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\appendix
\addtocounter{section}{1}
\section*{Appendix}

In case \AMSTeX\ is installed on your computer, the packages
\textsf{amsfonts} or \textsf{amssymb} will allow you 
to load \AMS\ fonts or \AMS\ fonts and  symbols  with \textsf{FBSart}.


\subsection{\AMS\ Fonts Notations}


The \AMS\ fonts  were developed by the American Mathematical 
Society and are  made available free of charge by the \AMS.
The \Metafont\ source files can be obtained, as are precompiled
.pk files. 

\subsection{Using {\protect\textsf{amsfonts}}}

The \textsf{amsfonts} class option provides
the \verb+\frak+ and \verb+\mathbb+ fonts and will also
use the extra Computer Modern fonts from the \AMS\ in order to provide
better access to bold math characters at smaller sizes and in
super- and subscripts.

With the \AMS\ fonts installed and employing either 
the \textsf{amsfonts} or \textsf{amssymb} (see Section\ref{amssymb} below) 
class option, 
the \verb+\mathfrak+ and \verb+\mathbb+ commands
are available. \verb+\mathfrak+ switches to the \AMS\ Fraktur font, while
\verb+\mathbb+ switches to the so-called ``Blackboard Bold'' font.
Only uppercase letters are available in Blackboard Bold, and there is
no bold version of this font. Fraktur has both uppercase and lowercase 
letters, and also a bold version is available.

Here are the letters ``ABCxyz'' from \verb+\mathfrak+: $\mathfrak{ABCxyz}$.
And here are the letters ``CRZN'' from \verb+\mathbb+: $\mathbb{CRZN}$.

Here is some mathemathics with superscripts and \verb+\mathfrak+. 
$$\mathfrak{E}=mc^{2\pi}.$$

To use \verb+\bm+ we have to switch to \verb+\normalsize+, otherwise no
bold fonts are available.
{\normalsize 
$$ \mbox{normal } {\mathfrak E}=mc^{2\pi} \mbox{ and  bold } 
{\bm {\mathfrak E}}={\bm m}{\bm c}^{{\bm 2}{\bm \pi}} $$
}   %% end \normalsize


\subsection{Using {\protect\textsf{amssymb}}}
\label{amssymb}

The \textsf{amssymb} class option defines  many extra symbols 
present in the \AMS\ fonts. These symbols and their names are shown in
the following tables.


Be aware that no bold versions are available for any of the symbols
in this section. A lot of \TeX's memory will be blocked by defining these
names. Therefore you should select this option with care.

\begin{table}[bp]
\beforetab
\begin{tabular}{*{2}{@{}c@{\,}l@{\,}}c@{\,}l@{}}
\firsthline 
$\digamma$ & \verb+\digamma+ & $\varkappa$ & \verb+\varkappa+ & \\
$\beth$ & \verb+\beth+ &     $\gimel$ & \verb+\gimel+ &
$\daleth$ & \verb+\daleth+ \\
$\hbar $ & \verb+\hbar+ &    $\hslash$ & \verb+\hslash+ &
$\backprime $ & \verb+\backprime+ \\
$\varnothing$ & \verb+\varnothing+ &$\vartriangle$ & \verb+\vartriangle+ &
$\blacktriangle$ & \verb+\blacktriangle+ \\
$\triangledown$ & \verb+\triangledown+ &
$\blacktriangledown$ & \verb+\blacktriangledown+ &
$\square$ & \verb+\square+ \\
$\blacksquare$ & \verb+\blacksquare+ & $\lozenge$ & \verb+\lozenge+ &
$\blacklozenge$ & \verb+\blacklozenge+ \\
$\circledS$ & \verb+\circledS+ &       $\bigstar$ & \verb+\bigstar+ &
$\angle $ & \verb+\angle+ \\
$\sphericalangle$ & \verb+\sphericalangle+ &
$\measuredangle$ & \verb+\measuredangle+ &  $\nexists$ & \verb+\nexists+ \\
$\complement$ & \verb+\complement+ & $\mho$ & \verb+\mho+ &
$\eth$ & \verb+\eth+ \\
$\Finv$ & \verb+\Finv+ & $\Game$ & \verb+\Game+ & $\diagup$ & \verb+\diagup+ \\
$\diagdown$ & \verb+\diagdown+ & $\Bbbk$ & \verb+\Bbbk+ &
$\varpropto$ & \verb+\varpropto+ \\
$\backepsilon$ & \verb+\backepsilon+ & 
$\blacktriangleleft$ & \verb+\blacktriangleleft+ &
$\blacktriangleright$ & \verb+\blacktriangleright+ \\
$\therefore$ & \verb+\therefore+ & $\because$ & \verb+\because+ & 
$\checkmark$ & \verb+\checkmark+ \\
  $\ulcorner$ & \verb+\ulcorner+ & $\urcorner$ & \verb+\urcorner+  &\\
  $\llcorner$ & \verb+\llcorner+ & $\lrcorner$ & \verb+\lrcorner+ & \\
  $\yen$ & \verb+\yen+ &           $\circledR$ & \verb+\circledR+ &
$\maltese$ & \verb+\maltese+\\
\lasthline 
\end{tabular}
\aftertab
\captionaftertab[]{Extra symbols available with 
{\protect\textsf{amssymb}}}
\end{table}

% Bin Op
\begin{table}
\beforetab
\begin{tabular}{*{2}{@{}c@{\,}l@{\,}}c@{\,}l@{}}
\firsthline
$\dotplus$ & \verb+\dotplus+ &
  $\ltimes$ & \verb+\ltimes+ &
$\smallsetminus$ & \verb+\smallsetminus+ \\
  $\rtimes$ & \verb+\rtimes+ &
$\barwedge$ & \verb+\barwedge+ &
  $\curlywedge$ & \verb+\curlywedge+ \\
$\veebar$ & \verb+\veebar+ &
  $\curlyvee$ & \verb+\curlyvee+ &
$\doublebarwedge$ & \verb+\doublebarwedge+ \\
$\Cap$ &   \verb+\Cap,\doublecap+ &
  $\leftthreetimes$ & \verb+\leftthreetimes+  &
$\Cup$ &   \verb+\Cup,\doublecup+ \\
  $\rightthreetimes$ & \verb+\rightthreetimes+ &
$\boxtimes$ & \verb+\boxtimes+ &
  $\circledast$ & \verb+\circledast+ \\
$\boxminus$ & \verb+\boxminus+ &
  $\circleddash$ & \verb+\circleddash+ &
$\boxplus$ & \verb+\boxplus+ \\
  $\centerdot$ & \verb+\centerdot+ &
$\boxdot$ & \verb+\boxdot+ &
  $\circledcirc$ & \verb+\circledcirc+ \\
$\divideontimes$ & \verb+\divideontimes+ &
  $\intercal$ & \verb+\intercal+    &\\
\lasthline
\end{tabular}
\aftertab
\captionaftertab[]{Binary operators available with the 
{\protect\textsf{amssymb}}}
\end{table}

%%  Arrows
\begin{table}[p]
\beforetab
\begin{tabular}{*{2}{@{}c@{}l@{}}c@{}l@{}}
\firsthline
$\leftrightarrows$ & \verb+\leftrightarrows+ &
  $\rightleftarrows$ & \verb+\rightleftarrows+ &
$\leftleftarrows$ & \verb+\leftleftarrows+ \\
  $\rightrightarrows$ & \verb+\rightrightarrows+ &
$\leftrightharpoons$ & \verb+\leftrightharpoons+ &
  $\rightleftharpoons$ & \verb+\rightleftharpoons+ \\
$\Lleftarrow$ & \verb+\Lleftarrow+ &
  $\Rrightarrow$ & \verb+\Rrightarrow+ &
$\twoheadleftarrow$ & \verb+\twoheadleftarrow+ \\
  $\twoheadrightarrow$ & \verb+\twoheadrightarrow+ &
$\leftarrowtail$ & \verb+\leftarrowtail+ &
  $\rightarrowtail$ & \verb+\rightarrowtail+ \\
$\looparrowleft$ & \verb+\looparrowleft+ &
  $\looparrowright$ & \verb+\looparrowright+ &
$\Lsh$ & \verb+\Lsh+ \\
  $\Rsh$ & \verb+\Rsh+ &
$\upuparrows$ & \verb+\upuparrows+ &
  $\downdownarrows$ & \verb+\downdownarrows+ \\
$\upharpoonleft$ & \verb+\upharpoonleft+ &
  $\upharpoonright$ & \verb+\upharpoonright,+ &
 $\upharpoonright$&\verb+\restriction+ \\
$\downharpoonleft$ & \verb+\downharpoonleft+ &
  $\downharpoonright$ & \verb+\downharpoonright+ &
$\curvearrowleft$ & \verb+\curvearrowleft+ \\
  $\curvearrowright$ & \verb+\curvearrowright+ &
$\circlearrowleft$ & \verb+\circlearrowleft+ &
  $\circlearrowright$ & \verb+\circlearrowright+ \\
$\multimap$ & \verb+\multimap+ &
  $\rightsquigarrow$ & \verb+\rightsquigarrow+ &
$\leftrightsquigarrow$ & \verb+\leftrightsquigarrow+ \\
$\dashrightarrow$ & \verb+\dashrightarrow+ &
  $\dashleftarrow$ & \verb+\dashleftarrow+ &
$\dasharrow$ & \verb+\dasharrow+ \\
$\nleftrightarrow$ & \verb+\nleftrightarrow+ &
  $\nLeftrightarrow$ & \verb+\nLeftrightarrow+&
$\nleftarrow$ & \verb+\nleftarrow+ \\
  $\nrightarrow$ & \verb+\nrightarrow+ &
$\nLeftarrow$ & \verb+\nLeftarrow+ &
  $\nRightarrow$ & \verb+\nRightarrow+ \\
\lasthline
\end{tabular}
\aftertab
\captionaftertab[]{Extra arrows available with the 
{\protect\textsf{amssymb}}} 
\end{table}

\begin{table}[p]
\beforetab
\begin{tabular}{*{2}{@{}c@{\,}l@{\,}}c@{\,}l@{}}
\firsthline
$\leqq$ & \verb+\leqq+ &
$\geqq$ & \verb+\geqq+ &
$\leqslant$ & \verb+\leqslant+ \\
$\geqslant$ & \verb+\geqslant+ &
$\eqslantless$ & \verb+\eqslantless+ &
$\eqslantgtr$ & \verb+\eqslantgtr+ \\
$\lesssim$ & \verb+\lesssim+ &
$\gtrsim$ & \verb+\gtrsim+ &
$\lessapprox$ & \verb+\lessapprox+ \\
$\gtrapprox$ & \verb+\gtrapprox+ &
$\approxeq$ & \verb+\approxeq+ &
$\lessdot$ & \verb+\lessdot+ \\
$\gtrdot$ & \verb+\gtrdot+ &
$\lll$ & \verb+\lll,\llless+ &
$\ggg$ & \verb+\ggg,\gggtr+ \\
$\lessgtr$ & \verb+\lessgtr+ &
$\gtrless$ & \verb+\gtrless+ &
$\lesseqgtr$ & \verb+\lesseqgtr+ \\
$\gtreqless$ & \verb+\gtreqless+ &
$\lesseqqgtr$ & \verb+\lesseqqgtr+ &
$\gtreqqless$ & \verb+\gtreqqless+ \\
$\preccurlyeq$ & \verb+\preccurlyeq+ &
$\succcurlyeq$ & \verb+\succcurlyeq+ &
$\curlyeqprec$ & \verb+\curlyeqprec+ \\
$\curlyeqsucc$ & \verb+\curlyeqsucc+ &
$\precsim$ & \verb+\precsim+ &
$\succsim$ & \verb+\succsim+ \\
$\precapprox$ & \verb+\precapprox+ &
$\succapprox$ & \verb+\succapprox+ &
$\subseteqq$ & \verb+\subseteqq+ \\
$\supseteqq$ & \verb+\supseteqq+ &
$\Subset$ & \verb+\Subset+ &
$\Supset$ & \verb+\Supset+ \\
$\sqsubset$ & \verb+\sqsubset+ &
$\sqsupset$ & \verb+\sqsupset+ &
$\backsim$ & \verb+\backsim+ \\
$\thicksim$ & \verb+\thicksim+ &
$\backsimeq$ & \verb+\backsimeq+ &
$\thickapprox$ & \verb+\thickapprox+ \\
$\doteqdot$ & \verb+\doteqdot,\Doteq+ &
$\eqcirc$ & \verb+\eqcirc+ &
$\risingdotseq$ & \verb+\risingdotseq+ \\
$\circeq$ & \verb+\circeq+ &
$\fallingdotseq$ & \verb+\fallingdotseq+ &
$\triangleq$ & \verb+\triangleq+ \\
$\vartriangleleft$ & \verb+\vartriangleleft+ &
$\vartriangleright$ & \verb+\vartriangleright+ &
$\trianglelefteq$ & \verb+\trianglelefteq+ \\
$\trianglerighteq$ & \verb+\trianglerighteq+ &
$\vDash$ & \verb+\vDash+ &
$\Vdash$ & \verb+\Vdash+ \\
$\Vvdash$ & \verb+\Vvdash+ &
$\smallsmile$ & \verb+\smallsmile+ &
$\smallfrown$ & \verb+\smallfrown+ \\
$\shortmid$ & \verb+\shortmid+ &
$\shortparallel$ & \verb+\shortparallel+ &
$\bumpeq$ & \verb+\bumpeq+ \\
$\Bumpeq$ & \verb+\Bumpeq+ &
$\between$ & \verb+\between+ &
$\pitchfork$ & \verb+\pitchfork+\\
$\nsim$ & \verb+\nsim+ &
  $\ncong$ & \verb+\ncong+ &
$\nless$ & \verb+\nless+ \\
  $\ngtr$ & \verb+\ngtr+ &
$\nleq$ & \verb+\nleq+ &
  $\ngeq$ & \verb+\ngeq+ \\
$\nleqslant$ & \verb+\nleqslant+ &
  $\ngeqslant$ & \verb+\ngeqslant+ &
$\nleqq$ & \verb+\nleqq+ \\
  $\ngeqq$ & \verb+\ngeqq+ &
$\lneq$ & \verb+\lneq+ &
  $\gneq$ & \verb+\gneq+ \\
$\lneqq$ & \verb+\lneqq+ &
  $\gneqq$ & \verb+\gneqq+ &
$\lvertneqq$ & \verb+\lvertneqq+ \\
  $\gvertneqq$ & \verb+\gvertneqq+ &
$\lnsim$ & \verb+\lnsim+ &
  $\gnsim$ & \verb+\gnsim+ \\
$\lnapprox$ & \verb+\lnapprox+ &
  $\gnapprox$ & \verb+\gnapprox+ &
$\nprec$ & \verb+\nprec+ \\
  $\nsucc$ & \verb+\nsucc+ &
$\npreceq$ & \verb+\npreceq+ &
  $\nsucceq$ & \verb+\nsucceq+ \\
$\precneqq$ & \verb+\precneqq+ &
  $\succneqq$ & \verb+\succneqq+ &
$\precnsim$ & \verb+\precnsim+ \\
  $\succnsim$ & \verb+\succnsim+ &
$\precnapprox$ & \verb+\precnapprox+ &
  $\succnapprox$ & \verb+\succnapprox+ \\
$\ntriangleleft$ & \verb+\ntriangleleft+ &
  $\ntriangleright$ & \verb+\ntriangleright+ &
$\ntrianglelefteq$ & \verb+\ntrianglelefteq+ \\
  $\ntrianglerighteq$ & \verb+\ntrianglerighteq+ &
$\nshortmid$ & \verb+\nshortmid+ &
$\nmid$ & \verb+\nmid+ \\
  $\nshortparallel$ & \verb+\nshortparallel+ &
  $\nparallel$ & \verb+\nparallel+ &
$\nvdash$ & \verb+\nvdash+ \\
  $\nvDash$ & \verb+\nvDash+ &
$\nVdash$ & \verb+\nVdash+ &
  $\nVDash$ & \verb+\nVDash+ \\
$\nsubseteq$ & \verb+\nsubseteq+ &
  $\nsupseteq$ & \verb+\nsupseteq+ &
$\nsubseteqq$ & \verb+\nsubseteqq+ \\
  $\nsupseteqq$ & \verb+\nsupseteqq+ &
$\varsubsetneq$ & \verb+\varsubsetneq+ &
  $\varsupsetneq$ & \verb+\varsupsetneq+ \\
$\subsetneq$ & \verb+\subsetneq+ &
  $\supsetneq$ & \verb+\supsetneq+ &
$\varsubsetneqq$ & \verb+\varsubsetneqq+ \\
  $\varsupsetneqq$ & \verb+\varsupsetneqq+ &
$\subsetneqq$ & \verb+\subsetneqq+ &
  $\supsetneqq$ & \verb+\supsetneqq+\\
\lasthline
\end{tabular}
\aftertab
\captionaftertab[]{Binary relations available with the 
{\protect\textsf{amssymb}}}
\end{table}


\clearpage
\endinput
