%% edited by LCP!!  
%%   Modified page break penalties
%%   Commented out the change to \newlinechar
%%   Increased space in Contents and List of Figures
%%   Changed \thebibliography to the defn in llncs.sty
%%   Added ttbox
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%   MATHSING.STY        Version 1.1
%
%   This LaTeX style option file contains necessary macros for writing
%   camera ready English single author math book manuscripts.
%
%
%   Usage:
%
%      \documentstyle[12pt,mathsing]{book}
%        ...
%
%   Change log:
%
%      90/11/04  pagestyle empty for first page of chapter
%      90/11/04  distinct figure and table captions
%      90/11/04  \small for captions and headings
%      90/11/04  improved definition of theorem-like environments
%      90/12/01  separation after chapter title changed to 5.1cm
%      90/12/01  page size changed to 45x14.4+10pt=23.05cm
%      90/12/01  references
%      90/12/01  common counter for theorem-like environments
%      90/12/02  table of contents
%      90/12/02  final improvements and corrections
%      90/12/26  two styles for equation numbers
%      91/02/05  \numberlikebook and \numberlikearticle replace
%                \eqnbook and \eqnarticle
%      91/10/07  \listoffigures, \listoftables made similar to
%                \tableofcontents,
%                running head of Index changed: Sachverzeichnis -> Index,
%                \newthe now uses \thechapter instead of \arabic{chapter}
%      91/02/05  binding: \tablebook, \tablearticle
%                \figurebook, \figurearticle added
%      91/10/07  holzwarth: \listoffigures, \listoftables
%                according to \tableofcontents,
%                \begin{theindex}
%                \newthe to produce correct numbers
%      91/12/03  \chapter, \section, and \subsection now do not
%                hyphenate the headings any more
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  change the catcode of @ (allows names containing @ after \begin{document})
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\makeatletter


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%     page layout and dimensions
%
% The following commands are redefined:
%
%   \ps@headings    (cf. BOOK.STY)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%
%     Layout
%
%     Note: The following values do not apply for English Springer
%     books on phsics; use \baselineskip=14pt, \textwidth=13.8cm,
%     \textheight=640pt (=45x14pt+10pt=22.5cm) instead!
%

\baselineskip=14.4pt          % LaTeX default

\topmargin=0cm
\textwidth=14.2cm             % 1.2 x 11.833 cm
\textheight=658pt             % 45x14.4pt+10pt = 658pt = 23.0554cm
%\textheight=23.2502cm         % 1.2x19.3752cm=23.2502cm (first version)
\oddsidemargin=0.7cm
\evensidemargin=0.7cm
\headsep=20pt                 % ?

\parindent=7mm                % 1.2 x 5.833mm

\hfuzz=2pt                    % supress "overfull box" messages below 2pt

\frenchspacing                % no large blanks at the end of a sentence


\tolerance=500

\abovedisplayskip=3.6 mm plus7.2pt minus 4.8pt
\belowdisplayskip=3.6 mm plus7.2pt minus 4.8pt
\abovedisplayshortskip=0.0 mm plus7.2pt minus 2.4pt
\belowdisplayshortskip=2.4 mm plus4.8pt minus 4.8pt

%%LCP: were 0, 10000, 10000
\predisplaypenalty=100        % penalties for page break
\clubpenalty=400              %
\widowpenalty=400             %


%
%     running titles
%

% binding 5.2.91 \hspace changed to 1.0 cm    |           |
% binding 5.2.91 dot deleted after \thesection                 |
\def\ps@headings{
    \let\@mkboth\markboth
    \def\@oddfoot{}
    \def\@evenfoot{}
    \def\@evenhead{\rm\small\thepage\hspace{1.0cm}\leftmark\hfil\hbox{}}
    \def\@oddhead{\hbox{}\hfil\rm\small\rightmark\hspace{1.0cm}\thepage}
    \def\chaptermark##1{\markboth
                        {\ifnum \c@secnumdepth >\m@ne \thechapter.\ \fi ##1}{}}
%hier punkt raus. binding                                      |
    \def\sectionmark##1{\markright
                        {\ifnum \c@secnumdepth >\z@ \thesection\ \fi ##1}}
    }

\pagestyle{headings}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Chapters and Sections
%
% The following commands are redefined:
%
%  \@makechapterhead    (cf. BK12.STY)
%  \@makeschapterhead   (cf. BK12.STY)
%  \chapter             (cf. BK12.STY)
%  \@sect               (cf. LATEX.TEX)
%  \section             (cf. BK12.STY)
%  \subsection          (cf. BK12.STY)
%  \subsubsection       (cf. BK12.STY)
%  \paragraph           (cf. BK12.STY)
%  \subparagraph        (cf. BK12.STY)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%
%     number of numbered section levels
%

\setcounter{secnumdepth}{3}


%
%     Adapt the font size for chapter titles and supress printing of
%     the word "chapter"
%

\def\@makechapterhead#1{ { \parindent 0pt \raggedright
% \pretolerance added 12/3/91 fuh
{\pretolerance=10000\Large \bf \thechapter.\hspace{0.3cm}#1\par}%
 \nobreak \vskip 4cm \vskip\baselineskip} }

\def\@makeschapterhead#1{ { \parindent 0pt \raggedright
% \pretolerance added 12/3/91 fuh
 \pretolerance=10000\Large \bf #1\par
 \nobreak \vskip 4cm \vskip\baselineskip} }

%
%     define pagestyle=empty for first page of a chapter
%

\def\chapter{\cleardoublepage \thispagestyle{empty} \global\@topnum\z@
\@afterindentfalse \secdef\@chapter\@schapter}

%
%     Change the distance between section number and title from 1em to 2mm
%     binding:  changed again to 1en=0.5em       |     5.2.91
%

\def\@sect#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth
     \def\@svsec{}\else
     \refstepcounter{#1}%
     \edef\@svsec{\csname the#1\endcsname\hskip 0.5em }\fi
     \@tempskipa #5\relax
      \ifdim \@tempskipa>\z@
        \begingroup #6\relax
% changed by Binding :) 20.3.91
% old:    \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par}
% \@hangfrom deleted to avoid hanging indentation \noindent added
          {\noindent\hskip #3\relax\@svsec}%
          {\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}\else
        \def\@svsechd{#6\hskip #3\@svsec #8\csname #1mark\endcsname
                      {#7}\addcontentsline
                           {toc}{#1}{\ifnum #2>\c@secnumdepth \else
                             \protect\numberline{\csname the#1\endcsname}\fi
                       #7}}\fi
     \@xsect{#5}}


%
%     Font size for section titles;
%     Increased vertical space before and after sections, subsections
%     and subsubsections by 1ex; run-in headings starting with subsubsection
%
%     (\@startsection{NAME}{LEVEL}{INDENT}{BEFORESKIP}{AFTERSKIP}{STYLE})
%

%binding, 18.3.91:  \boldmath inserted
\def\section{\@startsection{section}{1}{\z@}{
             -4.50ex plus -1ex minus -.2ex}{3.3ex plus .2ex}
             {\large\bf\boldmath\raggedright\pretolerance=10000}}
% \raggedright and \pretolerance added 12/3/91 fuh
\def\subsection{\@startsection{subsection}{2}{\z@}{
             -4.25ex plus -1ex minus -.2ex}{2.5ex plus .2ex}
             {\normalsize\bf\boldmath\raggedright\pretolerance=10000}}
% \raggedright and \pretolerance added 12/3/91 fuh
\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{
             -3.25ex plus -1ex minus -.2ex}{-0.5em}
             {\normalsize\bf\boldmath}}
\def\paragraph{\@startsection{paragraph}{4}{\z@}{
             -3.25ex plus -1ex minus -.2ex}{-0.5em}{\normalsize\it}}
\def\subparagraph{\@startsection{subparagraph}{5}{\@}{
             -3.25ex plus -1ex minus -.2ex}{-0.5em}{\normalsize\it}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%20.3.91, binding: \labelitemi changed
\renewcommand{\labelitemi}{$\bullet$}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Tables
%
% Change width of horizontal and vertical lines in arrays and tables
%
% The following commands are redefined:
%
%  \arrayrulewidth
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\arrayrulewidth0.15mm


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Figure and table captions (small)
%
% To meet the different requirements for table and figure captions
% new macros \@makefigurecaption and \@maketablecaption are introduced
% in addition to \@makecaption (cf. BOOK.STY). The \@caption macro is
% changed to check for figures and tables.
%
% The following commands are redefined:
%
%  \@caption         (cf. LATEX.TEX)
%  \fnum@figure      (cf. BOOK.STY)
%  \fnum@table       (cf. BOOK.STY)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\long\def\@caption#1[#2]#3{\addcontentsline{\csname
  ext@#1\endcsname}{#1}{\protect\numberline{\csname
  the#1\endcsname}{\ignorespaces #2}}\par
  \begingroup
    \@parboxrestore
    \normalsize
    \csname @make#1caption\endcsname
    {\csname fnum@#1\endcsname}{\ignorespaces #3}\par
  \endgroup}

\long\def\@makefigurecaption#1#2{
 \vskip 10pt                     % skip between figure and caption
 {\small                         % required here for correct \baselineskip !
 \setbox\@tempboxa\hbox{\small{\bf#1}#2}
 \ifdim \wd\@tempboxa >\hsize
   \unhbox\@tempboxa\par
 \else
   \hbox to\hsize{\hfil\box\@tempboxa\hfil}       % centered short caption !
 \fi}
 \vskip 10pt}                    % additional space between caption and text

\long\def\@maketablecaption#1#2{
 \vskip 10pt                     % additional space between text and caption
 {\small                         % required here for correct \baselineskip !
 \setbox\@tempboxa\hbox{\small{\bf#1}#2}
 \ifdim \wd\@tempboxa >\hsize
   \unhbox\@tempboxa\par
 \else \hbox  to\hsize{\box\@tempboxa\hfil}   % leftadjusted short caption !
 \fi}
 \vskip 10pt}                    % skip between caption and table

\def\fnum@figure{Fig.$\,$\thefigure.$\;$}
\def\fnum@table{Table$\,$\thetable.$\;$}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  Distance between text and floatings (tables, figures)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\floatsep 14pt plus 2pt minus 4pt        % LaTeX defaults values
\textfloatsep 20pt plus 2pt minus 4pt    %
\intextsep 14pt plus 4pt minus 4pt       %
\@maxsep 20pt                            %



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Table of contents
%
% The following commands are redefined:
%
%  \l@chapter        (cf. LATEX.STY)
%  \tableofcontents
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%
%     lowest level for table of contents entries
%
\setcounter{tocdepth}{3}

%
%     dotted line for chapters in table of contents
%     (cf. definition of \@dottedline in LATEX.STY)
%
\def\l@chapter#1#2{\pagebreak[3]
 \vskip 1.0em plus 1pt \@tempdima 1.5em \begingroup
 \parindent \z@ \rightskip \@pnumwidth
 \parfillskip -\@pnumwidth
 \rm \leavevmode #1
 \nobreak\leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern \@dotsep mu$}\hfill
 \nobreak
 \hbox to\@pnumwidth{\hss \rm #2}\par
 \endgroup}

%copied from book.sty to leave room for 12.11, etc. -- Frank Holzwarth via LCP
\def\l@section{\@dottedtocline{1}{1.5em}{2.8em}}
\def\l@figure{\@dottedtocline{1}{1.5em}{2.8em}}

%
%     Adaption of \tableofcontents (title,headings,pagenumber)
%

\def\tableofcontents{
     \@restonecolfalse
     \if@twocolumn\@restonecoltrue\onecolumn\fi
     \chapter*{Table of Contents}
     \markboth{Table of Contents}{Table of Contents}  % headline
     \renewcommand{\thepage}{\Roman{page}}            % roman page number
     \@starttoc{toc}\if@restonecol\twocolumn\fi}

%%%%%%%% added 91/10/07 fuh %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% List of figures
%
% The following commands are redefined:
%
%  \listoffigures
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\listoffigures{
     \@restonecolfalse
     \if@twocolumn\@restonecoltrue\onecolumn\fi
     \chapter*{List of Figures}
     \markboth{List of Figures}{List of Figures}      % headline
     \renewcommand{\thepage}{\Roman{page}}            % roman page number
     \@starttoc{lof}\if@restonecol\twocolumn\fi}

%%%%%%%% added 91/10/07 fuh %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% List of tables
%
% The following commands are redefined:
%
%  \listoftables
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\listoftables{
     \@restonecolfalse
     \if@twocolumn\@restonecoltrue\onecolumn\fi
     \chapter*{List of Tables}
     \markboth{List of Tables}{List of Tables}        % headline
     \renewcommand{\thepage}{\Roman{page}}            % roman page number
     \@starttoc{lot}\if@restonecol\twocolumn\fi}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Index (with table of contents entry)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\theindex{ \cleardoublepage
               \small
               \columnseprule \z@
               \columnsep=0.84cm
               \twocolumn[\@makeschapterhead{Index}]
               \addcontentsline{toc}{chapter}{Index}
               \@mkboth{Index}{Index}
               \thispagestyle{plain}\parindent\z@
               \parskip\z@ plus .3pt\relax\let\item\@idxitem}
\def\@idxitem{\par\hangindent 15pt}
\def\subitem{\par\hangindent 15pt -- }
\def\endtheindex{\clearpage}
\def\indexspace{\par \vskip 10pt plus 5pt minus 3pt\relax}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% References (Bibliography)
%
% Macros for creating a list of references in small print using LaTeX
% defaults or some special Springer commands.
%
% Usage:
%
%   \begin{thebibliography}{wide-label}      % LaTeX standard macros
%     \bibitem[label]{name} ... text ...
%     \bibitem[label]{name} ... text ...
%   \end{thebibliography}
%
%   or
%
%   \begin{references}{wide-label}           % Springer macros
%     \refer            ... text ...
%     \refno{no.}       ... text ...
%     \refmark{[label]} ... text ...
%   \end{references}
%
% New commands:
%
%   \refchapter      starts an unnumbered chapter "References"; small font
%   \refer           unlabeled item with hanging indentation
%   \refno           right adjusted label (for numbers)
%   \refmark         left adjusted label (for text labels)
%
% Changed commands
%
%   \thebibliography       (BOOK.STY)   (further edit by LCP!)
%   \endthebibliography    (BOOK.STY)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\refchapter{\chapter*{References}
\parindent0pt\parskip0pt\small
\addcontentsline{toc}{chapter}{References}
\markboth{References}{References}}


\def\thebibliography#1{\refchapter\small\list
  {\arabic{enumi}.}{\settowidth\labelwidth{#1.}\leftmargin\labelwidth
    \advance\leftmargin\labelsep
    \usecounter{enumi}}
    \def\newblock{\hskip .11em plus .33em minus -.07em}
    \sloppy
    \sfcode`\.=1000\relax}
\let\endthebibliography=\endlist


\newenvironment{references}[1]{\refchapter
                               \settowidth\labelwidth{#1\enspace}
                               \begingroup}{\endgraf\endgroup}
%
% The following macros are from REFER.TEX.
% \refindent is replaced by the predefined dimension \labelwidth
% that is also used by \thebibliography; \ref is replaced by \refer
% since \ref is already used for referencing lables!

%%%\newlinechar=`\|

% \refer produces ordinary entries, successive line are indented 1em
\def\refer{\goodbreak\hangindent1em\hangafter=1\noindent\ignorespaces}

% \refno produces entries with right-aligned marks in the margin
\def\refno#1{\goodbreak
\setbox0=\hbox{#1\enspace}\ifdim\labelwidth<\wd0\relax
\message{|Your reference `#1' is wider than you pretended in using
\string\begref.}\fi
\hangindent\labelwidth\hangafter=1\noindent
\kern\labelwidth\llap{#1\enspace}\ignorespaces}

% \refmark produces entries with left-aligned marks in the margin
\def\refmark#1{\goodbreak
\setbox0=\hbox{#1\enspace}\ifdim\labelwidth<\wd0\relax
\message{|Your reference `#1' is wider than you pretended in using
\string\begref.}\fi
\hangindent\labelwidth\hangafter=1\noindent
\hbox to\labelwidth{#1\hss}\ignorespaces}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  New environments
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%
%  The following lines define a new environment 'listing'
%
%         \begin{listing}
%               ...
%         \end{listing}
%
%  that prints listings using \footnotesize and takes care to reset
%  the \baselineskip. The macro definition is based on ALLTT.STY that
%  allows various TEX commands to be given within the environment
%  (e.g. '\input', '\index' or '\it'). '%' has been retained as a special
%  character within 'listing', however, to avoid unwanted line breaks.
%
%

\def\docspecials{\do\ \do\$\do\&%
  \do\#\do\^\do\^^K\do\_\do\^^A\do\~}

\newdimen\oldbaselineskip
\def\listing{\par\noindent\oldbaselineskip=\baselineskip \footnotesize%
\trivlist \item[]\if@minipage\else\vskip\parskip\fi
\leftskip\@totalleftmargin\rightskip\z@
\parindent\z@\parfillskip\@flushglue\parskip\z@
\@tempswafalse \def\par{\if@tempswa\hbox{}\fi\@tempswatrue\@@par}
\obeylines \tt \catcode``=13 \@noligs \let\do\@makeother \docspecials
 \frenchspacing\@vobeyspaces}

\def\endlisting{\endtrivlist\baselineskip=\oldbaselineskip}

%Add ttbox to Springer's macros!!  - LCP
\newenvironment{ttbox}{\par\nobreak\vskip-2pt%
           \vbox\bgroup\begin{listing}\leftskip\leftmargini}%
        {\end{listing}\egroup\vskip-7pt\@endparenv}
\newcommand\ttbreak{\end{ttbox}\goodbreak\vskip-8pt plus 3pt\begin{ttbox}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Acknowledgements ( = acknow.tex)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\ack#1{\vskip11pt\begingroup\noindent{\it Acknowledgements\/}.
\ignorespaces#1\vskip6pt\endgroup}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Definition of versal greek letters ( = ucgreek.tex)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Vectors ( = vector.tex)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% This is vector.tex
% it redefines the plain TeX \vec command
% to produce bold characters
%
\def\vec#1{\ifmmode
\mathchoice{\mbox{\boldmath$\displaystyle\bf#1$}}
{\mbox{\boldmath$\textstyle\bf#1$}}
{\mbox{\boldmath$\scriptstyle\bf#1$}}
{\mbox{\boldmath$\scriptscriptstyle\bf#1$}}\else
{\mbox{\boldmath$\bf#1$}}\fi}
%
%\def\vec#1{{\textfont0=\tenbf\scriptfont0=\sevenbf
%\scriptscriptfont0=\fivebf
%\textfont1=\tenbf\scriptfont1=\sevenbf
%\scriptscriptfont1=\fivebf
%\ifmmode % supply all varieties of math sizes
%   \mathchoice{\hbox{$\displaystyle#1$}}{\hbox{$\textstyle#1$}}
%   {\hbox{$\scriptstyle#1$}}{\hbox{$\scriptscriptstyle#1$}}
%\else\hbox{$#1$}\fi}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Symbols ( = symbols.tex )
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% This is symbols.tex
% the symbols not available in plain TeX are constructed
% by overprinting some characters

\def\sun{{\hbox{$\odot$}}}
\def\la{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.5pt}\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr
\noalign{\vskip1.0pt}\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr
\noalign{\vskip0.5pt}\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil
\cr<\cr\noalign{\vskip0.5pt}\sim\cr}}}}}
\def\ga{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.5pt}\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr
\noalign{\vskip1.0pt}\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr
\noalign{\vskip0.5pt}\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil
\cr>\cr\noalign{\vskip0.5pt}\sim\cr}}}}}
\def\sq{\hbox{\rlap{$\sqcap$}$\sqcup$}}
\def\degr{\hbox{$^\circ$}}
\def\arcmin{\hbox{$^\prime$}}
\def\arcsec{\hbox{$^{\prime\prime}$}}
\def\utw{\smash{\rlap{\lower5pt\hbox{$\sim$}}}}
\def\udtw{\smash{\rlap{\lower6pt\hbox{$\approx$}}}}
\def\fd{\hbox{$.\!\!^{\rm d}$}}
\def\fh{\hbox{$.\!\!^{\rm h}$}}
\def\fm{\hbox{$.\!\!^{\rm m}$}}
\def\fs{\hbox{$.\!\!^{\rm s}$}}
\def\fdg{\hbox{$.\!\!^\circ$}}
\def\farcm{\hbox{$.\mkern-4mu^\prime$}}
\def\farcs{\hbox{$.\!\!^{\prime\prime}$}}
\def\fp{\hbox{$.\!\!^{\scriptscriptstyle\rm p}$}}
\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\cor{\mathrel{\mathchoice {\hbox{$\widehat=$}}{\hbox{$\widehat=$}}
{\hbox{$\scriptstyle\hat=$}}
{\hbox{$\scriptscriptstyle\hat=$}}}}
\def\grole{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\noalign{\vskip-1.5pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
>\cr\noalign{\vskip-1.5pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
>\cr\noalign{\vskip-1pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr\noalign{\vskip-0.5pt}<\cr}}}}}
\def\lid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.5pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr
\noalign{\vskip1pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr
\noalign{\vskip0.5pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr\noalign{\vskip0.5pt}=\cr}}}}}
\def\gid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.5pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr
\noalign{\vskip1pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr
\noalign{\vskip0.5pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr\noalign{\vskip0.5pt}=\cr}}}}}
\def\sol{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr\sim\cr\noalign{\vskip-0.2mm}<\cr}}}
{\vcenter{\offinterlineskip
\halign{\hfil$\textstyle##$\hfil\cr\sim\cr<\cr}}}
{\vcenter{\offinterlineskip
\halign{\hfil$\scriptstyle##$\hfil\cr\sim\cr<\cr}}}
{\vcenter{\offinterlineskip
\halign{\hfil$\scriptscriptstyle##$\hfil\cr\sim\cr<\cr}}}}}
\def\sog{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr\sim\cr\noalign{\vskip-0.2mm}>\cr}}}
{\vcenter{\offinterlineskip
\halign{\hfil$\textstyle##$\hfil\cr\sim\cr>\cr}}}
{\vcenter{\offinterlineskip
\halign{\hfil$\scriptstyle##$\hfil\cr\sim\cr>\cr}}}
{\vcenter{\offinterlineskip
\halign{\hfil$\scriptscriptstyle##$\hfil\cr\sim\cr>\cr}}}}}
\def\lse{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.5pt}\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr
\noalign{\vskip1pt}\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr
\noalign{\vskip0.5pt}\simeq\cr}}}
{\vcenter{\offinterlineskip
\halign{\hfil$\scriptscriptstyle##$\hfil\cr<\cr
\noalign{\vskip0.5pt}\simeq\cr}}}}}
\def\gse{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.5pt}\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr
\noalign{\vskip1.0pt}\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr
\noalign{\vskip0.5pt}\simeq\cr}}}
{\vcenter{\offinterlineskip
\halign{\hfil$\scriptscriptstyle##$\hfil\cr>\cr
\noalign{\vskip0.5pt}\simeq\cr}}}}}
\def\grole{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\noalign{\vskip-1.5pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
>\cr\noalign{\vskip-1.5pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
>\cr\noalign{\vskip-1pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr\noalign{\vskip-0.5pt}<\cr}}}}}
\def\leogr{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\noalign{\vskip-1.5pt}>\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
<\cr\noalign{\vskip-1.5pt}>\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
<\cr\noalign{\vskip-1pt}>\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr\noalign{\vskip-0.5pt}>\cr}}}}}
\def\loa{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.5pt}\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr
\noalign{\vskip1.0pt}\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr
\noalign{\vskip0.5pt}\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr\noalign{\vskip0.5pt}\approx\cr}}}}}
\def\goa{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.5pt}\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr
\noalign{\vskip1.0pt}\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr
\noalign{\vskip0.5pt}\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr\noalign{\vskip0.5pt}\approx\cr}}}}}
\def\bbbr{{\rm I\!R}} %reelle Zahlen
\def\bbbn{{\rm I\!N}} %natuerliche Zahlen
\def\bbbm{{\rm I\!M}}
\def\bbbh{{\rm I\!H}}
\def\bbbf{{\rm I\!F}}
\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
to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle\rm C$}\hbox{\hbox
to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle\rm C$}\hbox{\hbox
to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm C$}\hbox{\hbox
to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}}}
\def\bbbe{{\mathchoice {\setbox0=\hbox{\smalletextfont e}\hbox{\raise
0.1\ht0\hbox to0pt{\kern0.4\wd0\vrule width0.3pt
height0.7\ht0\hss}\box0}}
{\setbox0=\hbox{\smalletextfont e}\hbox{\raise
0.1\ht0\hbox to0pt{\kern0.4\wd0\vrule width0.3pt
height0.7\ht0\hss}\box0}}
{\setbox0=\hbox{\smallescriptfont e}\hbox{\raise
0.1\ht0\hbox to0pt{\kern0.5\wd0\vrule width0.2pt
height0.7\ht0\hss}\box0}}
{\setbox0=\hbox{\smallescriptscriptfont e}\hbox{\raise
0.1\ht0\hbox to0pt{\kern0.4\wd0\vrule width0.2pt
height0.7\ht0\hss}\box0}}}}
\def\bbbq{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm Q$}\hbox{\raise
0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle\rm Q$}\hbox{\raise
0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle\rm Q$}\hbox{\raise
0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm Q$}\hbox{\raise
0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}}}
\def\bbbt{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm
T$}\hbox{\hbox to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle\rm T$}\hbox{\hbox
to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle\rm T$}\hbox{\hbox
to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm T$}\hbox{\hbox
to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}}}
\def\bbbs{{\mathchoice
{\setbox0=\hbox{$\displaystyle     \rm S$}\hbox{\raise0.5\ht0\hbox
to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox
to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle        \rm S$}\hbox{\raise0.5\ht0\hbox
to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox
to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle      \rm S$}\hbox{\raise0.5\ht0\hbox
to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox
to0pt{\kern0.5\wd0\vrule height0.45\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm S$}\hbox{\raise0.5\ht0\hbox
to0pt{\kern0.4\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox
to0pt{\kern0.55\wd0\vrule height0.45\ht0\hss}\box0}}}}

%
% note: changed \sans to \sf for LaTeX
%

\def\bbbz{{\mathchoice {\hbox{$\sf\textstyle Z\kern-0.4em Z$}}
{\hbox{$\sf\textstyle Z\kern-0.4em Z$}}
{\hbox{$\sf\scriptstyle Z\kern-0.3em Z$}}
{\hbox{$\sf\scriptscriptstyle Z\kern-0.2em Z$}}}}

\def\diameter{{\ifmmode\oslash\else$\oslash$\fi}}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% petit  (substitute for petit.tex)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\newenvironment{petit}{\vskip6pt\begingroup\small}{\endgroup\vskip6pt}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% New environments
%
%   lemma, proposition, theorem, corollary  (\bf,\it)  (numbered)
%   exercise, problem, solution, definition (\bf,\rm)
% 27.3.91 binding: example, note and question changed to (\bf, \rm)
%
%   lemma*, proposition*, theorem*, corollary*  (\bf,\it)   (unnumbered)
%   exercise*, problem*, solution*, definition* (\bf,\rm)
%   example*, note*, question* (\it,\rm)
%
%   remark, proof (\it,\rm)  (unnumbered)
%
%   usage:   \begin{lemma}  or  \begin{lemma}[COMMENT]
%              ...                ...
%            \end{lemma}        \end{lemma}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% currently one counter is used for all theorem like environments

\newcounter{lemmacount}[chapter]
\renewcommand{\thelemmacount}{\thechapter.\arabic{lemmacount}}


%
% short form for defininng new theorem like environments:
% \newthe{NAME}{NAME*}{TITLE}{COUNTER}{FONT1}{FONT2}
%
\def\@@begthe#1{\@ifnextchar[{\@optbegthe#1}{\@begthe#1}}
%27.3.91 binding: dot deleted
%def\@begthe#1{. #1}   old
\def\@begthe#1{ #1}
\def\@optbegthe#1[#2]{ {#2} #1}
\newcommand{\newthe}[6]{
 \def\nlni{\par\ifvmode\removelastskip\fi\vskip\baselineskip\noindent}
 \def\xxxend{\endgroup\vskip\baselineskip}
 \newenvironment{#1}{\nlni\begingroup\refstepcounter{#4}#5#3
%changed 91/10/7 fuh:\arabic{chapter}.\arabic{#4}\@@begthe{#6}}{\xxxend}
                     \thechapter.\arabic{#4}\@@begthe{#6}}{\xxxend}
 \newenvironment{#2}{\nlni\begingroup#5#3\@@begthe{#6}}{\xxxend}}


% Lemma, Proposition, Theorem, Corollary  (\bf,\it)

\newthe{lemma}{lemma*}{Lemma}{lemmacount}{\bf}{\it}
\newthe{proposition}{proposition*}{Proposition}{lemmacount}{\bf}{\it}
\newthe{theorem}{theorem*}{Theorem}{lemmacount}{\bf}{\it}
\newthe{corollary}{corollary*}{Corollary}{lemmacount}{\bf}{\it}


% Exercise, Problem, Solution, Definition (\bf,\rm)

\newthe{exercise}{exercise*}{exercise}{lemmacount}{\bf}{\it}
\newthe{problem}{problem*}{Problem}{lemmacount}{\bf}{\it}
\newthe{solution}{solution*}{Solution}{lemmacount}{\bf}{\it}
\newthe{definition}{definition*}{Definition}{lemmacount}{\bf}{\it}


% Example, Note, Question (\bf,\rm)

\newthe{example}{example*}{Example}{lemmacount}{\bf}{\rm}
\newthe{note}{note*}{Note}{lemmacount}{\bf}{\rm}
\newthe{question}{question*}{Question}{lemmacount}{\bf}{\rm}


% Remark, Proof

\newenvironment{remark}{\nlni\begingroup\it Remark. \rm}{
                        \endgroup\vskip\baselineskip}
\newenvironment{proof}{\nlni\begingroup\it Proof. \rm}{
                       \endgroup\vskip\baselineskip}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% qed
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\qed{\ifmmode\sq\else{\unskip\nobreak\hfil
\penalty50\hskip1em\null\nobreak\hfil\sq
\parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  \eqnarticle    simple equation numbers without chapter number
%  \eqnbook       structured equation numbers (default)
%   changed by binding 5.2.91: changed to \numberlikearticle and
%                                \numberlikebook, changing numbering of
%                              figures and tables also.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\numberlikearticle{\global\def\theequation{\arabic{equation}}
\global\def\thetable{\arabic{table}}
\global\def\thefigure{\arabic{figure}}}
\def\numberlikebook{\global\def\theequation{\thechapter.\arabic{equation}}
\global\def\thetable{\thechapter.\arabic{table}}
\global\def\thefigure{\thechapter.\arabic{figure}}}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  Redeclaration of \makeatletter; no @-expressions may be used from now on
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\makeatother




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%   End of MATHSING.STY
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



