<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">%%% ====================================================================
%%%  @LaTeX-style-file{
%%%     author          = "Silvano Balemi, balemi@aut.ee.ethz.ch",
%%%     version         = "1.2",
%%%     date            = "14-MAY-1993",
%%%     filename        = "birkhaus.sty",
%%%     address         = "Birk\"auser Verlag AG
%%%                        P.O.Box 133
%%%                        Klosterweg 23, 4010 Basel, Switzerland",
%%%     telephone       = "+41 (61) 271.74.00",
%%%     FAX             = "+41 (61) 271.76.66",
%%%     email           = "birkhauser@urz.unibas.ch (Internet)",
%%%     keywords        = "LaTeX, publisher style",
%%%     supported       = "yes. Please send comments via E-mail",
%%%     mainserver      = "ifa.ethz.ch"
%%%     docstring       = "document-style for books/ or conference/workshop
%%%                        proceedings according to the instructions of
%%%                        Birk\"auser Verlag.
%%%
%%%                        Usage:
%%%                           \documentstyle[birkhauser]{article}
%%%                           \begin{document}
%%%                           \author{...} 
%%%                           \title{...} 
%%%                           \maketitle
%%%                           \begin{abstract}...\end{abstract}
%%%                           ...
%%%                           \end{document}
%%%
%%%                        The command "\markboth{leftTEXT}{right}" puts the
%%%                        text "leftTEXT" and "rightTEXT" on the running heads
%%%                        together with the page number. The head on
%%%                        the first page is defined by "\head{firstHEAD}".
%%%                        In order to remove head and page number, insert
%%%                           \thispagestyle{empty}\pagestyle{empty} or
%%%                           \thispagestyle{plain}\pagestyle{plain}
%%%                        right after the \maketitle command!!
%%%
%%%  }
%%% ====================================================================
\typeout{Document Style `birkhaus' &lt;14-MAY-1993&gt;.}

% Dimensions of the text
\headheight 20mm
\oddsidemargin 2.5mm
\evensidemargin 2.5mm
\topmargin -20mm
\textheight 230mm
\textwidth 155mm
\pagestyle{myheadings}
\newdimen\headwidth
\newdimen\headrulewidth
\headrulewidth 0.4pt
\headwidth \textwidth
\def\footnoterule{\kern-3\p@
 \hrule width \columnwidth
 \kern 2.6\p@}

\def\head#1{\def\@head{#1}}
\head{\copyright Birkh\"auser Verlag Basel}

\def\ps@birkhauser{\let\@mkboth\@gobbletwo
\def\@oddhead{\hbox{}{\footnotesize\sc
\@head}\hfill\rm\thepage}}

%%% Definition of font sizes to 12 points for the normal size
\def\@normalsize{\@setsize\normalsize{14pt}\xiipt\@xiipt%
\abovedisplayskip 12pt plus3pt minus7pt\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus3pt\belowdisplayshortskip 6.5pt plus3.5pt
minus3pt}
\def\small{\@setsize\small{11.4pt}\xpt\@xpt%
\abovedisplayskip 11pt plus3pt minus6pt\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus3pt\belowdisplayshortskip 6.5pt plus3.5pt
minus3pt
}
\def\footnotesize{\@setsize\footnotesize{10pt}\ixpt\@ixpt%
\abovedisplayskip 10pt plus2pt minus5pt\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus3pt\belowdisplayshortskip 6pt plus3pt minus3pt
}
\def\large{\@setsize\large{18pt}\xivpt\@xivpt \def\bfsl{\frtnbfs}}
\def\Large{\@setsize\Large{22pt}\xviipt\@xviipt \def\bfsl{\svtnbfs}}
\def\LARGE{\@setsize\LARGE{25pt}\xxpt\@xxpt \def\bfsl{\twtybfs}}
\def\huge{\@setsize\huge{30pt}\xxvpt\@xxvpt \def\bfsl{\twfvbfs}}
\let\Huge=\huge

\def\@listI{\leftmargin\leftmargini 
 \topsep 6pt plus 2pt minus 2pt
 \parsep 1pt plus 1pt minus 1pt
 \itemsep 1pt plus 1pt minus 1pt}
\let\@listi\@listI
\@listi 

% Abstract defined to be left at the begining of a paragraph.
% Paragraph is 135mm wide
\def\abstract{
\advance \rightskip by 10mm
\advance \leftskip by 10mm
\vspace{-0.8em}
\noindent
\small{\bf Abstract.}
}
\def\endabstract{\par\normalsize\rm}

% Some additional definitions.
% \titlenewline enforces a new line in the title but not in the
% running heads. \headnewline enforces a new line in the
% running heads but not in the title
\def\commentout#1{}
\def\titlenewline{\\}
\def\headnewline{ }
\def\samethanks{\addtocounter{footnote}{-1}\footnotemark}%%%Same affilation%%%

% New definition of maketitle allowing the use of the definitions
% above
\def\maketitle{
\par
 \begingroup
 \def\thefootnote{\fnsymbol{footnote}}
 \def\@makefnmark{\hbox
 to 0pt{$^{\@thefnmark}$\hss}}
 \if@twocolumn
 \twocolumn[\@maketitle]
 \else \newpage
 \global\@topnum\z@ \@maketitle \fi
\thispagestyle{birkhauser}\@thanks
 \endgroup
 \setcounter{footnote}{0}
 \let\maketitle\relax
 \let\@maketitle\relax
\gdef\@thanks{}
%\gdef\@author{}
%\gdef\@title{}
%\let\thanks\relax
\def\titlenewline{ }
\def\and{,~} %%%used in \author, but reactivated in headings RS%%%
\let\thanks\commentout %%%\let instead of \def RS%%%
\let\samethanks\relax %%%also reactivated RS%%%
\def\headnewline{\\}
}

% title is 135mm wide like abstract paragraph
\def\@maketitle{
\newpage
 \null
\vskip 0em \begin{center}
 \advance \rightskip by 10mm
\advance \leftskip by 10mm
 {\Large\sc \@title \par} \vskip 2.5em {\normalsize \lineskip .5em
 \begin{tabular}[t]{c}\@author
 \end{tabular}\par}
 \end{center}
 \par
 \vskip 2.5em
}

\ds@twoside                     % Left- and right heads different


%\addtolength{\headwidth}{-60mm}

\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}}

% Definition for the running heads. The standard command
% \markboth{author's name}{title of the paper}
% can be used to manually set the headers
\def\@evenhead{\hbox to\headwidth{\vbox{\hbox
{\rlap{\parbox[b]{\headwidth}{\centering\sc\leftmark \strut}}}
\headrule}}\hss}
\def\@oddhead{\hbox to\headwidth{\vbox{\hbox
{\rlap{\parbox[b]{\headwidth}{\centering\sc\rightmark\strut}}}
\headrule}}\hss}
\def\headrule{\vskip 3pt{\hrule\@height\headrulewidth\@width\headwidth
               \vskip-\headrulewidth}}
\def\rightmark{\hfill\@title\hfill\thepage}
\def\leftmark{\thepage\hfill\@author\hfill}
\def\markboth#1#2{
\def\leftmark{\thepage\hfill#1\hfill}
\def\rightmark{\hfill#2\hfill\thepage}}

% defines the command for putting the header
% footernote{TEXT} is the same as markboth{TEXT}{TEXT}. Here for
% compatibility with other style files.
\def\footernote#1{\markboth{#1}{#1}}

% Redefinition of the sections, subsections and subsubsection in order
% to obtain different titles
\def\section{\@startsection {section}{1}{\z@}{-3.5ex plus -1ex minus
 -.2ex}{2.3ex plus .2ex}{\normalsize\bf}{}}
\def\subsection{\@startsection{subsection}{2}{\z@}{-3.25ex plus -1ex minus
 -.2ex}{1.5ex plus .2ex}{\normalsize\bf}{}}
\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-3.25ex plus
 -1ex minus -.2ex}{0ex plus 0ex}{\normalsize\bf}{.\mbox{~}}}%%%\it changed in \bf RS%%%

% Redefinition of startsection to allow an additional argument to
% put for instance ". " after the subsubsection name.
\def\@startsection#1#2#3#4#5#6#7{\if@noskipsec \leavevmode \fi
   \par \@tempskipa #4\relax
   \@afterindenttrue
   \ifdim \@tempskipa &lt;\z@ \@tempskipa -\@tempskipa \@afterindentfalse\fi
   \if@nobreak \everypar{}\else
     \addpenalty{\@secpenalty}\addvspace{\@tempskipa}\fi
     \vskip -\parskip\@ifstar
     {\@ssect{#3}{#4}{#5}{#6}{#7}}
     {\@dblarg{\@sect{#1}{#2}{#3}{#4}{#5}{#6}{}{#7}}}}

\def\@sect#1#2#3#4#5#6#7[#8]#9{\ifnum #2&gt;\c@secnumdepth
     \def\@svsec{}\else
     \refstepcounter{#1}\edef\@svsec{\csname the#1\endcsname\hskip 1em }\fi
     \@tempskipa #5\relax
      \ifdim \@tempskipa&gt;\z@
        \begingroup #6\relax
          \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M #9#7\par}%
        \endgroup
       \csname #1mark\endcsname{#8}\addcontentsline
         {toc}{#1}{\ifnum #2&gt;\c@secnumdepth \else
                      \protect\numberline{\csname the#1\endcsname}\fi
                    #8}\else
        \def\@svsechd{#6\hskip #3\@svsec #9#7\csname #1mark\endcsname
                      {#8}\addcontentsline
                           {toc}{#1}{\ifnum #2&gt;\c@secnumdepth \else
                             \protect\numberline{\csname the#1\endcsname}\fi
                       #8}}\fi
     \@xsect{#5}}

\def\@ssect#1#2#3#4#5#6{\@tempskipa #3\relax
   \ifdim \@tempskipa&gt;\z@
     \begingroup #4\@hangfrom{\hskip #1}{\interlinepenalty \@M
 #6#5\par}\endgroup
   \else \def\@svsechd{#4\hskip #1\relax #6#5}\fi
    \@xsect{#3}}


%Redefinition of the label for REFERENCE to be upper case as required
%for the section titles.
\def\thebibliography#1{\section*{REFERENCES\@mkboth
 {REFERENCES}{REFERENCES}}\list
 {[\arabic{enumi}]}{\settowidth\labelwidth{[#1]}\leftmargin\labelwidth
 \advance\leftmargin\labelsep
 \usecounter{enumi}}
 \def\newblock{\hskip .11em plus .33em minus .07em}
 \sloppy\clubpenalty4000\widowpenalty4000
 \sfcode`\.=1000\relax}

\long\def\@makecaption#1#2{
\vskip 10pt
\setbox\@tempboxa\hbox{\bf #1: \rm  #2}
\ifdim \wd\@tempboxa &gt;\hsize \bf #1: \rm #2\par \else \hbox
to\hsize{\hfil\box\@tempboxa\hfil}
\fi}

% Definition of the proof environment
\def\QED{~\rule[-1pt]{1.4ex}{1.4ex}\par\medskip}
\newenvironment{proof}{\noindent{\bf Proof:}}{ \hspace*{\fill} \QED}

\newtheorem{theorem}{Theorem}
\newtheorem{corollary}{Corollary}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{conjecture}{Conjecture}
\newtheorem{remark}{Remark}
\newtheorem{definition}{Definition}
\newtheorem{problem}{Problem}

\newcommand{\eqref}[1]{{\rm (\ref{#1})}}
\newcommand{\scp}[1]{\setcounter{page}{#1}}

</pre></body></html>