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They will be numbered automatically.{\it The figures\/} (line drawings and those containing halftone insertsas well as halftone figures) {\it should not be pasted into yourlaserprinter output}. They should be enclosed separately in camera-readyform (original artwork, glossy prints, photographs and/or slides). Thelettering should be suitable for reproduction, and after reduction theheight of capital letters should be at least1.8\,mm and not more than 2.5\,mm.Check that lines and other details are uniformly black andthat the lettering on figures is clearly legible.To leave the desired amount of space for the height ofyour figures, please use the coding described below.As can be seen in the output, we will automaticallyprovide 1\,cm space above and below the figure,so that you should only leave the space equivalent to the size of thefigure itself. Please note that ``\verb|x|'' in the followingcoding stands for the actual height of the figure:\begin{verbatim}\begin{figure}\vspace{x cm}\caption[ ]{...text of caption...}          (Do type [ ])\end{figure}\end{verbatim}\begin{flushleft}{\it Sample Input}\end{flushleft}\begin{verbatim}\begin{figure}\vspace{2.5cm}\caption{This is the caption of the figure displaying a whiteeagle and a white horse on a snow field}\end{figure}\end{verbatim}\begin{flushleft}{\it Sample Output}\end{flushleft}\begin{figure}\vspace{2.5cm}\caption{This is the caption of the figure displaying a white eagle anda white horse on a snow field}\end{figure}%\section{Tables}%Table captions should be treatedin the same way as figure legends, except thatthe table captions appear {\it above} the tables. The  tableswill be numbered automatically.%\subsection{Tables Coded with \protect\LaTeX{}}%Please use the following coding:\\[2mm]{\it Sample Input}\begin{verbatim}\begin{table}\caption{This is the example table taken out of {\it The\TeX{}book,} p.\,246}\vspace{2pt}\begin{tabular}{r@{\quad}rl}\hline\multicolumn{1}{l}{\rule{0pt}{12pt}                Year}&\multicolumn{2}{l}{World population}\\[2pt]\hline\rule{0pt}{12pt}8000 B.C.  &     5,000,000& \\  50 A.D.  &   200,000,000& \\1650 A.D.  &   500,000,000& \\1945 A.D.  & 2,300,000,000& \\1980 A.D.  & 4,400,000,000& \\[2pt]\hline\end{tabular}\end{table}Before continuing your text you need an empty line. \dots\end{verbatim}{\it Sample Output}\begin{table}\caption{This is the example table taken out of {\it The\TeX{}book,} p.\,246}\vspace{2pt}\begin{tabular}{r@{\quad}rl}\hline\multicolumn{1}{l}{\rule{0pt}{12pt}                Year}&\multicolumn{2}{l}{World population}\\[2pt]\hline\rule{0pt}{12pt}8000 B.C.  &     5,000,000& \\  50 A.D.  &   200,000,000& \\1650 A.D.  &   500,000,000& \\1945 A.D.  & 2,300,000,000& \\1980 A.D.  & 4,400,000,000& \\[2pt]\hline\end{tabular}\end{table}Before continuing your text you need an empty line. \dots\vspace{3mm}For further information you will find a complete description ofthe tabular environmenton p.~63~ff. and p.~182 of the {\em \LaTeX{} User's Guide \& ReferenceManual\/} by Leslie Lamport.%\subsection{Tables Not Coded with \protect\LaTeX{}}%If you do not wish to code your table using \LaTeX{}but prefer to have it reproduced separately,proceed as for figures and use the following coding:\\[2mm]{\it Sample Input}\begin{verbatim}\begin{table}\caption{text of your caption}\vspace{x cm}     % the actual height needed for your table\end{table}\end{verbatim}%\subsection{Signs and Characters}%\subsubsection*{Special Signs.}%You may need to use special signs.  The available ones are listed in the{\em \LaTeX{} User's Guide \& Reference Manual\/} by Leslie Lamport,pp.~44\,ff.We have created further symbols for math mode (enclosed in \$):\begin{center}\begin{tabular}{l@{\hspace{1em}yields\hspace{1em}}c@{\hspace{3em}}l@{\hspace{1em}yields\hspace{1em}}c}\verb|\grole| & $\grole$ & \verb|\getsto| & $\getsto$\\\verb|\lid|   & $\lid$   & \verb|\gid|    & $\gid$\end{tabular}\end{center}%\subsubsection*{Gothic (Fraktur).}%If gothic letters are {\it necessary}, please use those of therelevant \AmSTeX{} alphabet which are available from theAmerican Mathematical Society.In \LaTeX{} only the following gothic letters are available:\verb|$\Re$| yields $\Re$ and \verb|$\Im$| yields $\Im$. These should{\it not\/} be used when you need gothic letters for your contribution.Use \AmSTeX{} gothic as explained above. For the real and the imaginaryparts of a complex number within math mode you should use instead:\verb|$\rm Re$| (which yields Re) or \verb|$\rm Im$| (which yields Im).%\subsubsection*{Script.}%For script capitals use the coding\begin{center}\begin{tabular}{l@{\hspace{1em}which yields\hspace{1em}}c}\verb|$\cal AB$| & $\cal AB$\end{tabular}\end{center}(see p.~43 of  the \LaTeX{} book).%\subsubsection*{Special Roman.}%If you need other symbols than those below, you could usethe blackboard bold characters of \AmSTeX{},  but there might arisecapacity problemsin loading additional \AmSTeX{} fonts. Therefore  we createdthe blackboard bold characters listed below.Some of them are not estheticallysatisfactory. This need not deter you from using them:in the final printed form they will bereplaced by the well-designed MT (monotype) characters ofthe phototypesetting machine.\begin{flushleft}\begin{tabular}{@{}ll@{ yields }c@{\hspace{1.1em}}ll@{ yields }c}\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| & (whole numbers)     & $\bbbz$\\\verb|\bbbone| & (symbol one)      & $\bbbone$\end{tabular}\end{flushleft}\begin{displaymath}\begin{array}{c}\bbbc^{\bbbc^{\bbbc}} \otimes\bbbf_{\bbbf_{\bbbf}} \otimes\bbbh_{\bbbh_{\bbbh}} \otimes\bbbk_{\bbbk_{\bbbk}} \otimes\bbbm^{\bbbm^{\bbbm}} \otimes\bbbn_{\bbbn_{\bbbn}} \otimes\bbbp^{\bbbp^{\bbbp}}\\[2mm]\otimes\bbbq_{\bbbq_{\bbbq}} \otimes\bbbr^{\bbbr^{\bbbr}} \otimes\bbbs^{\bbbs_{\bbbs}} \otimes\bbbt^{\bbbt^{\bbbt}} \otimes\bbbz \otimes\bbbone^{\bbbone_{\bbbone}}\end{array}\end{displaymath}%\subsubsection*{Sans Serif.}%Using our macros you can also choose this font family;use the command \verb|\sf| for {\sf sans serif}(like \verb|\it| for {\it italic style}).%\section{References}\label{refer}%There are three reference systems available; only one, of course,should be used for your contribution. With each system (bynumber only, by letter-number or by author-year) a reference listcontaining all citations in thetext, should be included at the end of your contribution placing the\LaTeX{} environment \verb|thebibliography| there.For an overall information on that environmentsee the {\em \LaTeX{} User's Guide \& ReferenceManual\/} by Leslie Lamport, p.~73.%\subsection{References by Letter-Number or by Number Only}%References are cited in the text -- using the \verb|\cite|command of \LaTeX{} -- by number or by letter-number in squarebrackets, e.g.\ [1] or [E1, S2], [P1], according to your use of the\verb|\bibitem| command in the \verb|thebibliography| environment. Thecoding is as follows: if you choose your own label for the sources bygiving an optional argument to the \verb|\bibitem| command the citationsin the text are marked with the label you supplied. Otherwise a simplenumbering is done, which is preferred.\begin{verbatim}The results in this section are a refined versionof \cite{clar:eke}; the minimality result of Proposition~14was the first of its kind.\end{verbatim}The above input produces the citation: ``\dots\ refined version of[CE1]; the min\-i\-mality\dots''. Then the \verb|\bibitem| entry ofthe \verb|thebibliography| environment should read:\begin{verbatim}\begin{thebibliography}{[MT1]}..\bibitem[CE1]{clar:eke}Clarke, F., Ekeland, I.:Nonlinear oscillations and boundary-value problems forHamiltonian systems.Arch. Rat. Mech. Anal. {\bf 78} (1982) 315--333..\end{thebibliography}\end{verbatim}The complete bibliography looks like this:%\begin{thebibliography}{[MT1]}%\bibitem[CE1]{clar:eke}Clarke, F., Ekeland, I.:Nonlinear oscillations andboundary-value problems for Hamiltonian systems.Arch. Rat. Mech. Anal. {\bf 78} (1982) 315--333%\bibitem[CE2]{clar:eke:2}Clarke, F., Ekeland, I.:Solutions p\'{e}riodiques, dup\'{e}riode donn\'{e}e, des \'{e}quations hamiltoniennes.Note CRAS Paris {\bf 287} (1978) 1013--1015%\bibitem[MT1]{mich:tar}Michalek, R., Tarantello, G.:Subharmonic solutions with prescribed minimalperiod for nonautonomous Hamiltonian systems.J. Diff. Eq. {\bf 72} (1988) 28--55%\bibitem[Ta1]{tar}Tarantello, G.:Subharmonic solutions for Hamiltoniansystems via a $\bbbz_{p}$ pseudoindex theory.Annali di Matematica Pura (to appear)%\bibitem[Ra1]{rab}Rabinowitz, P.:On subharmonic solutions of a Hamiltonian system.Comm. Pure Appl. Math. {\bf 33} (1980) 609--633\end{thebibliography}%\subsubsection*{Number-Only System.}%For this preferred system do not use the optional argumentin the \verb|\bibitem| command: then, only numbers willappear for the citations in the text (enclosed in square brackets)as well as for the marks in yourbibliography (here the number is only end-punctuated withoutsquare brackets).\begin{verbatim}\begin{thebibliography}{1}\bibitem {clar:eke}Clarke, F., Ekeland, I.:Nonlinear oscillations and boundary-value problems forHamiltonian systems.Arch. Rat. Mech. Anal. {\bf 78} (1982) 315--333\end{thebibliography}\end{verbatim}%\subsection{Author-Year System}%References are cited in the text by name and year in parenthesesand should look as follows:(Smith 1970, 1980), (Ekeland et al. 1985, Theorem 2), (Jones and Jaffe1986; Farrow 1988, Chap.\,2). If the name is part of the sentenceonly the year may appear in parentheses,e.g.\ Ekeland et al. (1985, Sect.\,2.1)The reference list should contain all citations occurring in the text,ordered alphabetically by surname (with initials following). If thereare several works by the same author(s) the references should be listedin the appropriate order indicated below:\begin{alpherate}\setlength{\hfuzz}{5pt}\itemOne author: list works chronologically;\itemAuthor and same co-author(s): list works chronologically;\itemAuthor and different co-authors: list works alphabeticallyaccording to co-authors.\end{alpherate}If there are several works by the same author(s) and in the same year,but which are cited separately, they should be distinguished by the useof ``a'', ``b'' etc., e.g.\ (Smith 1982a), (Ekeland et al. 1982b).%\subsubsection*{How to Code Author-Year System.}%If you want to use this system you have to specify in\verb|documentstyle| the option \verb|[citeauthoryear]|, like:\begin{verbatim}\documentstyle[citeauthoryear]{llncs}\end{verbatim}Write your citations in the text explicitly except for the year, leavingthat up to \LaTeX{} with the \verb|\cite| command. Then give only theappropriate year as the optional argument (i.e. the label in squarebrackets) with the \verb|\bibitem| command(s).\\[2mm]{\it Sample Input}\begin{verbatim}The results in this section are a refined versionof Clarke and Ekeland (\cite{clar:eke}); the minimality result ofProposition~14 was the first of its kind.\end{verbatim}The above input produces the citation: ``\dots\ refined version ofClarke and Ekeland (1982); the minimality\dots''. Then the\verb|\bibitem|entry of the \verb|thebibliography| environment should read:\begin{verbatim}\begin{thebibliography}{}  % (do not forget {})..\bibitem[1982]{clar:eke}Clarke, F., Ekeland, I.:Nonlinear oscillations and boundary-value problems forHamiltonian systems.Arch. Rat. Mech. Anal. {\bf 78} (1982) 315--333..\end{thebibliography}\end{verbatim}{\it Sample Output}\bibauthoryear%\end{document}

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