%%% Document option for  proceedings after  Birkhaeuser 
%%% Bengt M{\aa}rtensson  bengt@mathematik.uni-Bremen.de  g09e@dhbrrz41.bitnet

\typeout{Document Option `BIRK <10 June 1989>}

% For the title page:
%
% There is a new command \dedication, the command \date is ignored

\newfont{\titlefont}{cmr17}	% Like Birkhauser wants it
\newfont{\authorfont}{cmr12}

\def\maketitle{\par
 \begingroup
   \def\thefootnote{\fnsymbol{footnote}}
   \def\@makefnmark{\hbox   
       to 0pt{$^{\@thefnmark}$\hss}}   
   \if@twocolumn               
     \twocolumn[\@maketitle]   
     \else \newpage
     \global\@topnum\z@        % Prevents figures from going at top of page.
     \@maketitle \fi\thispagestyle{empty}\@thanks
 \endgroup
 \setcounter{footnote}{0}
 \let\maketitle\relax
 \let\@maketitle\relax
 \gdef\@thanks{}\gdef\@author{}\gdef\@title{}\let\thanks\relax}

\def\@maketitle{\newpage
 \null
 \vskip 2em                 % Vertical space above title.
 \begin{center}
  {\LARGE\titlefont \@title \par}     % Title set in \LARGE size. 
  \vskip 4em                % Vertical space after title.
  {\large\authorfont            % each author set in \large, in a
   \lineskip .5em           % tabular environment
   \begin{tabular}[t]{c}\@author 
   \end{tabular}\par}                   
  \vskip 2em              % Vertical space after author.
   \begin{flushright}
	\normalsize\it\@dedication
   \end{flushright}
%  {\large \@date}           % Date set in \large size.
\end{center}
 \par
 \vskip 1.5em}                % Vertical space after date.

\def\abstract{\if@twocolumn
\section*{Abstract}
\else \small 
\begin{center}
{\normalsize\bf Abstract\vspace{-.5em}\vspace{0pt}} 
\end{center}
\small
\quotation\noindent\ignorespaces
\fi}

\def\endabstract{\if@twocolumn\else\endquotation\fi}

\def\dedication#1{\gdef\@dedication{#1}}
\gdef\@dedication{\mbox{}}          %Default is empty

%%% For the end of the article:

\def\authorinfo#1{\par\bigskip\noindent\ignorespaces#1}

%%% Theorem- and Remark like environments (also see the file remark.sty)
%%% The following theorem-like environments are pre-defined: theorem,
%%% lemma, corollary, proposition.
%%% The following remark-like environments are pre-defined:
%%% definition, remark, example.
%%% There is also a proof environement and an acknowledgement
%%% environment.

\input remark.sty

\def\@beginremark#1#2{\trivlist \item[\hskip \labelsep{\it #1\ #2.\ }]}
\def\@opargbeginremark#1#2#3{\trivlist
      \item[\hskip \labelsep{\it #1\ #2\ (#3).\ }]}

\newremark{definition}{Definition}
\newremark{remark}{Remark}
\newremark{example}[remark]{Example}


% We put periods after the number, as opposed to standard LaTeX.
\def\@begintheorem#1#2{\it \trivlist \item[\hskip \labelsep{\bf #1\ #2.\ }]}
\def\@opargbegintheorem#1#2#3{\it \trivlist
      \item[\hskip \labelsep{\bf #1\ #2.\ (#3)\ }]}
\def\@endtheorem{\endtrivlist}

\newtheorem{theorem}{Theorem}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}

\def\@rectangle {\hbox{\vrule \vbox to 0.4em
                              {\hrule\hbox to 0.4em{\hfil}\vfil\hrule}\vrule}}
\xdef\@endgadget #1{{\unskip\nobreak\hfil\penalty50\hskip1em\hbox{}\nobreak
                     \hfil#1\parfillskip=0pt\finalhyphendemerits=0\par}}
%
%\def\@qedsymbol{\@rectangle}
\def\@qedsymbol{Q.E.D.}
\def\qed{\@endgadget{\@qedsymbol}}
%
\newenvironment{declaration}[1]{\trivlist \item[\hskip \labelsep{\bf #1 }]\ignorespaces}{\endtrivlist}
%\newenvironment{definition}{\begin{declaration}{Definition}}{\end{declaration}}
\newenvironment{proofof}[1]{\begin{declaration}{#1}}{\qed\end{declaration}}
\newenvironment{proof}{\begin{proofof}{Proof.}}{\end{proofof}}
%
\newenvironment{acknowledgement}{\trivlist \item[\hskip \labelsep{\it Acknowledgement:\quad}]\ignorespaces}{\endtrivlist}

% Somewhat changed appearance
\def\thebibliography#1{\begin{center}
{REFERENCES\vspace{-.5em}\vspace{0pt}} 
\end{center}
\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}

\ds@twoside			% Left- and right heads different

\def\@threepart#1#2#3{\rlap{#1} \hfil {#2} \hfil \llap{#3}}
\def\@oddfoot{}\def\@evenfoot{}
\def\runningtitle#1#2{\def\@oddhead{\@threepart{}{\uppercase{#2}}{\thepage}}
    \def\@evenhead{\@threepart{\thepage}{\uppercase{#1}}{}}}

%%% Measures the way Birkhauser wants it

\textheight = 42\baselineskip
\advance\textheight by \topskip
\textwidth 4.5in
\let\footnotesize=\normalsize
\def\footnoterule{\kern-3\p@   
  \hrule width 2in%.4\columnwidth 
  \kern 2.6\p@}                 % The \hrule has default height of .4pt .
