%% 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%now redefines \{ and \}\newenvironment{ttbox}{\par\nobreak\vskip-2pt% \vbox\bgroup\begin{listing}\chardef\{=`\{\chardef\}=`\}% \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{\hboxto0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}{\setbox0=\hbox{$\textstyle\rm C$}\hbox{\hboxto0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}{\setbox0=\hbox{$\scriptstyle\rm C$}\hbox{\hboxto0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}{\setbox0=\hbox{$\scriptscriptstyle\rm C$}\hbox{\hboxto0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}}}\def\bbbe{{\mathchoice {\setbox0=\hbox{\smalletextfont e}\hbox{\raise0.1\ht0\hbox to0pt{\kern0.4\wd0\vrule width0.3ptheight0.7\ht0\hss}\box0}}{\setbox0=\hbox{\smalletextfont e}\hbox{\raise0.1\ht0\hbox to0pt{\kern0.4\wd0\vrule width0.3ptheight0.7\ht0\hss}\box0}}{\setbox0=\hbox{\smallescriptfont e}\hbox{\raise0.1\ht0\hbox to0pt{\kern0.5\wd0\vrule width0.2ptheight0.7\ht0\hss}\box0}}{\setbox0=\hbox{\smallescriptscriptfont e}\hbox{\raise0.1\ht0\hbox to0pt{\kern0.4\wd0\vrule width0.2ptheight0.7\ht0\hss}\box0}}}}\def\bbbq{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm Q$}\hbox{\raise0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}}{\setbox0=\hbox{$\textstyle\rm Q$}\hbox{\raise0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}}{\setbox0=\hbox{$\scriptstyle\rm Q$}\hbox{\raise0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}{\setbox0=\hbox{$\scriptscriptstyle\rm Q$}\hbox{\raise0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}}}\def\bbbt{{\mathchoice {\setbox0=\hbox{$\displaystyle\rmT$}\hbox{\hbox to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}{\setbox0=\hbox{$\textstyle\rm T$}\hbox{\hboxto0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}{\setbox0=\hbox{$\scriptstyle\rm T$}\hbox{\hboxto0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}{\setbox0=\hbox{$\scriptscriptstyle\rm T$}\hbox{\hboxto0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}}}\def\bbbs{{\mathchoice{\setbox0=\hbox{$\displaystyle \rm S$}\hbox{\raise0.5\ht0\hboxto0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hboxto0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}}{\setbox0=\hbox{$\textstyle \rm S$}\hbox{\raise0.5\ht0\hboxto0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hboxto0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}}{\setbox0=\hbox{$\scriptstyle \rm S$}\hbox{\raise0.5\ht0\hboxto0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hboxto0pt{\kern0.5\wd0\vrule height0.45\ht0\hss}\box0}}{\setbox0=\hbox{$\scriptscriptstyle\rm S$}\hbox{\raise0.5\ht0\hboxto0pt{\kern0.4\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hboxto0pt{\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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%