%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This is a sample input file for your contribution to a multi-
% author book to be published by Springer Verlag.
%
% Please use it as a template for your own input, and please
% follow the instructions for the formal editing of your
% manuscript as described in the file "1readme".
%
% Please send the Tex and figure files of your manuscript
% together with any additional style files as well as the
% PS file to the editor of your book.
%
% He or she will collect all contributions for the planned
% book, possibly compile them all in one go and pass the
% complete set of manuscripts on to Springer.
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%RECOMMENDED%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\documentclass[runningheads,fleqn]{cl2emult}

\usepackage{makeidx}  % allows index generation
\usepackage{graphicx} % standard LaTeX graphics tool
                      % for including eps-figure files
\usepackage{subeqnar} % subnumbers individual equations
                      % within an array
\usepackage{multicol} % used for the two-column index
\usepackage{cropmark} % cropmarks for pages without
                      % pagenumbers
\usepackage{engi}     % flushleft layout of math and captions
\makeindex            % used for the subject index
                      % please use the style sprmidx.sty with
                      % your makeindex program

%upright Greek letters (example below: upright "mu")
\newcommand{\euler}[1]{{\usefont{U}{eur}{m}{n}#1}}
\newcommand{\eulerbold}[1]{{\usefont{U}{eur}{b}{n}#1}}
\newcommand{\umu}{\mbox{\euler{\char22}}}
\newcommand{\umub}{\mbox{\eulerbold{\char22}}}

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%OPTIONAL%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\usepackage{amstex}   % useful for coding complex math
%\mathindent\parindent % needed in case "Amstex" is used
%
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%AUTHOR_STYLES_AND_DEFINITIONS%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%Please reduce your own definitions and macros to an absolute
%minimum since otherwise the editor will find it rather
%strenuous to compile all individual contributions to a
%single book file
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{document}
%
\title*{Focusing of a Parallel Beam to Form\protect\newline a Point
in the Particle Deflection Plane}
%
%
\toctitle{Focusing of a Parallel Beam to Form a Point
\protect\newline in the Particle Deflection Plane}
% allows explicit linebreak for the table of content
%
%
\titlerunning{Focusing of a Parallel Beam}
% allows abbreviation of title, if the full title is too long
% to fit in the running head
%
\author{Ivar Ekeland\inst{1}
\and Roger Temam\inst{2}
\and Jeffrey Dean\inst{2}
\and David Grove\inst{1}
\and Craig Chambers\inst{2}
\and Kim~B.~Bruce\inst{2}
\and Elsa Bertino\inst{1}}
%
\authorrunning{Ivar Ekeland et al.}
% if there are more than two authors,
% please abbreviate author list for running head
%
%
\institute{Princeton University, Princeton NJ 08544, USA
\and Universit\'{e} de Paris-Sud,
     Laboratoire d'Analyse Num\'{e}rique,
     B\^{a}timent 425,\\
     F-91405 Orsay Cedex, France}

\maketitle              % typesets the title of the contribution

\begin{abstract}
The abstract\index{abstract} should summarize the contents of the paper
in at least 70 and at most 150 words; neither too long
nor too short but to the point!
\end{abstract}

\section{Fixed-Period Problems: The Sublinear Case}
%
Of course this text has no scientific relevance but should be used
as a practical example of the Springer layout specifications for
{\itshape engineering books}~\cite{JL1.2}. We begin now the
search for periodic solutions to Hamiltonian systems\index{Hamiltonian
systems}. All this will be done
in the convex case; that is, we shall study the
boundary-value\index{boundary-value problem} problem
\begin{eqnarray*}
  \dot{x}&=&JH' (t,x)\\
  x(0) &=& x(T)
\end{eqnarray*}
with $H(t,\cdot)$ a convex function of $x$, going to $+\infty$ when
$\left\|x\right\| \to \infty$.


\section{Equations}
The following equation is the compiled result of using the command
\verb|\vec| and using the newly defined command \verb|\umu|:

\begin{equation}
\vec{A}=\mu y = 50\ts \umu {\rm m}\ts  .
\end{equation}

\subsection{Sub-equations}
As you have seen above, equations are numbered automatically
when the equations are defined with \verb|\begin{equation}|
(but not when \verb|$$| is used). Here you will find an example
for the automatic sub-numbering of equation arrays, using the style \verb|subeqnar.sty|:

\begin{subeqnarray}
a & = & c + d \ts , \label{f1a}\\
e & = & f - d \ts  .\label{f1b}
\end{subeqnarray}

In order to refer to the equations within the main text you must simply label your
equations (within the equation's environment) and quote the labels within the text
environment. Upon running \TeX\ you should receive the corresponding
subnumbers, e.g.
(\ref{f1a}) and (\ref{f1b}).

\subsubsection*{No Sub-numbering.}
If you want to suppress the sub-numbering of an equation
array you use the original \verb|\begin{eqnarray}| environment, put \verb|\nonumber|
at the end of the line that is to have no number, and set the sub-counter to zero:

\begin{eqnarray}
a & = & c + d \ts , \nonumber \\
e & = & f - d \ts .
\setcounter{eqsubcnt}{0}
\end{eqnarray}



\section{Figures}

If your figures are available as electronic data it is advisable to
convert them to eps-format and include them directly into the text with
the help of the graphicx package (see the following example in
Fig.~\ref{eps1})

\begin{figure}
\includegraphics[width=.4\textwidth]{figure.eps}
\caption[]{Example of an electronically included eps-figure}
\label{eps1}
\end{figure}

In order to mark the desired amount of space for a (flushleft!) figure
which has to be pasted into the manuscript manually please provide a
vertical line on the lefthand side of the figure. This
is reached by using the commands
\verb|\sidecaption\mpicplace{width in cm}{height in cm}|.

This way the figure caption automatically will be placed at the righthand side
of the figure if there is
enough space left ($>$ 3\,cm).

For further instructions
e.g. on the structure and layout of the caption see Fig.~\ref{partfig1}
und~\ref{labelfig1}.

\begin{figure}
\mpicplace{9 cm}{3 cm}
\caption{General description. ({\bf a}) The \lq name' of the sub-figure should be set
boldface and in round brackets. ({\bf b}) In general the last
sentence of a figure caption should not
end with a fullstop}
\label{partfig1}
\end{figure}

\begin{figure}
\sidecaption
\mpicplace{4 cm}{5 cm}
\caption{This could show a figure consisting of different types of
lines to describe individual aspects. These descriptive lines ({\it
dotted line\,}) should be set italic and put into round brackets
as shown in this sample figure caption. In general the last
sentence of a figure caption ({\it straight line\,}) should not
end with a fullstop}
\label{labelfig1}
\end{figure}

\section{Tables}
In {\itshape Springer engineering books} tables as well as
equations and figures should be set {\it flushleft}. Table
captions should be treated in the same way as figure legends, except that the
table captions appear {\it above} the tables. Overwide tables should
be reduced to the page width, if possible, or exceed the type area by a
maximum of 5\,mm. Please check the \TeX\ files of the following
tables
(Table~\ref{Tab1a} and ~\ref{Tab1b}) and use them as an example for
setting your own tables.

\begin{table}
\caption{Critical $N$ values}
\renewcommand{\arraystretch}{1.4}
\setlength\tabcolsep{5pt}
\begin{tabular}{llllll}
\hline\noalign{\smallskip}
${\mathrm M}_\odot$ & $\beta_{0}$ & $T_{\mathrm c6}$ & $\gamma$
  & $N_{\mathrm{crit}}^{\mathrm L}$
  & $N_{\mathrm{crit}}^{\mathrm{Te}}$\\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
 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 \\
\hline
\end{tabular}
\label{Tab1a}
\end{table}


\begin{table}
\caption{Please write your table caption here. Multi-line captions as
well as single-line captions automatically will be set flushleft}
\renewcommand{\arraystretch}{1.4}
\setlength\tabcolsep{15pt}
\begin{tabular}{@{}llp{1.8cm}l}
\hline\noalign{\smallskip}
Nominal dimension & Angle & Tolerance & Evaluation factor \\
(mm) & & (\umu m) & \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
$10^1$ & $1^\circ$ & Untoleranced dimension& $c_1 =0$ \\
$10^{-1}$ & $1^{\prime\, {\rm a}}$ & 101--200 & $c_1 = 1$ \\
$10^{-2}$ & $1^{\prime\prime\, {\rm b}}$ & 40--100 & $c_1 = 2$ \\
$10^{-3}$ & & $< 50 $ & $c_1 = 3$ \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
\end{tabular}\\
$^{\rm a}$ One minute of arc. \\
$^{\rm b}$ One second of arc.
\label{Tab1b}
\end{table}




\section{Lists}
We have redefined the {\it itemize} environment (labelitemi) so that you
will
receive bullets instead of dashes to introduce the individual items.
We think that this way the list
\begin{itemize}
\item
is clearer
\item
looks better
\item
is more noticeable
\end{itemize}

\begin{thebibliography}{7}
%
\addcontentsline{toc}{section}{References}


\bibitem{JL1.2} Holzwarth F., Lenz J. et al. (1998) 1readme. Further
Details on Layout and \LaTeX\, code. Springer, Berlin Heidelberg

\bibitem{ref1.1} Turner, J.~S. (1974) Double--diffusive phenomena. Ann.
Rev. Fluid Mech. {\bf6}, 37--56

\bibitem{ref1.2} Turner, J.~S. (1968) Double--diffusive phenomena. Ann.
Rev. Fluid Mech. {\bf33}, 168--200

\bibitem{ref1.3} Normand, C., Pomeau, Y. (1977)
Convective instability: a physicist's approach. Rev. Mod. Phys. {\bf
49}, 581--623

\end{thebibliography}

%INDEX%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\clearpage
\addcontentsline{toc}{section}{Index}
\flushbottom
\printindex
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\end{document}

