% SVMULT DOCUMENT CLASS -- version 5.15 (7-May-25)
% Springer Verlag global LaTeX2e support for multi authored books
%%
%%
%% \CharacterTable
%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
%%   Digits        \0\1\2\3\4\5\6\7\8\9
%%   Exclamation   \!     Double quote  \"     Hash (number) \#
%%   Dollar        \$     Percent       \%     Ampersand     \&
%%   Acute accent  \'     Left paren    \(     Right paren   \)
%%   Asterisk      \*     Plus          \+     Comma         \,
%%   Minus         \-     Point         \.     Solidus       \/
%%   Colon         \:     Semicolon     \;     Less than     \<
%%   Equals        \=     Greater than  \>     Question mark \?
%%   Commercial at \@     Left bracket  \[     Backslash     \\
%%   Right bracket \]     Circumflex    \^     Underscore    \_
%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
%%   Right brace   \}     Tilde         \~}
%%
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
\ProvidesClass{svmult}[2025/05/07 v5.15
^^JSpringer Verlag global LaTeX document class for multi authored books]
% Options
% citations
\DeclareOption{natbib}{\ExecuteOptions{oribibl}%
\AtEndOfClass{% Loading package 'NATBIB'
\RequirePackage{natbib}
% Changing some parameters of NATBIB
\setlength{\bibhang}{\parindent}
%\setlength{\bibsep}{0mm}
\let\bibfont=\small
\def\@biblabel#1{#1.}
\newcommand{\etal}{\textit{et al}.}
%\bibpunct[,]{(}{)}{;}{a}{}{,}}}
}}
% Springer environment
\let\if@spthms\iftrue
\DeclareOption{nospthms}{\let\if@spthms\iffalse}
%
\let\envankh\@empty   % no anchor for "theorems"
%
\let\if@envcntreset\iffalse % environment counter is not reset
\let\if@envcntresetsect=\iffalse % reset each section
\DeclareOption{envcountresetchap}{\let\if@envcntreset\iftrue}
\DeclareOption{envcountresetsect}{\let\if@envcntreset\iftrue
\let\if@envcntresetsect=\iftrue}
%
\let\if@envcntsame\iffalse  % NOT all environments work like "Theorem",
                            % each using its own counter
\DeclareOption{envcountsame}{\let\if@envcntsame\iftrue}
%
\let\if@envcntshowhiercnt=\iffalse % do not show hierarchy counter at all
%
% enhance theorem counter
\DeclareOption{envcountchap}{\def\envankh{chapter}% show \thechapter along with theorem number
\let\if@envcntshowhiercnt=\iftrue}
%
\DeclareOption{envcountsect}{\def\envankh{section}% show \thesection along with theorem number
\let\if@envcntshowhiercnt=\iftrue
\ExecuteOptions{envcountresetsect}}
% reset environment counters every new contribution by default
\ExecuteOptions{envcountresetchap}
%
% languages
\let\switcht@@therlang\relax
\let\svlanginfo\relax
\def\ds@deutsch{\def\switcht@@therlang{\switcht@deutsch}%
\gdef\svlanginfo{\typeout{Man spricht deutsch.}\global\let\svlanginfo\relax}}
\def\ds@francais{\def\switcht@@therlang{\switcht@francais}%
\gdef\svlanginfo{\typeout{On parle francais.}\global\let\svlanginfo\relax}}
\def\ds@italiano{\def\switcht@@therlang{\switcht@italian}%
\gdef\svlanginfo{\typeout{Noi parliamo italiano.}\global\let\svlanginfo\relax}}
%
\AtBeginDocument{\@ifundefined{url}{\def\url#1{#1}}{}%
\@ifpackageloaded{babel}{%
\@ifundefined{extrasamerican}{}{\addto\extrasamerican{\switcht@albion}}%
\@ifundefined{extrasaustralian}{}{\addto\extrasaustralian{\switcht@albion}}%
\@ifundefined{extrasbritish}{}{\addto\extrasbritish{\switcht@albion}}%
\@ifundefined{extrascanadian}{}{\addto\extrascanadian{\switcht@albion}}%
\@ifundefined{extrasenglish}{}{\addto\extrasenglish{\switcht@albion}}%
\@ifundefined{extrasnewzealand}{}{\addto\extrasnewzealand{\switcht@albion}}%
\@ifundefined{extrasUKenglish}{}{\addto\extrasUKenglish{\switcht@albion}}%
\@ifundefined{extrasUSenglish}{}{\addto\extrasUSenglish{\switcht@albion}}%
\@ifundefined{captionsfrench}{}{\addto\captionsfrench{\switcht@francais}}%
\@ifundefined{extrasgerman}{}{\addto\extrasgerman{\switcht@deutsch}}%
\@ifundefined{extrasngerman}{}{\addto\extrasngerman{\switcht@deutsch}}%
\@ifundefined{captionsitalian}{}{\addto\captionsitalian{\switcht@italian}}%
}{\switcht@@therlang}%
}
\DeclareOption{italian}{\bbl@load@language{italian}}%
% numbering style of floats, equations
% \newif\if@numart   \@numartfalse
% \DeclareOption{numart}{\@numarttrue}
% numbering of headings
\let\if@chapnum=\iftrue
\def\nixchapnum{\let\if@chapnum\iffalse}
\def\numstyle{0}
\DeclareOption{nosecnum}{\def\numstyle{1}}%
% \DeclareOption{nochapnum}{\def\numstyle{2}}%
% \DeclareOption{nonum}{\def\numstyle{3}}%
\def\set@numbering{\ifcase\numstyle %\if@numart\else\num@book\fi %default
\or % 1-case - no \section-numbers
\setcounter{secnumdepth}{0}% \if@numart\else\num@book\fi
% \or % 2-case
% % chapter not numbered, but \sections are
% \def\thesection{\@arabic\c@section}%
% \nixchapnum
% \or % 3-case
% % neither chapter nor sections numbered + "numart"
% \nixchapnum
% \setcounter{secnumdepth}{0}%
\else\fi}
\AtEndOfClass{\set@numbering}
% style for vectors
\DeclareOption{vecphys}{\def\vec@style{phys}}
\DeclareOption{vecarrow}{\def\vec@style{arrow}}
% running heads
\let\if@runhead\iftrue
\DeclareOption{norunningheads}{\let\if@runhead\iffalse}
% referee option
\let\if@referee\iffalse
\def\makereferee{\def\baselinestretch{2}\selectfont
\newbox\refereebox
\setbox\refereebox=\vbox to\z@{\vskip0.5cm%
  \hbox to\textwidth{\normalsize\tt\hrulefill\lower0.5ex
        \hbox{\kern5\p@ referee's copy\kern5\p@}\hrulefill}\vss}%
\def\@oddfoot{\copy\refereebox}\let\@evenfoot=\@oddfoot}
\DeclareOption{referee}{\let\if@referee\iftrue
\AtBeginDocument{\makereferee\small\normalsize}}
% modification of thebibliography
\let\if@openbib\iffalse
\DeclareOption{openbib}{\let\if@openbib\iftrue}
% LaTeX standard, sectionwise references
\DeclareOption{oribibl}{\let\oribibl=Y}
\DeclareOption{chaprefs}{\let\chpbibl=Y}
%
% footinfo option (provides an informatory line on every page)
\def\SpringerMacroPackageNameA{svmult.cls}
% \thetime, \thedate and \timstamp are macros to include
% time, date (or both) of the TeX run in the document
\def\maketimestamp{\count255=\time
\divide\count255 by 60\relax
\edef\thetime{\the\count255:}%
\multiply\count255 by-60\relax
\advance\count255 by\time
\edef\thetime{\thetime\ifnum\count255<10 0\fi\the\count255}
\edef\thedate{\number\day-\ifcase\month\or Jan\or Feb\or Mar\or
             Apr\or May\or Jun\or Jul\or Aug\or Sep\or Oct\or
             Nov\or Dec\fi-\number\year}
\def\timstamp{\hbox to\hsize{\tt\hfil\thedate\hfil\thetime\hfil}}}
\maketimestamp
%
% \footinfo generates a info footline on every page containing
% pagenumber, jobname, macroname, and timestamp
\DeclareOption{footinfo}{\AtBeginDocument{\maketimestamp
   \def\ps@empty{\let\@mkboth\@gobbletwo
   \let\@oddhead\@empty\let\@evenhead\@empty}%
   \def\@oddfoot{\scriptsize\tt Page:\,\thepage\space\hfil
                 job:\,\jobname\space\hfil
                 macro:\,\SpringerMacroPackageNameA\space\hfil
                 date/time:\,\thedate/\thetime}%
   \let\@evenfoot=\@oddfoot}}
%
% start new chapter on any page
\newif\if@openright \@openrighttrue
\DeclareOption{openany}{\@openrightfalse}
%
% no size changing allowed
\DeclareOption{11pt}{\OptionNotUsed}
\DeclareOption{12pt}{\OptionNotUsed}
% options for the article class
\def\@rticle@options{10pt,twoside}
% fleqn
\DeclareOption{fleqn}{\def\@rticle@options{10pt,twoside,fleqn}%
\AtEndOfClass{\let\leftlegendglue\relax}%
\AtBeginDocument{\mathindent\parindent}}
% hanging sectioning titles
\let\if@sechang\iftrue
\DeclareOption{nosechang}{\let\if@sechang\iffalse}
% hanging sectioning titles
\def\ClassInfoNoLine#1#2{%
   \ClassInfo{#1}{#2\@gobble}%
}
%
\DeclareOption{graybox}{%
\AtEndOfClass{% Loading color package
\RequirePackage{color}%
% defining values of gray
\definecolor{shadecolor}{gray}{.85}%
\definecolor{tintedcolor}{gray}{.80}%
\RequirePackage{framed}%
%
\newenvironment{tinted}{%
  \def\FrameCommand{\colorbox{tintedcolor}}%
  \MakeFramed {\FrameRestore}}%
 {\endMakeFramed}%
%
\renewenvironment{svgraybox}%
       {\fboxsep=12pt\relax
        \begin{shaded}%
        \list{}{\leftmargin=12pt\rightmargin=2\leftmargin\leftmargin=\z@\topsep=\z@\relax}%
        \expandafter\item\parindent=\svparindent
        \hskip-\listparindent}%
       {\endlist\end{shaded}}%
%
\renewenvironment{svtintedbox}%
       {\fboxsep=12pt\relax
        \begin{tinted}%
        \list{}{\leftmargin=12pt\rightmargin=2\leftmargin\leftmargin=\z@\topsep=\z@\relax}%
        \expandafter\item\parindent=\svparindent
        \relax}%
       {\endlist\end{tinted}}%
%
}}
%

\setlength{\textwidth}{117mm}
%\setlength{\textheight}{12pt}\multiply\textheight by 45\relax
\setlength{\textheight}{191mm}
\setlength{\topmargin}{0cm}
\setlength\oddsidemargin   {63\p@}
\setlength\evensidemargin  {63\p@}
\setlength\marginparwidth{90\p@}
\setlength\headsep   {12\p@}

\DeclareOption{RBook}{%
\AtEndOfClass{%
\setlength{\textwidth}{117mm}%
\setlength{\textheight}{191mm}%
\setlength{\topmargin}{0cm}%
\setlength\oddsidemargin   {63\p@}%
\setlength\evensidemargin  {63\p@}%
}}%

\DeclareOption{MBook}{%
\AtEndOfClass{%
\setlength{\textwidth}{126mm}%
\setlength{\textheight}{192mm}%
\setlength{\topmargin}{1.5cm}%
\setlength\oddsidemargin   {60\p@}%
\setlength\evensidemargin  {60\p@}%
}}%

\DeclareOption{LBook}{%
\AtEndOfClass{%
\setlength{\textwidth}{142mm}%
\setlength{\textheight}{211mm}%
\setlength{\topmargin}{-0.5cm}%
\setlength\oddsidemargin   {43\p@}%
\setlength\evensidemargin  {43\p@}%
}}%

\DeclareOption{HBook}{%
\AtEndOfClass{%
\setlength{\textwidth}{174mm}%
\setlength{\textheight}{234mm}%
\setlength{\topmargin}{-1.5cm}%
\setlength\oddsidemargin   {-12\p@}%
\setlength\evensidemargin  {-12\p@}%
}}%

\let\SVMultOpt\@empty
\DeclareOption*{\InputIfFileExists{sv\CurrentOption.clo}{%
\global\let\SVMultOpt\CurrentOption}{%
\ClassWarning{Springer-SVMult}{Specified option or subpackage
"\CurrentOption" \MessageBreak not found -
passing it to article class \MessageBreak
-}\PassOptionsToClass{\CurrentOption}{article}%
}}
\ProcessOptions\relax
\ifx\SVMultOpt\@empty\relax
\ClassInfoNoLine{Springer-SVMult}{extra/valid Springer sub-package
\MessageBreak not found in option list - using "global" style}{}
\fi
\LoadClass[\@rticle@options]{article}
\raggedbottom

% various sizes and settings for contributed works

\newdimen\svparindent
\setlength{\svparindent}{12\p@}
\parindent\svparindent

\newdimen\bibindent
\setlength\bibindent{\parindent}

\setlength{\parskip}{\z@ \@plus \p@}
\setlength{\hfuzz}{2\p@}
\setlength{\arraycolsep}{1.5\p@}

\frenchspacing

\tolerance=500

\predisplaypenalty=0
\clubpenalty=10000
\widowpenalty=10000

\setlength\footnotesep{7.7\p@}

\newdimen\betweenumberspace          % dimension for space between
\betweenumberspace=5\p@              % number and text of titles
\newdimen\headlineindent             % dimension for space of
\headlineindent=2.5cc                % number and gap of running heads

% fonts, sizes, and the like
\renewcommand\normalsize{%
   \@setfontsize\normalsize\@xpt\@xiipt
   \abovedisplayskip 10\p@ % \@plus2\p@ \@minus5\p@
   \abovedisplayshortskip \z@ % \@plus3\p@
   \belowdisplayshortskip 6\p@ %\@plus3\p@ \@minus3\p@
   \belowdisplayskip \abovedisplayskip
   \let\@listi\@listI}
\normalsize
\renewcommand\small{%
   \@setfontsize\small{8.5}{10}%
   \abovedisplayskip 8.5\p@ % \@plus3\p@ \@minus4\p@
   \abovedisplayshortskip \z@ %\@plus2\p@
   \belowdisplayshortskip 4\p@ %\@plus2\p@ \@minus2\p@
   \def\@listi{\leftmargin\leftmargini
               \parsep \z@ \@plus\p@ \@minus\p@
               \topsep 6\p@ \@plus2\p@ \@minus4\p@
               \itemsep\z@}%
   \belowdisplayskip \abovedisplayskip
}
%
\let\footnotesize=\small
%
\renewcommand\Large{\@setfontsize\large{14}{16}}
\newcommand\LArge{\@setfontsize\Large{16}{18}}
\renewcommand\LARGE{\@setfontsize\LARGE{18}{20}}
%
\newenvironment{petit}{\par\addvspace{6\p@}\small}{\par\addvspace{6\p@}}
%

% modification of automatic positioning of floating objects
\setlength\@fptop{\z@ }
\setlength\@fpsep{12\p@ }
\setlength\@fpbot{\z@ \@plus 1fil }
\def\textfraction{.01}
\def\floatpagefraction{.8}
\setlength{\intextsep}{20\p@ \@plus 2\p@ \@minus 2\p@}
\setlength\textfloatsep{24\p@ \@plus 2\p@ \@minus 4\p@}
\setcounter{topnumber}{4}
\def\topfraction{.9}
\setcounter{bottomnumber}{2}
\def\bottomfraction{.7}
\setcounter{totalnumber}{6}
%
% size and style of headings
\newcommand{\partnumsize}{\LArge}
\newcommand{\partnumstyle}{\bfseries\boldmath}
\newcommand{\partsize}{\LARGE}
\newcommand{\partstyle}{\bfseries\boldmath}
\newcommand{\chapnumsize}{\Large}
\newcommand{\chapnumstyle}{\bfseries\boldmath}
\newcommand{\chapsize}{\LArge}
\newcommand{\chapstyle}{\bfseries\boldmath}
\newcommand{\chapauthsize}{\normalsize}
\newcommand{\chapauthstyle}{\bfseries\boldmath}
\newcommand{\mottosize}{\small}
\newcommand{\mottostyle}{\itshape\unboldmath\raggedright}
\newcommand{\secsize}{\large}
\newcommand{\secstyle}{\bfseries\boldmath}
%%\newcommand{\subsecsize}{\large}
\newcommand{\subsecsize}{\fontsize{11}{13}\selectfont}
\newcommand{\subsecstyle}{\bfseries\boldmath}
\newcommand{\subsubsecstyle}{\bfseries\boldmath}
%
\def\cleardoublepage{\clearpage\if@twoside \ifodd\c@page\else
    \hbox{}\newpage\if@twocolumn\hbox{}\newpage\fi\fi\fi}

\newcommand{\clearemptydoublepage}{%
        \clearpage{\pagestyle{empty}\cleardoublepage}}
\newcommand{\startnewpage}{\if@openright\clearemptydoublepage\else\clearpage\fi}

% MiniTOC
% one outputstream for all minitocs
\newwrite\minitoc
\let\MiniTOC=N % switch for MT processing in .aux files
\newcounter{minitocdepth}
\setcounter{minitocdepth}{0}

% stolen from LaTeX.ltx - read miniTOC and redirect output stream
\long\def \protected@immwrite#1#2#3{%
      \begingroup
       \let\thepage\relax
       #2%
       \let\protect\@unexpandable@protect
       \edef\reserved@a{\immediate\write#1{#3}}%
       \reserved@a
      \endgroup
      \if@nobreak\ifvmode\nobreak\fi\fi}
%
\newcommand{\@mtstarttoc}[1]
{\begingroup
 \makeatletter
 \immediate\write\@auxout{\string\immediate\string\closeout\string\minitoc}%
 \typeout{input jobname.#1}%
\small
 \@input{\jobname.#1}%
 \protected@immwrite\@auxout
   {\let\label\@gobble \let\index\@gobble
    \let\glossary\@gobble}%
   {\immediate\openout\minitoc \jobname.#1\relax}
 \global\@nobreakfalse\endgroup}
%
\newcommand{\@mtstarttocquiet}[1]
{\begingroup
 \makeatletter
 \protected@write\@auxout
   {\let\label\@gobble \let\index\@gobble
    \let\glossary\@gobble}%
   {\immediate\openout\minitoc \jobname.#1\relax}
 \global\@nobreakfalse\endgroup}
%
\newcommand{\mtaddtocont}[1]
{\protected@write \@auxout
  {\let\label\@gobble \let\index\@gobble
   \let\glossary\@gobble}%
  {\string\@mtwritefile{#1}}}
%
\newcommand{\@mtwritefile}[1]{\if Y\MiniTOC
\@temptokena{#1} \immediate\write\minitoc{\the\@temptokena}\fi}

\AtEndDocument{\immediate\write\@auxout{\string\immediate\string\closeout\string\minitoc}}

\newcommand{\dominitoc}{% switch \let\MiniTOC=Y
    \protected@immwrite\@auxout{}{\let\MiniTOC=Y}%
    \ifnum \c@minitocdepth<1
        \@mtstarttocquiet{t\thecontribution}\relax
    \else
        \@mtstarttoc{t\thecontribution}\par\addvspace\bigskipamount
    \fi}

% redefinition of \part
\renewcommand\part{\clearemptydoublepage
         \thispagestyle{empty}
         \if@twocolumn
            \onecolumn
            \@tempswatrue
         \else
            \@tempswafalse
         \fi
         \@ifundefined{thispagecropped}{}{\thispagecropped}
         \secdef\@part\@spart}

\def\@part[#1]#2{\ifnum \c@secnumdepth >-2\relax
        \refstepcounter{part}
        \addcontentsline{toc}{part}{\partname\
        \thepart\thechapterend\hspace{\betweenumberspace}%
        #1}\else
        \addcontentsline{toc}{part}{#1}\fi
   \markboth{}{}
   {\raggedleft
    \hyphenpenalty \@M
    \interlinepenalty\@M
    \ifnum \c@secnumdepth >-2\relax
      \normalfont\partnumsize\partnumstyle %\vrule height 34pt width 0pt depth 0pt%
     \partname\ \thepart %\llap{\smash{\lower 5pt\hbox to\textwidth{\hrulefill}}}
    \par
    \vskip 2\p@ \fi
    \partsize\partstyle #2\par}\@endpart}
%
% \@endpart finishes the part page
%
\def\@endpart{\vfil\newpage
   \if@twoside
       \hbox{}
       \thispagestyle{empty}
       \newpage
   \fi
   \if@tempswa
     \twocolumn
   \fi}
%
\def\@spart#1{{\raggedleft
   \normalfont\partsize\partstyle
   #1\par}\@endpart}
%
\newenvironment{partbacktext}{\def\@endpart{\vfil\newpage}}
{\thispagestyle{empty} \newpage}
%
% (re)define sectioning
\setcounter{secnumdepth}{3}

\def\seccounterend{}
\def\seccountergap{\hskip\betweenumberspace}
\def\@seccntformat#1{\csname the#1\endcsname\seccounterend\seccountergap\ignorespaces}
%
\let\firstmark=\botmark
%
\@ifundefined{thechapterend}{\def\thechapterend{}}{}
%
\if@sechang
   \def\sec@hangfrom#1{\setbox\@tempboxa\hbox{#1}%
         \hangindent\wd\@tempboxa\noindent\box\@tempboxa}
\else
   \def\sec@hangfrom#1{\setbox\@tempboxa\hbox{#1}%
         \hangindent\z@\noindent\box\@tempboxa}
\fi

\def\chap@hangfrom#1{\if!#1!\else
\@chapapp\ #1\vskip2pt\fi}
\def\schap@hangfrom{\chap@hangfrom{}}

\newcounter{chapter}

\newif\if@mainmatter \@mainmattertrue
\newcommand\frontmatter{\startnewpage
            \@mainmatterfalse\pagenumbering{roman}
            \setcounter{page}{5}}
%
\newcommand\mainmatter{\clearemptydoublepage
            \@mainmattertrue
            \markboth{}{}
            \pagenumbering{arabic}}
%
\newcommand\backmatter{%
\setcounter{minitocdepth}{0}%
\pagestyle{headings}%
\clearemptydoublepage %\@mainmatterfalse
\let\appendix=\bppendix
\def\bibsection{\chapter*{\refname}\@mkboth{\refname}{\refname}%
     \addcontentsline{toc}{chapter}{\refname}%
     \csname biblst@rthook\endcsname\par}%
}

\renewenvironment{titlepage}
    {%
      \cleardoublepage
      \if@twocolumn
        \@restonecoltrue\onecolumn
      \else
        \@restonecolfalse\newpage
      \fi
      \thispagestyle{empty}%
      \addtocounter{page}\m@ne
  \def\and{\unskip, }
  \parindent=\z@
  \pretolerance=10000
  \rightskip=0pt plus 1fil
  \large                    % default size for titlepage
  \vspace*{2em}             % Vertical space above title.
 }{{\LARGE                   % each author set in \LARGE
   \lineskip .5em
   \@author
   \par}%
  \vskip 2cm                % Vertical space after author.
  {\Huge\bfseries\@title \par}% Title set in \Huge size and bold face
  \vskip 1cm                % Vertical space after title.
  \if!\@subtitle!\else
   {\LARGE\ignorespaces\@subtitle \par}
   \vskip 1cm               % Vertical space after subtitle.
  \fi
  \if!\@date!\else
    \@date
    \par
    \vskip 1.5em            % Vertical space after date.
  \fi
 \vfill
 {\Large\bfseries Springer\par}
%\vskip 3pt
%\itshape
%  Berlin\enspace Heidelberg\enspace New\kern0.1em York\\
%  Hong\kern0.2em Kong\enspace London\\
%  Milan\enspace Paris\enspace Tokyo\par
     \if@restonecol\twocolumn \else \newpage \fi
     \if@twoside\else
        \setcounter{page}\@ne
     \fi
 \clearheadinfo
}

\def\@chapapp{\chaptername}

\newdimen\mottowidth
\newcommand\motto[2][77mm]{%
\setlength{\mottowidth}{#1}%
\gdef\m@ttotext{#2}}
%
\newcommand{\processmotto}{\@ifundefined{m@ttotext}{}{%
    \setbox0=\hbox{\vbox{\hyphenpenalty=50
    \begin{flushright}
    \begin{minipage}{\mottowidth}
       \vrule\@width\z@\@height21\p@\@depth\z@
       \normalfont\mottosize\mottostyle\m@ttotext
    \end{minipage}
    \end{flushright}}}%
    \@tempdima=\pagetotal
    \advance\@tempdima by\ht0
    \ifdim\@tempdima<157\p@
       \multiply\@tempdima by-1
       \advance\@tempdima by157\p@
       \vskip\@tempdima
    \fi
    \box0\par
    \global\let\m@ttotext=\undefined}}

\newcommand{\chapsubtitle}[1]{%
\gdef\ch@psubtitle{#1}}
%
\newcommand{\processchapsubtit}{\@ifundefined{ch@psubtitle}{}{%
    {\normalfont\chapnumsize\chapnumstyle
    \vskip 14\p@
    \ch@psubtitle
    \par}
    \global\let\ch@psubtitle=\undefined}}

\newcommand{\chapauthor}[1]{%
\gdef\ch@pauthor{#1}}
%
\newcommand{\processchapauthor}{\@ifundefined{ch@pauthor}{}{%
    {\normalfont\chapauthsize\chapauthstyle
    \vskip 20\p@
    \ch@pauthor
    \par}
    \global\let\ch@pauthor=\undefined}}

\newcommand\chapter{\startnewpage
                    \@ifundefined{thispagecropped}{}{\thispagecropped}
                    \thispagestyle{bchap}%
                    \if@chapnum\else
                       \begingroup
                         \let\@elt\@stpelt
                         \csname cl@chapter\endcsname
                       \endgroup
                    \fi
                    \global\@topnum\z@
                    \@afterindentfalse
                    \secdef\@chapter\@schapter}

\def\@chapter[#1]#2{\if@chapnum  % war mal \ifnum \c@secnumdepth >\m@ne
                       \refstepcounter{chapter}%
                       \if@mainmatter
                         \typeout{\@chapapp\space\thechapter.}%
                         \addcontentsline{toc}{chapter}{\protect
                                  \numberline{\thechapter\thechapterend}#1}%
                       \else
                         \addcontentsline{toc}{chapter}{#1}%
                       \fi
                    \else
                      \addcontentsline{toc}{chapter}{#1}%
                    \fi
                    \chaptermark{#1}%
                    \addtocontents{lof}{\protect\addvspace{10\p@}}%
                    \addtocontents{lot}{\protect\addvspace{10\p@}}%
                    \if@twocolumn
                      \@topnewpage[\@makechapterhead{#2}]%
                    \else
                      \@makechapterhead{#2}%
                      \@afterheading
                    \fi}

\def\@schapter#1{\if@twocolumn
                   \@topnewpage[\@makeschapterhead{#1}]%
                 \else
                   \@makeschapterhead{#1}%
                   \@afterheading
                 \fi}

%%changes position and layout of numbered chapter headings
\def\@makechapterhead#1{{\parindent\z@\raggedright\normalfont
  \hyphenpenalty \@M
  \interlinepenalty\@M
  \if@chapnum
     \chapnumsize\chapnumstyle
     \@chapapp\ \thechapter\thechapterend\par
     \vskip 2\p@
  \fi
  \chapsize\chapstyle
  \ignorespaces#1\par\nobreak
  \processchapsubtit
  \processchapauthor
  \processmotto
  \ifdim\pagetotal>167\p@
     \vskip 11\p@
  \else
     \@tempdima=167\p@\advance\@tempdima by-\pagetotal
     \vskip\@tempdima
  \fi}}

%%changes position and layout of unnumbered chapter headings
\def\@makeschapterhead#1{{\parindent \z@ \raggedright\normalfont
  \hyphenpenalty \@M
  \interlinepenalty\@M
  \chapsize\chapstyle
  \ignorespaces#1\par\nobreak
  \processmotto
  \ifdim\pagetotal>167\p@
     \vskip 11\p@
  \else
     \@tempdima=168\p@\advance\@tempdima by-\pagetotal
     \vskip\@tempdima
  \fi}}
%
% dedication environment
\newenvironment{dedication}
{\clearemptydoublepage
\thispagestyle{empty}
\vspace*{13\baselineskip}
\large\itshape
\let\\\@centercr\@rightskip\@flushglue \rightskip\@rightskip
\leftskip4cm\parindent\z@\relax
\everypar{\parindent=\svparindent\let\everypar\empty}}{\clearpage}
%
% predefined unnumbered headings
\newcommand{\preface}[1][\prefacename]{\chapter*{#1}\markboth{#1}{#1}}
\newcommand{\foreword}[1][\forewordname]{\chapter*{#1}\markboth{#1}{#1}}
\newcommand{\contributors}[1][\contriblistname]{\chapter*{#1}\markboth{#1}{#1}}
\newcommand{\extrachap}[1]{\chapter*{#1}\markboth{#1}{#1}}
% same with TOC entry
\newcommand{\Extrachap}[1]{\chapter*{#1}\markboth{#1}{#1}%
\addcontentsline{toc}{chapter}{#1}}

% measures and setting of sections
\renewcommand\section{\@startsection{section}{1}{\z@}%
                       {-30\p@}% \p@lus -4\p@ \@minus -4\p@}%
                       {16\p@}% \p@lus 4\p@ \@minus 4\p@}%
                       {\normalfont\secsize\secstyle
                        \rightskip=\z@ \@plus 8em\pretolerance=10000 }}
\renewcommand\subsection{\@startsection{subsection}{2}{\z@}%
                       {-30\p@}% \p@lus -4\p@ \@minus -4\p@}%
                       {16\p@}% \p@lus 4\p@ \@minus 4\p@}%
                       {\normalfont\subsecsize\subsecstyle
                        \rightskip=\z@ \@plus 8em\pretolerance=10000 }}
\renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}%
                       {-24\p@}% \p@lus -4\p@ \@minus -4\p@}%
                       {12\p@}% \p@lus 4\p@ \@minus 4\p@}%
                       {\normalfont\normalsize\subsubsecstyle
                        \rightskip=\z@ \@plus 8em\pretolerance=10000 }}
\renewcommand\paragraph{\@startsection{paragraph}{4}{\z@}%
                       {-24\p@}% \p@lus -4\p@ \@minus -4\p@}%
                       {12\p@}% \p@lus 4\p@ \@minus 4\p@}%
                       {\normalfont\normalsize\upshape
                        \rightskip=\z@ \@plus 8em\pretolerance=10000 }}
\renewcommand\subparagraph{\@startsection{paragraph}{4}{\z@}%
                       {-18\p@}% \p@lus -4\p@ \@minus -4\p@}%
                       {6\p@}% \p@lus 4\p@ \@minus 4\p@}%
                       {\normalfont\normalsize\itshape
                        \rightskip=\z@ \@plus 8em\pretolerance=10000 }}
\newcommand\runinhead{\@startsection{paragraph}{4}{\z@}%
                       {-6\p@}% \p@lus -4\p@ \@minus -4\p@}%
                       {-6\p@}%
                       {\normalfont\normalsize\bfseries\boldmath
                        \rightskip=\z@ \@plus 8em\pretolerance=10000 }}
\newcommand\subruninhead{\@startsection{paragraph}{4}{\z@}%
                       {-6\p@}% \p@lus -4\p@ \@minus -4\p@}%
                       {-6\p@}%
                       {\normalfont\normalsize\bfseries\itshape
                        \rightskip=\z@ \@plus 8em\pretolerance=10000 }}

\newcommand\subsubruninhead{\@startsection{paragraph}{4}{\z@}%
                       {-6\p@}% \p@lus -4\p@ \@minus -4\p@}%
                       {0.1\p@}%
                       {\normalfont\normalsize\bfseries
                        \rightskip=\z@ \@plus 8em\pretolerance=10000 }}
                        
% Appendix
\renewcommand\appendix{\par}         %article appendix

\newcommand\bppendix{\startnewpage            %book appendix
                \pagestyle{headings}
                \stepcounter{chapter}
                \setcounter{chapter}{0}
                \stepcounter{section}
                \setcounter{section}{0}
                \setcounter{equation}{0}
                \setcounter{figure}{0}
                \setcounter{table}{0}
                \setcounter{footnote}{0}
\let\if@chapnum=\iftrue
\def\@chapapp{\appendixname}
\renewcommand\thechapter{\@Alph\c@chapter}
\renewcommand\thesection{\thechapter.\@arabic\c@section}
\renewcommand\thesubsection{\thesection.\@arabic\c@subsection}
\renewcommand\theequation{\thechapter.\@arabic\c@equation}
\renewcommand\thefigure{\thechapter.\@arabic\c@figure}
\renewcommand\thetable{\thechapter.\@arabic\c@table}}

\def\hyperhrefextend{\ifx\hyper@anchor\@undefined\else
{\@currentHref}\fi}

\def\runinsep{}
\def\aftertext{\unskip\runinsep}
%
%
\def\@ssect#1#2#3#4#5{%
  \@tempskipa #3\relax
  \ifdim \@tempskipa>\z@
    \begingroup
      #4{%
        \@hangfrom{\hskip #1}%
          \raggedright
          \hyphenpenalty \@M
          \interlinepenalty \@M #5\@@par}%
    \endgroup
  \else
    \def\@svsechd{#4{\hskip #1\relax #5}}%
  \fi
      \addcontentsline{toc}{section}{#5}%
  \@xsect{#3}}
%
\def\@sect#1#2#3#4#5#6[#7]#8{%
   \ifnum #2>\c@secnumdepth
      \let\@svsec\@empty
   \else
      \refstepcounter{#1}%
      \protected@edef\@svsec{\@seccntformat{#1}\relax}%
   \fi
   \@tempskipa #5\relax
   \ifdim \@tempskipa>\z@
      \begingroup #6\relax
         \sec@hangfrom{\hskip #3\relax\@svsec}%
         {\raggedright
          \hyphenpenalty \@M
          \interlinepenalty \@M #8\@@par}%
      \endgroup
      \csname #1mark\endcsname{#7}%
      \addcontentsline{toc}{#1}{%
        \ifnum #2>\c@secnumdepth \else
          \protect\numberline{\csname the#1\endcsname}%
        \fi
        #7}%
      \ifnum #2>\c@minitocdepth \else
         \mtaddtocont{\protect\contentsline
             \ifnum #2>\@ne{mtsec}\else{mtchap}\fi
             \ifnum #2>\c@secnumdepth
                {#7}%
             \else
                {\protect\numberline{\csname the#1\endcsname}#7}%
             \fi
             {\thepage}\hyperhrefextend}%
      \fi
   \else
      \def\@svsechd{%
         #6\hskip #3\relax
         \@svsec #8\aftertext\ignorespaces
         \csname #1mark\endcsname{#7}%
         \addcontentsline{toc}{#1}{%
            \ifnum #2>\c@secnumdepth \else
                \protect\numberline{\csname the#1\endcsname}%
            \fi
            #7}}%
   \fi
   \@xsect{#5}}

% figures and tables are processed in small print
\def \@floatboxreset {%
        \reset@font
        \small
        \@setnobreak
        \@setminipage
}
\def\fps@figure{htbp}
\def\fps@table{htbp}
%
% Frame for paste-in figures or tables
\def\mpicplace#1#2{%  #1 =width   #2 =height
\vbox{\hbox to #1{\vrule\@width \fboxrule \@height #2\hfill}}}
%
\newenvironment{svgraybox}%
       {\ClassWarning{Springer-SVMono}{Environment "svgraybox" not available,\MessageBreak
         switching over to "quotation" environment;\MessageBreak
         specify documentclass option "graybox",\MessageBreak
         see SVMono documentation -}%
                \par\addvspace{6pt}
                \list{}{\listparindent12\p@%
                        \leftmargin=12\p@%
                        \itemindent    \listparindent
                        \rightmargin   \leftmargin
                        \parsep        \z@ \@plus\p@}%
                \expandafter\item\parindent=\svparindent
                \relax\hskip-\listparindent}%
       {\endlist}%
%
\newenvironment{svtintedbox}%
       {\ClassWarning{Springer-SVMono}{Environment "svtintedbox" not available,\MessageBreak
         switching over to "quotation" environment;\MessageBreak
         specify documentclass option "graybox",\MessageBreak
         see SVMono documentation -}%
                \par\addvspace{6pt}
                \list{}{\listparindent12\p@%
                        \leftmargin=12\p@%
                        \itemindent    \listparindent
                        \rightmargin   \leftmargin
                        \parsep        \z@ \@plus\p@}%
                \expandafter\item\parindent=\svparindent
                \relax\hskip-\listparindent}%
       {\endlist}%
%
\renewenvironment{quotation}
               {\par\addvspace{6pt}
                \list{}{\listparindent12\p@%
                        \leftmargin=12\p@%
                        \itemindent    \listparindent
                        \rightmargin   \leftmargin
                        \parsep        \z@ \@plus\p@%
                        \small}%
                \item\relax\hskip-\listparindent}
               {\endlist}
%
\renewenvironment{quote}
               {\par\addvspace{6pt}
                \list{}{\leftmargin=12\p@%
                \rightmargin\leftmargin
                \parsep=3\p@
                \small}%
                \item\relax}
               {\endlist}

% labels of enumerate
\renewcommand\labelenumii{\theenumii.}
\renewcommand\theenumii{\@alph\c@enumii}

% labels of itemize
\renewcommand\labelitemi{\textbullet}
\renewcommand\labelitemii{\textendash}
\let\labelitemiii=\labelitemiv

% labels of description
\renewcommand*\descriptionlabel[1]{\hspace\labelsep #1\hfil}

% fixed indentation for standard itemize-environment
\newdimen\svitemindent \setlength{\svitemindent}{\parindent}


% make indentations changeable

\def\setitemindent#1{\settowidth{\labelwidth}{#1}%
        \let\setit@m=Y%
        \leftmargini\labelwidth
        \advance\leftmargini\labelsep
   \def\@listi{\leftmargin\leftmargini
        \labelwidth\leftmargini\advance\labelwidth by -\labelsep
        \parsep=\parskip
        \topsep=\medskipamount
        \itemsep=\parskip \advance\itemsep by -\parsep}}
\def\setitemitemindent#1{\settowidth{\labelwidth}{#1}%
        \let\setit@m=Y%
        \leftmarginii\labelwidth
        \advance\leftmarginii\labelsep
\def\@listii{\leftmargin\leftmarginii
        \labelwidth\leftmarginii\advance\labelwidth by -\labelsep
        \parsep=\parskip
        \topsep=6\p@
        \itemsep=\parskip \advance\itemsep by -\parsep}}
%
% adjusted environment "description"
% if an optional parameter (at the first two levels of lists)
% is present, its width is considered to be the widest mark
% throughout the current list.
\def\description{\@ifnextchar[{\@describe}{\list{}{\labelwidth\z@
\labelsep=12pt\relax  %!!!!!!!!!
\leftmargini=12pt\relax  %!!!!!!!!!
\leftmargin=12pt\relax  %!!!!!!!!!
          \itemindent-\leftmargin \let\makelabel\descriptionlabel}}}
%
\def\describelabel#1{#1\hfil}
\def\@describe[#1]{\labelsep=12pt\relax
\relax\ifnum\@listdepth=0
\setitemindent{#1}\else\ifnum\@listdepth=1
\setitemitemindent{#1}\fi\fi
\list{--}{\let\makelabel\describelabel}}
%
\def\itemize{%
  \ifnum \@itemdepth >\thr@@\@toodeep\else
    \advance\@itemdepth\@ne
    \ifx\setit@m\undefined
       \ifnum \@itemdepth=1 \leftmargini=\svitemindent
          \labelwidth\leftmargini\advance\labelwidth-\labelsep
          \leftmarginii=\leftmargini \leftmarginiii=\leftmargini
       \fi
    \fi
    \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%
    \expandafter\list
      \csname\@itemitem\endcsname
      {\def\makelabel##1{\rlap{##1}\hss}}%
  \fi}
%
\def\enumerate{%
  \ifnum \@enumdepth >\thr@@\@toodeep\else
    \advance\@enumdepth\@ne
    \ifx\setit@m\undefined
       \ifnum \@enumdepth=1 \leftmargini=\svitemindent
          \labelwidth\leftmargini\advance\labelwidth-\labelsep
          \leftmarginii=\leftmargini \leftmarginiii=\leftmargini
       \fi
    \fi
    \edef\@enumctr{enum\romannumeral\the\@enumdepth}%
      \expandafter
      \list
        \csname label\@enumctr\endcsname
        {\usecounter\@enumctr\def\makelabel##1{\hss\llap{##1}}}%
  \fi}
%
\newdimen\verbatimindent \verbatimindent\parindent
\def\verbatim{\advance\@totalleftmargin by\verbatimindent
\@verbatim \frenchspacing\@vobeyspaces \@xverbatim}

%
%  special signs and characters
\newcommand{\D}{\mathrm{d}}
\newcommand{\E}{\mathrm{e}}
\let\eul=\E
\newcommand{\I}{{\rm i}}
\let\imag=\I
%
% the definition of uppercase Greek characters
% Springer likes them as italics to depict variables
\DeclareMathSymbol{\Gamma}{\mathalpha}{letters}{"00}
\DeclareMathSymbol{\Delta}{\mathalpha}{letters}{"01}
\DeclareMathSymbol{\Theta}{\mathalpha}{letters}{"02}
\DeclareMathSymbol{\Lambda}{\mathalpha}{letters}{"03}
\DeclareMathSymbol{\Xi}{\mathalpha}{letters}{"04}
\DeclareMathSymbol{\Pi}{\mathalpha}{letters}{"05}
\DeclareMathSymbol{\Sigma}{\mathalpha}{letters}{"06}
\DeclareMathSymbol{\Upsilon}{\mathalpha}{letters}{"07}
\DeclareMathSymbol{\Phi}{\mathalpha}{letters}{"08}
\DeclareMathSymbol{\Psi}{\mathalpha}{letters}{"09}
\DeclareMathSymbol{\Omega}{\mathalpha}{letters}{"0A}
% the upright forms are defined here as \var<Character>
\DeclareMathSymbol{\varGamma}{\mathalpha}{operators}{"00}
\DeclareMathSymbol{\varDelta}{\mathalpha}{operators}{"01}
\DeclareMathSymbol{\varTheta}{\mathalpha}{operators}{"02}
\DeclareMathSymbol{\varLambda}{\mathalpha}{operators}{"03}
\DeclareMathSymbol{\varXi}{\mathalpha}{operators}{"04}
\DeclareMathSymbol{\varPi}{\mathalpha}{operators}{"05}
\DeclareMathSymbol{\varSigma}{\mathalpha}{operators}{"06}
\DeclareMathSymbol{\varUpsilon}{\mathalpha}{operators}{"07}
\DeclareMathSymbol{\varPhi}{\mathalpha}{operators}{"08}
\DeclareMathSymbol{\varPsi}{\mathalpha}{operators}{"09}
\DeclareMathSymbol{\varOmega}{\mathalpha}{operators}{"0A}
% Upright Lower Case Greek letters without using a new MathAlphabet
\newcommand{\greeksym}[1]{\usefont{U}{psy}{m}{n}#1}
\newcommand{\greeksymbold}[1]{{\usefont{U}{psy}{b}{n}#1}}
\newcommand{\allmodesymb}[2]{\relax\ifmmode{\mathchoice
{\mbox{\fontsize{\tf@size}{\tf@size}#1{#2}}}
{\mbox{\fontsize{\tf@size}{\tf@size}#1{#2}}}
{\mbox{\fontsize{\sf@size}{\sf@size}#1{#2}}}
{\mbox{\fontsize{\ssf@size}{\ssf@size}#1{#2}}}}
\else
\mbox{#1{#2}}\fi}
% Definition of lower case Greek letters
\newcommand{\ualpha}{\allmodesymb{\greeksym}{a}}
\newcommand{\ubeta}{\allmodesymb{\greeksym}{b}}
\newcommand{\uchi}{\allmodesymb{\greeksym}{c}}
\newcommand{\udelta}{\allmodesymb{\greeksym}{d}}
\newcommand{\ugamma}{\allmodesymb{\greeksym}{g}}
\newcommand{\umu}{\allmodesymb{\greeksym}{m}}
\newcommand{\unu}{\allmodesymb{\greeksym}{n}}
\newcommand{\upi}{\allmodesymb{\greeksym}{p}}
\newcommand{\utau}{\allmodesymb{\greeksym}{t}}
% redefines the \vec accent to a bold character - if desired
\def\vec@type{arrow}% temporarily abused
\AtBeginDocument{\ifx\vec@style\vec@type\else
\@ifundefined{vec@style}{%
 \def\vec#1{\ensuremath{\mathchoice
                     {\mbox{\boldmath$\displaystyle\mathbf{#1}$}}
                     {\mbox{\boldmath$\textstyle\mathbf{#1}$}}
                     {\mbox{\boldmath$\scriptstyle\mathbf{#1}$}}
                     {\mbox{\boldmath$\scriptscriptstyle\mathbf{#1}$}}}}%
}
{\def\vec#1{\ensuremath{\mathchoice
                     {\mbox{\boldmath$\displaystyle#1$}}
                     {\mbox{\boldmath$\textstyle#1$}}
                     {\mbox{\boldmath$\scriptstyle#1$}}
                     {\mbox{\boldmath$\scriptscriptstyle#1$}}}}%
}
\fi}
% tensor
\def\tens#1{\relax\ifmmode\mathsf{#1}\else\textsf{#1}\fi}

% end of proof symbol
\newcommand\qedsymbol{\hbox{\rlap{$\sqcap$}$\sqcup$}}
\newcommand\qed{\relax\ifmmode\else\unskip\quad\fi\qedsymbol}
\newcommand\smartqed{\renewcommand\qed{\relax\ifmmode\qedsymbol\else
  {\unskip\nobreak\hfil\penalty50\hskip1em\null\nobreak\hfil\qedsymbol
  \parfillskip=\z@\finalhyphendemerits=0\endgraf}\fi}}
%
\newif\if@numart   \@numarttrue
\def\ds@numart{\@numarttrue
  \@takefromreset{figure}{chapter}%
  \@takefromreset{table}{chapter}%
  \@takefromreset{equation}{chapter}%
  \def\thesection{\@arabic\c@section}%
  \def\thefigure{\@arabic\c@figure}%
  \def\thetable{\@arabic\c@table}%
  \def\theequation{\arabic{equation}}%
  \def\thesubequation{\arabic{equation}\alph{subequation}}}
%
\def\ds@book{\@numartfalse
\def\thesection{\thechapter.\@arabic\c@section}%
\def\thefigure{\thechapter.\@arabic\c@figure}%
\def\thetable{\thechapter.\@arabic\c@table}%
\def\theequation{\thechapter.\arabic{equation}}%
\@addtoreset{section}{chapter}%
\@addtoreset{figure}{chapter}%
\@addtoreset{table}{chapter}%
\@addtoreset{equation}{chapter}}
%
% Ragged bottom for the actual page
\def\thisbottomragged{\def\@textbottom{\vskip\z@ \@plus.0001fil
\global\let\@textbottom\relax}}

% This is texte.tex
% it defines various texts and their translations
% called up with documentstyle options
\def\switcht@albion{%
\def\abbrsymbname{List of Abbreviations and Symbols}%
\def\abstractname{Abstract}%
\def\ackname{Acknowledgements}%
\def\andname{and}%
\def\bibname{References}%
\def\lastandname{, and}%
\def\appendixname{Appendix}%
\def\chaptername{Chapter}%
\def\claimname{Claim}%
\def\conjecturename{Conjecture}%
\def\contentsname{Contents}%
\def\corollaryname{Corollary}%
\def\definitionname{Definition}%
\def\emailname{e-mail}%
\def\examplename{Example}%
\def\exercisename{Exercise}%
\def\figurename{Fig.}%
\def\forewordname{Foreword}%
\def\keywordname{{\bf Key words:}}%
\def\indexname{Index}%
\def\lemmaname{Lemma}%
\def\contriblistname{List of Contributors}%
\def\listfigurename{List of Figures}%
\def\listtablename{List of Tables}%
\def\mailname{{\it Correspondence to\/}:}%
\def\noteaddname{Note added in proof}%
\def\notename{Note}%
\def\partname{Part}%
\def\prefacename{Preface}%
\def\problemname{Problem}%
\def\proofname{Proof}%
\def\propertyname{Property}%
\def\propositionname{Proposition}%
\def\questionname{Question}%
\def\refname{References}%
\def\remarkname{Remark}%
\def\seename{see}%
\def\solutionname{Solution}%
\def\subclassname{{\it Subject Classifications\/}:}%
\def\tablename{Table}%
\def\theoremname{Theorem}}
\switcht@albion
% Names of theorem like environments are already defined
% but must be translated if another language is chosen
%
% French section
\def\switcht@francais{\svlanginfo
 \def\abbrsymbname{Liste des abbr\'eviations et symboles}%
 \def\abstractname{R\'esum\'e.}%
 \def\ackname{Remerciements.}%
 \def\andname{et}%
 \def\lastandname{ et}%
 \def\appendixname{Appendice}%
 \def\bibname{Bibliographie}%
 \def\chaptername{Chapitre}%
 \def\claimname{Pr\'etention}%
 \def\conjecturename{Hypoth\`ese}%
 \def\contentsname{Table des mati\`eres}%
 \def\corollaryname{Corollaire}%
 \def\definitionname{D\'efinition}%
 \def\emailname{e-mail}%
 \def\examplename{Exemple}%
 \def\exercisename{Exercice}%
 \def\figurename{Fig.}%
 \def\forewordname{Avant-propos}%
 \def\keywordname{{\bf Mots-cl\'e:}}%
 \def\indexname{Index}%
 \def\lemmaname{Lemme}%
 \def\contriblistname{Liste des contributeurs}%
 \def\listfigurename{Liste des figures}%
 \def\listtablename{Liste des tables}%
 \def\mailname{{\it Correspondence to\/}:}%
 \def\noteaddname{Note ajout\'ee \`a l'\'epreuve}%
 \def\notename{Remarque}%
 \def\partname{Partie}%
 \def\prefacename{Pr\'eface}%
 \def\problemname{Probl\`eme}%
 \def\proofname{Preuve}%
 \def\propertyname{Caract\'eristique}%
%\def\propositionname{Proposition}%
 \def\questionname{Question}%
 \def\refname{Litt\'erature}%
 \def\remarkname{Remarque}%
 \def\seename{voir}%
 \def\solutionname{Solution}%
 \def\subclassname{{\it Subject Classifications\/}:}%
 \def\tablename{Tableau}%
 \def\theoremname{Th\'eor\`eme}%
}
%
% German section
\def\switcht@deutsch{\svlanginfo
 \def\abbrsymbname{Abk\"urzungs- und Symbolverzeichnis}%
 \def\abstractname{Zusammenfassung}%
 \def\ackname{Danksagung}%
 \def\andname{und}%
 \def\lastandname{ und}%
 \def\appendixname{Anhang}%
 \def\bibname{Literaturverzeichnis}%
 \def\chaptername{Kapitel}%
 \def\claimname{Behauptung}%
 \def\conjecturename{Hypothese}%
 \def\contentsname{Inhaltsverzeichnis}%
 \def\corollaryname{Korollar}%
%\def\definitionname{Definition}%
 \def\emailname{E-Mail}%
 \def\examplename{Beispiel}%
 \def\exercisename{\"Ubung}%
 \def\figurename{Abb.}%
 \def\forewordname{Geleitwort}%
 \def\keywordname{{\bf Schl\"usselw\"orter:}}%
 \def\indexname{Sachverzeichnis}%
%\def\lemmaname{Lemma}%
 \def\contriblistname{Mitarbeiter}%
 \def\listfigurename{Abbildungsverzeichnis}%
 \def\listtablename{Tabellenverzeichnis}%
 \def\mailname{{\it Correspondence to\/}:}%
 \def\noteaddname{Nachtrag}%
 \def\notename{Anmerkung}%
 \def\partname{Teil}%
 \def\prefacename{Vorwort}%
%\def\problemname{Problem}%
 \def\proofname{Beweis}%
 \def\propertyname{Eigenschaft}%
%\def\propositionname{Proposition}%
 \def\questionname{Frage}%
 \def\refname{Literaturverzeichnis}%
 \def\remarkname{Anmerkung}%
 \def\seename{siehe}%
 \def\solutionname{L\"osung}%
 \def\subclassname{{\it Subject Classifications\/}:}%
 \def\tablename{Tabelle}%
%\def\theoremname{Theorem}%
}

% Italian section
\def\switcht@italian{\svlanginfo
\def\abstractname{Estratto}%
\def\ackname{Ringraziamenti}%
\def\andname{E}%
\def\bibname{Bibliografia}%
\def\lastandname{, E}%
\def\appendixname{Appendice}%
\def\chaptername{Capitolo}%
\def\claimname{Reclamo}%
\def\conjecturename{Congettura}%
\def\contentsname{Contenuti}%
\def\corollaryname{Corollario}%
\def\definitionname{Definizione}%
\def\emailname{e-mail}%
\def\examplename{Esempio}%
\def\exercisename{Esercizio}%
\def\figurename{Figura}%
\def\forewordname{Prefazione}%
\def\keywordname{{\bf Parole chiave:}}%
\def\indexname{Indice}%
\def\lemmaname{Lemma}%
\def\contriblistname{Elenco dei collaboratori}%
\def\listfigurename{Elenco delle figure}%
\def\listtablename{Elenco delle tabelle}%
\def\mailname{{\it Corrispondenza a\/}:}%
\def\noteaddname{Nota aggiunta nelle bozze}%
\def\notename{Nota}%
\def\partname{Parte}%
\def\prefacename{Prefazione}%
\def\problemname{Problema}%
\def\proofname{Prova}%
\def\propertyname{Propriet\`{a}}%
\def\propositionname{Proposizione}%
\def\questionname{Domanda}%
\def\refname{Riferimenti bibliografici}%
\def\remarkname{Commento}%
\def\seename{Vedi}%
\def\solutionname{Soluzione}%
\def\subclassname{{\it Classificazioni degli argomenti\/}:}%
\def\tablename{Tabella}%
\def\theoremname{Teorema}%
%\def\enclname{Allegati}%
%\def\ccname{e~p.~c.}%
%\def\headtoname{Per}%
%\def\pagename{Pag.}%
%\def\alsoname{vedi anche}%
%\def\glossaryname{Glossario}%
}

\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{\vskip1.2\p@}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr
\noalign{\vskip1.2\p@}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr
\noalign{\vskip\p@}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr
\noalign{\vskip0.9\p@}=\cr}}}}}
\def\gid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.2\p@}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr
\noalign{\vskip1.2\p@}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr
\noalign{\vskip\p@}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr
\noalign{\vskip0.9\p@}=\cr}}}}}
\def\grole{\mathrel{\mathchoice {\vcenter{\offinterlineskip
\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\noalign{\vskip-\p@}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
>\cr\noalign{\vskip-\p@}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
>\cr\noalign{\vskip-0.8\p@}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr\noalign{\vskip-0.3\p@}<\cr}}}}}
\def\bbbr{{\rm I\!R}} %reelle Zahlen
\def\bbbm{{\rm I\!M}}
\def\bbbn{{\rm I\!N}} %natuerliche Zahlen
\def\bbbf{{\rm I\!F}}
\def\bbbh{{\rm I\!H}}
\def\bbbk{{\rm I\!K}}
\def\bbbp{{\rm I\!P}}
\def\bbbone{{\mathchoice {\rm 1\mskip-4mu l} {\rm 1\mskip-4mu l}
{\rm 1\mskip-4.5mu l} {\rm 1\mskip-5mu l}}}
\def\bbbc{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm C$}\hbox{\hbox
to\z@{\kern0.4\wd0\vrule\@height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle\rm C$}\hbox{\hbox
to\z@{\kern0.4\wd0\vrule\@height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle\rm C$}\hbox{\hbox
to\z@{\kern0.4\wd0\vrule\@height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm C$}\hbox{\hbox
to\z@{\kern0.4\wd0\vrule\@height0.9\ht0\hss}\box0}}}}
\def\bbbq{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm
Q$}\hbox{\raise
0.15\ht0\hbox to\z@{\kern0.4\wd0\vrule\@height0.8\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle\rm Q$}\hbox{\raise
0.15\ht0\hbox to\z@{\kern0.4\wd0\vrule\@height0.8\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle\rm Q$}\hbox{\raise
0.15\ht0\hbox to\z@{\kern0.4\wd0\vrule\@height0.7\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm Q$}\hbox{\raise
0.15\ht0\hbox to\z@{\kern0.4\wd0\vrule\@height0.7\ht0\hss}\box0}}}}
\def\bbbt{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm
T$}\hbox{\hbox to\z@{\kern0.3\wd0\vrule\@height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle\rm T$}\hbox{\hbox
to\z@{\kern0.3\wd0\vrule\@height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle\rm T$}\hbox{\hbox
to\z@{\kern0.3\wd0\vrule\@height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm T$}\hbox{\hbox
to\z@{\kern0.3\wd0\vrule\@height0.9\ht0\hss}\box0}}}}
\def\bbbs{{\mathchoice
{\setbox0=\hbox{$\displaystyle     \rm S$}\hbox{\raise0.5\ht0\hbox
to\z@{\kern0.35\wd0\vrule\@height0.45\ht0\hss}\hbox
to\z@{\kern0.55\wd0\vrule\@height0.5\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle        \rm S$}\hbox{\raise0.5\ht0\hbox
to\z@{\kern0.35\wd0\vrule\@height0.45\ht0\hss}\hbox
to\z@{\kern0.55\wd0\vrule\@height0.5\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle      \rm S$}\hbox{\raise0.5\ht0\hbox
to\z@{\kern0.35\wd0\vrule\@height0.45\ht0\hss}\raise0.05\ht0\hbox
to\z@{\kern0.5\wd0\vrule\@height0.45\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm S$}\hbox{\raise0.5\ht0\hbox
to\z@{\kern0.4\wd0\vrule\@height0.45\ht0\hss}\raise0.05\ht0\hbox
to\z@{\kern0.55\wd0\vrule\@height0.45\ht0\hss}\box0}}}}
\def\bbbz{{\mathchoice {\hbox{$\textstyle\sf Z\kern-0.4em Z$}}
{\hbox{$\textstyle\sf Z\kern-0.4em Z$}}
{\hbox{$\scriptstyle\sf Z\kern-0.3em Z$}}
{\hbox{$\scriptscriptstyle\sf Z\kern-0.2em Z$}}}}

\let\ts\,

\setlength\arrayrulewidth{.5\p@}
\def\svhline{%
  \noalign{\ifnum0=`}\fi\hrule \@height2\arrayrulewidth \futurelet
   \reserved@a\@xhline}

\setlength \labelsep     {5\p@}
\setlength\leftmargini   {17\p@}
\setlength\leftmargin    {\leftmargini}
\setlength\leftmarginii  {\leftmargini}
\setlength\leftmarginiii {\leftmargini}
\setlength\leftmarginiv  {\leftmargini}
\setlength\labelwidth    {\leftmargini}
\addtolength\labelwidth{-\labelsep}

\def\@listI{\leftmargin\leftmargini
        \parsep=\parskip
        \topsep=\medskipamount
        \itemsep=\parskip \advance\itemsep by -\parsep}
\let\@listi\@listI
\@listi

\def\@listii{\leftmargin\leftmarginii
        \labelwidth\leftmarginii
        \advance\labelwidth by -\labelsep
        \parsep=\parskip
        \topsep=6\p@
        \itemsep=\parskip
        \advance\itemsep by -\parsep}

\def\@listiii{\leftmargin\leftmarginiii
        \labelwidth\leftmarginiii\advance\labelwidth by -\labelsep
        \parsep=\parskip
        \topsep=\z@
        \itemsep=\parskip
        \advance\itemsep by -\parsep
        \partopsep=\topsep}

\setlength\arraycolsep{1.5\p@}
\setlength\tabcolsep{1.5\p@}

\def\tableofcontents{\chapter*{\contentsname\markboth{{\contentsname}}%
                                                    {{\contentsname}}}
 \def\authcount##1{\setcounter{auco}{##1}\setcounter{@auth}{1}}
 \def\lastand{\ifnum\value{auco}=2\relax
                 \unskip{} \andname\
              \else
                 \unskip \lastandname\
              \fi}%
 \def\and{\stepcounter{@auth}\relax
          \ifnum\value{@auth}=\value{auco}%
             \lastand
          \else
             \unskip,
          \fi}%
 \@starttoc{toc}\if@restonecol\twocolumn\fi}

\setcounter{tocdepth}{2}

\def\l@part#1#2{\addpenalty{\@secpenalty}%
   \addvspace{1em \@plus\p@}%
   \begingroup
     \parindent \z@
     \rightskip \z@ \@plus 5em
%    \hrule\vskip5\p@
     \bfseries\boldmath
     \leavevmode
     #1\par
%    \vskip5\p@
%    \hrule
     \vskip\p@
     \nobreak
   \addvspace{1em \@plus\p@}%
   \endgroup}

\def\@dotsep{2}

\def\addnumcontentsmark#1#2#3{%
\addtocontents{#1}{\protect\contentsline{#2}{\protect\numberline
                                    {\thechapter}#3}{\thepage}}}
\def\addcontentsmark#1#2#3{%
\addtocontents{#1}{\protect\contentsline{#2}{#3}{\thepage}}}
\def\addcontentsmarkwop#1#2#3{%
\addtocontents{#1}{\protect\contentsline{#2}{#3}{0}}}

\def\@adcmk[#1]{\ifcase #1 \or
\def\@gtempa{\addnumcontentsmark}%
  \or    \def\@gtempa{\addcontentsmark}%
  \or    \def\@gtempa{\addcontentsmarkwop}%
  \fi\@gtempa{toc}{chapter}}
\def\addtocmark{\@ifnextchar[{\@adcmk}{\@adcmk[3]}}

\def\l@chapter#1#2{\par\addpenalty{-\@highpenalty}
 \addvspace{1.0em \@plus \p@}
 \@tempdima \tocchpnum \begingroup
 \parindent \z@ \rightskip \@tocrmarg
 \advance\rightskip by \z@ \@plus 2cm
 \parfillskip -\rightskip \pretolerance=10000
 \leavevmode \advance\leftskip\@tempdima \hskip -\leftskip
 {\bfseries\boldmath#1}\ifx0#2\hfil\null
 \else
      \nobreak
      \leaders\hbox{$\m@th \mkern \@dotsep mu\hbox{.}\mkern
      \@dotsep mu$}\hfill
      \nobreak\hbox to\@pnumwidth{\hfil #2}%
 \fi\par
 \penalty\@highpenalty \endgroup}

\newcommand{\tocauthorstyle}{\upshape}
\newcommand{\toctitlestyle}{\bfseries}

\def\l@title#1#2{\addpenalty{-\@highpenalty}
 \addvspace{8\p@ \@plus \p@}
 \@tempdima \z@
 \begingroup
 \tocchpnum \z@ \calctocindent
 \parindent \z@ \rightskip \@tocrmarg
 \advance\rightskip by \z@ \@plus 2cm
 \pretolerance=10000
 \parfillskip -\@tocrmarg
 \leavevmode \advance\leftskip\@tempdima \hskip -\leftskip
 {\toctitlestyle#1}%\nobreak
 \leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern
 \@dotsep mu$}\hfill
 \nobreak\hbox to\@pnumwidth{\hss #2}%
 \par
 \penalty\@highpenalty \endgroup}

\def\l@titlech#1#2{\addpenalty{-\@highpenalty}
 \addvspace{8\p@ \@plus \p@}
 \@tempdima=\tocchpnum
 \begingroup
 \parindent \z@ \rightskip \@tocrmarg
 \advance\rightskip by \z@ \@plus 2cm
 \pretolerance=10000
 \parfillskip -\@tocrmarg
 \leavevmode \advance\leftskip\@tempdima \hskip -\leftskip
 {\toctitlestyle#1}%\nobreak
 \leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern
 \@dotsep mu$}\hfill
 \nobreak\hbox to\@pnumwidth{\hss #2}%
 \par
 \penalty\@highpenalty \endgroup}

\newcommand{\tocaftauthskip}{\z@}
\def\l@author#1#2{%\addpenalty{\@highpenalty}
 \@tempdima \z@
 \begingroup
 \pretolerance=10000
 \parindent \z@ \rightskip \@tocrmarg
 \advance\rightskip by \z@ \@plus 2cm
%\parfillskip -\@tocrmarg
 \leavevmode \advance\leftskip\@tempdima \hskip -\leftskip
 {\tocauthorstyle#1}\nobreak
%\leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern
%\@dotsep mu$}\hfill
%\nobreak\hbox to\@pnumwidth{\hss #2}%
 \par
 \penalty\@highpenalty
 \addvspace{\tocaftauthskip}\endgroup}

\def\l@authorch#1#2{%\addpenalty{\@highpenalty}
 \@tempdima=\tocchpnum
 \begingroup
 \pretolerance=10000
 \parindent \z@ \rightskip \@tocrmarg
 \advance\rightskip by \z@ \@plus 2cm
%\parfillskip -\@tocrmarg
 \leavevmode \advance\leftskip\@tempdima %\hskip -\leftskip
 {\tocauthorstyle#1}\nobreak
%\leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern
%\@dotsep mu$}\hfill
%\nobreak\hbox to\@pnumwidth{\hss #2}%
 \par
 \penalty\@highpenalty
 \addvspace{\tocaftauthskip}\endgroup}

\newdimen\tocchpnum
\newdimen\tocsecnum
\newdimen\tocsectotal
\newdimen\tocsubsecnum
\newdimen\tocsubsectotal
\newdimen\tocsubsubsecnum
\newdimen\tocsubsubsectotal
\newdimen\tocparanum
\newdimen\tocparatotal
\newdimen\tocsubparanum
\tocchpnum=20\p@            % chapter {\bf 88.} \@plus 5.3\p@
\tocsecnum=28.5\p@          % section 88.8. plus 4.722\p@
\tocsubsecnum=36.5\p@       % subsection 88.8.8 plus 4.944\p@
\tocsubsubsecnum=43\p@      % subsubsection 88.8.8.8 plus 4.666\p@
\tocparanum=45\p@           % paragraph 88.8.8.8.8 plus 3.888\p@
\tocsubparanum=53\p@        % subparagraph 88.8.8.8.8.8 plus 4.11\p@
\def\calctocindent{%
\tocsectotal=\tocchpnum
\advance\tocsectotal by\tocsecnum
\tocsubsectotal=\tocsectotal
\advance\tocsubsectotal by\tocsubsecnum
\tocsubsubsectotal=\tocsubsectotal
\advance\tocsubsubsectotal by\tocsubsubsecnum
\tocparatotal=\tocsubsubsectotal
\advance\tocparatotal by\tocparanum}
\calctocindent

\def\@dottedtocline#1#2#3#4#5{%
  \ifnum #1>\c@tocdepth \else
    \vskip \z@ \@plus.2\p@
    {\leftskip #2\relax \rightskip \@tocrmarg \advance\rightskip by \z@ \@plus 2cm
               \parfillskip -\rightskip \pretolerance=10000
     \parindent #2\relax\@afterindenttrue
     \interlinepenalty\@M
     \leavevmode
     \@tempdima #3\relax
     \advance\leftskip \@tempdima \null\nobreak\hskip -\leftskip
     {#4}\nobreak
     \leaders\hbox{$\m@th
        \mkern \@dotsep mu\hbox{.}\mkern \@dotsep
        mu$}\hfill
     \nobreak
     \hb@xt@\@pnumwidth{\hfil\normalfont \normalcolor #5}%
     \par}%
  \fi}
%
\def\l@section{\@dottedtocline{1}{\tocchpnum}{\tocsecnum}}
\def\l@subsection{\@dottedtocline{2}{\tocsectotal}{\tocsubsecnum}}
\def\l@subsubsection{\@dottedtocline{3}{\tocsubsectotal}{\tocsubsubsecnum}}
\def\l@paragraph{\@dottedtocline{4}{\tocsubsubsectotal}{\tocparanum}}
\def\l@subparagraph{\@dottedtocline{5}{\tocparatotal}{\tocsubparanum}}

\renewcommand\listoffigures{%
    \chapter*{\listfigurename
      \markboth{\listfigurename}{\listfigurename}}%
    \@starttoc{lof}%
    }

\renewcommand\listoftables{%
    \chapter*{\listtablename
      \markboth{\listtablename}{\listtablename}}%
    \@starttoc{lot}%
    }

\newenvironment{thecontriblist}
               {\par
                \addvspace{\bigskipamount}
                \parindent\z@
                \rightskip\z@ \@plus 40\p@
                \def\iand{\\[\medskipamount]\let\and=\nand}%
                \def\nand{\ifhmode\unskip\nobreak\fi\ $\cdot$ }%
                \let\and=\nand
                \def\at{\\\let\and=\iand}%
                }
               {\par
                \addvspace{\bigskipamount}}

\renewcommand\footnoterule{%
    \kern-3\p@
    \hrule\@width 36mm
    \kern2.6\p@}

\newdimen\foot@parindent
\foot@parindent 10.83\p@
\footnotesep 9\p@

\AtBeginDocument{%
\renewcommand\@makefntext[1]{%
    \parindent 12\p@
    \noindent
    \mbox{\@makefnmark} #1}}
%
\if@spthms
% Definition of the "\spnewtheorem" command.
%
% Usage:
%
%     \spnewtheorem{env_nam}{caption}[within]{cap_font}{body_font}
% or  \spnewtheorem{env_nam}[numbered_like]{caption}{cap_font}{body_font}
% or  \spnewtheorem*{env_nam}{caption}{cap_font}{body_font}
%
% New is "cap_font" and "body_font". It stands for
% fontdefinition of the caption and the text itself.
%
% "\spnewtheorem*" gives a theorem without number.
%
% A defined spnewthoerem environment is used as described
% by Lamport.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\@thmcountersep{.}
%\def\@thmcounterend{.}
\def\@thmcounterend{}%%As per request email dated 27 Feb 2018%%
\newcommand\nocaption{\noexpand\@gobble}
%\newdimen\spthmsep \spthmsep=3pt

\def\spnewtheorem{\@ifstar{\@sthm}{\@Sthm}}

% definition of \spnewtheorem with number

\def\@spnthm#1#2{%
  \@ifnextchar[{\@spxnthm{#1}{#2}}{\@spynthm{#1}{#2}}}
\def\@Sthm#1{\@ifnextchar[{\@spothm{#1}}{\@spnthm{#1}}}

\def\@spxnthm#1#2[#3]#4#5{\expandafter\@ifdefinable\csname #1\endcsname
   {\@definecounter{#1}\@addtoreset{#1}{#3}%
   \expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand
     \csname the#3\endcsname \noexpand\@thmcountersep \@thmcounter{#1}}%
   \expandafter\xdef\csname #1name\endcsname{#2}%
   \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#4}{#5}}%
                              \global\@namedef{end#1}{\@endtheorem}}}

\def\@spynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname
   {\@definecounter{#1}%
   \expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}%
   \expandafter\xdef\csname #1name\endcsname{#2}%
   \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#3}{#4}}%
                               \global\@namedef{end#1}{\@endtheorem}}}

\def\@spothm#1[#2]#3#4#5{%
  \@ifundefined{c@#2}{\@latexerr{No theorem environment `#2' defined}\@eha}%
  {\expandafter\@ifdefinable\csname #1\endcsname
  {\global\@namedef{the#1}{\@nameuse{the#2}}%
  \expandafter\xdef\csname #1name\endcsname{#3}%
  \global\@namedef{#1}{\@spthm{#2}{\csname #1name\endcsname}{#4}{#5}}%
  \global\@namedef{end#1}{\@endtheorem}}}}

\def\@spthm#1#2#3#4{\topsep 7\p@ \@plus2\p@ \@minus4\p@
%\labelsep=\spthmsep
\refstepcounter{#1}%
\@ifnextchar[{\@spythm{#1}{#2}{#3}{#4}}{\@spxthm{#1}{#2}{#3}{#4}}}

\def\@spxthm#1#2#3#4{\@spbegintheorem{#2}{\csname the#1\endcsname}{#3}{#4}%
                    \ignorespaces}

\def\@spythm#1#2#3#4[#5]{\@spopargbegintheorem{#2}{\csname
       the#1\endcsname}{#5}{#3}{#4}\ignorespaces}

\def\normalthmheadings{\def\@spbegintheorem##1##2##3##4{\trivlist
                 \item[\hskip\labelsep{##3##1\ ##2\@thmcounterend}]##4}
\def\@spopargbegintheorem##1##2##3##4##5{\trivlist
      \item[\hskip\labelsep{##4##1\ ##2}]{##4\hspace*{-2pt}(##3)\@thmcounterend\ }##5}}
\normalthmheadings

\def\reversethmheadings{\def\@spbegintheorem##1##2##3##4{\trivlist
                 \item[\hskip\labelsep{##3##2\ ##1\@thmcounterend}]##4}
\def\@spopargbegintheorem##1##2##3##4##5{\trivlist
      \item[\hskip\labelsep{##4##2\ ##1}]{##4\hspace*{-2pt}(##3)\@thmcounterend\ }##5}}

% definition of \spnewtheorem* without number

\def\@sthm#1#2{\@Ynthm{#1}{#2}}

\def\@Ynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname
   {\global\@namedef{#1}{\@Thm{\csname #1name\endcsname}{#3}{#4}}%
    \expandafter\xdef\csname #1name\endcsname{#2}%
    \global\@namedef{end#1}{\@endtheorem}}}

\def\@Thm#1#2#3{\topsep 7\p@ \@plus2\p@ \@minus4\p@
\@ifnextchar[{\@Ythm{#1}{#2}{#3}}{\@Xthm{#1}{#2}{#3}}}

\def\@Xthm#1#2#3{\@Begintheorem{#1}{#2}{#3}\ignorespaces}

\def\@Ythm#1#2#3[#4]{\@Opargbegintheorem{#1}
       {#4}{#2}{#3}\ignorespaces}

\def\@Begintheorem#1#2#3{#3\trivlist
                           \item[\hskip\labelsep{#2#1\@thmcounterend}]}

\def\@Opargbegintheorem#1#2#3#4{#4\trivlist
      \item[\hskip\labelsep{#3#1}]{#3\hspace*{-2pt}(#2)\@thmcounterend\ }}

% initialize theorem environment

\if@envcntshowhiercnt % show hierarchy counter
   \def\@thmcountersep{.}
   \spnewtheorem{theorem}{Theorem}[\envankh]{\bfseries}{\itshape}
   \@addtoreset{theorem}{chapter}
\else          % theorem counter only
   \spnewtheorem{theorem}{Theorem}{\bfseries}{\itshape}
   \if@envcntreset
      \@addtoreset{theorem}{chapter}
      \if@envcntresetsect
         \@addtoreset{theorem}{section}
      \fi
   \fi
\fi

%definition of divers theorem environments
\spnewtheorem*{claim}{Claim}{\itshape}{\rmfamily}
%\spnewtheorem*{proof}{Proof}{\itshape}{\rmfamily}
%
\if@envcntsame % all environments like "Theorem" - using its counter
   \def\spn@wtheorem#1#2#3#4{\@spothm{#1}[theorem]{#2}{#3}{#4}}
\else % all environments with their own counter
   \if@envcntshowhiercnt % show hierarchy counter
      \def\spn@wtheorem#1#2#3#4{\@spxnthm{#1}{#2}[\envankh]{#3}{#4}}
   \else          % environment counter only
      \if@envcntreset % environment counter is reset each section
         \if@envcntresetsect
            \def\spn@wtheorem#1#2#3#4{\@spynthm{#1}{#2}{#3}{#4}
             \@addtoreset{#1}{chapter}\@addtoreset{#1}{section}}
         \else
            \def\spn@wtheorem#1#2#3#4{\@spynthm{#1}{#2}{#3}{#4}
                                      \@addtoreset{#1}{chapter}}
         \fi
      \else
         \let\spn@wtheorem=\@spynthm
      \fi
   \fi
\fi
%
\let\spdefaulttheorem=\spn@wtheorem
%
\spn@wtheorem{case}{Case}{\itshape}{\rmfamily}
\spn@wtheorem{conjecture}{Conjecture}{\itshape}{\rmfamily}
\spn@wtheorem{corollary}{Corollary}{\bfseries}{\itshape}
\spn@wtheorem{definition}{Definition}{\bfseries}{\rmfamily}
\spn@wtheorem{example}{Example}{\itshape}{\rmfamily}
\spn@wtheorem{exercise}{Exercise}{\bfseries}{\rmfamily}
\spn@wtheorem{lemma}{Lemma}{\bfseries}{\itshape}
\spn@wtheorem{note}{Note}{\itshape}{\rmfamily}
\spn@wtheorem{problem}{Problem}{\bfseries}{\rmfamily}
\spn@wtheorem{property}{Property}{\itshape}{\rmfamily}
\spn@wtheorem{proposition}{Proposition}{\bfseries}{\itshape}
\spn@wtheorem{question}{Question}{\itshape}{\rmfamily}
\spn@wtheorem{solution}{Solution}{\bfseries}{\rmfamily}
\spn@wtheorem{remark}{Remark}{\itshape}{\rmfamily}
%
\newenvironment{theopargself}
    {\def\@spopargbegintheorem##1##2##3##4##5{\trivlist
         \item[\hskip\labelsep{##4##1\ ##2}]{##4##3\@thmcounterend\ }##5}
     \def\@Opargbegintheorem##1##2##3##4{##4\trivlist
         \item[\hskip\labelsep{##3##1}]{##3##2\@thmcounterend\ }}}{}
\newenvironment{theopargself*}
    {\def\@spopargbegintheorem##1##2##3##4##5{\trivlist
         \item[\hskip\labelsep{##4##1\ ##2}]{\hspace*{-\labelsep}##4##3\@thmcounterend}##5}
     \def\@Opargbegintheorem##1##2##3##4{##4\trivlist
         \item[\hskip\labelsep{##3##1}]{\hspace*{-\labelsep}##3##2\@thmcounterend}}}{}
%
\spn@wtheorem{prob}{\nocaption}{\bfseries}{\rmfamily}
\newcommand{\probref}[1]{\textbf{\ref{#1}} }
\newenvironment{sol}{\par\addvspace{6pt}\noindent\probref}{\par\addvspace{6pt}}
%
\fi

\def\@takefromreset#1#2{%
    \def\@tempa{#1}%
    \let\@tempd\@elt
    \def\@elt##1{%
        \def\@tempb{##1}%
        \ifx\@tempa\@tempb\else
            \@addtoreset{##1}{#2}%
        \fi}%
    \expandafter\expandafter\let\expandafter\@tempc\csname cl@#2\endcsname
    \expandafter\def\csname cl@#2\endcsname{}%
    \@tempc
    \let\@elt\@tempd}

% redefininition of the captions for "figure" and "table" environments
%
\@ifundefined{floatlegendstyle}{\def\floatlegendstyle{\bfseries}}{}
\def\floatcounterend{\enspace}
\def\capstrut{\vrule\@width\z@\@height\topskip}
\@ifundefined{captionstyle}{\def\captionstyle{\normalfont\small}}{}
\@ifundefined{instindent}{\newdimen\instindent}{}

\long\def\@caption#1[#2]#3{\par\addcontentsline{\csname
  ext@#1\endcsname}{#1}{\protect\numberline{\csname
  the#1\endcsname}{\ignorespaces #2}}\begingroup
    \@parboxrestore\if@minipage\@setminipage\fi
    \@makecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par
  \endgroup}

\def\twocaptionwidth#1#2{\def\first@capwidth{#1}\def\second@capwidth{#2}}
% Default: .46\textwidth
\twocaptionwidth{.46\textwidth}{.46\textwidth}

\def\leftcaption{\refstepcounter\@captype\@dblarg%
            {\@leftcaption\@captype}}

\def\rightcaption{\refstepcounter\@captype\@dblarg%
            {\@rightcaption\@captype}}

\long\def\@leftcaption#1[#2]#3{\addcontentsline{\csname
  ext@#1\endcsname}{#1}{\protect\numberline{\csname
  the#1\endcsname}{\ignorespaces #2}}\begingroup
    \@parboxrestore
    \vskip\figcapgap
    \@maketwocaptions{\csname fnum@#1\endcsname}{\ignorespaces #3}%
    {\first@capwidth}\ignorespaces\hspace{.073\textwidth}\hfill%
  \endgroup}

\long\def\@rightcaption#1[#2]#3{\addcontentsline{\csname
  ext@#1\endcsname}{#1}{\protect\numberline{\csname
  the#1\endcsname}{\ignorespaces #2}}\begingroup
    \@parboxrestore
    \@maketwocaptions{\csname fnum@#1\endcsname}{\ignorespaces #3}%
    {\second@capwidth}\par
  \endgroup}

\long\def\@maketwocaptions#1#2#3{%
   \parbox[t]{#3}{{\floatlegendstyle #1\floatcounterend}#2}}

\def\fig@pos{l}
\newcommand{\leftfigure}[2][\fig@pos]{\makebox[.4635\textwidth][#1]{#2}}
\let\rightfigure\leftfigure

\newdimen\figgap\figgap=0.5cm  % hgap between figure and sidecaption
%
\long\def\@makesidecaption#1#2{\@tempdimb=3.6cm
   \setbox0=\vbox{\hsize=\@tempdimb
                  \captionstyle{\floatlegendstyle
                                         #1\floatcounterend}#2}%
   \ifdim\instindent<\z@
      \ifdim\ht0>-\instindent
         \advance\instindent by\ht0
         \typeout{^^JClass-Warning: Legend of \string\sidecaption\space for
                     \@captype\space\csname the\@captype\endcsname
                  ^^Jis \the\instindent\space taller than the corresponding float -
                  ^^Jyou'd better switch the environment. }%
         \instindent\z@
      \fi
   \else
      \ifdim\ht0<\instindent
         \advance\instindent by-\ht0
         \advance\instindent by-\dp0\relax
         \advance\instindent by\topskip
         \advance\instindent by-11\p@
      \else
         \advance\instindent by-\ht0
         \instindent=-\instindent
         \typeout{^^JClass-Warning: Legend of \string\sidecaption\space for
                     \@captype\space\csname the\@captype\endcsname
                  ^^Jis \the\instindent\space taller than the corresponding float -
                  ^^Jyou'd better switch the environment. }%
         \instindent\z@
      \fi
   \fi
   \parbox[b]{\@tempdimb}{\captionstyle{\floatlegendstyle
                                        #1\floatcounterend}#2%
                          \ifdim\instindent>\z@ \\
                               \vrule\@width\z@\@height\instindent
                                     \@depth\z@
                          \fi}}
\def\sidecaption{\@ifnextchar[\sidec@ption{\sidec@ption[t]}}
%
\newbox\bildb@x
%
\def\sidec@ption[#1]#2\caption{%
\setbox\bildb@x=\hbox{\ignorespaces#2\unskip}%
\if@twocolumn
 \ifdim\hsize<\textwidth\else
   \ifdim\wd\bildb@x<\columnwidth
      \typeout{Double column float fits into single column -
            ^^Jyou'd better switch the environment. }%
   \fi
 \fi
\fi
  \instindent=\ht\bildb@x
  \advance\instindent by\dp\bildb@x
\if t#1
\else
  \instindent=-\instindent
\fi
\@tempdimb=\hsize
\advance\@tempdimb by-\figgap
\advance\@tempdimb by-\wd\bildb@x
\ifdim\@tempdimb<3.6cm
   \ClassWarning{SVMult}{\string\sidecaption: No sufficient room for the legend;
             ^^Jusing normal \string\caption}%
   \unhbox\bildb@x
   \let\@capcommand=\@caption
\else
%  \ifdim\@tempdimb<4.5cm
%     \ClassWarning{SVMono}{\string\sidecaption: Room for the legend very narrow;
%              ^^Jusing \string\raggedright}%
      \toks@\expandafter{\captionstyle\sloppy
                         \rightskip=\z@\@plus6mm\relax}%
      \def\captionstyle{\the\toks@}%
%  \fi
   \let\@capcommand=\@sidecaption
%  \leavevmode
%  \unhbox\bildb@x
%  \hfill
\fi
\refstepcounter\@captype
\@dblarg{\@capcommand\@captype}}
\long\def\@sidecaption#1[#2]#3{\addcontentsline{\csname
  ext@#1\endcsname}{#1}{\protect\numberline{\csname
  the#1\endcsname}{\ignorespaces #2}}\begingroup
    \@parboxrestore
    \@makesidecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}%
    \hfill
    \unhbox\bildb@x
    \par
  \endgroup}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\fig@type{figure}

\def\leftlegendglue{\relax}
\newdimen\figcapgap\figcapgap=5\p@   % vgap between figure and caption
\newdimen\tabcapgap\tabcapgap=3\p@ % vgap between caption and table

\long\def\@makecaption#1#2{%
 \captionstyle
 \ifx\@captype\fig@type
   \vskip\figcapgap
 \fi
 \setbox\@tempboxa\hbox{{\floatlegendstyle #1\floatcounterend}%
 \capstrut #2}%
 \ifdim \wd\@tempboxa >\hsize
   {\floatlegendstyle #1\floatcounterend}\capstrut #2\par
 \else
   \hbox to\hsize{\leftlegendglue\unhbox\@tempboxa\hfil}%
 \fi
 \ifx\@captype\fig@type\else
   \vskip\tabcapgap
 \fi}

\newcounter{merk}

\def\endfigure{\resetsubfig\end@float}

\@namedef{endfigure*}{\resetsubfig\end@dblfloat}

\def\resetsubfig{\global\let\last@subfig=\undefined}

\def\r@setsubfig{\xdef\last@subfig{\number\value{figure}}%
\setcounter{figure}{\value{merk}}%
\setcounter{merk}{0}}

\def\subfigures{\refstepcounter{figure}%
   \@tempcnta=\value{merk}%
   \setcounter{merk}{\value{figure}}%
   \setcounter{figure}{\the\@tempcnta}%
   \def\thefigure{\if@numart\else\thechapter.\fi
   \@arabic\c@merk\alph{figure}}%
   \let\resetsubfig=\r@setsubfig}

\def\samenumber{\addtocounter{\@captype}{-1}%
\@ifundefined{last@subfig}{}{\setcounter{merk}{\last@subfig}}}

% redefinition of the "bibliography" environment
%
\def\biblstarthook#1{\gdef\biblst@rthook{#1}}
%
\AtBeginDocument{%
\ifx\chpbibl\undefined
  \def\bibsection{\section*{\refname}\ifx\sectionmark\@gobble\else
      \markright{\refname}\fi
      \addcontentsline{toc}{section}{\refname}%
      \mtaddtocont{\protect\contentsline{mtchap}{\refname}{\thepage}\hyperhrefextend}%
      \csname biblst@rthook\endcsname\par}
\else
 \def\bibsection{\chapter*{\refname}\@mkboth{\refname}{\refname}%
     \addcontentsline{toc}{chapter}{\refname}%
     \csname biblst@rthook\endcsname\par}
\fi}
\ifx\oribibl\undefined % Springer way of life
   \renewenvironment{thebibliography}[1]{\bibsection
         \global\let\biblst@rthook=\undefined
         \def\@biblabel##1{##1.}
         \small
         \list{\@biblabel{\@arabic\c@enumiv}}%
              {\settowidth\labelwidth{\@biblabel{#1}}%
               \leftmargin\labelwidth
               \advance\leftmargin\labelsep
               \if@openbib
                 \advance\leftmargin\bibindent
                 \itemindent -\bibindent
                 \listparindent \itemindent
                 \parsep \z@
               \fi
               \usecounter{enumiv}%
               \let\p@enumiv\@empty
               \renewcommand\theenumiv{\@arabic\c@enumiv}}%
         \if@openbib
           \renewcommand\newblock{\par}%
         \else
           \renewcommand\newblock{\hskip .11em \@plus.33em \@minus.07em}%
         \fi
         \sloppy\clubpenalty4000\widowpenalty4000%
         \sfcode`\.=\@m}
        {\def\@noitemerr
          {\@latex@warning{Empty `thebibliography' environment}}%
         \endlist}
   \def\@lbibitem[#1]#2{\item[{[#1]}\hfill]\if@filesw
        {\let\protect\noexpand\immediate
        \write\@auxout{\string\bibcite{#2}{#1}}}\fi\ignorespaces}
\else % original bibliography is required
   \let\bibname=\refname
   \renewenvironment{thebibliography}[1]
     {\chapter*{\bibname
        \markboth{\bibname}{\bibname}}%
      \list{\@biblabel{\@arabic\c@enumiv}}%
           {\settowidth\labelwidth{\@biblabel{#1}}%
            \leftmargin\labelwidth
            \advance\leftmargin\labelsep
            \@openbib@code
            \usecounter{enumiv}%
            \let\p@enumiv\@empty
            \renewcommand\theenumiv{\@arabic\c@enumiv}}%
      \sloppy
      \clubpenalty4000
      \@clubpenalty \clubpenalty
      \widowpenalty4000%
      \sfcode`\.\@m}
     {\def\@noitemerr
       {\@latex@warning{Empty `thebibliography' environment}}%
      \endlist}
\fi

\let\if@threecolind\iffalse
\def\threecolindex{\let\if@threecolind\iftrue}
\def\indexstarthook#1{\gdef\indexst@rthook{#1}}
\renewenvironment{theindex}
               {\if@twocolumn
                  \@restonecolfalse
                \else
                  \@restonecoltrue
                \fi
                \columnseprule \z@
                \columnsep 1cc
                \@nobreaktrue
                \if@threecolind
                   \begin{multicols}{3}[\chapter*{\indexname}%
                \else
                   \begin{multicols}{2}[\chapter*{\indexname}%
                \fi
                {\csname indexst@rthook\endcsname}]%
                \global\let\indexst@rthook=\undefined
                \markboth{\indexname}{\indexname}%
                \addcontentsline{toc}{chapter}{\indexname}%
                \parindent\z@
                \rightskip\z@ \@plus 40\p@
                \parskip\z@ \@plus .3\p@\relax
                \flushbottom
                \let\item\@idxitem
                \def\,{\relax\ifmmode\mskip\thinmuskip
                             \else\hskip0.2em\ignorespaces\fi}%
                \normalfont\small}
               {\end{multicols}
                \global\let\if@threecolind\iffalse
                \if@restonecol\onecolumn\else\clearpage\fi}

\def\idxquad{\hskip 10\p@}% space that divides entry from number

\def\@idxitem{\par\setbox0=\hbox{--\,--\,--\enspace}%
                  \hangindent\wd0\relax}

\def\subitem{\par\noindent\setbox0=\hbox{--\enspace}% second order
                \kern\wd0\setbox0=\hbox{--\,--\,--\enspace}%
                \hangindent\wd0\relax}% indexentry

\def\subsubitem{\par\noindent\setbox0=\hbox{--\,--\enspace}% third order
                \kern\wd0\setbox0=\hbox{--\,--\,--\enspace}%
                \hangindent\wd0\relax}% indexentry

\def\indexspace{\par \vskip 10\p@ \@plus5\p@ \@minus3\p@\relax}

% LaTeX does not provide a command to enter the authors institute
% addresses. The \institute command is defined here.

\newcounter{@inst}
\newcounter{@auth}
\newcounter{auco}
\newdimen\instindent
\newbox\authrun
\newtoks\authorrunning
\newtoks\tocauthor
\newbox\titrun
\newtoks\titlerunning
\newtoks\toctitle

\def\clearheadinfo{\gdef\@author{No Author Given}%
                   \gdef\@title{No Title Given}%
                   \gdef\@subtitle{}%
                   \gdef\@institute{}%
                   \gdef\@thanks{}%
                   \global\titlerunning={}\global\authorrunning={}%
                   \global\toctitle={}\global\tocauthor={}}

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

\def\title{\@ifstar\s@title\n@title}
\def\s@title#1{\gdef\@title{#1}\ds@numart}
\def\n@title#1{\gdef\@title{#1}\ds@book}

\def\institutename
 {\begingroup
 \if!\@institute!\else
 \def\thanks##1{\unskip{}}%
 \def\iand{\\[5pt]\let\and=\nand}%
 \def\nand{\ifhmode\unskip\nobreak\fi\ $\cdot$ }%
 \let\and=\nand
 \def\at{\\\let\and=\iand}%
 \footnotetext[0]{\kern-\bibindent
 \ignorespaces\@institute}\vspace{5dd}\fi
 \endgroup
 }%

\def\@fnsymbol#1{\ensuremath{\ifcase#1\or\star\or{\star\star}\or
   {\star{\star}\star}\or \dagger\or \ddagger\or
   \mathchar "278\or \mathchar "27B\or \|\or **\or \dagger\dagger
   \or \ddagger\ddagger \else\@ctrerr\fi}}

\def\inst#1{\unskip$^{#1}$}
\def\orcidID#1{\unskip$^{[#1]}$}% 
\def\fnmsep{\unskip$^,$}

\def\subtitle#1{\gdef\@subtitle{#1}}
\clearheadinfo

\def\@bfdottedtocline#1#2#3#4#5{%
  \ifnum #1>\c@minitocdepth \else
    \par
    \if@minipage\else\addvspace{5\p@}\fi
    {\leftskip #2\relax \rightskip \@tocrmarg \advance\rightskip by \z@ \@plus 2cm
               \parfillskip -\rightskip \pretolerance=10000
     \parindent #2\relax\@afterindenttrue
     \interlinepenalty\@M
     \leavevmode
     \@tempdima #3\relax
     \advance\leftskip \@tempdima \null\nobreak\hskip -\leftskip
     {\bfseries#4}\nobreak
     \leaders\hbox{$\m@th
        \mkern \@dotsep mu\hbox{.}\mkern \@dotsep
        mu$}\hfill
     \nobreak
     \hb@xt@\@pnumwidth{\hfil\normalfont \normalcolor #5}%
     \par\addvspace{5\p@}}%
  \fi}

\def\@rmdottedtocline#1#2#3#4#5{%
  \ifnum #1>\c@minitocdepth \else
    \vskip \z@ \@plus.2\p@
    {\leftskip #2\relax \rightskip \@tocrmarg \advance\rightskip by \z@ \@plus 2cm
               \parfillskip -\rightskip \pretolerance=10000
     \parindent #2\relax\@afterindenttrue
     \interlinepenalty\@M
     \leavevmode
     \@tempdima #3\relax
     \advance\leftskip \@tempdima \null\nobreak\hskip -\leftskip
     {#4}\nobreak
     \leaders\hbox{$\m@th
        \mkern \@dotsep mu\hbox{.}\mkern \@dotsep
        mu$}\hfill
     \nobreak
     \hb@xt@\@pnumwidth{\hfil\normalfont \normalcolor #5}%
     \par}%
  \fi}

%def\l@mtchap{\@bfdottedtocline{1}{\z@}{\tocsectotal}}
\def\l@mtchap{\@rmdottedtocline{1}{\z@}{\tocsecnum}}
\def\l@mtsec{\@rmdottedtocline{1}{\tocsecnum}{\tocsubsecnum}}

\newcounter{contribution}

\renewcommand\maketitle{\par\startnewpage
  \stepcounter{section}%
  \setcounter{section}{0}%
  \setcounter{subsection}{0}%
  \setcounter{figure}{0}
  \setcounter{table}{0}
  \setcounter{equation}{0}
  \setcounter{footnote}{0}%
  \if@numart
     \stepcounter{chapter}%
     \addtocounter{chapter}{-1}%
  \else
     \refstepcounter{chapter}%
  \fi
  \stepcounter{contribution}%
  \immediate\write\@auxout{\string\immediate\string\closeout\string\minitoc}%
  \immediate\write\@auxout{\let\MiniTOC=N}%
% try to be hyperref-compatible
  \csname phantomsection\endcsname
  \begingroup
    \parindent=\z@
%%%%%%%%%    \renewcommand\thefootnote{\@fnsymbol\c@footnote}%
%
    \renewcommand\thefootnote{\@fnsymbol\c@footnote}%
    \def\@makefnmark{$^{\@thefnmark}$}%
    \renewcommand\@makefntext[1]{%
    \noindent
    \hb@xt@\bibindent{\hss\@makefnmark\enspace}##1\vrule height0pt
    width0pt depth8pt}
%
    \if@twocolumn
      \ifnum \col@number=\@ne
        \@maketitle
      \else
        \twocolumn[\@maketitle]%
      \fi
    \else
      \newpage
      \global\@topnum\z@   % Prevents figures from going at top of page.
      \@maketitle
    \fi
    \@ifundefined{thispagecropped}{}{\thispagecropped}
    \thispagestyle{bchap}\@thanks
%
    \def\\{\unskip\ \ignorespaces}\def\inst##1{\unskip{}}%
    \def\thanks##1{\unskip{}}\def\fnmsep{\unskip}%
    \instindent=\hsize
    \advance\instindent by-\headlineindent
    \if@numart % keine Nummer
        \if!\the\toctitle!\addcontentsline{toc}{title}{\@title}\else
        \addcontentsline{toc}{title}{\the\toctitle}\fi
    \else
        \if!\the\toctitle!\addcontentsline{toc}{titlech}{\protect\numberline{\thechapter\thechapterend}\@title}\else
        \addcontentsline{toc}{titlech}{\protect\numberline{\thechapter\thechapterend}\the\toctitle}\fi
    \fi
    \if@runhead
       \if!\the\titlerunning!\else
         \edef\@title{\the\titlerunning}%
       \fi
       \global\setbox\titrun=\hbox{\small\rm\unboldmath\if@numart\else
                                   \@seccntformat{chapter}\fi
                                   \ignorespaces\@title}%
       \ifdim\wd\titrun>\instindent
          \typeout{Title too long for running head. Please supply}%
          \typeout{a shorter form with \string\titlerunning\space prior to
                   \string\maketitle}%
          \global\setbox\titrun=\hbox{\small\rm
          Title Suppressed Due to Excessive Length}%
       \fi
       \xdef\@title{\copy\titrun}%
    \fi
%
    \if!\the\tocauthor!\relax
      {\def\and{\noexpand\protect\noexpand\and}%
      \protected@xdef\toc@uthor{\@author}}%
    \else
      \def\\{\noexpand\protect\noexpand\newline}%
      \protected@xdef\scratch{\the\tocauthor}%
      \protected@xdef\toc@uthor{\scratch}%
    \fi
    \addtocontents{toc}{\noexpand\protect\noexpand\authcount{\the\c@auco}}%
    \if@numart
       \addcontentsline{toc}{author}{\toc@uthor}%
    \else
       \addcontentsline{toc}{authorch}{\toc@uthor}%
    \fi
    \if@runhead
       \if!\the\authorrunning!
         \value{@inst}=\value{@auth}%
         \setcounter{@auth}{1}%
       \else
         \edef\@author{\the\authorrunning}%
       \fi
       \global\setbox\authrun=\hbox{\small\unboldmath\@author\unskip}%
       \ifdim\wd\authrun>\instindent
          \typeout{Names of authors too long for running head. Please supply}%
          \typeout{a shorter form with \string\authorrunning\space prior to
                   \string\maketitle}%
          \global\setbox\authrun=\hbox{\small\rm
          Authors Suppressed Due to Excessive Length}%
       \fi
       \xdef\scratch{\copy\authrun}%
       \markboth{\scratch}{\@title}%
     \fi
  \endgroup
% \setcounter{footnote}{0}% footnote starts at (\inst+1)
  \@afterindentfalse\@afterheading
  \clearheadinfo}
%
\def\@maketitle{\newpage
 \markboth{}{}%
 \def\lastand{\ifnum\value{@inst}=2\relax
                 \unskip{} \andname\
              \else
                 \unskip \lastandname\
              \fi}%
 \def\and{\stepcounter{@auth}\relax
          \ifnum\value{@auth}=\value{@inst}%
             \lastand
          \else
             \unskip,
          \fi}%
  \raggedright
 {\chapnumsize
  \chapnumstyle
  \pretolerance=10000
  \let\\=\newline
% \@hangfrom{\@svsec}%
%%%  \@svsec
  \raggedright
  \hyphenpenalty \@M
  \interlinepenalty \@M
  \if@numart
     \chap@hangfrom{}%!!!
  \else
     \chap@hangfrom{\thechapter\thechapterend\hskip\betweenumberspace}%!!!
  \fi
  \ignorespaces
  \chapsize
  \chapstyle
  \@title \par}\vskip .8cm
\if!\@subtitle!\else {\chapnumsize\chapnumstyle
  \vskip -.65cm
  \pretolerance=10000
  \@subtitle \par}\vskip .8cm\fi
 \setbox0=\vbox{\setcounter{@auth}{1}\def\and{\stepcounter{@auth}}%
 \def\thanks##1{}\@author}%
 \global\value{@inst}=\value{@auth}%
 \global\value{auco}=\value{@auth}%
 \setcounter{@auth}{1}%
{\lineskip .5em
 \noindent\ignorespaces
 \@author\vskip.35cm}
 \processmotto % {\small\institutename\par}
 \institutename
 \ifdim\pagetotal>157\p@
     \vskip 11\p@
 \else
     \@tempdima=168\p@\advance\@tempdima by-\pagetotal
     \vskip\@tempdima
 \fi
}

\def\email#1{\emailname: \url{#1}}

% Useful environments
\newenvironment{abbrsymblist}[1][\qquad]
   {\section*{\abbrsymbname}
    \mtaddtocont{\protect\contentsline{mtchap}{\abbrsymbname}{\thepage}\hyperhrefextend}
    \begin{description}[#1]}{\end{description}\addvspace{10\p@}}
%
\newenvironment{acknowledgement}{\par\addvspace{17\p@}\small\rm
\trivlist\item[\hskip\labelsep{\bfseries\ackname}]}
{\endtrivlist\addvspace{6\p@}}
%
\newenvironment{noteadd}{\par\addvspace{17\p@}\small\rm
\trivlist\item[\hskip\labelsep{\it\noteaddname}]}
{\endtrivlist\addvspace{6\p@}}
%
\DeclareRobustCommand\abstract{\@ifstar\@abstgobl\@abstract}
\def\@abstract#1{\noindent\textbf{\abstractname} #1\par
%\@afterindentfalse
%\@afterheading
}
\def\@abstgobl#1{\par
%\@afterindentfalse
%\@afterheading
}
%
\newcommand{\keywords}[1]{\par\addvspace\baselineskip
\noindent\keywordname\enspace\ignorespaces#1}
%
% define the running headings of a twoside text
\def\runheadsize{\small}
\def\runheadstyle{\rmfamily\upshape}
\def\customizhead{\hspace{\headlineindent}}

\def\ps@bchap{%\let\@mkboth\@gobbletwo
     \let\@oddhead\@empty\let\@evenhead\@empty
     \def\@oddfoot{\reset@font\small\hfil\thepage}%
     \let\@evenfoot\@oddfoot}

\def\ps@headings{\let\@mkboth\markboth
   \let\@oddfoot\@empty\let\@evenfoot\@empty
   \def\@evenhead{\runheadsize\runheadstyle\rlap{\thepage}\hfil
                  \leftmark}
   \def\@oddhead{\runheadsize\runheadstyle\rightmark\hfil
                  \llap{\thepage}}
   \def\chaptermark##1{\markboth{{\ifnum\c@secnumdepth>\m@ne
      \thechapter\thechapterend\hskip\betweenumberspace\fi ##1}}{{\ifnum %!!!
      \c@secnumdepth>\m@ne\thechapter\thechapterend\hskip\betweenumberspace\fi ##1}}}%!!!
   \def\sectionmark##1{\markright{{\ifnum\c@secnumdepth>\z@
      \thesection\hskip\betweenumberspace\fi ##1}}}}

\def\ps@myheadings{\let\@mkboth\@gobbletwo
   \let\@oddfoot\@empty\let\@evenfoot\@empty
   \def\@evenhead{\runheadsize\runheadstyle\rlap{\thepage}\hfil
                  \leftmark}
   \def\@oddhead{\runheadsize\runheadstyle\rightmark\hfil
                  \llap{\thepage}}
   \let\chaptermark\@gobble
   \let\sectionmark\@gobble
   \let\subsectionmark\@gobble}

\if@runhead\ps@myheadings\else
\ps@empty\fi

%%%SOPHIE TEMPLATE BEGIN%%%

\RequirePackage[x11names]{xcolor}

\definecolor{trailer}{gray}{0.9}
\definecolor{example}{gray}{0.85}
\definecolor{questype}{gray}{0.8}
\definecolor{important}{gray}{0.75}
\definecolor{warning}{gray}{0.7}
\definecolor{programcode}{gray}{0.65}
\definecolor{tips}{gray}{0.6}
\definecolor{overview}{gray}{0.55}
\definecolor{backgroundinformation}{gray}{0.5}
\definecolor{legaltext}{gray}{0.45}

\newcommand\circledmark[2][white]{%
  \ooalign{%
    \hidewidth
    \kern0.65ex\raisebox{-1.3ex}{\scalebox{3}{\textcolor{#1}{\textbullet}}}
    \hidewidth\cr
    #2\cr
  }%
}

\def\formtmp#1#2{{\vskip12pt\noindent\fboxsep=0pt\colorbox{#1}{\vbox{\vskip3pt\hbox to \textwidth{\hskip3pt\vbox{\raggedright\noindent\textbf{#2\vphantom{Qy}}}\hfill}\vspace*{3pt}}}\par\vskip2pt%
\noindent\kern0pt}}

\newenvironment{trailer}[1]{\ignorespaces\def\stmtopen##1{##1}%
\formtmp{trailer}{#1}}{\par\noindent\textcolor{trailer}{\rule{\columnwidth}{1pt}}\vskip2pt\par\addvspace{\baselineskip}}%

%\renewenvironment{example}[1]{\ignorespaces\def\stmtopen##1{##1}%
%\formtmp{example}{#1}}{\par\noindent\textcolor{example}{\rule{\columnwidth}{1pt}}\vskip2pt\par\addvspace{\baselineskip}}%

\newenvironment{questype}[1]{\ignorespaces\def\stmtopen##1{##1}%
\formtmp{questype}{\ \circledmark[white]{\textcolor{black}{\sf\bfseries?}}{\kern6pt}#1}}{\par\noindent\textcolor{questype}{\rule{\columnwidth}{1pt}}\vskip2pt\par\addvspace{\baselineskip}}%

\newenvironment{important}[1]{\ignorespaces\def\stmtopen##1{##1}%
\formtmp{important}{\ \circledmark{\textcolor{black}{$\ >$}}{\kern6pt}#1}}{\par\noindent\textcolor{important}{\rule{\columnwidth}{1pt}}\vskip2pt\par\addvspace{\baselineskip}}%

\newenvironment{warning}[1]{\ignorespaces\def\stmtopen##1{##1}%
\formtmp{warning}{\ \circledmark[white]{\textcolor{black}{!}}{\kern6pt}#1}}{\par\noindent\textcolor{warning}{\rule{\columnwidth}{1pt}}\vskip2pt\par\addvspace{\baselineskip}}%

\newenvironment{programcode}[1]{\ignorespaces\def\stmtopen##1{##1}%
\formtmp{programcode}{#1}}{\noindent\textcolor{programcode}{\rule{\columnwidth}{1pt}}\vskip2pt\par\addvspace{\baselineskip}}%

\newenvironment{tips}[1]{\ignorespaces\def\stmtopen##1{##1}%
\formtmp{tips}{#1}}{\par\noindent\textcolor{tips}{\rule{\columnwidth}{1pt}}\vskip2pt\par\addvspace{\baselineskip}}%

\newenvironment{overview}[1]{\ignorespaces\def\stmtopen##1{##1}%
\formtmp{overview}{#1}}{\par\noindent\textcolor{overview}{\rule{\columnwidth}{1pt}}\vskip2pt\par\addvspace{\baselineskip}}%
 
\newenvironment{backgroundinformation}[1]{\ignorespaces\def\stmtopen##1{##1}%
\formtmp{backgroundinformation}{#1}}{\par\noindent\textcolor{backgroundinformation}{\rule{\columnwidth}{1pt}}\vskip2pt\par\addvspace{\baselineskip}}%

\newenvironment{legaltext}[1]{\ignorespaces\def\stmtopen##1{##1}%
\formtmp{legaltext}{#1}}{\par\noindent\textcolor{legaltext}{\rule{\columnwidth}{1pt}}\vskip2pt\par\addvspace{\baselineskip}}%

\newenvironment{newshaded}{%
  \def\FrameCommand{\fboxsep=12pt\relax\colorbox{shadecolor}}%
  \MakeFramed
{\advance\hsize-\width\FrameRestore}}%
{\endMakeFramed}
\AtBeginDocument{\renewenvironment{svgraybox}%
       {%\fboxsep=12pt\relax
        \begin{newshaded}%\vspace*{10pt}%
        \list{}{\leftmargin=0mm\rightmargin=0mm%\leftmargin=12pt\rightmargin=12pt%
        \topsep=\z@\relax}%
        \expandafter\item\parindent=\svparindent
        \hskip-\listparindent}%
        {%\vspace*{10pt}
        \endlist\end{newshaded}}}%

\def\boxtext#1{\vskip\baselineskip\moveleft26pt\vbox{\fboxsep3pt\fbox{#1}}}%

\newcommand\guisection{\@startsection{section}{1}{\z@}%
                       {-18\p@}% \p@lus -4\p@ \@minus -4\p@}%
                       {4\p@}% \p@lus 4\p@ \@minus 4\p@}%
                       {\normalfont\secsize\secstyle
                        \rightskip=\z@ \@plus 8em\pretolerance=10000 }}
\newcommand\guisubsection{\@startsection{subsection}{2}{\z@}%
                       {-18\p@}% \p@lus -4\p@ \@minus -4\p@}%
                       {4\p@}% \p@lus 4\p@ \@minus 4\p@}%
                       {\normalfont\subsecsize\subsecstyle
                        \rightskip=\z@ \@plus 8em\pretolerance=10000 }}

\newenvironment{refguide}
{\let\section\guisection%
\let\subsection\guisubsection}
{}

                        %%%SOPHIE TEMPLATE END%%%

\usepackage{amsthm}

%\usepackage[thmmarks,thref]{ntheorem} 
%\theoremstyle{nonumberplain}
%\theoremheaderfont{\bfseries\itshape}
%\theorembodyfont{\upshape}
%\theoremsymbol{\ensuremath{\square}}
%\newtheorem{proof}{Proof} 
%\gdef\NoneSymbol{}

\makeatletter

\let\@ethics\@empty%
\def\ethicssubhead#1#2{\vskip9pt\noindent{\bf #1}\enspace#2}%
\def\ethics#1#2{\bgroup\small\parskip0pt\if!#1!\vskip-9pt\else\vspace*{11pt}\noindent{{\bf#1}}\enspace\nobreak\fi{\noindent #2\endgraf}%
\egroup}%

\long\def\addtocontents#1#2{%
\def\orcidID##1{}% 
  \protected@write\@auxout
      {\let\label\@gobble \let\index\@gobble \let\glossary\@gobble}%
      {\string\@writefile{#1}{#2}}}

\newwrite\DescriptionTexts%
\immediate\openout\DescriptionTexts=DescriptionTexts.txt%
\newcounter{Dfigchecks}%

\def\Description#1{\stepcounter{Dfigchecks}\stepcounter{figure}%
\immediate\write\DescriptionTexts{\arabic{Dfigchecks} (Fig. \thefigure) - \detokenize{#1}}%
\addtocounter{figure}{-1}}%

\makeatother

\endinput
%end of file svmult.cls
