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+\documentstyle[12pt,mathsing]{book}
+%
+\numberlikebook
+\let\ts=\thinspace
+\let\picplace=\vspace
+%
+\newfont{\fivebf}{cmbx7 scaled 714} %Fonts fuer die Vektor-definition
+\newfont{\sevenbf}{cmbx7}
+%
+\makeatletter
+
+\def\laTeX{{\rm L\kern-.35em\raise.3ex\hbox{\LARGE A}\kern-.15em
+T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}}
+
+\newcommand{\BibTeX}{{\rm B\kern-.05em{\sc i\kern-.025em b}\kern-.08em
+ T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}}
+%
+\def\textfontii{\the\textfont\tw@}
+\def\AmSTeX{{\textfontii A}\kern-.1667em\lower.5ex\hbox
+ {\textfontii M}\kern-.125em{\textfontii S}-\TeX}
+%
+\def\runnheadl{Single-Author Mathematics -- \LaTeX{} Style File}
+\def\runnheadr{Documentation}
+\def\@evenhead{\rm\small\thepage\hspace{1.5cm}\runnheadl\hfil\hbox{}}
+\def\@oddhead{\hbox{}\hfil\rm\small\runnheadr\hspace{1.5cm}\thepage}
+%
+% braik: \tableofcontents changed to produce arabic page numbers
+\def\tableofcontents{
+ \@restonecolfalse
+ \if@twocolumn\@restonecoltrue\onecolumn\fi
+ \chapter*{Table of Contents}
+ \markboth{Table of Contents}{Table of Contents} % headline
+ \renewcommand{\thepage}{\arabic{page}} % arabic page numbers
+ \@starttoc{toc}\if@restonecol\twocolumn\fi
+ }
+% braik: \chapter should not start new page
+\def\chapter{\vskip18pt \global\@topnum\z@
+\@afterindentfalse \secdef\@chapter\@schapter}
+%
+\def\@makechapterhead#1{{\parindent 0pt \noindent\raggedright
+{\Large \bf \thechapter.\hspace{0.3cm}#1\par}%
+ \nobreak\vskip\baselineskip} }
+
+\def\@makeschapterhead#1{{\parindent 0pt \raggedright
+ \Large \bf #1\par
+ \nobreak \vskip\baselineskip} }
+%%%
+\makeatother
+%
+\begin{document}
+% hier geht's dann los!
+\thispagestyle{empty}
+\noindent
+\rule{\textwidth}{1pt}
+\vspace*{11mm}
+
+\noindent
+{\Huge \bf Single - Author Mathematics}
+
+\vspace*{11mm} \noindent
+{\huge \laTeX{} MathSing Style File}
+
+\vspace*{11mm} \noindent
+\rule{\textwidth}{1pt}
+
+\vspace*{11mm}\noindent
+Version 1.1
+\vfill
+\noindent
+{
+{\huge Springer-\kern-1pt Verlag}\\
+\LARGE
+Berlin\enspace Heidelberg\enspace New~Y\kern-2.5pt ork\\
+London\enspace Paris\enspace Tokyo\enspace Hong~Kong \\
+Barcelona\enspace Budapest}
+\newpage \noindent
+\rule{\textwidth}{1pt}
+\section*{For further information please contact us\newline
+at Springer-Verlag, Heidelberg:}
+%
+%begin{flushleft}
+\begin{tabular}{@{}l@{\hspace{.35cm}}p{0.75\textwidth}}
+Mailing address: & Springer-Verlag\\
+ & New Technologies/Product Developement\\
+ & P.O.~Box 105280\\
+ & D-6900 Heidelberg 1, FRG\\[2mm]
+bitnet/EARN: & SPRINGER @ DHDSPRI6 \\[2mm]
+Telex: & 46\,17\,23 \\[2mm]
+Telefax: & (0) 62\,21 43\,982
+\end{tabular}
+
+\bigskip\noindent
+All Springer macros are also available through our mailserver
+
+SVSERV@DHDSPRI6.bitnet.
+
+\noindent Send an e-mail just containing the word "help"
+to this e-mail address and you will receive further information.
+%end{flushleft}
+
+\bigskip\bigskip\noindent
+Once you have completed your work using this style file, please
+submit your own printout of the {\it final version together with the
+disk/magnetic tape\/}$^*$ containing your \LaTeX{} input (source) file
+and
+the final DVI file and make sure that the text is {\it identical in both
+cases}. Moreover, please check that you have also copied the dataset
+containing your macros on the disk.
+\vfill
+\begin{itemize}
+\item[$^*$] {\it The following formats are acceptable:}
+%\smallskip
+\item[] $5.25^{\prime\prime}$ or $3.5^{\prime\prime}$ diskette MS-DOS,
+$5.25^{\prime\prime}$ CP/M, $3.5^{\prime\prime}$ diskette Apple
+Macintosh, 9-track 1600 bpi magnetic tape VAX/VMS, 9-track 1600 bpi
+magnetic tape ANSI with label, SUN-Streamer Tape.\par
+\end{itemize}
+\bigskip\bigskip
+\rule{\textwidth}{1pt}
+%%%
+\newpage
+\tableofcontents
+\newpage
+%
+%
+\chapter{Introduction}
+%
+Authors wishing to code their book
+with \LaTeX{}, as well as
+those who have already coded it with \LaTeX{},
+will be provided with a style file that will give the text the
+desired layout. Authors are requested
+to adhere strictly to these instructions; {\em the \LaTeX{}-mathsing file must not be changed}.
+
+For the main body of the text
+you should use the commands of standard \LaTeX{}.
+Even if you are familiar with these commands, we urge you to read
+this entire document thoroughly. It contains many suggestions on
+how to use our commands properly; thus with little work your book
+will be formatted exactly to the Springer standard.
+
+If you are already familiar with \LaTeX{}, then the \LaTeX{}
+MathSing file should not give you any major difficulties.
+This style file will change the layout to the required MathSing style
+(for instance it will define the layout of \verb|\section|).
+We have also invented some extra commands,
+which are not provided by \LaTeX{}.
+
+The majority of these hints are not specific for MathSing; they may improve
+your use of \LaTeX{} in general.
+Furthermore, the documentation provides suggestions for the proper
+editing and use
+of the input files (capitalization, abbreviation, etc. -- see
+Sects.~\ref{refedit} ff).
+
+\vspace{12pt}
+\chapter{How to Begin}
+
+Please insert the enclosed diskette or tape into your computer. You will
+find the following files:
+%end{document}
+\begin{flushleft}
+\begin{tabular}{@{}l@{\hspace{1cm}}l}
+{\em mathsing.doc} & General instructions (this document).\\
+{\em mathsing.dem} & Run this to get a sample output.\\
+{\em mathsing.sty} & \LaTeX{} MathSing file for use with normal CM-Fonts.\\
+\end{tabular}
+\end{flushleft}
+You need to run your file with the command:
+\verb|latex filename|.
+If you have citations or references run it
+once more with the same command.
+
+\section{How to invoke the \LaTeX{} MathSing style file}
+
+The \LaTeX{} MathSing style file is substyle for the \LaTeX{}
+``book'' style.
+Therefore you may use all ``book'' style commands to prepare your
+manuscript except the command \verb|\part|. \LaTeX{} MathSing style file
+is invoked by requesting ``book'' in the
+\verb|documentstyle|-command:
+\begin{verbatim}
+\documentstyle[12pt,mathsing]{book}
+ \begin{document}
+ <your book>
+ \end{document}
+\end{verbatim}
+Do not use any other document-style options!
+
+\section{Text Already Coded with \LaTeX{} Without
+the \LaTeX{} mathsing file}
+
+If your file is already coded with \LaTeX{}
+you can easily adapt it a posteriori to \LaTeX{} MathSing style.
+
+Please refrain from using any \LaTeX{} or \TeX{} commands
+that affect the layout or formatting of your document (i.e. commands
+like \verb|\textheight|, \verb|\vspace|, \verb|\hoffset|, etc.).
+There may nevertheless be exceptional occasions
+when some of them may be used.
+
+The \LaTeX{}-MathSing style file has been carefully designed to produce
+the right layout
+from your \LaTeX{} input. If there is anything specific you would like
+to do and for which the style file does not provide a command,
+{\em please contact us.\/}
+
+If you have your own macros or definitions, insert them as shown here:
+\begin{verbatim}
+\documentstyle[12pt, mathsing]{book}
+ <your own macros or definitions>
+ \begin{document}
+ <your book>
+ \end{document}
+\end{verbatim}
+
+ or, if your macros are in a separate file:
+
+\begin{verbatim}
+\documentstyle[12pt, mathsing, <macrofilename>]{book}
+\begin{document}
+ <your book>
+ \end{document}
+\end{verbatim}
+
+\noindent
+Please supply comments with your macros to help us understand them.
+
+\section{Problems with PC\ts\TeX{}}
+In PC\ts\TeX{} the default memory capacity is not sufficient to
+accommodate
+our fonts. To cope with this problem, invoke \TeX{} with the following
+command:
+\begin{verbatim}
+latex file.tex /f=26000 /m=65000
+\end{verbatim}
+
+
+\chapter{General Rules for Coding Formulas}
+
+With mathematical formulas, you may proceed as described
+in Sect.~3.3 of the {\em \LaTeX{} User's Guide \& Reference
+Manual\/} by Leslie Lamport (1986), Addison-Wesley Publishing
+Company, Reading, Mass.
+
+A formula that appears in the running text is produced by enclosing
+it in \verb|$| signs, e.g. \verb|$ x^{2} $|
+produces $x^{2}$.\label{math}
+
+Displayed formulas are produced by the
+equation environment; here
+equations are automatically numbered sequentially throughout
+the chapters of your book using arabic
+numerals in parentheses on the right-hand side.
+
+You can choose between two kinds of numbering:
+\begin{itemize}
+\item the command \verb|\numberlikebook| at the beginning of your file,
+after the
+\verb|\documentstyle| and before the \verb|\begin{document}| command
+invokes structured numbering, e.g. (1.1), (1.2) of equations, tables
+and figures.
+\item Replacing this command by the command
+\verb|\numberlikearticle| results in ``ordinary" numbering e.g. (1),
+(2).
+\end{itemize}
+
+If you have to break equations, please use the eqnarray environment
+described in Sect.~3.3.5 on p.~49 of the \LaTeX{} book.
+
+If you wish to start a new paragraph immediately after a displayed
+equation, insert a blank line to produce the required
+indention. If there is no new paragraph either do not insert
+a blank line or insert a blank line and
+type \verb|\noindent| immediately before continuing the text.
+
+Please punctuate a displayed equation in the same way as
+ordinary text.
+
+Note that the sizes of the parentheses or other delimiter
+symbols used in equations should ideally match the height of the
+formulas being enclosed. This is automatically taken care of by
+the following \LaTeX{} commands, e.g.\ \
+\verb|\left(| \quad or \quad \verb|\left[| \quad and \quad
+\verb|\right)| \quad or \quad \verb|\right]|.
+
+\section{Italic and Roman Type in the Math Mode}
+
+\begin{itemize}
+\item[a)]
+In the math mode \TeX{} and \LaTeX{} treat all letters as though they
+were mathematical or physical variables; hence they are typeset in
+italics. However, any textual elements within formulas should be
+set in roman. Roman should also be used for
+subscripts and superscripts {\em in formulas\/} where these are
+merely labels and not in themselves variables, e.g.\\
+\verb|$T_{\rm eff} = 5\,10^{9} \mbox{ K}$|\quad produce\quad
+$T_{\rm eff} = 5 \cdot 10^{9} \mbox{ K}$\\
+\verb|$T_{\rm K}$|\quad produce\quad $T_{\rm K}$ (K = Kelvin)\\
+\verb|$m_{\rm e}$|\quad produce\quad $m_{\rm e}$ (e = electron).
+
+\paragraph{Sample Input}
+\begin{verbatim}
+\begin{equation}
+ \left(\frac{a^{2} + b^{2}}{c^{3}} \right) = 1 \quad
+ \mbox{ if } c\neq 0 \mbox{ and if } a,b,c\in \bbbr.
+\end{equation}
+\end{verbatim}
+
+\paragraph{Sample Output}
+\begin{equation}
+ \left(\frac{a^{2} + b^{2}}{c^{3}} \right) = 1 \quad
+ \mbox{ if } c\neq 0 \mbox{ and if } a,b,c\in \bbbr.
+\end{equation}
+
+%\begin{itemize}
+\item[b)]
+Please ensure that {\em physical units\/} (e.g.\ pc, erg\ts s$^{-1}$\ts
+K, cm$^{-3}$, W\ts m$^{-2}$\ts Hz$^{-1}$, m\ts kg\ts s$^{-2}$\ts
+A$^{-2}$) and
+{\em abbreviations} such as Ord, Var, GL, SL, sgn, const.\
+are always set in roman type. To ensure
+this use the \verb|\mbox| command: \verb|\mbox{Hz}|.
+On p.\ 46 of the {\em \LaTeX{} User's Guide \& Reference
+Manual\/} by Leslie Lamport you will find the names of
+common mathe\-matical functions, such as log, sin, exp, max and sup.
+These should be coded as \verb|\log|,
+\verb|\sin|, \verb|\exp|, \verb|\max|, \verb|\sup|
+and will then automatically appear in roman.
+
+\item[c)]
+In order
+to distinguish ``d'' used as ``differential sign'' and ``e''
+used as ``exponential function'' from normal variables,
+please set those in roman.
+%
+\item[d)]
+Chemical symbols and formulas should be set in roman,
+e.g.\ Fe not $Fe$, H$_{2}$O not {\em H$_{2}$O\/}, H$\alpha$ not
+{\em H${\alpha}$}.
+\end{itemize}
+
+
+\chapter{How to Edit Your Input (Source) File}
+
+\section{Headings}
+
+All words in headings should be capitalized except for conjunctions,
+prepositions up to five letters (e.g. on, of, by, and, or, but, from,
+with, with, under) and definite and indefinite articles (the, a, an)
+unless they appear at the beginning of a sentence. Formula letters must
+be typeset as in the text.
+
+\section{Capitalization and Non-capitalization}\label{refedit}
+\begin{itemize}
+\item[a)] The following should always be capitalized:
+\begin{itemize}
+\item Headings (see preceding Sect.\ts 4.1)
+\item Abbreviations and expressions in the text such as
+Fig(s).,
+Table(s), Sect(s)., Chap(s)., Theorem, Corollary, Definition, etc. when
+used with numbers, e.g. Fig.\ts 3.1, Table 1.1, Theorem 2.1.
+\end{itemize}
+\item[] Please see below the special rules in Sect.\ts 4.3 for
+referring to equations.
+\item[b)] The following should {\it not\/} be capitalized:
+\begin{itemize}
+\item The words figure(s), table(s), equation(s),
+theorem(s) in the text when used without an accompanying number.
+\item Figure legends and table captions except for names and
+abbreviations.
+\end{itemize}
+\end{itemize}
+\section{Abbreviation of Words}
+\begin{itemize}
+\item[a)] The following {\it should\/} be abbreviated in the running
+text
+{\it unless\/} they come at the beginning of a sentence: Chap., Sect.,
+Fig.; e.g. The results are depicted in Fig.\ts 5. Figure 9 reveals that
+\dots
+\item[] {\it Please note\/}: Equations should be referred to solely by
+their number in parentheses e.g. (14). However, when the reference comes
+at the beginning of a sentence, the unabbreviated word ``Equation"
+should be used: e.g. Equation (14) is very important. However, (15)
+makes it clear that \dots
+\item[b)] If abbreviations of names or concepts are used throughout the
+text, they should be defined at first occurrence, e.g. Plurisubharmonic
+(PSH) Functions, Strong Optimization (SOPT) Problem.
+\end{itemize}
+
+\section{Foreign Words and Phrases}
+Foreign words that have not come into general use are italicized.
+If a word or phrase or its abbrevation can be found in the main body
+of {\em Webster's\/} (and this also applies to British usage),
+it and its abbrevation are considered to be in general use and
+are not italicized. E.g. et al., cf., e.g.,
+a priori, in situ, brems\-strah\-lung, eigenvalues, should not be
+italicized.
+
+
+\chapter{Sectioning Commands}
+
+Main headings will be automatically numbered by the following macros.
+
+\paragraph{Sample Input}
+\begin{verbatim}
+\chapter{This is a First-Order Title}
+\section{This is a Second-Order Title}
+\subsection{This is a Third-Order Title}
+\subsubsection{This is an Bold Run-in Heading.}
+\paragraph{This is an Italic Run-in Heading}
+\end{verbatim}
+
+\newpage
+\paragraph{Sample Output}\
+
+
+\chapter*{1. This is a First-Order Title}
+\section*{1.1 This is a Second-Order Title}
+\subsection*{1.1.1 This is a Third-Order Title}
+\subsubsection*{This is an Bold Run-in Heading.} The text continues in
+regular roman typeface.
+\paragraph{This is an italic run-in heading.} The text
+continues \dots
+
+
+\chapter{Minienvironments}
+We have defined a number of minienvironments, namely for lemma,
+propositions, theorems, corollaries, exercises, problems, solutions,
+definitions, examples, notes and questions.
+
+These commands automatically provide the correct fonts and print the
+appropriate run-in headings. They all come in two flavors: without an
+asterisk they produce automatically numbered run-in heading.
+
+An optional argument is enclosed in [\ ] brackets. Note that unlike
+the standard \LaTeX syntax, no brackets or fullstops are provided
+automatically but have to be typed by the user.
+
+Using an asterisk will turn off the automatic numbering:
+
+General syntax:
+\begin{verbatim}
+\begin{<env.name>}
+ <text>
+\end{<env.name}
+\end{verbatim}
+ or
+\begin{verbatim}
+\begin{<env.name>}[<text>]
+ <text>
+\end{<env.name}
+\end{verbatim}
+ or
+\begin{verbatim}
+\begin{<env.name>*}
+ <text>
+\end{<env.name*}
+\end{verbatim}
+
+\paragraph{Sample Input}
+\begin{verbatim}
+\begin{lemma}
+Every day the night falls
+\end{lemma}
+\begin{lemma}[(Proverb).]
+At night, all cats are grey
+\end{lemma}
+\begin{theorem*}
+Every day the cats are grey
+\end{theorem*}
+\end{verbatim}
+
+\paragraph{Sample Output}\
+
+
+\begin{lemma}
+Every day the night falls
+\end{lemma}
+\begin{lemma}[(Proverb).]
+At night, all cats are grey
+\end{lemma}
+\begin{theorem*}
+Every day the cats are grey
+\end{theorem*}
+
+\section{Defining new minienvironments}
+If you want to define similar minienvironments or alter existing ones,
+you can do so by using the command
+\begin{verbatim}
+\newthe{<environmentname>}{<environmentname>}
+ {lemmacount}{<title of heading>}
+ {<font of heading>}
+ {<font of text>}
+\end{verbatim}
+
+
+\chapter{Fine Tuning of the Text}
+
+The following should be used to improve the readability of the text:
+\begin{flushleft}
+\begin{tabular}{@{}l@{\hspace{.5cm}}p{.7\textwidth}}
+\verb|\,| & a thin space, e.g.\ between numbers with more than
+ 5 digits; a line division will not be made
+ following this space,\\
+\verb|--| & en-dash; two strokes, without a space at either end,\\
+\verb*| -- | & em-dash; two strokes, with a space at either end,\\
+\verb|-| & hyphen; one stroke, no space at either end,\\
+\verb|$-$| & minus, in the text {\em only},\\
+\verb|~| & tilde between parts of names.
+\end{tabular}
+\end{flushleft}
+
+\paragraph{Sample Input}
+\begin{verbatim}
+20\,000 km, 1\,000\,000 s, NGC 468\,324
+1950--1985, p.~11--21
+this -- written on a computer -- is now printed
+signal-to-noise ratio, early-type, metal-poor, non-relativistic
+$-30$ K, $-5^{\circ}$C
+Dr~h.c.~Rockefeller-Smith and Prof.~Dr~Mallory
+\end{verbatim}
+
+\paragraph{Sample Output}
+\begin{flushleft}
+20\,000 km, 1\,000\,000 s, NGC 468\,324\\
+1950--1985, p.~11--21\\
+this -- written on a computer -- is now printed\\
+signal-to-noise ratio, early-type, metal-poor, non-relativistic\\
+$-30$ K, $-5^{\circ}$C\\
+Dr~h.c.~Rockefeller-Smith and Prof.~Dr~Mallory
+\end{flushleft}
+
+
+\chapter{Special Typefaces}
+
+Normal type (roman) need not be specified. {\em Italic\/}
+(not {\sl slanted\/}) should be used for emphasis in the text or, if
+not avoidable, {\bf boldface} could be used too.
+\begin{flushleft}
+\begin{tabular}{@{}l@{\hspace{.5cm}}l}
+\verb|{\em <text>}| & {\em Emphasized Text}.\\
+
+\verb|\begin{petit}| & Paragraph in small print (petit) for passages in the \\
+\verb|<text>| & text that the reader may skip upon first reading or for \\
+\verb|\end{petit}| & exercises or sections of similar
+importance.\\
+\end{tabular}
+\end{flushleft}
+
+For the use of further typefaces, please refer to Sect. 3.1 of the
+\LaTeX manual by Lamport.
+
+\chapter{Footnotes}
+
+Footnotes need to be punctuated at the end.
+Footnotes within the text should be coded
+\begin{verbatim}
+\footnote{<text>}
+\end{verbatim}
+
+\paragraph{Sample Input}
+\begin{verbatim}
+Text with a footnote\footnote{The footnote is automatically
+numbered.} and text continues \dots
+\end{verbatim}
+
+\noindent
+{\bf Remark}: Please avoid using footnotes in headings.
+
+\paragraph{Sample Output}
+\begin{flushleft}
+Text with a footnote\footnote{The footnote is automatically
+numbered.} and text continues \dots
+\end{flushleft}
+
+
+\chapter{Lists}
+
+Please code lists as described below:
+
+\paragraph{Sample Input}
+\begin{verbatim}
+\begin{enumerate}
+ \item First item.
+ \item Second item.
+ \begin{enumerate}
+ \item First nested item.
+ \item Second nested item.
+ \end{enumerate}
+ \item Third item.
+\end{enumerate}
+\end{verbatim}
+
+\paragraph{Sample Output}
+\begin{enumerate}
+\item First item.
+\item Second item.
+\begin{enumerate}
+\item First nested item.
+\item Second nested item.
+\end{enumerate}
+\item Third item.
+\end{enumerate}
+
+
+\chapter{Figures}
+
+{\it The figures\/} (line drawings and those containing halftone inserts
+as well as halftone figures) {\it should not be pasted into your
+laserprinter output}. They should be enclosed separately in camera-ready
+form (original artwork, glossy prints, photographs and/or slides). The
+lettering should be suitable for reproduction, and after reduction the
+capital letters should be at least 1.8 mm and not more than 2.5 mm in
+height. Check that lines and other details are uniformly black and that
+the lettering on figures is clearly legible.
+
+To leave the desired amount of space for the height of your figures,
+please use the following coding. As can be seen in the output, we will
+automatically provide 1\ts cm space above and below the figure, so that
+you should only leave the space corresponding to the size of the figure
+itself.
+
+If the figure is narrower than the page-width, please do not try to fill
+up the empty space with text.
+
+The final positioning of floating objects (i.e. figures and tables)
+should be done at the end of development of your text.
+
+For further information see also Sect.~3.6.2 on p.~63 of the
+{\em \LaTeX{} User's Guide \& Reference
+Manual\/} by Leslie Lamport (1986), Addison-Wesley Publishing
+Company, Reading, Mass.
+Figure legends should be inserted after or before
+(not in) the paragraph in which the figure is first mentioned.
+They will be numbered automatically.
+
+The figure, including the legend, must not exceed 23~cm in height.
+Taller figures will be swallowed by \LaTeX{} without warning.
+
+Please code as follows:
+\begin{flushleft}
+\verb|\begin{figure}|\\
+\verb|\picplace{<height> cm}|\\
+\verb|\caption[ ]{<text of caption>}| \quad
+ (Type [ ] to save auxiliary space)\\
+\verb|\end{figure}|
+\end{flushleft}
+
+\paragraph{Sample Input}
+\begin{verbatim}
+\begin{figure}
+\picplace{2.5cm}
+\caption[ ]{This is the caption.}
+\end{figure}
+\end{verbatim}
+
+\noindent
+Please use the minipage environment to place two figures next to each
+other.
+
+\paragraph{Sample Output}\ \\[2mm]
+see fig.\ts 11.1
+\begin{figure}%\label{table11.1}
+\picplace{2.5cm}
+\caption[ ]{This is the caption.}
+\end{figure}
+
+\chapter{Tables}
+
+Tables should be treated
+in the same way as figure legends, except that
+the table captions appear {\em above\/} the tables. The tables
+will be numbered automa\-tically.
+
+Table columns should be set flush left. Vertical lines
+are normally not necessary and should only be inserted
+in exceptional cases for the sake of clarity. Please note that tables
+should be set in small print using the \verb|\small| command.
+
+For further information you will find a complete description of
+the table and tabular environment
+on p.~63~ff. and p.~182 of the {\em \LaTeX{} User's Guide \&
+Reference Manual\/} by Leslie Lamport.
+
+Height of tables must not exceed 23 cm. Taller tables will be swallowed
+by \LaTeX{} without warning.
+
+\section{Tables coded with \LaTeX{}}
+
+As an example for simple coding of a table we give you
+the following advice for the coding.
+(Before continuing your text after the
+table environment you need an empty line.)
+
+\paragraph{Sample Input}
+
+\begin{verbatim}
+\begin{table}
+\caption[ ]{Critical $N$ values}
+\begin{flushleft}
+\small
+\begin{tabular}{llllll}
+\hline
+\noalign{\vskip 3pt}
+$M_$\sun & $beta_{0}$ & $T_{\rm c6}$ & $\gamma$
+ & $N_{\rm crit}^{\rm L}$
+ & $N_{\rm crit}^{\rm Te}$\\
+\noalign{\vskip 3pt}
+\hline
+\noalign{\vskip 3pt}
+ 30 & 0.82 & 38.4 & 35.7 & 154 & 320 \\
+ 60 & 0.67 & 42.1 & 34.7 & 138 & 340 \\
+120 & 0.52 & 45.1 & 34.0 & 124 & 370 \\
+\noalign{\vskip 3pt}
+\hline
+\end{tabular}
+\end{flushleft}
+\end{table}
+\end{verbatim}
+
+\paragraph{Sample Output}\ \\[2mm]
+See table\ts12.1
+\begin{table}
+%\label{table12.1}
+\caption[ ]{Critical $N$ values}
+\begin{flushleft}
+\small
+\begin{tabular}{llllll}
+\hline
+\noalign{\vskip 3pt}
+$M_\sun$ & $beta_{0}$ & $T_{\rm c6}$ & $\gamma$
+ & $N_{\rm crit}^{\rm L}$
+ & $N_{\rm crit}^{\rm Te}$\\
+\noalign{\vskip 3pt}
+\hline
+\noalign{\vskip 3pt}
+ 30 & 0.82 & 38.4 & 35.7 & 154 & 320 \\
+ 60 & 0.67 & 42.1 & 34.7 & 138 & 340 \\
+120 & 0.52 & 45.1 & 34.0 & 124 & 370 \\
+\noalign{\vskip 3pt}
+\hline
+\end{tabular}
+\end{flushleft}
+\end{table}
+
+\newpage
+\paragraph{Sample Input}
+
+\begin{verbatim}
+\begin{table}
+\caption[ ]{Observational results from NGC 4827}
+\small
+\begin{flushleft}
+\renewcommand{\arraystretch}{1.2}
+\begin{tabular}{lllllllllllll}
+\hline
+ & & \multicolumn{3}{l}{RA (1950)} &\
+ & \multicolumn{3}{l}{Dec (1950)}
+ & $S$ & Pol & \% & $\log P$\\
+ \cline{3-5}\cline{7-9}
+ & &(h) & (m) & (s) & & (\degr) & (\arcmin)
+ & (\arcsec) & (mJy) & (mJy) & & (W Hz$^{-1}$)\\
+\hline
+Core & (5 GHz) & 12 & 54 & 18.0 & & 27 & 26 & 56.2
+ & 8 & & & 21.64 \\
+Total&(327 MHz)& & & & & & &
+ & 210 & & & 23.13 \\
+ &(1.4 GHz)& & & & & & &
+ & 57 & 1.3 & 2 & 22.49 \\
+ & (5 GHz) & & & & & & &
+ & 26 & 0.73 & 3 & 22.15 \\
+\hline
+\end{tabular}
+\renewcommand{\arraystretch}{1}
+\end{flushleft}
+\end{table}
+\end{verbatim}
+
+\paragraph{Sample Output}\ \\[2mm]
+See table\ts 12.2
+\begin{table}
+\label{table12.2}
+\caption[ ]{Observational results from NGC 4827}
+\small
+\begin{flushleft}
+\renewcommand{\arraystretch}{1.2}
+\tabcolsep=0.9\tabcolsep
+\begin{tabular}{lllllllllllll}
+\hline
+ & & \multicolumn{3}{l}{RA (1950)} &\
+ & \multicolumn{3}{l}{Dec (1950)}
+ & $S$ & Pol & \% & $\log P$\\
+ \cline{3-5}\cline{7-9}
+ & &(h) & (m) & (s) & & (\degr) & (\arcmin)
+ & (\arcsec) & (mJy) & (mJy) & & (W Hz$^{-1}$)\\
+\hline
+Core & (5 GHz) & 12 & 54 & 18.0 & & 27 & 26 & 56.2
+ & 8 & & & 21.64 \\
+Total&(327 MHz)& & & & & & &
+ & 210 & & & 23.13 \\
+ &(1.4 GHz)& & & & & & &
+ & 57 & 1.3 & 2 & 22.49 \\
+ & (5 GHz) & & & & & & &
+ & 26 & 0.73 & 3 & 22.15 \\
+\hline
+\end{tabular}
+\renewcommand{\arraystretch}{1}
+\end{flushleft}
+\end{table}
+\section{Tables Not Coded with \LaTeX{}}
+
+If you do not wish to code your table using \LaTeX{}
+but prefer to have it reproduced separately,
+proceed similarily as for figures and use the following coding:
+
+\paragraph{Sample Input}
+\begin{flushleft}
+\verb|\begin{table}| \\
+\verb|\caption[ ]{<text of caption>}|\\
+\verb|\vspace{<actual height of table> cm}| \\
+\verb|\end{table}|
+\end{flushleft}
+
+
+\chapter{Appendices}
+
+Type \verb|\appendix| to set all sectioncounter etc to 0.
+Begin the actual appendix by typing\\
+\verb|\section{Appendix}|
+
+
+\chapter{Signs and Characters}
+
+\section{Special Signs}
+
+You may need to use special signs. Though quite a number is supplied by
+{\em \LaTeX{}} (see
+{\em \LaTeX{} User's Guide \& Reference Manual\/} by Leslie Lamport, pp.~44~ff.) we have created further
+symbols.
+
+\section{Mathematical Symbols}
+\begin{flushleft}
+%\small
+\footnotesize
+\renewcommand{\arraystretch}{1.25}
+\begin{tabular}{lll@{\hspace{1.5cm}}lll}
+\hline
+Input & Explanation & Output & Input & Explanation & Output\\
+\hline
+\verb|\la| & less or approx & $\la$ &
+ \verb|\ga| & greater or approx & $\ga$\\
+\verb|\getsto| & gets over to & $\getsto$ &
+ \verb|\cor| & corresponds to & $\cor$\\
+\verb|\lid| & less or equal & $\lid$ &
+ \verb|\gid| & greater or equal & $\gid$\\
+\verb|\sol| & similar over less & $\sol$ &
+ \verb|\sog| & similar over greater & $\sog$\\
+\verb|\lse| & less over simeq & $\lse$ &
+ \verb|\gse| & greater over simeq & $\gse$\\
+\verb|\grole| & greater over less & $\grole$ &
+ \verb|\leogr| & less over greater & $\leogr$\\
+\verb|\loa| & less over approx & $\loa$ &
+ \verb|\goa| & greater over approx & $\goa$\\
+\verb|\qed| & less over approx & $\qed$ & \\
+\hline
+\end{tabular}
+\renewcommand{\arraystretch}{1}
+\end{flushleft}
+
+\section{Special Roman or Blackboard Bold}
+
+\begin{flushleft}
+%\small
+\footnotesize
+\renewcommand{\arraystretch}{1.25}
+\begin{tabular}{lll@{\hspace{1cm}}lll}
+\hline
+Input & Explanation & Output & Input & Explanation & Output\\
+\hline
+\verb|$\bbbc$| & complex numbers & $\bbbc$ &
+\verb|$\bbbf$| & blackboard bold F & $\bbbf$ \\
+\verb|$\bbbh$| & blackboard bold H & $\bbbh$ &
+\verb|$\bbbk$| & blackboard bold K & $\bbbk$ \\
+\verb|$\bbbm$| & blackboard bold M & $\bbbm$ &
+\verb|$\bbbn$| & natural numbers N & $\bbbn$ \\
+\verb|$\bbbp$| & blackboard bold P & $\bbbp$ &
+\verb|$\bbbq$| & rational numbers & $\bbbq$ \\
+\verb|$\bbbr$| & real numbers & $\bbbr$ &
+\verb|$\bbbs$| & blackboard bold S & $\bbbs$ \\
+\verb|$\bbbt$| & blackboard bold T & $\bbbt$ &
+\verb|$\bbbz$| & integer numbers & $\bbbz$ \\
+\verb|$\bbbone$| & symbol one & $\bbbone$ & & & \\
+\hline
+\end{tabular}
+\renewcommand{\arraystretch}{1}
+\end{flushleft}
+
+\section{Gothic (Fraktur)}
+If gothic letters are {\em necessary}, please
+use those from \AmSTeX{},
+available from the American Mathematical Society.
+
+For the real and imaginary parts
+of a complex number within math mode the commands \verb|$\Re$|
+and \verb|$\Im$| have been redefined to produce Re and Im
+instead of gothic letters.
+
+\section{Script}
+
+For script capitals use the coding\\
+\verb|${\cal AB}$| which yields ${\cal AB}$
+(see p.~43 of the \LaTeX{} book).
+
+\section{Vectors}
+\begin{flushleft}
+\begin{tabular}{@{}l@{\hspace{.5cm}}l}
+\verb|\vec{<Symbol>}| & Vectors may only appear in math mode.\\
+\end{tabular}
+\end{flushleft}
+\verb|$\vec{A} \times \vec{B} \cdot \vec{C}|\quad
+ yields $\vec{A}\times\vec{B}\cdot\vec{C}$.\\
+\verb|$\vec{A\/}^{\rm T} \otimes \vec{B} \otimes \vec{\hat D}$|\\
+yields $\vec{A\/}^{\rm T} \otimes \vec{B} \otimes
+\vec{\hat D}$.
+
+
+\def\refchapter{\chapter*{References}
+\parindent0pt\parskip0pt\small}
+\chapter{References}
+
+There are three reference systems available; only one, of course,
+should be used. With each system (by author-year,
+by number only or by letter-number) a reference list
+containing all citations in the
+text, should be included at the end of your book.
+
+\newpage
+\paragraph{Examples of Typical Text Containing Reference Citations}\
+\\[2mm]
+This is implicit in recent work of Arnold (1968) and Lerch et al. (1983)
+\dots\\
+Consider as an example the following theorem [1].\\
+We refer now to the hypothesis as given in [S1].
+
+\section{Author-Year System}
+References are cited in the text by name and year in parentheses, e.g.
+(Smith 1970, 1980), (Ekeland et al. 1985, Theorem 2), (Jones and Jaffe
+1986; Farrow 1988, Chap.\ts 2) or only the year in parentheses if the
+name is part of the sentence, e.g. Ekeland et al. (1985, Sect.\ts 2.1).
+The reference list should contain all citations contained in the text,
+ordered alphabetically by surname (with initials following). If there
+are several works by the same author(s) the references should be listed
+in the appropriate order indicated below:
+\medskip
+\begin{itemize}
+\item[a)] One author: list works chronologically;
+\item[b)] Author and same co-author(s): list works chronologically;
+\item[c)] Author and different co-authors: list works alphabetically
+according to co-authors.
+\end{itemize}
+\medskip
+If there are several works by the same author(s) and in the same year,
+but cited separately, they should be distinguished by
+the use of ``a", ``b" etc., e.g. (Smith 1982a), (Ekeland et al. 1982b).
+
+To achieve a reference list in the author-year system, please use the
+following springer macro syntax
+
+\noindent
+\verb|\begin{references}{}|\quad Don't forget those empty braces\\
+\verb|\refer <text>|\\
+\verb|\refer ...|\\
+\quad $\vdots$\\
+\verb|\end{references}|
+
+\paragraph{Sample Input}
+
+\begin{verbatim}
+\begin{references}{}
+ \refer Clarke, F., Ekeland, I. 1982, Nonlinear oscillations
+ and boundary-value problems for Hamiltonian systems,
+ Arch. Rat. Mech. Anal. {\bf 78}, (1982) 315--333
+ \refer Rabinowitz, P.: On subharmonic solutions
+ of a Hamiltonian system. Comm. Pure Appl. Math.
+ {\bf 33} (1980) 609--633
+\end{references}
+\end{verbatim}
+
+\paragraph{Sample Output}\
+
+\begin{references}{}
+
+ \refer Clarke, F., Ekeland, I. 1982, Nonlinear oscillations and
+ boundary-value problems for Hamiltonian systems,
+ Arch. Rat. Mech. Anal. {\bf 78}, (1982) 315--333
+ \refer Rabinowitz, P.: On subharmonic solutions of a Hamiltonian
+ system. Comm. Pure Appl. Math. {\bf 33} (1980) 609--633
+
+\end{references}
+
+\section{References by Number Only or by Letter-Number}
+The author-year system is probably the most convenient to the reader.
+However,\newline
+ refer\-en{}ces may instead be cited in the text by
+numbers
+in square brackets, e.g. [1], [2] etc. used sequentially throughout your
+text or by letter-number, e.g. [E1, S2], [P1] etc. or a
+similar version.
+For example, the first two references are given as [1] and [2] in the
+text, and as 1. and 2. (i.e. the brackets are dropped) in the reference
+list.
+
+\subsection{Syntax for Number-Only System}
+
+\verb|\begin{references}{<widest number used in ref. list>}|\\
+\verb|\refno{<no.>}<text>|\\
+\verb|\refno ...|\\
+\quad $\vdots$\\
+\verb|\end{references}|
+
+\paragraph{Sample Input}
+\begin{verbatim}
+%
+\begin{references}{1.}
+ \refno{1.} Clarke, F., Ekeland, I. 1982, Nonlinear oscillations
+ and boundary-value problems for Hamiltonian systems,
+ Arch. Rat. Mech. Anal. {\bf 78}, (1982) 315--333
+ \refno{2.} Rabinowitz, P.: On subharmonic solutions
+ of a Hamiltonian system. Comm. Pure Appl. Math.
+ {\bf 33} (1980) 609--633
+\end{references}
+\end{verbatim}
+
+\newpage
+\paragraph{Sample Output}\
+
+\begin{references}{1.} %Springer macros
+ \refno{1.} Clarke, F., Ekeland, I. 1982, Nonlinear oscillations and
+ boundary-value problems for Hamiltonian systems,
+ Arch. Rat. Mech. Anal. {\bf 78}, (1982) 315--333
+ \refno{2.} Rabinowitz, P.: On subharmonic solutions of a Hamiltonian
+ system. Comm. Pure Appl. Math. {\bf 33} (1980) 609--633
+\end{references}
+
+\subsection{Letter-Number system}
+Here you have the choice between the traditional \LaTeX{}-way of doing
+things and Springer macros.
+
+\smallskip\noindent
+Traditional \LaTeX{} syntax
+
+\begin{verbatim}
+\begin{thebibliography}{widest-label} % \LaTeX{} standard macros
+ \bibitem[<label>]{name}<text>
+ \bibitem[<label>]{name}<text>
+\end{thebibliography}
+\end{verbatim}
+
+\paragraph{Sample Input}
+
+\begin{verbatim}
+\begin{thebibliography}{[MT1]}
+\bibitem[CE1]{CE1} Clarke, F., Ekeland, I. 1982,
+ Nonlinear oscillations and boundary-value
+ problems for Hamiltonian systems,
+ Arch. Rat. Mech. Anal. {\bf 78},
+ (1982) 315--333
+\bibitem[Ra1]{Ra1} Rabinowitz, P.: On subharmonic solutions
+ of a Hamiltonian system. Comm. Pure Appl.
+ Math. {\bf 33} (1980) 609--633
+\end{thebibliography}
+\end{verbatim}
+
+\paragraph{Sample Ouput}\
+
+\begin{thebibliography}{[MT1]}
+\bibitem[CE1]{CE1} Clarke, F., Ekeland, I. 1982, Nonlinear oscillations and
+boundary-value problems for Hamiltonian systems, Arch. Rat. Mech. Anal.
+{\bf 78}, (1982) 315--333
+\bibitem[Ra1]{Ra1} Rabinowitz, P.: On subharmonic solutions of a
+Hamiltonian system. Comm. Pure Appl. Math. {\bf 33} (1980) 609--633
+\end{thebibliography}
+
+\noindent
+For overall information on the reference environment
+see the {\em \LaTeX{} User's Guide \& Reference
+Manual\/} by Leslie Lamport, p.~73.
+
+\subsection{Springer macros syntax}
+
+\verb|\begin{references}{[<widest label used in your list>]}|\\
+\verb|\refmark{[<label>]}<text>|\\
+\verb|\refmark ...|\\
+\quad $\vdots$\\
+\verb|\end{references}|
+
+\paragraph{Sample Input}
+\begin{verbatim}
+%
+\begin{references}{[CEW]}
+ \refmark{[Aa]} Clarke, F., Ekeland, I. 1982,
+ Nonlinear oscillations and boundary-value
+ problems for Hamiltonian systems,
+ Arch. Rat. Mech. Anal. {\bf 78}, (1982) 315--333
+ \refmark{[Bi]} Rabinowitz, P.: On subharmonic solutions
+ of a Hamiltonian system. Comm. Pure Appl. Math.
+ {\bf 33} (1980) 609--633
+ \end{references}
+\end{verbatim}
+
+\noindent{\em Sample Output}
+
+\begin{references}{[CEW]}
+ \refmark{[Aa]} Clarke, F., Ekeland, I. 1982, Nonlinear oscillations and
+ boundary-value problems for Hamiltonian systems,
+ Arch. Rat. Mech. Anal. {\bf 78}, (1982) 315--333
+ \refmark{[Bi]} Rabinowitz, P.: On subharmonic solutions of a Hamiltonian
+ system. Comm. Pure Appl. Math. {\bf 33} (1980) 609--633
+ \end{references}
+
+\smallskip
+In reality, all these references start at the top of a new right page
+thus creating an empty page if necessary.
+
+\smallskip\noindent
+{\it Very important\/}: For each entry in the reference list please
+follow {\it exactly\/} the order shown in the examples and
+ensure that the references cited in the text (name-year,
+number or letter-number) correspond exactly with the entries
+in the reference list.
+
+\section{The use of\/ {\rm\BibTeX{}}}
+
+If you normally use \BibTeX{} to produce your references please
+customize its bibliography style according to the things mentioned
+above.
+
+\chapter{Postscriptum}
+
+We include a file named mathsing.dem on the diskette containing the
+\TeX{} -- input for an example of a text being formatted with the
+MathSing style-file.
+\end{document}
+ \ No newline at end of file