%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                 %
%    This is a LaTeX input file called FBSSUPPL.STY               %
%                                (version of April 28th, 1995)    %
%                                                                 %
%    Save this file under the name FBSSUPPL.STY into your LaTeX   %
%    input directory/folder. It will generate your documents in   %
%    the style required for FEW-BODY SYSTEMS SUPPLEMENTUM.        %
%    For further instructions see the manual that can be          %
%    generated by executing the source file EXAMPLE.TEX.          %
%                                                                 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% ARTICLE STANDARD DOCUMENT STYLE -- Released 14 Jan 1992
%    for LaTeX version 2.09
% Copyright (C) 1992 by Leslie Lamport
%
% Adapted by
%    Gerhard A. Bachmaier
%    Institute for Medical Informatics,
%    Statistics and Documentation
%    University of Graz
%    Graz, Austria
%
%    for Springer-Verlag  Wien, New York
  

\typeout{Document Style `fbssuppl' <28 April 95>.}

\def\@errmess#1#2{\typeout{FBS Suppl #1: #2}}

\def\AmS{{\protect\the\textfont2 
A\kern-.1667em\lower.5ex\hbox{M}\kern-.125emS}\,}
\def\AMSTeX{\AmS\TeX}

\def\partname{Part}
\def\contentsname{Contents}
\def\listfigurename{List of Figures}
\def\listtablename{List of Tables}
\def\refname{References}
\def\figurename{Figure}
\def\tablename{Table}
\def\abstractname{Abstract}

\newif\if@amsfonts  \@amsfontsfalse
\def\ds@amsfonts{\@amsfontstrue}

\newif\if@amssymbols  \@amssymbolsfalse
\def\ds@amssymb{\@amssymbolstrue}

\newif\if@psfig  \@psfigfalse
\def\ds@psfig{\@psfigstrue}

\def\ds@draft{\overfullrule 5\p@}

\newif\if@widenlines \@widenlinesfalse
\def\ds@widen{\@widenlinestrue}
\newif\if@tightenlines \@tightenlinesfalse
\def\ds@tighten{\@tightenlinestrue}

\newif\if@secnumeq \global\@secnumeqfalse
\def\ds@secnumeq{\global\@secnumeqtrue}
\newif\if@secnumfig \global\@secnumfigfalse
\def\ds@secnumfig{\global\@secnumfigtrue}
\newif\if@secnumtab \global\@secnumtabfalse
\def\ds@secnumtab{\global\@secnumtabtrue}

\@options
\@twosidetrue

\newcounter{numdate}
\setcounter{numdate}{\number\year}
\addtocounter{numdate}{-1990}
\multiply \value{numdate} by 12
\addtocounter{numdate}{\number\month}
\multiply \value{numdate} by 31
\addtocounter{numdate}{\number\day}

\def\widenlines{\def\baselinestretch{2.5}\small\normalsize}
\let\widen\widenlines
\def\tightenlines{\def\baselinestretch{1}\small\normalsize}
\let\tighten\tightenlines

\def\labelenumi{\theenumi.}
\def\theenumi{\arabic{enumi}}

\def\labelenumii{(\theenumii)}
\def\theenumii{\alph{enumii}}
\def\p@enumii{\theenumi}

\def\labelenumiii{\theenumiii.}
\def\theenumiii{\roman{enumiii}}
\def\p@enumiii{\theenumi(\theenumii)}

\def\labelenumiv{\theenumiv.}
\def\theenumiv{\Alph{enumiv}}
\def\p@enumiv{\p@enumiii\theenumiii}

\def\labelitemi{$\m@th\bullet$}
\def\labelitemii{\bf --}
\def\labelitemiii{$\m@th\ast$}
\def\labelitemiv{$\m@th\cdot$}

\def\verse{\let\\=\@centercr
  \list{}{\itemsep\z@ \itemindent -1.5em\listparindent \itemindent
          \rightmargin\leftmargin\advance\leftmargin 1.5em}\item[]}
\let\endverse\endlist

\def\quotation{\list{}{\listparindent 1.5em
    \itemindent\listparindent
    \rightmargin\leftmargin  % for both sided indent
    \parsep \z@ plus\p@}\item[]}
\let\endquotation=\endlist

\def\Quotation{\list{}{\listparindent 1.5em
    \itemindent\listparindent
    \parsep \z@ plus\p@}\item[]}
\let\endQuotation=\endlist

\def\quote{\list{}{\rightmargin\leftmargin}\item[]}
\let\endquote=\endlist

\def\descriptionlabel#1{\hspace\labelsep \bf #1}
\def\description{\list{}{\labelwidth\z@ \itemindent-\leftmargin
       \let\makelabel\descriptionlabel}}

\let\enddescription\endlist

\def\theequation{\arabic{equation}}

\arraycolsep 5pt

\tabcolsep 6pt

\arrayrulewidth .4pt
\doublerulesep 2pt

\tabbingsep \labelsep

\skip\@mpfootins = \skip\footins

\fboxsep = 3pt

\fboxrule = .4pt

\newcounter{part}
\newcounter {section}
\newcounter {subsection}[section]
\newcounter {subsubsection}[subsection]
\newcounter {paragraph}[subsubsection]
\newcounter {subparagraph}[paragraph]

\def\thepart          {\Roman{part}}
\def\thesection       {\arabic{section}}
\def\thesubsection    {\thesection.\arabic{subsection}}
\def\thesubsubsection {\thesubsection.\arabic{subsubsection}}
\def\theparagraph     {\thesubsubsection.\arabic{paragraph}}
\def\thesubparagraph  {\theparagraph.\arabic{subparagraph}}

\def\part{\par
   \addvspace{4ex}
   \@afterindentfalse
   \secdef\@part\@spart}

\def\@part[#1]#2{\ifnum \c@secnumdepth >\m@ne
        \refstepcounter{part}
        \addcontentsline{toc}{part}{\thepart
        \hspace{1em}#1}\else
      \addcontentsline{toc}{part}{#1}\fi
   {\parindent \z@ \raggedright
    \interlinepenalty \@M
    \ifnum \c@secnumdepth >\m@ne
      \Large \bf \partname~\thepart%   THEN Print '\partname' and
      \par\nobreak
    \fi
    \huge \bf
    #2%
    \markboth{}{}\par
   }\nobreak
   \vskip 5ex
   \@afterheading
  }

\def\@spart#1{{\parindent \z@ \raggedright
    \interlinepenalty \@M
    \huge \bf
    #1\par}
    \nobreak
    \vskip 3ex
    \@afterheading
  }

\def\@pnumwidth{1.55em}
\def\@tocrmarg {2.55em}
\def\@dotsep{4.5}
\setcounter{tocdepth}{3}

\def\tableofcontents{\section*{\contentsname
        \@mkboth{\uppercase{\contentsname}}{\uppercase{\contentsname}}}%
  \@starttoc{toc}}

\def\l@part#1#2{\addpenalty{\@secpenalty}%
   \addvspace{2.25em plus\p@}%
   \begingroup
   \@tempdima 3em
     \parindent \z@ \rightskip \@pnumwidth
     \parfillskip -\@pnumwidth
     {\large \bf
     \leavevmode
     #1\hfil \hbox to\@pnumwidth{\hss #2}}\par
     \nobreak
   \endgroup}

\def\l@section#1#2{\addpenalty{\@secpenalty}% good place for page break
   \addvspace{1.0em plus\p@}%
   \@tempdima 1.5em
   \begingroup
     \parindent \z@ \rightskip \@pnumwidth
     \parfillskip -\@pnumwidth
     \bf
     \leavevmode
      \advance\leftskip\@tempdima
      \hskip -\leftskip
     #1\nobreak\hfil \nobreak\hbox to\@pnumwidth{\hss #2}\par
   \endgroup}

\def\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}}
\def\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}}
\def\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}}
\def\l@subparagraph{\@dottedtocline{5}{10em}{5em}}

\def\listoffigures{\section*{\listfigurename
    \@mkboth{\uppercase{\listfigurename}}{\uppercase{\listfigurename}}}%
  \@starttoc{lof}}

\def\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}

\def\listoftables{\section*{\listtablename\@mkboth
   {\uppercase{\listtablename}}{\uppercase{\listtablename}}}%
  \@starttoc{lot}}
\let\l@table\l@figure

\def\thebibliography#1{\@appendixfalse\section*{\refname\@mkboth{}{}}\list
  {\@biblabel{\arabic{enumiv}}}{\settowidth\labelwidth{\@biblabel{#1}}%
    \leftmargin\labelwidth
    \advance\leftmargin\labelsep
    \usecounter{enumiv}%
    \let\p@enumiv\@empty
    \def\theenumiv{\arabic{enumiv}}}%
    \def\newblock{\hskip .11em plus.33em minus.07em}%
    \sloppy\clubpenalty4000\widowpenalty4000
    \sfcode`\.=1000\relax}

\def\@biblabel#1{#1.}

\def\endthebibliography{%
  \def\@noitemerr{\@warning{Empty `thebibliography' environment}}%
  \endlist}

\def\@checkdate{\ifnum \value{numdate} > 2015 
\@errmess{error}{Evaluation time expired! Contact your TeX wizard %
immediately!}\enddocument \else\relax\fi}

\newif\if@restonecol

\def\footnoterule{\kern-3\p@
  \hrule width .4\columnwidth
  \kern 2.6\p@}

\def\Fnsymbol#1{\@Fnsymbol{\@nameuse{c@#1}}}
\def\@Fnsymbol#1{\ifcase#1\or * \or \dagger \or ** \or \dagger\dagger %
\or *** \or \dagger\dagger\dagger \or **** \or \dagger\dagger\dagger\dagger %
\or ***** \or \dagger\dagger\dagger\dagger\dagger \else\@ctrerr\fi\relax}

\newcounter{thanks}
\newlength\@fnindent
\def\get@fnindent{%
\ifnum \value{thanks} <3 \setlength{\@fnindent}{4pt} \else%
  \ifnum \value{thanks} <5 \setlength{\@fnindent}{8pt} \else%
    \ifnum \value{thanks} <7 \setlength{\@fnindent}{12pt} \else%
      \ifnum \value{thanks} <9 \setlength{\@fnindent}{16pt} \else%
        \setlength{\@fnindent}{20pt}%
\fi\fi\fi\fi}

\long\def\@makefntext#1{\@setpar{\get@fnindent\@@par\@tempdima \hsize
  \advance\@tempdima-\@fnindent\parshape \@ne \@fnindent \@tempdima}\par 
  \parindent 0pt\noindent
            \hbox to\z@{\hss$\m@th^{\@thefnmark}$}#1}

\setcounter{topnumber}{4}
\def\topfraction{.9}
\setcounter{bottomnumber}{4}
\def\bottomfraction{.9}
\setcounter{totalnumber}{8}
\def\textfraction{.1}
\def\floatpagefraction{.7}
\setcounter{dbltopnumber}{2}
\def\dbltopfraction{.7}
\def\dblfloatpagefraction{.5}


\long\def\@makecaption#1#2{%
   \vskip 10\p@
   {\small {\bf #1.} #2\par\vskip5\p@}}

\newcounter{figure}
\@definecounter{figure}%
\if@secnumfig %
\@addtoreset{figure}{section} %
\def\thefigure@prefix{\arabic{section}.} %
\else %
\def\thefigure@prefix{}
\fi

\def\thefigure{\thefigure@prefix\@arabic\c@figure}%

\def\fps@figure{tbp}
\def\ftype@figure{1}
\def\ext@figure{lof}
\def\fnum@figure{\figurename~\thefigure}
\def\figure{\@float{figure}}
\let\endfigure\end@float

\newcounter{table}
\@definecounter{table}%
\if@secnumtab %
\@addtoreset{table}{section} %
\def\thetable@prefix{\arabic{section}.} %
\else %
\def\thetable@prefix{}
\fi

\def\thetable{\thetable@prefix\@arabic\c@table}%

\def\tabstrut{\rule[-3mm]{0mm}{8mm}}
\renewcommand{\arraystretch}{1.1}

\def\fps@table{tbp}
\def\ftype@table{2}
\def\ext@table{lot}
\def\fnum@table{\tablename~\thetable}
\def\table{\@float{table}}
\let\endtable\end@float

\newcounter{pageskip}
\def\emptyfloatpages#1#2#3{%
\if #1+#2<1 \@errmess{error}{No floats selected, command ignored!}\relax
\else 
 \if #3<1 \@errmess{warning}{Number of empty pages reset to one!}%
 \setcounter{pageskip}{1}\else\setcounter{pageskip}{#3}\fi
 \@errmess{information}{There will be #1 skipped figures.}
 \@errmess{information}{There will be #2 skipped tables.}
 \@errmess{information}{There will be #3 skipped pages.}
 \addtocounter{figure}{#1}
 \addtocounter{table}{#2}
 \loop\ifnum\value{pageskip}>0 \@emptyfloat\advance\value{pageskip}-1\repeat
\fi}

\def\@emptyfloat{\begin{figure}[p]\vspace*{180mm}\end{figure}}

\newcounter{instnum}
\setcounter{instnum}{1}
\def\theinstnum{\arabic{instnum}}

\newif\if@singleinst
\@singleinsttrue

\def\instnr#1{$\m@th{}^{#1}$}
\def\thanksnr#1{$\m@th{}^{\Fnsymbol{#1}}$}

\def\institute#1{\gdef\@institute{#1}}
\def\instlist#1{\gdef\@instlist{#1\@singleinstfalse}}

\def\@checkinst{%\let\and\mbox{}
\@ifundefined{@institute}{\@singleinstfalse}{\@singleinsttrue}}

\newlength{\@tablength}
\setlength{\@tablength}{114mm}
\renewcommand\and{%
\end{tabular}\par\noindent\vspace{1pt}\addtocounter{instnum}{1}%
\begin{tabular}[t]{@{}p{3mm}@{\,}p{\@tablength}}\hfil${}^{\theinstnum}$&%
}

\def\SaveFinalPage{%
 \write\@mainaux{\string\SetFinalPage{\arabic{page}}}}
 \def\SetFinalPage#1{\gdef\FinalPage{#1}}
 \SetFinalPage{??}

\newcounter{volume}
\setcounter{volume}{99}

\def\@year{\number\year}

\newcommand\FBSlogo{\unitlength=1mm
\begin{picture}(28,3)(0,15)\put(0,0){\line(1,0){28}}
\put(0,18){\line(1,0){28}}\put(13,13){\Large Few-}
\put(14.5,9.8){\Large Body}\put(9.3,7.3){\Large Systems}
\put(0,4){\hbox to 28mm{\tiny\copyright\ by Springer-Verlag \@year}}
\put(0,2){\tiny Printed in Austria}
\end{picture}} % end FBS-Logo

\def\maketitle{\par
 \begingroup
   \def\thefootnote{\Fnsymbol{footnote}}%
   \def\@makefnmark{${}^{\@thefnmark}$}%
     \newpage
     \global\@topnum\z@
     \@maketitle 
     \setcounter{thanks}{\value{footnote}}
     \thispagestyle{myheadings}\@thanks
 \endgroup
 \setcounter{footnote}{0}%
 \let\maketitle\relax
 \let\@maketitle\relax
 \gdef\@thanks{}\gdef\@author{}\gdef\@title{}\gdef\@institute{}%
 \gdef\@instlist{}\let\thanks\relax}

\def\@maketitle{\newpage
 \null
 \vskip 20mm
 \begin{flushleft}%
  {\Large \@title \par}%
  \vskip 10mm
  \normalsize
   \lineskip .5em
   \@author \par\vskip 5pt\noindent
   \@checkinst
   \if@singleinst%
     \@institute\par\end{flushleft}% 
   \else
     \end{flushleft}
     \begin{tabular}[t]{@{}p{3mm}@{\,}p{\@tablength}}\hfil${}^1$&\@instlist
     \end{tabular}\par%   
   \fi
  \vskip 2em}

\def\abstract{\small\Quotation%
\noindent {\bf \abstractname.}
}

\def\endabstract{\endQuotation\normalsize}

\def\acknowledge{\par\vskip1em\normalsize%
\noindent {\it Acknowledgement.}}

\def\endacknowledge{\par\vskip1em}

\mark{{}{}}

 \def\ps@headings{\let\@mkboth\markboth
  \def\@oddfoot{}\def\@evenfoot{}%       No feet.
  \def\@evenhead{\hbox{}{\rm\small \thepage} \hfil}%   Left heading.
  \def\@oddhead{\hbox{}\hfil {\rm\small\thepage}}% Right heading.
 }

 \def\ps@myheadings{\let\@mkboth\markboth
  \def\@oddfoot{}\def\@evenfoot{}%       No feet.
  \def\@evenhead{This page (\thepage) should be an odd one!}%        
  %                  Left heading should not occur for 1st page!
  \def\@oddhead{{\small \bf Few-Body Systems Suppl.\ \thevolume, \thepage--%
  \FinalPage\ (\@year)} \hfil \FBSlogo}% Right heading.
  }

\def\today{\ifcase\month\or
  January\or February\or March\or April\or May\or June\or
  July\or August\or September\or October\or November\or December\fi
  \space\number\day, \number\year}

\ps@headings
\pagenumbering{arabic}
\onecolumn
\flushbottom
\frenchspacing

%
% Additional mathematical stuff
%  
\newdimen\fdxvi
\newdimen\fdxvii
%\newcommand{\chemical}[1]{%
%\@ifundefined{selectfont}%
% {\fdxvi=\fontdimen16\tensy \fdxvii=\fontdimen17\tensy%  
% {$\fontdimen16\tensy=.3\fontdimen5\tensy 
% \fontdimen17\tensy=.3\fontdimen5\tensy \rm #1$} 
% \fontdimen16\tensy=\fdxvi \fontdimen17\tensy=\fdxvii}
%{\relax}
%}

\let\@Realpart\Re
\let\@Imagpart\Im
\renewcommand{\Re}{\mbox{\rm Re}}
\renewcommand{\Im}{\mbox{\rm Im}}

\let\Ohm\Omega
\let\Laplace\Delta

\let\rmGamma\Gamma
\let\rmDelta\Delta
\let\rmTheta\Theta
\let\rmLambda\Lambda
\let\rmXi\Xi
\let\rmPi\Pi
\let\rmSigma\Sigma
\let\rmUpsilon\Upsilon
\let\rmPhi\Phi
\let\rmPsi\Psi
\let\rmOmega\Omega

\mathchardef\Gamma="0100
\mathchardef\Delta="0101
\mathchardef\Theta="0102
\mathchardef\Lambda="0103
\mathchardef\Xi="0104
\mathchardef\Pi="0105
\mathchardef\Sigma="0106
\mathchardef\Upsilon="0107
\mathchardef\Phi="0108
\mathchardef\Psi="0109
\mathchardef\Omega="010A

\let\inodot\i%
\let\jnodot\j%
\renewcommand{\i}{\ifmmode{\rm i}\else\inodot\fi}
\renewcommand{\j}{\ifmmode{\rm j}\else\jnodot\fi}

\def\putilde#1{\oalign{$#1$\crcr\hidewidth 
   \vbox to.2ex{\hbox{\char126}\vss}\hidewidth}}
\def\utilde{\protect\putilde}

\def\bm#1{%
\mathchoice
{{\hbox{\boldmath$\displaystyle#1$\unboldmath}}}%
{{\hbox{\boldmath$\textstyle#1$\unboldmath}}}%
{{\hbox{\boldmath$\scriptstyle#1$\unboldmath}}}%
{{\hbox{\boldmath$\scriptscriptstyle#1$\unboldmath}}}%
}

\let\polarize\vec
\def\tensor#1{\protect\@ontopof{#1}{\leftrightarrow}{1.15}\mathord{\box2}}
\def\loarrow#1{\protect\@ontopof{#1}{\leftarrow}{1.15}\mathord{\box2}}
\def\roarrow#1{\protect\@ontopof{#1}{\rightarrow}{1.15}\mathord{\box2}}

\def\@ontopof#1#2#3{%
{\mathchoice
{\@@ontopof{#1}{#2}{#3}\displaystyle\scriptstyle}%
{\@@ontopof{#1}{#2}{#3}\textstyle\scriptstyle}%
{\@@ontopof{#1}{#2}{#3}\scriptstyle\scriptscriptstyle}%
{\@@ontopof{#1}{#2}{#3}\scriptscriptstyle\scriptscriptstyle}%
}%
}

\def\@@ontopof#1#2#3#4#5{%
\setbox0=\hbox{$#4#1$}%
\setbox1=\hbox{$#5#2$}%
\setbox2=\hbox{}\ht2=\ht0 \dp2=\dp0 %
\ifdim\wd0>\wd1 %
\setbox1=\hbox to\wd0{\hss\box1\hss}%
\mathord{\rlap{\raise#3\ht0\box1}\box0}%
\else     %
\setbox1=\hbox to.9\wd1{\hss\box1\hss}%
\setbox0=\hbox to\wd1{\hss$#4\relax#1$\hss}%
\mathord{\rlap{\copy0}\raise#3\ht0\box1}%
\fi
}

%  Redine vectors as boldface letters 
\def\vec#1{\bm{#1}}

\def\openone{\leavevmode\hbox{\small1\kern-3.3pt\normalsize1}}%

%  Additional symbols (if you do not use AMS-TeX)
\def\squareforqed{\hbox{\rlap{$\sqcap$}$\sqcup$}}
\def\qed{\ifmmode\squareforqed\else{\unskip\nobreak\hfil
\penalty50\hskip1em\null\nobreak\hfil\squareforqed
\parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi}
\def\getsto{\mathrel{\mathchoice {\vcenter{\offinterlineskip
\halign{\hfil
$\displaystyle##$\hfil\cr\gets\cr\to\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr\gets
\cr\to\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr\gets
\cr\to\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
\gets\cr\to\cr}}}}}
\def\lid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr
\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr
\noalign{\vskip1pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr
\noalign{\vskip0.9pt}=\cr}}}}}
\def\gid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr
\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr
\noalign{\vskip1pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr
\noalign{\vskip0.9pt}=\cr}}}}}
\def\grole{\mathrel{\mathchoice {\vcenter{\offinterlineskip
\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\noalign{\vskip-1pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
>\cr\noalign{\vskip-1pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
>\cr\noalign{\vskip-0.8pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr\noalign{\vskip-0.3pt}<\cr}}}}}

\newcommand{\Lesim}{\raisebox{-.3ex}[1.ex][1.ex]{%
\mbox{$\,\stackrel{\scriptstyle<}{\scriptscriptstyle \approx}\,$}}}
\newcommand{\Gesim}{\raisebox{-.3ex}[1.ex][1.ex]{%
\mbox{$\,\stackrel{\scriptstyle>}{\scriptscriptstyle \approx}\,$}}}
\newcommand{\lesim}{\raisebox{-.3ex}[1.ex][1.ex]{%
\mbox{$\,\stackrel{\scriptstyle<}{\scriptscriptstyle \sim}\,$}}}
\newcommand{\gesim}{\raisebox{-.3ex}[1.ex][1.ex]{%
\mbox{$\,\stackrel{\scriptstyle>}{\scriptscriptstyle \sim}\,$}}}

\def\Prom{\leavevmode{\kern-.05em
 \raise.5ex\hbox{\the\scriptfont0 0}\kern-.15em/\kern-.15em
 \lower.25ex\hbox{\the\scriptfont0 00}}}
\def\prom{\leavevmode{\kern-.05em
 \raise.5ex\hbox{\the\scriptscriptfont0 0}\kern-.15em/\kern-.15em
 \lower.25ex\hbox{\the\scriptscriptfont0 00}}}
\def\Perc{\leavevmode{\kern-.05em
 \raise.5ex\hbox{\the\scriptfont0 0}\kern-.15em/\kern-.15em
 \lower.25ex\hbox{\the\scriptfont0 0}}}
\def\perc{\leavevmode{\kern-.05em
 \raise.5ex\hbox{\the\scriptscriptfont0 0}\kern-.15em/\kern-.15em
 \lower.25ex\hbox{\the\scriptscriptfont0 0}}}

%AMS-Notation for relations and symbols defined above
\if@amssymbols\relax
\else
 \@ifundefined{square}{\let\square\squareforqed}{\relax}
 \@ifundefined{leftrightarrows}{\let\leftrightarrows\getsto}{\relax}
 \@ifundefined{leqq}{\let\leqq\lid}{\relax}
 \@ifundefined{geqq}{\let\geqq\gid}{\relax}
 \@ifundefined{gtrless}{\let\gtrless\grole}{\relax}
 \@ifundefined{lessapprox}{\let\lessapprox\Lesim}{\relax}
 \@ifundefined{gtrapprox}{\let\gtrapprox\Gesim}{\relax}
 \@ifundefined{lesssim}{\let\lesssim\lesim}{\relax}
 \@ifundefined{gtrsim}{\let\gtrsim\gesim}{\relax}
\fi

\newcounter{eqletter} \setcounter{eqletter}{0}

\def\@eqnnum{\hbox{\reset@font\rm(\theequation)}}
\let\make@eqnnum=\@eqnnum %
\def\eqnum#1{\dec@eqnnum \global\def\make@eqnnum{\reset@font\rm(#1)}%
\def\@currentlabel{#1}%
}
\def\inc@eqnnum{\addtocounter{equation}{1}}
\def\dec@eqnnum{\addtocounter{equation}{-1}}
\@definecounter{equation}%
\if@secnumeq %
\@addtoreset{equation}{section} %
\def\theequation@prefix{\arabic{section}.} %
\else %
\def\theequation@prefix{}
\fi

\def\theequation{\theequation@prefix\arabic{equation}}%

\def\equation{$$ %% $$ brace matching hack
\inc@eqnnum%
\let\@currentlabel=\theequation%
}

\def\endequation{\eqno\hbox{\@eqnnum} %% $$ brace matching hack
$$\global\@ignoretrue}

\def\mathletters{%
\inc@eqnnum      \setcounter{eqletter}{0}%
\edef\@currentlabel{\theequation}%
\def\theequation{\theequation@prefix\arabic{equation}\alph{eqletter}}%
\def\inc@eqnnum{\addtocounter{eqletter}{1}}%
\def\dec@eqnnum{\addtocounter{eqletter}{-1}}%
}

\let\endmathletters\relax

\def\Equation#1{$$ %% $$ brace matching hack
\let\save@number\theequation
\def\theequation{\mbox{#1}}
\let\@currentlabel=\theequation
}

\def\endEquation{\eqno\hbox{\@eqnnum} %% $$ brace matching hack
$$\global\@ignoretrue%
\let\theequation\save@number}

%   End of mathematical stuff
%
%   Following definitions are based on art10.sty 

\lineskip 1pt
\normallineskip 1pt
\def\baselinestretch{1}

\def\@normalsize{\@setsize\normalsize{12pt}\xpt\@xpt
\abovedisplayskip 10\p@ plus2\p@ minus5\p@
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip  \z@ plus3\p@
\belowdisplayshortskip  6\p@ plus3\p@ minus3\p@
\let\@listi\@listI}

\def\small{\@setsize\small{11pt}\ixpt\@ixpt
\abovedisplayskip 8.5\p@ plus3\p@ minus4\p@
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus2\p@
\belowdisplayshortskip 4\p@ plus2\p@ minus2\p@
\def\@listi{\leftmargin\leftmargini
\topsep 4\p@ plus2\p@ minus2\p@\parsep 2\p@ plus\p@ minus\p@
\itemsep \parsep}}

\def\footnotesize{\@setsize\footnotesize{9.5pt}\viiipt\@viiipt
\abovedisplayskip 6\p@ plus2\p@ minus4\p@
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus\p@
\belowdisplayshortskip 3\p@ plus\p@ minus2\p@
\def\@listi{\leftmargin\leftmargini
\topsep 3\p@ plus\p@ minus\p@\parsep 2\p@ plus\p@ minus\p@
\itemsep \parsep}}

\def\scriptsize{\@setsize\scriptsize{8pt}\viipt\@viipt}
\def\tiny{\@setsize\tiny{6pt}\vpt\@vpt}
\def\large{\@setsize\large{14pt}\xiipt\@xiipt}
\def\Large{\@setsize\Large{18pt}\xivpt\@xivpt}
\def\LARGE{\@setsize\LARGE{22pt}\xviipt\@xviipt}
\def\huge{\@setsize\huge{25pt}\xxpt\@xxpt}
\def\Huge{\@setsize\Huge{30pt}\xxvpt\@xxvpt}

\normalsize

\oddsidemargin  50pt
\evensidemargin 50pt
\marginparwidth 107pt

\marginparsep 11pt

\topmargin 30pt

\headheight 10pt
\headsep 10pt
\topskip = 10pt

\footskip 0pt

\textheight = 45\baselineskip
\advance\textheight by \topskip
\textwidth 120mm

\footnotesep 6.65pt

\skip\footins 9pt plus 4pt minus 2pt

\floatsep 12pt plus 2pt minus 2pt

\textfloatsep 20pt plus 2pt minus 4pt

\intextsep 12pt plus 2pt minus 2pt

\@maxsep 20pt

\dblfloatsep 0pt
\dbltextfloatsep 0pt
\@dblmaxsep 0pt

\@fptop 0pt plus 1fil

\@fpsep 8pt plus 2fil
\@fpbot 0pt plus 1fil

\@dblfptop 0pt plus 1fil
\@dblfpsep 0pt plus 2fil
\@dblfpbot 0pt plus 1fil

\marginparpush 5pt

\parskip 0pt 

\parindent 15pt

\partopsep 2pt plus 1pt minus 1pt

\@lowpenalty   51
\@medpenalty  151
\@highpenalty 301

\@beginparpenalty -\@lowpenalty

\@endparpenalty   -\@lowpenalty

\@itempenalty     -\@lowpenalty

\newif\if@appendix
\@appendixfalse
\if@appendix
\def\section{\@startsection {section}{1}{\z@}{-3.5ex plus-1ex minus
    -.2ex}{2.3ex plus.2ex}{\noindent\reset@font\normalsize\bf Appendix }}
\else
\def\section{\@startsection {section}{1}{\z@}{-3.5ex plus-1ex minus
    -.2ex}{2.3ex plus.2ex}{\reset@font\normalsize\bf}}
\fi

\def\subsection{\@startsection{subsection}{2}{\z@}{-3.25ex plus-1ex
    minus-.2ex}{1.5ex plus.2ex}{\reset@font\normalsize\sl}}
\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-3.25ex plus
    -1ex minus-.2ex}{1.5ex plus.2ex}{\reset@font\normalsize}}
\def\paragraph{\@startsection
     {paragraph}{4}{\z@}{3.25ex plus1ex minus.2ex}{-1em}{\reset@font
     \normalsize}}
\def\subparagraph{\@startsection
     {subparagraph}{5}{\parindent}{3.25ex plus1ex minus
     .2ex}{-1em}{\reset@font\normalsize}}

\setcounter{secnumdepth}{3}

\def\appendix{\par\@afterindentfalse
  \setcounter{section}{0}
  \setcounter{subsection}{0}
  \setcounter{subsubsection}{0}
  \setcounter{figure}{0}
  \setcounter{table}{0}
  \def\thesection{\Alph{section}}
  \def\thesubsection{\thesection.\arabic{subsection}}
  \def\thesubsubsection{\thesubsection.\arabic{subsubsection}}
  \def\theequation@prefix{\thesection.}
  \def\thefigure@prefix{\thesection.}
  \def\thetable@prefix{\thesection.}
  \@addtoreset{equation}{section}
  \@addtoreset{figure}{section}
  \@addtoreset{table}{section}
  \@secnumeqtrue
  \@secnumfigtrue
  \@secnumtabtrue
  \@appendixtrue
  }

\leftmargini 25pt
\leftmarginii 22pt
\leftmarginiii 18.7pt
\leftmarginiv 17pt
\leftmarginv 10pt
\leftmarginvi 10pt

\leftmargin\leftmargini
\labelsep 5pt
\labelwidth\leftmargini\advance\labelwidth-\labelsep

\def\@listI{\leftmargin\leftmargini \parsep 4\p@ plus2\p@ minus\p@
\topsep 8\p@ plus2\p@ minus4\p@
\itemsep 4\p@ plus2\p@ minus\p@}

\let\@listi\@listI
\@listi

\def\@listii{\leftmargin\leftmarginii
   \labelwidth\leftmarginii\advance\labelwidth-\labelsep
   \topsep 4\p@ plus2\p@ minus\p@
   \parsep 2\p@ plus\p@ minus\p@
   \itemsep \parsep}

\def\@listiii{\leftmargin\leftmarginiii
    \labelwidth\leftmarginiii\advance\labelwidth-\labelsep
    \topsep 2\p@ plus\p@ minus\p@
    \parsep \z@ \partopsep \p@ plus\z@ minus\p@
    \itemsep \topsep}

\def\@listiv{\leftmargin\leftmarginiv
     \labelwidth\leftmarginiv\advance\labelwidth-\labelsep}

\def\@listv{\leftmargin\leftmarginv
     \labelwidth\leftmarginv\advance\labelwidth-\labelsep}

\def\@listvi{\leftmargin\leftmarginvi
     \labelwidth\leftmarginvi\advance\labelwidth-\labelsep}

%
%   definitions for AMSTeX
%
\ifx\selectfont\undefined %
\@errmess{message}{NFSS not detected. Assuming OFSS.}
\let\reset@font\relax
\def\mathhexbox{\protect\mathhexbox@}
\def\mathhexbox@#1#2#3{\relax
\ifmmode\mathpalette{}{\m@th\mathchar"#1#2#3}%
\else\leavevmode\hbox{$\m@th\mathchar"#1#2#3$}\fi}
\def\text#1{%
\relax
\ifmmode %
\mathchoice
{\hbox{\everymath{\displaystyle}\rm #1}}%
{\hbox{\everymath{\textstyle}\rm #1}}%
{\hbox{\everymath{\scriptstyle}%
\def\prm{\fam\z@ \the\scriptfont\z@ \relax}%
\def\pit{\fam\itfam \the\scriptfont\itfam \relax}%
\rm #1}%
}%
{\hbox{\everymath{\scriptscriptstyle}%
\def\prm{\fam\z@ \the\scriptscriptfont\z@ \relax}%
\def\pit{\fam\itfam \the\scriptscriptfont\itfam \relax}%
\rm #1}%
}%
\else %
\leavevmode\hbox{#1}%
\fi
}
\def\bbox#1{%
\leavevmode\text{%
\textfont0 \the\textfont\bffam
\scriptfont0 \the\scriptfont\bffam
\scriptscriptfont0 \the\scriptscriptfont\bffam
\@temptokena\everymath \boldmath \everymath\@temptokena
{$\m@th\relax#1$}%
}%
}
\font\fivbf=cmbx5 \font\sixbf=cmbx6 \font\sevbf=cmbx7 \font\egtbf=cmbx8
\expandafter\def\expandafter\ixpt\expandafter{\ixpt
\scriptfont\bffam\sixbf \scriptscriptfont\bffam\fivbf}
\expandafter\def\expandafter\xpt\expandafter{\xpt
\scriptfont\bffam\sevbf \scriptscriptfont\bffam\fivbf}
\expandafter\def\expandafter\xipt\expandafter{\xipt
\scriptfont\bffam\egtbf \scriptscriptfont\bffam\sixbf}
\expandafter\def\expandafter\xiipt\expandafter{\xiipt
\scriptfont\bffam\egtbf \scriptscriptfont\bffam\sixbf}
\expandafter\def\expandafter\xivpt\expandafter{\xivpt
\scriptfont\bffam\tenbf \scriptscriptfont\bffam\sevbf}
\else %
\@errmess{message}{NFSS detected! Assuming NFSS.}
\def\text#1{%
\relax\ifmmode
\mathchoice
{\hbox{{\everymath{\displaystyle}#1}}}%
{\hbox{{\everymath{\textstyle}#1}}}%
{\hbox{{\everymath{\scriptstyle}\let\f@size\sf@size\selectfont#1}}}%
{\hbox{{\everymath{\scriptscriptstyle}\let\f@size\ssf@size\selectfont#1}}}%
\glb@settings
\else
\mbox{#1}%
\fi
}
\def\bbox#1{%
\relax\ifmmode
\mathchoice
{{\hbox{\boldmath$\displaystyle#1$}}}%
{{\hbox{\boldmath$\textstyle#1$}}}%
{{\hbox{\boldmath$\scriptstyle#1$}}}%
{{\hbox{\boldmath$\scriptscriptstyle#1$}}}%
\glb@settings
\else
\mbox{#1}%
\fi
}

\def\mathhexbox{\protect\mathhexbox@}
\def\mathhexbox@#1#2#3{\relax
\ifmmode\mathpalette{}{\m@th\mathchar"#1#2#3}%
\else\leavevmode\hbox{$\m@th\mathchar"#1#2#3$}\fi}
\fi

\if@amssymbols %
\def\@tempa{%
\let\gtrsim\undefined \let\lesssim\undefined
\let\precsim\undefined \let\succsim\undefined
\def\corresponds{\triangleq}%
\@ifundefined{selectfont}%
{}%
{\input{amssymb.sty}%
\let\Finv\undefined      \newsymbol\Finv 2060
\let\Game\undefined      \newsymbol\Game 2061
\let\Bbbk\undefined      \newsymbol\Bbbk 207C
\let\diagup\undefined    \newsymbol\diagup 231E
\let\diagdown\undefined  \newsymbol\diagdown 231F
\endinput}%
}
\else %
\if@amsfonts %
\def\@tempa{\@ifundefined{selectfont}{}{\input{amsfonts.sty}\endinput}}
\else %
\let\@tempa\endinput
\fi
\fi
\@tempa

\def\frak{\protect\pfrak} \def\Bbb{\protect\pBbb}

\newfam\msamfam
\font\twlmsam=msam10\@magscale1 \font\tenmsam=msam10 \font\ninmsam=msam9
\font\sevmsam=msam7 \font\fivmsam=msam5

\newfam\msbmfam
\font\twlmsbm=msbm10\@magscale1 \font\tenmsbm=msbm10 \font\ninmsbm=msbm9
\font\sevmsbm=msbm7 \font\fivmsbm=msbm5

\newfam\euffam
\font\twleufm=eufm10\@magscale1 \font\teneufm=eufm10 \font\nineufm=eufm9
\font\seveufm=eufm7 \font\fiveufm=eufm5

\def\fontextras#1{%
\def\pfrak{\fam\euffam\nineufm}\textfont\euffam\nineufm
\scriptfont\euffam\seveufm \scriptscriptfont\euffam\fiveufm
\textfont\msamfam\ninmsam \scriptfont\msamfam\sevmsam
\scriptscriptfont\msamfam\fivmsam
\def\pBbb{\fam\msbmfam\ninmsbm}\textfont\msbmfam\ninmsbm
\scriptfont\msbmfam\sevmsbm \scriptscriptfont\msbmfam\fivmsbm
\def\boldmath{\@ifundefined{#1ninmib}%
{\expandafter\global\expandafter\def\csname#1ninmib\endcsname{}%
\global\font\ninmib=cmmib9\global\font\sevmib=cmmib7\global
\font\fivmib=cmmib5%
\global\font\ninbsy=cmbsy9\global\font\sevbsy=cmbsy7\global
\font\fivbsy=cmbsy5%
\global\font\nineufb=eufb9\global\font\seveufb=eufb7\global
\font\fiveufb=eufb5\relax
\expandafter\@addfontinfo\csname#1\endcsname
{\def\boldmath{\@prtct\@nomathbold
\everymath{\mit}\everydisplay{\mit}%
\textfont\@ne\ninmib \scriptfont\@ne\sevmib \scriptscriptfont\@ne\fivmib
\textfont\tw@\ninbsy \scriptfont\tw@\sevbsy \scriptscriptfont\tw@\fivbsy
\textfont\euffam\nineufb \scriptfont\euffam\seveufb
\scriptscriptfont\euffam\fiveufb
\@prtct\@boldtrue}%
}%
}%
{}\csname#1\endcsname\boldmath
}%
}

\expandafter\def\expandafter\viiipt\expandafter{\viiipt \fontextras{@viiipt}}

\expandafter\def\expandafter\ixpt\expandafter{\ixpt \fontextras{@ixpt}}

\expandafter\def\expandafter\xpt\expandafter{\xpt%
\def\pfrak{\fam\euffam\teneufm}\textfont\euffam\teneufm
\scriptfont\euffam\seveufm \scriptscriptfont\euffam\fiveufm
\textfont\msamfam\tenmsam \scriptfont\msamfam\sevmsam
\scriptscriptfont\msamfam\fivmsam
\def\pBbb{\fam\msbmfam\tenmsbm}\textfont\msbmfam\tenmsbm
\scriptfont\msbmfam\sevmsbm \scriptscriptfont\msbmfam\fivmsbm
\def\boldmath{\@ifundefined{tenmib}%
{\global\font\tenmib=cmmib10\global\font\sevmib=cmmib7\global
\font\fivmib=cmmib5%
\global\font\tenbsy=cmbsy10\global\font\sevbsy=cmbsy7\global
\font\fivbsy=cmbsy5%
\global\font\teneufb=eufb10\global\font\seveufb=eufb7\global
\font\fiveufb=eufb5
\global\font\tenlyb=lasyb10\relax
\@addfontinfo\@xpt{\def\boldmath{\@prtct\@nomathbold
\everymath{\mit}\everydisplay{\mit}%
\textfont\@ne\tenmib \scriptfont\@ne\sevmib \scriptscriptfont\@ne\fivmib
\textfont\tw@\tenbsy \scriptfont\tw@\sevbsy \scriptscriptfont\tw@\fivbsy
\textfont\euffam\teneufb \scriptfont\euffam\seveufb
\scriptscriptfont\euffam\fiveufb
\textfont\lyfam\tenlyb
\@prtct\@boldtrue}%
}%
}%
{}\@xpt\boldmath
}%
}

\expandafter\def\expandafter\xiipt\expandafter{\xiipt%
\def\pfrak{\fam\euffam\twleufm}\textfont\euffam\twleufm
\scriptfont\euffam\nineufm \scriptscriptfont\euffam\seveufm
\textfont\msamfam\twlmsam \scriptfont\msamfam\ninmsam
\scriptscriptfont\msamfam\sevmsam
\def\pBbb{\fam\msbmfam\twlmsbm}\textfont\msbmfam\twlmsbm
\scriptfont\msbmfam\ninmsbm \scriptscriptfont\msbmfam\sevmsbm
\def\boldmath{\@ifundefined{twlmib}%
{\global\font\twlmib=cmmib10\@magscale1\global\font\ninmib=cmmib9\global
\font\sevmib=cmmib7%
\global\font\twlbsy=cmbsy10\@magscale1\global\font\ninbsy=cmbsy9\global
\font\sevbsy=cmbsy7%
\global\font\twleufb=eufb10\@magscale1\global\font\nineufb=eufb9\global
\font\seveufb=eufb7
\global\font\twllyb=lasyb10\@magscale1\relax
\@addfontinfo\@xiipt{\def\boldmath{\@prtct\@nomathbold
\everymath{\mit}\everydisplay{\mit}%
\textfont\@ne\twlmib \scriptfont\@ne\ninmib \scriptscriptfont\@ne\sevmib
\textfont\tw@\twlbsy \scriptfont\tw@\ninbsy \scriptscriptfont\tw@\sevbsy
\textfont\euffam\twleufb \scriptfont\euffam\nineufb
\scriptscriptfont\euffam\seveufb
\textfont\lyfam\twllyb
\@prtct\@boldtrue}%
}%
}%
{}\@xiipt\boldmath
}%
}

\def\undefine#1{\let#1\undefined}
\def\newsymbol#1#2#3#4#5{\let\next@\relax
\ifnum#2=\@ne\let\next@\msafam@\else
\ifnum#2=\tw@\let\next@\msbfam@\fi\fi
\mathchardef#1="#3\next@#4#5}
\def\hexnumber@#1{\ifcase#1 0\or 1\or 2\or 3\or 4\or 5\or 6\or 7\or 8\or
9\or A\or B\or C\or D\or E\or F\fi}
\edef\msafam@{\hexnumber@\msamfam}
\mathchardef\dabar@"0\msafam@39
\def\dashrightarrow{\mathrel{\dabar@\dabar@\mathchar"0\msafam@4B}}
\def\dashleftarrow{\mathrel{\mathchar"0\msafam@4C\dabar@\dabar@}}
\let\dasharrow\dashrightarrow
\def\ulcorner{\delimiter"4\msafam@70\msafam@70 }
\def\urcorner{\delimiter"5\msafam@71\msafam@71 }
\def\llcorner{\delimiter"4\msafam@78\msafam@78 }
\def\lrcorner{\delimiter"5\msafam@79\msafam@79 }
\def\yen{{\mathhexbox\msafam@55 }}
\def\checkmark{{\mathhexbox\msafam@58 }}
\def\circledR{{\mathhexbox\msafam@72 }}
\def\maltese{{\mathhexbox\msafam@7A }}
\edef\msbfam@{\hexnumber@\msbmfam}
\def\widehat#1{\setbox\z@\hbox{$\m@th#1$}%
\ifdim\wd\z@>\tw@ em\mathaccent"0\msbfam@5B{#1}%
\else\mathaccent"0362{#1}\fi}
\def\widetilde#1{\setbox\z@\hbox{$\m@th#1$}%
\ifdim\wd\z@>\tw@ em\mathaccent"0\msbfam@5D{#1}%
\else\mathaccent"0365{#1}\fi}
\undefine\Box           \newsymbol\Box 1203
\undefine\Diamond       \newsymbol\Diamond 1206
\undefine\leadsto       \newsymbol\leadsto 1320
\undefine\lhd           \newsymbol\lhd 1343
\undefine\unlhd         \newsymbol\unlhd 1345
\undefine\rhd           \newsymbol\rhd 1342
\undefine\unrhd         \newsymbol\unrhd 1344
\edef\Join{\mathrel{\mathchar"0\msbfam@ 6F\mkern-13.8mu%
\mathchar"0\msbfam@ 6E}}

\if@amssymbols %
\@amsfontstrue
\undefine\square
\undefine\leftrightarrows
\undefine\leqq
\undefine\geqq
\undefine\gtrless
\undefine\lessapprox
\undefine\gtrapprox
\undefine\lesssim
\undefine\gtrsim
\expandafter\def\csname amsfonts.sty\endcsname{}
\input{amssymb.sty}
\undefine\Finv          \newsymbol\Finv 2060
\undefine\Game          \newsymbol\Game 2061
\undefine\Bbbk          \newsymbol\Bbbk 207C
\undefine\diagup        \newsymbol\diagup 231E
\undefine\diagdown      \newsymbol\diagdown 231F
\fi

\endinput

    

