% This is LLNCS.DOC the documentation file of % the LaTeX2e class from Springer-Verlag % for Lecture Notes in Computer Science, version 2.4 \documentclass{llncs} \usepackage{llncsdoc} % \begin{document} \markboth{\LaTeXe{} Class for Lecture Notes in Computer Science}{\LaTeXe{} Class for Lecture Notes in Computer Science} \thispagestyle{empty} \begin{flushleft} \LARGE\bfseries Instructions for Authors\\ Coding with \LaTeX\\[2cm] \end{flushleft} \rule{\textwidth}{1pt} \vspace{2pt} \begin{flushright} \Huge \begin{tabular}{@{}l} \LaTeXe{} Class\\ for Lecture Notes\\ in Computer Science\\[6pt] {\Large Version 2.4} \end{tabular} \end{flushright} \rule{\textwidth}{1pt} \vfill %\begin{flushleft} %\large\itshape %\begin{tabular}{@{}l} %{\Large\upshape\bfseries Springer}\\[8pt] %Berlin\enspace Heidelberg\enspace New\kern0.1em York\\[5pt] %Barcelona\enspace Budapest\enspace Hong\kern0.2em Kong\\[5pt] %London\enspace Milan\enspace Paris\enspace\\[5pt] %Santa\kern0.2em Clara\enspace Singapore\enspace Tokyo %\end{tabular} %\end{flushleft} \newpage % \section*{For further information please contact us:} % \begin{flushleft} \begin{tabular}{l@{\quad}l@{\hspace{3mm}}l@{\qquad}l} $\bullet$&\multicolumn{3}{@{}l}{\bfseries LNCS Editorial Office}\\[1mm] &\multicolumn{3}{@{}l}{Springer-Verlag}\\ &\multicolumn{3}{@{}l}{Computer Science Editorial}\\ &\multicolumn{3}{@{}l}{Tiergartenstra�e 17}\\ &\multicolumn{3}{@{}l}{69121 Heidelberg}\\ &\multicolumn{3}{@{}l}{Germany}\\[0.5mm] & Tel: & +49-6221-487-8706\\ & Fax: & +49-6221-487-8588\\ & e-mail: & \tt lncs@springer.com & for editorial questions\\ & & \tt texhelp@springer.de & for \TeX{} problems\\[2mm] \noalign{\rule{\textwidth}{1pt}} \noalign{\vskip2mm} % %{\tt svserv@vax.ntp.springer.de}\hfil first try the \verb|help| %command. % $\bullet$&\multicolumn{3}{@{}l}{\bfseries We are also reachable through the world wide web:}\\[1mm] &\multicolumn{2}{@{}l}{\texttt{http://www.springer.com}}&Springer Global Website\\ &\multicolumn{2}{@{}l}{\texttt{http://www.springer.com/lncs}}&LNCS home page\\ &\multicolumn{2}{@{}l}{\texttt{http://www.springerlink.com}}&data repository\\ &\multicolumn{2}{@{}l}{\texttt{ftp://ftp.springer.de}}&FTP server \end{tabular} \end{flushleft} % \newpage \tableofcontents \newpage % \section{Introduction} % Authors wishing to code their contribution with \LaTeX{}, as well as those who have already coded with \LaTeX{}, will be provided with a document class that will give the text the desired layout. Authors are requested to adhere strictly to these instructions; {\em the class file must not be changed}. The text output area is automatically set within an area of 12.2\,cm horizontally and 19.3\,cm vertically. If you are already familiar with \LaTeX{}, then the LLNCS class should not give you any major difficulties. It will change the layout to the required LLNCS style (it will for instance define the layout of \verb|\section|). We had to invent some extra commands, which are not provided by \LaTeX{} (e.g.\ \verb|\institute|, see also Sect.\,\ref{contbegin}) For the main body of the paper (the text) you should use the commands of the standard \LaTeX{} article'' class. Even if you are familiar with those commands, we urge you to read this entire documentation thoroughly. It contains many suggestions on how to use our commands properly; thus your paper will be formatted exactly to LLNCS standard. For the input of the references at the end of your contribution, please follow our instructions given in Sect.\,\ref{refer} References. The majority of these hints are not specific for LLNCS; they may improve your use of \LaTeX{} in general. Furthermore, the documentation provides suggestions about the proper editing and use of the input files (capitalization, abbreviation etc.) (see Sect.\,\ref{refedit} How to Edit Your Input File). % \section{How to Proceed} % The package consists of the following files: \begin{flushleft} \begin{tabular}{@{}p{2.5cm}l} {\tt history.txt}& the version history of the package\\[2pt] {\tt llncs.cls} & class file for \LaTeX{}\\[2pt] {\tt llncs.dem} & an example showing how to code the text\\[2pt] {\tt llncs.doc} & general instructions (source of this document),\\ & {\tt llncs.doc} means {\itshape l\/}atex {\itshape doc\/}umentation for\\ & {\itshape L\/}ecture {\itshape N}otes in {\itshape C\/}omputer {\itshape S\/}cience\\ {\tt llncsdoc.pdf}& the documentation of the class (PDF version),\\ {\tt llncs.doc} & general instructions (source of this document),\\ {\tt llncsdoc.sty} & class modifications to help for the instructions\\ {\tt llncsind.tex} & an external (faked) author index file\\ {\tt subjidx.tex} & subject index demo from the Springer book package\\ {\tt llncs.dvi} & the resultig DVI file (remember to use binary transfer!)\\[2pt] {\tt sprmindx.sty} & supplementary style file for MakeIndex\\ & (usage: {\tt makeindex -s sprmindx.sty }) \end{tabular} \end{flushleft} % \subsection{How to Invoke the LLNCS Document Class} % The LLNCS class is an extension of the standard \LaTeX{} article'' document class. Therefore you may use all article'' commands for the body of your contribution to prepare your manuscript. LLNCS class is invoked by replacing article'' by llncs'' in the first line of your document: \begin{verbatim} \documentclass{llncs} % \begin{document} \end{document} \end{verbatim} % \subsection{Contributions Already Coded with \protect\LaTeX{} without the LLNCS document class} % If your file is already coded with \LaTeX{} you can easily adapt it a posteriori to the LLNCS document class. 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|\headsep| etc.). There may nevertheless be exceptional occasions on which to use some of them. The LLNCS document class 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}. Same holds for any error and bug you discover (there is however no reward for this -- sorry). % \section{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 (2nd~ed. 1994), Addison-Wesley Publishing Company, Inc. Equations are automatically numbered sequentially throughout your contribution using arabic numerals in parentheses on the right-hand side. When you are working in math mode everything is typeset in italics. Sometimes you need to insert non-mathematical elements (e.g.\ words or phrases). Such insertions should be coded in roman (with \verb|\mbox|) as illustrated in the following example: \begin{flushleft} {\itshape Sample Input} \end{flushleft} \begin{verbatim} \left(\frac{a^{2} + b^{2}}{c^{3}} \right) = 1 \quad \mbox{ if } c\neq 0 \mbox{ and if } a,b,c\in \bbbr \enspace . \end{verbatim} {\itshape 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 \enspace . \end{equation} If you wish to start a new paragraph immediately after a displayed equation, insert a blank line so as to produce the required indentation. If there is no new paragraph either do not insert a blank line or code \verb|\noindent| immediately before continuing the text. Please punctuate a displayed equation in the same way as other ordinary text but with an \verb|\enspace| before end punctuation. 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:\\[2mm] \verb|\left(| or \verb|\left[| and \verb|\right)| or \verb|\right]|. % \subsection{Italic and Roman Type in Math Mode} % \begin{alpherate} \item In math mode \LaTeX{} treats all letters as though they were mathematical or physical variables, hence they are typeset as characters of their own in italics. However, for certain components of formulas, like short texts, this would be incorrect and therefore coding in roman is required. Roman should also be used for subscripts and superscripts {\em in formulas\/} where these are merely labels and not in themselves variables, e.g. $T_{\mathrm{eff}}$ \emph{not} $T_{eff}$, $T_{\mathrm K}$ \emph{not} $T_K$ (K = Kelvin), $m_{\mathrm e}$ \emph{not} $m_e$ (e = electron). However, do not code for roman if the sub/superscripts represent variables, e.g.\ $\sum_{i=1}^{n} a_{i}$. \item Please ensure that {\em physical units\/} (e.g.\ pc, erg s$^{-1}$ K, cm$^{-3}$, W m$^{-2}$ Hz$^{-1}$, m kg s$^{-2}$ 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|\mathrm| command: \verb|\mathrm{Hz}|. On p.\ 44 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 appear in roman automatically. \item Chemical symbols and formulas should be coded for roman, e.g.\ Fe not $Fe$, H$_2$O not {\em H$_2$O}. \item Familiar foreign words and phrases, e.g.\ et al., a priori, in situ, brems\-strah\-lung, eigenvalues should not be italicized. \end{alpherate} % \section{How to Edit Your Input (Source) File} \label{refedit} % \subsection{Headings}\label{headings} % All words in headings should be capitalized except for conjunctions, prepositions (e.g.\ on, of, by, and, or, but, from, with, without, under) and definite and indefinite articles (the, a, an) unless they appear at the beginning. Formula letters must be typeset as in the text. % \subsection{Capitalization and Non-capitalization} % \begin{alpherate} \item The following should always be capitalized: \begin{itemize} \item Headings (see preceding Sect.\,\ref{headings}) \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.\,3, Table\,1, Theorem 2. \end{itemize} Please follow the special rules in Sect.\,\ref{abbrev} for referring to equations. \item The following should {\em 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{alpherate} % \subsection{Abbreviation of Words}\label{abbrev} % \begin{alpherate} \item The following {\em should} be abbreviated when they appear in running text {\em unless\/} they come at the beginning of a sentence: Chap., Sect., Fig.; e.g.\ The results are depicted in Fig.\,5. Figure 9 reveals that \dots .\\ {\em Please note\/}: Equations should usually 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 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{alpherate} % \section{How to Code the Beginning of Your Contribution} \label{contbegin} % The title of a single contribution (it is mandatory) should be coded as follows: \begin{verbatim} \title{} \end{verbatim} All words in titles should be capitalized except for conjunctions, prepositions (e.g.\ on, of, by, and, or, but, from, with, without, under) and definite and indefinite articles (the, a, an) unless they appear at the beginning. Formula letters must be typeset as in the text. Titles have no end punctuation. If a long \verb|\title| must be divided please use the code \verb|\\| (for new line). If you are to produce running heads for a specific volume the standard (of no such running heads) is overwritten with the \verb|[runningheads]| option in the \verb|\documentclass| line. For long titles that do not fit in the single line of the running head a warning is generated. You can specify an abbreviated title for the running head on odd pages with the command \begin{verbatim} \titlerunning{} \end{verbatim} There is also a possibility to change the text of the title that goes into the table of contents (that's for volume editors only -- there is no table of contents for a single contribution). For this use the command \begin{verbatim} \toctitle{} \end{verbatim} An optional subtitle may follow then: \begin{verbatim} \subtitle{} \end{verbatim} Now the name(s) of the author(s) must be given: \begin{verbatim} \author{} \end{verbatim} Numbers referring to different addresses or affiliations are to be attached to each author with the \verb|\inst{}| command. If there is more than one author, the order is up to you; the \verb|\and| command provides for the separation. If you have done this correctly, this entry now reads, for example: \begin{verbatim} \author{Ivar Ekeland\inst{1} \and Roger Temam\inst{2}} \end{verbatim} The first name\footnote{Other initials are optional and may be inserted if this is the usual way of writing your name, e.g.\ Alfred J.~Holmes, E.~Henry Green.} is followed by the surname. As for the title there exist two additional commands (again for volume editors only) for a different author list. One for the running head (on odd pages) -- if there is any: \begin{verbatim} \authorrunning{} \end{verbatim} And one for the table of contents where the affiliation of each author is simply added in braces. \begin{verbatim} \tocauthor{} \end{verbatim} Next the address(es) of institute(s), company etc. is (are) required. If there is more than one address, the entries are numbered automatically with \verb|\and|, in the order in which you type them. Please make sure that the numbers match those placed next to to the authors' names to reflect the affiliation. \begin{verbatim} \institute{ \and \and } \end{verbatim} In addition, you can use \begin{verbatim} \email{} \end{verbatim} to provide your email address within \verb|\institute|. If you need to typeset the tilde character -- e.g. for your web page in your unix system's home directory -- the \verb|\homedir| command will happily do this. Please note that, if your email address is given in your paper, it will also be included in the meta data of the online version. \enlargethispage*{6mm} \medskip If footnote like things are needed anywhere in the contribution heading please code (immediately after the word where the footnote indicator should be placed): \begin{verbatim} \thanks{} \end{verbatim} \verb|\thanks| may only appear in \verb|\title|, \verb|\author| and \verb|\institute| to footnote anything. If there are two or more footnotes or affiliation marks to a specific item separate them with \verb|\fnmsep| (i.e. {\itshape f}oot\emph note \emph mark \emph{sep}arator). \medskip\noindent The command \begin{verbatim} \maketitle \end{verbatim} then formats the complete heading of your article. If you leave it out the work done so far will produce \emph{no} text. Then the abstract should follow. Simply code \begin{verbatim} \begin{abstract} \end{abstract} \end{verbatim} or refer to the demonstration file {\tt llncs.dem} for an example or to the {\em Sample Input\/} on p.~\pageref{samppage}. \subsubsection{Remark to Running Heads and the Table of Contents} \leavevmode\\[\medskipamount] If you are the author of a single contribution you normally have no running heads and no table of contents. Both are done only by the editor of the volume or at the printers. % \section{Special Commands for the Volume Editor} The volume editor can produce a complete camera ready output including running heads, a table of contents, preliminary text (frontmatter), and index or glossary. For activating the running heads there is the class option \verb|[runningheads]|. The table of contents of the volume is printed wherever \verb|\tableofcontents| is placed. A simple compilation of all contributions (fields \verb|\title| and \verb|\author|) is done. If you wish to change this automatically produced list use the commands \begin{verbatim} \titlerunning \toctitle \authorrunning \tocauthor \end{verbatim} to enhance the information in the specific contributions. See the demonstration file \verb|llncs.dem| for examples. An additional structure can be added to the table of contents with the \verb|\addtocmark{}| command. It has an optional numerical argument, a digit from 1 through 3. 3 (the default) makes an unnumbered chapter like entry in the table of contents. If you code \verb|\addtocmark[2]{text}| the corresponding page number is listed also, \verb|\addtocmark[1]{text}| even introduces a chapter number beyond it. % \section{How to Code Your Text} % The contribution title and all headings should be capitalized except for conjunctions, prepositions (e.g.\ on, of, by, and, or, but, from, with, without, under) and definite and indefinite articles (the, a, an) unless they appear at the beginning. Formula letters must be typeset as in the text. Headings will be automatically numbered by the following codes.\\[2mm] {\itshape Sample Input} \begin{verbatim} \section{This is a First-Order Title} \subsection{This is a Second-Order Title} \subsubsection{This is a Third-Order Title.} \paragraph{This is a Fourth-Order Title.} \end{verbatim} \verb|\section| and \verb|\subsection| have no end punctuation.\\ \verb|\subsubsection| and \verb|\paragraph| need to be punctuated at the end. In addition to the above-mentioned headings your text may be structured by subsections indicated by run-in headings (theorem-like environments). All the theorem-like environments are numbered automatically throughout the sections of your document -- each with its own counter. If you want the theorem-like environments to use the same counter just specify the documentclass option \verb|envcountsame|: \begin{verbatim} \documentclass[envcountsame]{llncs} \end{verbatim} If your first call for a theorem-like environment then is e.g. \verb|\begin{lemma}|, it will be numbered 1; if corollary follows, this will be numbered 2; if you then call lemma again, this will be numbered 3. But in case you want to reset such counters to 1 in each section, please specify the documentclass option \verb|envcountreset|: \begin{verbatim} \documentclass[envcountreset]{llncs} \end{verbatim} Even a numbering on section level (including the section counter) is possible with the documentclass option \verb|envcountsect|. \section{Predefined Theorem like Environments}\label{builtintheo} The following variety of run-in headings are at your disposal: \begin{alpherate} \item {\bfseries Bold} run-in headings with italicized text as built-in environments: \begin{verbatim} \begin{corollary} \end{corollary} \begin{lemma} \end{lemma} \begin{proposition} \end{proposition} \begin{theorem} \end{theorem} \end{verbatim} \item The following generally appears as {\itshape italic} run-in heading: \begin{verbatim} \begin{proof} \qed \end{proof} \end{verbatim} It is unnumbered and may contain an eye catching square (call for that with \verb|\qed|) before the environment ends. \item Further {\itshape italic} or {\bfseries bold} run-in headings with roman environment body may also occur: \begin{verbatim} \begin{definition} \end{definition} \begin{example} \end{example} \begin{exercise} \end{exercise} \begin{note} \end{note} \begin{problem} \end{problem} \begin{question} \end{question} \begin{remark} \end{remark} \begin{solution} \end{solution} \end{verbatim} \end{alpherate} \section{Defining your Own Theorem like Environments} We have enhanced the standard \verb|\newtheorem| command and slightly changed its syntax to get two new commands \verb|\spnewtheorem| and \verb|\spnewtheorem*| that now can be used to define additional environments. They require two additional arguments namely the type style in which the keyword of the environment appears and second the style for the text of your new environment. \verb|\spnewtheorem| can be used in two ways. \subsection{Method 1 {\itshape (preferred)}} You may want to create an environment that shares its counter with another environment, say {\em main theorem\/} to be numbered like the predefined {\em theorem\/}. In this case, use the syntax \begin{verbatim} \spnewtheorem{}[]{} {}{} \end{verbatim} \noindent Here the environment with which the new environment should share its counter is specified with the optional argument \verb|[]|. \paragraph{Sample Input} \begin{verbatim} \spnewtheorem{mainth}[theorem]{Main Theorem}{\bfseries}{\itshape} \begin{theorem} The early bird gets the worm. \end{theorem} \begin{mainth} The early worm gets eaten. \end{mainth} \end{verbatim} \medskip\noindent {\em Sample Output} \medskip\noindent {\bfseries Theorem 3.}\enspace {\em The early bird gets the worm.} \medskip\noindent {\bfseries Main Theorem 4.} The early worm gets eaten. \bigskip The sharing of the default counter (\verb|[theorem]|) is desired. If you omit the optional second argument of \verb|\spnewtheorem| a separate counter for your new environment is used throughout your document. \subsection[Method 2]{Method 2 {\itshape (assumes {\tt[envcountsect]} documentstyle option)}} \begin{verbatim} \spnewtheorem{}{}[] {}{} \end{verbatim} \noindent This defines a new environment \verb|| which prints the caption \verb|| in the font \verb|| and the text itself in the font \verb||. The environment is numbered beginning anew with every new sectioning element you specify with the optional parameter \verb||. \medskip\noindent \paragraph{Example} \leavevmode \medskip\noindent \verb|\spnewtheorem{joke}{Joke}[subsection]{\bfseries}{\rmfamily}| \medskip \noindent defines a new environment called \verb|joke| which prints the caption {\bfseries Joke} in boldface and the text in roman. The jokes are numbered starting from 1 at the beginning of every subsection with the number of the subsection preceding the number of the joke e.g. 7.2.1 for the first joke in subsection 7.2. \subsection{Unnumbered Environments} If you wish to have an unnumbered environment, please use the syntax \begin{verbatim} \spnewtheorem*{}{}{}{} \end{verbatim} \section{Program Codes} In case you want to show pieces of program code, just use the \verb|verbatim| environment or the \verb|verbatim| package of \LaTeX. (There also exist various pretty printers for some programming languages.) % \noindent \subsection*{Sample Input {\rmfamily(of a simple contribution)}}\label{samppage} \begin{verbatim} \title{Hamiltonian Mechanics} \author{Ivar Ekeland\inst{1} \and Roger Temam\inst{2}} \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 % \begin{abstract} This paragraph shall summarize the contents of the paper in short terms. \end{abstract} % \section{Fixed-Period Problems: The Sublinear Case} % With this chapter, the preliminaries are over, and we begin the search for periodic solutions \dots % \subsection{Autonomous Systems} % In this section we will consider the case when the Hamiltonian $H(x)$ \dots % \subsubsection*{The General Case: Nontriviality.} % We assume that $H$ is $\left(A_{\infty}, B_{\infty}\right)$-subqua\-dra\-tic at infinity, for some constant \dots % \paragraph{Notes and Comments.} The first results on subharmonics were \dots % \begin{proposition} Assume $H'(0)=0$ and $H(0)=0$. Set \dots \end{proposition} \begin{proof}[of proposition] Condition (8) means that, for every $\delta'>\delta$, there is some $\varepsilon>0$ such that \dots \qed \end{proof} % \begin{example}[\rmfamily (External forcing)] Consider the system \dots \end{example} \begin{corollary} Assume $H$ is $C^{2}$ and $\left(a_{\infty}, b_{\infty}\right)$-subquadratic at infinity. Let \dots \end{corollary} \begin{lemma} Assume that $H$ is $C^{2}$ on $\bbbr^{2n}\backslash \{0\}$ and that $H''(x)$ is \dots \end{lemma} \begin{theorem}[(Ghoussoub-Preiss)] Let $X$ be a Banach Space and $\Phi:X\to\bbbr$ \dots \end{theorem} \begin{definition} We shall say that a $C^{1}$ function $\Phi:X\to\bbbr$ satisfies \dots \end{definition} \end{verbatim} {\itshape Sample Output\/} (follows on the next page together with examples of the above run-in headings) \newcounter{save}\setcounter{save}{\value{section}} {\def\addtocontents#1#2{}% \def\addcontentsline#1#2#3{}% \def\markboth#1#2{}% % \title{Hamiltonian Mechanics} \author{Ivar Ekeland\inst{1} \and Roger Temam\inst{2}} \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 % \begin{abstract} This paragraph shall summarize the contents of the paper in short terms. \end{abstract} % \section{Fixed-Period Problems: The Sublinear Case} % With this chapter, the preliminaries are over, and we begin the search for periodic solutions \dots % \subsection{Autonomous Systems} % In this section we will consider the case when the Hamiltonian $H(x)$ \dots % \subsubsection{The General Case: Nontriviality.} % We assume that $H$ is $\left(A_{\infty}, B_{\infty}\right)$-subqua\-dra\-tic at infinity, for some constant \dots % \paragraph{Notes and Comments.} The first results on subharmonics were \dots % \begin{proposition} Assume $H'(0)=0$ and $H(0)=0$. Set \dots \end{proposition} \begin{proof}[of proposition] Condition (8) means that, for every $\delta'>\delta$, there is some $\varepsilon>0$ such that \dots \qed \end{proof} % \begin{example}[{{\rmfamily External forcing}}] Consider the system \dots \end{example} \begin{corollary} Assume $H$ is $C^{2}$ and $\left(a_{\infty}, b_{\infty}\right)$-subquadratic at infinity. Let \dots \end{corollary} \begin{lemma} Assume that $H$ is $C^{2}$ on $\bbbr^{2n}\backslash \{0\}$ and that $H''(x)$ is \dots \end{lemma} \begin{theorem}[Ghoussoub-Preiss] Let $X$ be a Banach Space and $\Phi:X\to\bbbr$ \dots \end{theorem} \begin{definition} We shall say that a $C^{1}$ function $\Phi:X\to\bbbr$ satisfies \dots \end{definition} % }\setcounter{section}{\value{save}} \section{Fine Tuning of the Text} % The following should be used to improve the readability of the text: \begin{flushleft} \begin{tabular}{@{}p{.19\textwidth}p{.79\textwidth}} \verb|\,| & a thin space, e.g.\ between numbers or between units and num\-bers; a line division will not be made following this space\\ \verb|--| & en dash; two strokes, without a space at either end\\ \verb*| -- |& en 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} \\[8mm] {\em Input} & \verb|21\,$^{\circ}$C etc.,|\\ & \verb|Dr h.\,c.\,Rockefellar-Smith \dots|\\ & \verb|20,000\,km and Prof.\,Dr Mallory \dots|\\ & \verb|1950--1985 \dots|\\ & \verb|this -- written on a computer -- is now printed|\\ & \verb|$-30$\,K \dots|\\[3mm] {\em Output}& 21\,$^{\circ}$C etc., Dr h.\,c.\,Rockefellar-Smith \dots\\ & 20,000\,km and Prof.\,Dr Mallory \dots\\ & 1950--1985 \dots\\ & this -- written on a computer -- is now printed\\ & $-30$\,K \dots \end{tabular} \end{flushleft} % \section {Special Typefaces} % Normal type (roman text) need not be coded. {\itshape Italic} (\verb|{\em }| better still \verb|\emph{}|) or, if necessary, {\bfseries boldface} should be used for emphasis.\\[6pt] \begin{minipage}[t]{\textwidth} \begin{flushleft} \begin{tabular}{@{}p{.25\textwidth}@{\hskip6pt}p{.73\textwidth}@{}} \verb|{\itshape Text}| & {\itshape Italicized Text}\\[2pt] \verb|{\em Text}| & {\em Emphasized Text -- if you would like to emphasize a {\em definition} within an italicized text (e.g.\ of a {\em theorem)} you should code the expression to be emphasized by} \verb|\em|.\\[2pt] \verb|{\bfseries Text}|& {\bfseries Important Text}\\[2pt] \verb|\vec{Symbol}| & Vectors may only appear in math mode. The default \LaTeX{} vector symbol has been adapted\footnotemark\ to LLNCS conventions.\\[2pt] & \verb|$\vec{A \times B\cdot C}| yields$\vec{A\times B\cdot C}$\\ & \verb|$\vec{A}^{T} \otimes \vec{B} \otimes|\\ & \verb|\vec{\hat{D}}$|yields$\vec{A}^{T} \otimes \vec{B} \otimes \vec{\hat{D}}$\end{tabular} \end{flushleft} \end{minipage} \footnotetext{If you absolutely must revive the original \LaTeX{} design of the vector symbol (as an arrow accent), please specify the option \texttt{[orivec]} in the \texttt{documentclass} line.} \newpage % \section {Footnotes} % Footnotes within the text should be coded: \begin{verbatim} \footnote{Text} \end{verbatim} {\itshape Sample Input} \begin{flushleft} Text with a footnote\verb|\footnote{The |{\tt footnote is automatically numbered.}\verb|}| and text continues \dots \end{flushleft} {\itshape Sample Output} \begin{flushleft} Text with a footnote\footnote{The footnote is automatically numbered.} and text continues \dots \end{flushleft} % \section {Lists} % Please code lists as described below:\\[2mm] {\itshape 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} {\itshape 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} % \section {Figures} % Figure environments should be inserted after (not in) the paragraph in which the figure is first mentioned. They will be numbered automatically. Preferably the images should be enclosed as PostScript files -- best as EPS data using the epsfig package. If you cannot include them into your output this way and use other techniques for a separate production, the figures (line drawings and those containing halftone inserts as well as halftone figures) {\em 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 a probably necessary reduction the height of capital letters should be at least 1.8\,mm and not more than 2.5\,mm. 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 coding described below. As can be seen in the output, we will automatically provide 1\,cm space above and below the figure, so that you should only leave the space equivalent to the size of the figure itself. Please note that \verb|x|'' in the following coding 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} {\itshape Sample Input} \end{flushleft} \begin{verbatim} \begin{figure} \vspace{2.5cm} \caption{This is the caption of the figure displaying a white eagle and a white horse on a snow field} \end{figure} \end{verbatim} \begin{flushleft} {\itshape Sample Output} \end{flushleft} \begin{figure} \vspace{2.5cm} \caption{This is the caption of the figure displaying a white eagle and a white horse on a snow field} \end{figure} % \section{Tables} % Table captions should be treated in the same way as figure legends, except that the table captions appear {\itshape above} the tables. The tables will be numbered automatically. % \subsection{Tables Coded with \protect\LaTeX{}} % Please use the following coding:\\[2mm] {\itshape Sample Input} \begin{verbatim} \begin{table} \caption{Critical$Nvalues} \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} \end{table} \end{verbatim} \medskip\noindent{\itshape Sample Output} \begin{table} \caption{CriticalNvalues} \begin{center} \renewcommand{\arraystretch}{1.4} \setlength\tabcolsep{3pt} \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} \end{center} \end{table} Before continuing your text you need an empty line. \dots \vspace{3mm} For further information you will find a complete description of the tabular environment on p.~62~ff. and p.~204 of the {\em \LaTeX{} User's Guide \& Reference Manual\/} 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] {\itshape 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.~41\,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 {\itshape necessary}, please use those of the relevant \AmSTeX{} alphabet which are available using the amstex package of the American Mathematical Society. In \LaTeX{} only the following gothic letters are available: \verb|$\Re$| yields $\Re$ and \verb|$\Im$| yields $\Im$. These should {\itshape not\/} be used when you need gothic letters for your contribution. Use \AmSTeX{} gothic as explained above. For the real and the imaginary parts of a complex number within math mode you should use instead: \verb|$\mathrm{Re}$| (which yields Re) or \verb|$\mathrm{Im}$| (which yields Im). % \subsubsection*{Script.} % For script capitals use the coding \begin{center} \begin{tabular}{l@{\hspace{1em}which yields\hspace{1em}}c} \verb|$\mathcal{AB}$| & $\mathcal{AB}$ \end{tabular} \end{center} (see p.~42 of the \LaTeX{} book). % \subsubsection*{Special Roman.} % If you need other symbols than those below, you could use the blackboard bold characters of \AmSTeX{}, but there might arise capacity problems in loading additional \AmSTeX{} fonts. Therefore we created the blackboard bold characters listed below. Some of them are not esthetically satisfactory. This need not deter you from using them: in the final printed form they will be replaced by the well-designed MT (monotype) characters of the phototypesetting machine. \begin{flushleft} \begin{tabular}{@{}ll@{ yields } c@{\hspace{1.em}}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} % \section{References} \label{refer} % There are three reference systems available; only one, of course, should be used for your contribution. With each system (by number only, by letter-number or by author-year) a reference list containing all citations in the text, should be included at the end of your contribution placing the \LaTeX{} environment \verb|thebibliography| there. For an overall information on that environment see the {\em \LaTeX{} User's Guide \& Reference Manual\/} by Leslie Lamport, p.~71. There is a special {\sc Bib}\TeX{} style for LLNCS that works along with the class: \verb|splncs.bst| -- call for it with a line \verb|\bibliographystyle{splncs}|. If you plan to use another {\sc Bib}\TeX{} style you are customed to, please specify the option \verb|[oribibl]| in the \verb|documentclass| line, like: \begin{verbatim} \documentclass[oribibl]{llncs} \end{verbatim} This will retain the original \LaTeX{} code for the bibliographic environment and the \verb|\cite| mechanism that many {\sc Bib}\TeX{} applications rely on. % \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 square brackets, e.g.\ [1] or [E1, S2], [P1], according to your use of the \verb|\bibitem| command in the \verb|thebibliography| environment. The coding is as follows: if you choose your own label for the sources by giving an optional argument to the \verb|\bibitem| command the citations in the text are marked with the label you supplied. Otherwise a simple numbering is done, which is preferred. \begin{verbatim} The results in this section are a refined version of \cite{clar:eke}; the minimality result of Proposition~14 was 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 of the \verb|thebibliography| environment should read: \begin{verbatim} \begin{thebibliography}{[MT1]} . . \bibitem[CE1]{clar:eke} Clarke, F., Ekeland, I.: Nonlinear oscillations and boundary-value problems for Hamiltonian systems. Arch. Rat. Mech. Anal. 78, 315--333 (1982) . . \end{thebibliography} \end{verbatim} The complete bibliography looks like this: % \begin{thebibliography}{[MT1]} % \bibitem[CE1]{clar:eke} Clarke, F., Ekeland, I.: Nonlinear oscillations and boundary-value problems for Hamiltonian systems. Arch. Rat. Mech. Anal. 78, 315--333 (1982) % \bibitem[CE2]{clar:eke:2} Clarke, F., Ekeland, I.: Solutions p\'{e}riodiques, du p\'{e}riode donn\'{e}e, des \'{e}quations hamiltoniennes. Note CRAS Paris 287, 1013--1015 (1978) % \bibitem[MT1]{mich:tar} Michalek, R., Tarantello, G.: Subharmonic solutions with prescribed minimal period for nonautonomous Hamiltonian systems. J. Diff. Eq. 72, 28--55 (1988) % \bibitem[Ta1]{tar} Tarantello, G.: Subharmonic solutions for Hamiltonian systems 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. 33, 609--633 (1980) \end{thebibliography} % \subsubsection*{Number-Only System.} % For this preferred system do not use the optional argument in the \verb|\bibitem| command: then, only numbers will appear for the citations in the text (enclosed in square brackets) as well as for the marks in your bibliography (here the number is only end-punctuated without square brackets). Subsequent citation numbers in the text are collapsed to ranges. Non-numeric and undefined labels are handled correctly but no sorting is done. E.g., \verb|\cite{n1,n3,n2,n3,n4,n5,foo,n1,n2,n3,?,n4,n5}| -- where \verb|n|$x$ is the key of the $x^{\mathrm{th}}$ \verb|\bibitem| command in sequence, \verb|foo| is the key of a \verb|\bibitem| with an optional argument, and \verb|?| is an undefined reference -- gives 1,3,2-5,foo,1-3,?,4,5 as the citation reference. \begin{verbatim} \begin{thebibliography}{1} \bibitem {clar:eke} Clarke, F., Ekeland, I.: Nonlinear oscillations and boundary-value problems for Hamiltonian systems. Arch. Rat. Mech. Anal. 78, 315--333 (1982) \end{thebibliography} \end{verbatim} % \subsection{Author-Year System} % References are cited in the text by name and year in parentheses and should look as follows: (Smith 1970, 1980), (Ekeland et al. 1985, Theorem 2), (Jones and Jaffe 1986; Farrow 1988, Chap.\,2). If the name is part of the sentence only 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 there are several works by the same author(s) the references should be listed in the appropriate order indicated below: \begin{alpherate} \setlength{\hfuzz}{5pt} \item One author: list works chronologically; \item Author and same co-author(s): list works chronologically; \item Author and different co-authors: list works alphabetically according 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 use of 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 the option \verb|[citeauthoryear]| in the \verb|documentclass|, like: \begin{verbatim} \documentclass[citeauthoryear]{llncs} \end{verbatim} Write your citations in the text explicitly except for the year, leaving that up to \LaTeX{} with the \verb|\cite| command. Then give only the appropriate year as the optional argument (i.e. the label in square brackets) with the \verb|\bibitem| command(s).\\[2mm] {\itshape Sample Input} \begin{verbatim} The results in this section are a refined version of Clarke and Ekeland (\cite{clar:eke}); the minimality result of Proposition~14 was the first of its kind. \end{verbatim} The above input produces the citation: \dots\ refined version of Clarke and Ekeland (1982); the minimality\dots''. Then the \verb|\bibitem| entry of \verb|clar:eke| in 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 for Hamiltonian systems. Arch. Rat. Mech. Anal. 78, 315--333 (1982) . . \end{thebibliography} \end{verbatim} {\itshape Sample Output} \bibauthoryear % \end{document}