symbols; used in math mode. }
\begin{tabular}%
  {c@{\hspace{\xxx}}lc@{\hspace{\xxx}}lc@{\hspace{\xxx}}lc@{\hspace{\xxx}}l}
$\leq$ &amp; \verb+\leq+ &amp;
 $\geq$ &amp; \verb+\geq+ &amp;
$\ll$ &amp; \verb+\ll+ &amp;
 $\gg$ &amp; \verb+\gg+ \\
 $\equiv$ &amp; \verb+\equiv+ &amp;
 $\asymp$ &amp; \verb+\asymp+ &amp;
   $\neq$ &amp; \verb+\neq+ &amp;
   $\doteq$ &amp; \verb+\doteq+  \\
$\subset$ &amp; \verb+\subset+ &amp;
 $\supset$ &amp; \verb+\supset+ &amp;
$\subseteq$ &amp; \verb+\subseteq+ &amp;
 $\supseteq$ &amp; \verb+\supseteq+  \\
$\sqsubset$ &amp; \verb+\sqsubset+ &amp;
 $\sqsupset$ &amp; \verb+\sqsupset+ &amp;
$\sqsubseteq$ &amp; \verb+\sqsubseteq+ &amp;
 $\sqsupseteq$ &amp; \verb+\sqsupseteq+\hidewidth \\
   $\models$ &amp; \verb+\models+ &amp;
   $\perp$ &amp; \verb+\perp+  &amp;
 $\mid$ &amp; \verb+\mid+  &amp;
   $\parallel$ &amp; \verb+\parallel+ \\
$\prec$ &amp; \verb+\prec+ &amp;
 $\succ$ &amp; \verb+\succ+ &amp;
$\preceq$ &amp; \verb+\preceq+ &amp;
 $\succeq$ &amp; \verb+\succeq+ \\
 $\sim$ &amp; \verb+\sim+ &amp;
   $\simeq$ &amp; \verb+\simeq+ &amp;
   $\approx$ &amp; \verb+\approx+ &amp;
   $\cong$ &amp; \verb+\cong+ \\
 $\bowtie$ &amp; \verb+\bowtie+  &amp;
 $\Join$ &amp; \verb+\Join+  &amp;
 $\smile$ &amp; \verb+\smile+ &amp;
 $\frown$ &amp; \verb+\frown+ \\
$\in$ &amp; \verb+\in+ &amp;
 $\ni$ &amp; \verb+\ni+ &amp;
$\vdash$ &amp; \verb+\vdash+ &amp;
 $\dashv$ &amp; \verb+\dashv+  \\
 $\propto$ &amp; \verb+\propto+ &amp;
\end{tabular}
%\end{table}

 Negated relations can sometimes
be constructed with \verb+\not+. For example,
\[
\hbox{\verb+If $x \not&lt; y$ then $x \not\leq z$.+}
\]
gives
\[
\hbox{If $x \not&lt; y$ then $x \not\leq z$.}
\]

\end{table}

\newpage

\begin{table}
\caption{Arrow symbols; used in math mode.}
\begin{tabular}{c@{\hspace{\xxx}}lc@{\hspace{\xxx}}l}
$\leftarrow$ &amp; \verb+\leftarrow+ &amp;
$\rightarrow$ &amp; \verb+\rightarrow+ \\
 $\longleftarrow$ &amp; \verb+\longleftarrow+ &amp;
 $\longrightarrow$ &amp; \verb+\longrightarrow+ \\
$\Leftarrow$ &amp; \verb+\Leftarrow+ &amp;
$\Rightarrow$ &amp; \verb+\Rightarrow+ \\
 $\Longleftarrow$ &amp; \verb+\Longleftarrow+ &amp;
 $\Longrightarrow$ &amp; \verb+\Longrightarrow+ \\
$\hookleftarrow$ &amp; \verb+\hookleftarrow+ &amp; $\hookrightarrow$
  &amp; \verb+\hookrightarrow+ \\
$\leftharpoonup$ &amp; \verb+\leftharpoonup+ &amp; $\rightharpoonup$
  &amp; \verb+\rightharpoonup+\\
$\leftharpoondown$ &amp; \verb+\leftharpoondown+ &amp; $\rightharpoondown$
  &amp; \verb+\rightharpoondown+ \\
$\rightleftharpoons$&amp;\verb+\rightleftharpoons+&amp;$\leadsto$&amp;\verb+\leadsto+ \\
$\leftrightarrow$ &amp; \verb+\leftrightarrow+ &amp; $\longleftrightarrow$
  &amp; \verb+\longleftrightarrow+  \\
$\Leftrightarrow$ &amp; \verb+\Leftrightarrow+ &amp; $\Longleftrightarrow$
  &amp; \verb+\Longleftrightarrow+  \\
$\mapsto$ &amp; \verb+\mapsto+ &amp; $\longmapsto$ &amp; \verb+\longmapsto+ \\
\multicolumn{4}{c}{%
   \begin{tabular}{c@{\hspace{\xxx}}l}
   $\uparrow$ &amp; \btt{uparrow}\\
   $\downarrow$ &amp; \btt{downarrow} \\
   $\Uparrow$ &amp; \btt{Uparrow}\\
   $\Downarrow$ &amp; \btt{Downarrow}\\
   $\updownarrow$ &amp; \btt{updownarrow}\\
   $\Updownarrow$ &amp; \btt{Updownarrow}\\
   $\nearrow$ &amp; \btt{nearrow}\\
   $\searrow$ &amp; \btt{searrow}\\
   $\swarrow$ &amp; \btt{swarrow}\\
   $\nwarrow$ &amp; \btt{nwarrow}
   \end{tabular}%
} % end of multicolumn
%
\end{tabular}
\end{table}



\newpage

\begin{table}
\caption{Miscellaneous symbols; used in math mode.}
\begin{tabular}%
  {c@{\hspace{\xxx}}lc@{\hspace{\xxx}}lc@{\hspace{\xxx}}lc@{\hspace{\xxx}}l}
 $\flat$ &amp; \verb+\flat+ &amp;
 $\natural$ &amp; \verb+\natural+ &amp;
 $\sharp$ &amp; \verb+\sharp+ &amp;
 $\prime$ &amp; \verb+\prime+ \\
 $\backslash$ &amp; \verb+\backslash+ &amp;
 $\forall$ &amp; \verb+\forall+ &amp;
  $\infty$ &amp; \verb+\infty+ &amp;
 $\exists$ &amp; \verb+\exists+\\
 $\emptyset$ &amp; \verb+\emptyset+ &amp;
  $\Box$ &amp; \verb+\Box+ &amp;
 $\nabla$ &amp; \verb+\nabla+ &amp;
 $\neg$ &amp; \verb+\neg+ \\
  $\Diamond$ &amp; \verb+\Diamond+ &amp;
 $\surd$ &amp; \verb+\surd+ &amp;
  $\triangle$ &amp; \verb+\triangle+&amp;
 $\|$ &amp; \verb+\|+ \\
  $\clubsuit$ &amp; \verb+\clubsuit+ &amp;
$\aleph$ &amp; \verb+\aleph+ &amp;
$\wp$ &amp; \verb+\wp+ &amp;
 $\top$ &amp; \verb+\top+\\
  $\diamondsuit$ &amp; \verb+\diamondsuit+&amp;
$\Re$ &amp; \verb+\Re+ &amp;
$\ell$ &amp; \verb+\ell+ &amp;
 $\bot$ &amp; \verb+\bot+ \\
  $\heartsuit$ &amp; \verb+\heartsuit+ &amp;
$\Im$ &amp; \verb+\Im+ &amp;
$\imath$ &amp; \verb+\imath+ &amp;
 $\partial$ &amp; \verb+\partial+ \\
  $\spadesuit$ &amp; \verb+\spadesuit+ &amp;
$\hbar$ &amp; \verb+\hbar+ &amp;
$\jmath$ &amp; \verb+\jmath+ &amp;
 $\angle$ &amp; \verb+\angle+ \\
$\mho$ &amp; \verb+\mho+
\end{tabular}
\end{table}

\newpage

\begin{table}
\caption{Log-like functions; used in math mode.}
\begin{tabular}{llllllll}
\verb+\arccos+ &amp;
\verb+\arcsin+ &amp;
\verb+\arctan+ &amp;
\verb+\arg+ &amp;
 \verb+\cos+ \\
 \verb+\cosh+ &amp;
 \verb+\cot+ &amp;
 \verb+\coth+ &amp;
 \verb+\csc+ &amp;
 \verb+\deg+ \\
 \verb+\det+ &amp;
 \verb+\dim+ &amp;
 \verb+\exp+ &amp;
 \verb+\gcd+ &amp;
 \verb+\hom+ \\
 \verb+\inf+ &amp;
 \verb+\ker+ &amp;
 \verb+\lg+ &amp;
 \verb+\lim+ &amp;
 \verb+\liminf+ \\
  \verb+\limsup+ &amp;
  \verb+\ln+ &amp;
  \verb+\log+ &amp;
  \verb+\max+ &amp;
 \verb+\min+ \\
 \verb+\Pr+ &amp;
 \verb+\sec+ &amp;
 \verb+\sin+ &amp;
 \verb+\sinh+ &amp;
 \verb+\sup+ \\
 \verb+\tan+ &amp;
 \verb+\tanh+
\end{tabular}
\end{table}

\newpage

\begin{table}
\caption{Delimiters; used in math mode.}
\begin{tabular}{c@{\hspace{\xxx}}lc@{\hspace{\xxx}}lc@{\hspace{\xxx}}l}
$($ &amp; \verb+(+ &amp;
 $)$ &amp; \verb+)+ &amp;
$/$ &amp; \verb+/+ \\
$[$ &amp; \verb+[+ &amp;
 $]$ &amp; \verb+]+ &amp;
 $\backslash$ &amp; \verb+\backslash+ \\
$\{$ &amp; \verb+\{+ &amp;
 $\}$ &amp; \verb+\}+ &amp;
$|$ &amp; \verb+|+ \\
$\langle$ &amp; \verb+\langle+ &amp;
 $\rangle$ &amp; \verb+\rangle+ &amp;
 $\|$ &amp; \verb+\|+ \\
 $\uparrow$ &amp; \verb+\uparrow+ &amp;
  $\Uparrow$ &amp; \verb+\Uparrow+&amp;
$\lfloor$ &amp; \verb+\lfloor+ \\
 $\downarrow$ &amp; \verb+\downarrow+ &amp;
  $\Downarrow$ &amp; \verb+\Downarrow+ &amp;
 $\rfloor$ &amp; \verb+\rfloor+ \\
 $\updownarrow$ &amp; \verb+\updownarrow+ &amp;
  $\Updownarrow$ &amp; \verb+\Updownarrow+ &amp;
$\lceil$ &amp; \verb+\lceil+ \\
 &amp; &amp; &amp; &amp; $\rceil$ &amp; \verb+\rceil+
\end{tabular}
\end{table}


\newpage

\begin{table}
\caption{Miscellaneous symbols; used in math mode.}
\begin{tabular}{c@{\hspace{\xxx}}lc@{\hspace{\xxx}}lc@{\hspace{\xxx}}l}
$\textstyle\sum$ $\displaystyle\sum$ &amp; \verb+\sum+ &amp;
$\textstyle\prod$ $\displaystyle\prod$ &amp; \verb+\prod+ &amp;
$\textstyle\coprod$ $\displaystyle\coprod$ &amp; \verb+\coprod+ \\
$\textstyle\int$ $\displaystyle\int$ &amp; \verb+\int+ &amp;
$\textstyle\oint$ $\displaystyle\oint$ &amp; \verb+\oint+ &amp;
$\textstyle\biguplus$ $\displaystyle\biguplus$ &amp; \verb+\biguplus+ \\
  $\textstyle\bigcap$ $\displaystyle\bigcap$ &amp; \verb+\bigcap+ &amp;
  $\textstyle\bigcup$ $\displaystyle\bigcup$ &amp; \verb+\bigcup+ &amp;
  $\textstyle\bigsqcup$ $\displaystyle\bigsqcup$ &amp; \verb+\bigsqcup+ \\
  $\textstyle\bigodot$ $\displaystyle\bigodot$ &amp; \verb+\bigodot+ &amp;
  $\textstyle\bigotimes$ $\displaystyle\bigotimes$ &amp; \verb+\bigotimes+ &amp;
  $\textstyle\bigoplus$ $\displaystyle\bigoplus$ &amp; \verb+\bigoplus+ \\
  $\textstyle\bigvee$ $\displaystyle\bigvee$ &amp; \verb+\bigvee+ &amp;
  $\textstyle\bigwedge$ $\displaystyle\bigwedge$ &amp; \verb+\bigwedge+
\end{tabular}
\end{table}

\newpage

\subsubsection[Standard \protect\LaTeX{} typefaces]{Standard LaTeX typefaces}

You can access a pair of special typefaces in \LaTeX.

% only math mode?
You can switch to script (calligraphic) letters by using the \verb+\cal+
command (note the $\cal L$):
\begin{verbatim}
{\cal L}_{\text{int}} = e F^{3}_{\pi} r^{2}
  B^{0}(r,t) \epsilon \sin(\Omega t)
  \exp(\eta t),
\end{verbatim}
gives
\[
{\cal L}_{\text{int}} = eF^{3}_{\pi} r^{2}
 B^{0}(r,t)\epsilon\sin(\Omega t)\exp(\eta t),
\]
Only uppercase letters are available in the \verb+\cal+ font.


% only math mode?
You can switch to sans serif letters by using the \verb+\sf+
command (note the $\sf M$):

% \case -&gt; \frac for portability

\begin{verbatim}
R({\cal Q}-{\cal Q}_{0})
=R_{0} \exp\left(-\frac{1}{2}\Delta {\cal Q}
 \cdot{\sf M}\cdot\Delta{\cal Q}\right).
  \label{eq:rdef}
\end{verbatim}
gives
\[
  R({\cal Q}-{\cal Q}_{0}) =
%  R_{0} \exp\left(-\case1/2\Delta {\cal Q} \cdot {\sf M}
  R_{0} \exp\left(-\frac{1}{2}\Delta {\cal Q} \cdot {\sf M}
  \cdot \Delta {\cal Q}\right).
\]
Both uppercase and lowercase letters are available with \verb+\sf+.

\newpage

\subsubsection{Other notations}

% math mode only?
The \verb+\overline+ command puts a horizontal line above its argument
in math mode:
\begin{verbatim}
$\overline{x}+\overline{y}$
\end{verbatim}
gives
\[
\overline{x}+\overline{y}
\]

There is an analogous \verb+\underline+ command that works in text
or math mode:
\begin{verbatim}
The equation \underline{is} $\underline{x+y}$.
\end{verbatim}
gives
\[
\hbox{The equation \underline{is} $\underline{x+y}$.}
\]

% math mode?
Horizontal braces are put above or below an expression with the
\verb+\overbrace+ and \verb+\underbrace+ commands:
\begin{verbatim}
$\underbrace{a_{1} + \overbrace{a_{2}+a_{3}}
  + a_{4}}$
\end{verbatim}
gives
\[
\underbrace{a_{1} + \overbrace{a_{2}+a_{3}} + a_{4}}
\]
and in displayed math, a subscript or a superscript puts a label on
the brace:
\begin{verbatim}
$\underbrace{a_{1} +
  \overbrace{a_{2}+\cdots+a_{n-1}}^{n-2}
   + a_{n}}_{n}$
\end{verbatim}
gives
\[
\underbrace{a_{1} + \overbrace{a_{2}+\cdots+a_{n-1}}^{n-2} + a_{n}}_{n}
\]

Wide versions of the \verb+\hat+ and \verb+\tilde+ commands are available.
They are called \verb+\widehat+ and \verb+\widetilde+, respectively.
Here is an example:
\begin{verbatim}
$\widehat{a} + \widehat{ab}
 + \widehat{abc} + \widehat{abcd}$
\end{verbatim}
gives
\[
\widehat{a} + \widehat{ab} + \widehat{abc} + \widehat{abcd}
\]

\end{document}
% end of file charset.tex

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