% This is JNS.DOC the documentation file of % the plain TeX macro package from Springer-Verlag % for the Journal of Nonlinear Science % version of 16 July 1990 \input jns.cmm \def\degr{\hbox{$^\circ$}} \def\arcmin{\hbox{$^\prime$}} \def\arcsec{\hbox{$^{\prime\prime}$}} \def\bs{\ifmmode\backslash\else$\backslash$\fi} \newdimen\einrueck\setbox0=\hbox{\kern6.5mm DATEX-P dial: } \einrueck=\wd0\relax \def\jtem#1{\par\hangindent\einrueck\hangafter=1\noindent\hbox to\einrueck{\kern6.5mm#1\hss}\ignorespaces} \chardef\other=12 \def\BlankIsSpace{\def\blankmeaning{\space}} \def\BlankIsControlSpace{\def\blankmeaning{\ }} \def\BlankIsVisible{\def\blankmeaning{{\tt\char32}}} \def\theblankmeaning{\blankmeaning} {\obeyspaces\global\let =\theblankmeaning} \def\obeyspaces{\BlankIsSpace\catcode`\ =\active} {\catcode`\`=\active \gdef`{\relax\lq}} \def\setupverbatim{\begingroup\catcode`\\=\other \catcode`\{=\other \catcode`\}=\other \catcode`\$=\other \catcode`\&=\other \catcode`\#=\other \catcode`\%=\other \catcode`\~=\other \catcode`\_=\other \catcode`\^=\other \obeyspaces \tt} \def\doverbatim#1{\def\next##1#1{##1\endgroup}\next} \def\verb{\setupverbatim\doverbatim} \def\verbb{\setupverbatim\BlankIsVisible\doverbatim} {\catcode`\|=0 |catcode`|\=\other |obeylines |gdef|ttfinish#1\endtt{#1|strut|endgroup|smallskip}} \def\begintt{\strut\smallskip\let\par=\endgraf \setupverbatim\parindent=0pt\obeylines \parskip=0pt\catcode`\|=0 \ttfinish} \def\listing#1{\par\setupverbatim\obeylines\input#1 \endgroup} \def\ident{Macro Package for Authors Coding with Plain\TeX} \headline={\hfill} \let\header=N \output={\if N\header%gar nix \else\if F\header\headline={{\petit\rm \ifodd\pageno\hfil \folio\else\folio\hfil\fi}} \else\headline={{\petit\rm \ifodd\pageno\ident\hfil \folio\else\folio\hfil\ident\fi}}\fi\fi\plainoutput\global\let\header=Y \if Y\FIG\topinsert\unvbox\figbox\endinsert\global\let\FIG=N\fi} \def\leaderfill{\kern0.5em\leaders\hbox to 0.5em{\hss.\hss}\hfill\kern 0.5em} \newdimen\chapindent \newdimen\sectindent \newdimen\subsecindent \newdimen\thousand \setbox0=\hbox{\bf 10. }\chapindent=\wd0\advance\chapindent by-4true pt \setbox0=\hbox{10.10 }\sectindent=\wd0\advance\sectindent by-4true pt \setbox0=\hbox{10.10.1 }\subsecindent=\wd0 \advance\subsecindent by-4true pt \setbox0=\hbox{\enspace 100}\thousand=\wd0 % \def\conttitlea#1#2#3{\if N\lasttitle\if!#1!\else\vskip8true pt\fi \fi\let\lasttitle=N\line{\hbox to \chapindent{\strut\bf#1\hss}{\textfont1=\tams \scriptfont1=\tamss\scriptscriptfont1=\tbmss\bf#2}% \if!#3!\hfill\else\leaderfill\hbox to\thousand{\hss#3}\fi}} % \def\conttitleb#1#2#3{\line{\kern\chapindent\hbox to\sectindent{\strut#1\hss}{#2}% \if!#3!\hfill\else\leaderfill\hbox to\thousand{\hss#3}\fi}\par} % \def\conttitlec#1#2#3{\line{\kern\chapindent\kern\sectindent \hbox to\subsecindent{\strut#1\hss}{#2}% \if!#3!\hfill\else\leaderfill\hbox to\thousand{\hss#3}\fi}\par} \def\LaTeX{{\rm L\kern-.36em\raise.3ex\hbox{\petit A}\kern-.15em T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}}% \def\AmSTeX{{\tensy A}\kern-.1667em\lower.5ex\hbox {\tensy M}\kern-.125em{\tensy S}-\TeX} \font \titelfont = cmr10 scaled\magstep3 \font \titelbffont = cmbx10 scaled\magstep4%at 20true pt \font \titelbigfont = cmr10 scaled\magstep5%at 24true pt {\parindent=0pt\titelbffont Macro Package for\medskip \leftline{Authors Coding with Plain\TeX} \vskip2.2cm \hrule height1pt\bigskip\bigskip \rightline{\vbox{\titelbigfont\hbox{The Journal of}\bigskip \hbox{Nonlinear Science}}} \bigskip\bigskip\hrule height1pt \vfil \rightline{\vbox{\titelfont\hbox{Springer-Verlag}\bigskip \hbox{New \kern-4pt Y\kern-2pt ork Berlin Heidelberg Tokyo} \smallskip\vskip1true mm \hbox{London Paris Hong \kern-3pt Kong}}}\eject}% \titlea{}{For further information please contact us:} \noindent\hbox to6.5mm{$\bullet$\hfil}{\bf Springer-Verlag New \kern-3pt York} \vskip0.5\baselineskip \jtem{Springer-Verlag} New \kern-2pt York, 175 Fifth Avenue,\newline New \kern-2pt York, New \kern-2pt York 10010 USA \vskip0.5\baselineskip \jtem{Telex:} 232235 \jtem{Fax:} (212)437-6272 \jtem{Editorial:} (Mon--Fr; preferably between 9 a.m. and 4 p.m. --\newline Eastern Standard Time)\newline Telephone (212)460-1565 \jtem{net-address:} TROWBRIDGE@COMPUSERVE.COM \vskip0.5\baselineskip \noindent\hbox to6.5mm{$\bullet$\hfil}{\bf Springer-Verlag Heidelberg} \vskip0.5\baselineskip \item{}Springer-Verlag, Postfach 105280, D-6900 Heidelberg 1, FRG \vskip0.5\baselineskip \jtem{DATEX-P dial:} FRG 456 221 4305 If you do not yet have an account, press RETURN when asked for your name; then simply leave a message. The file name should be your name and country or state, e.g.\ smith-texas \jtem{Telex:} 461723 \jtem{Telefax:} (06221)43982 \jtem{Editorial:} (Mon--Fr; preferably between 9 a.m. and\newline 4 p.m. - European local time),\newline Telephone (0049)(0)6221-487534 \item{}\TeX{}nical information (Mon--Fri; preferably between\newline 9 a.m. and 1 p.m. -- European local time):\newline Telephone (0049)(0)6221-487478 \jtem{bitnet:} SPRINGER@DHDSPRI6 \bigskip\hrule \titlea{}{Mailing address for your disk/magnetic tape and output:} {\leftskip=\oldparindent Springer-Verlag New \kern-2pt York, Inc.\newline 175 Fifth Avenue,\newline New \kern-2pt York, New \kern-2pt York 10010 USA \medskip} The following formats are acceptable: 5.25$^{\prime\prime}$ diskette MS-DOS, 5.25$^{\prime\prime}$ CP/M, 3.5$^{\prime\prime}$ diskette MS-DOS, 3.5$^{\prime\prime}$ diskette Apple MacIntosh, 9-track 1600 bpi magnetic tape VAX/VMS, 9-track 1600 bpi magnetic tape ANSI with label, 9-track 1600 bpi magnetic tape, SUN-Streamer Tape. Once you have completed your work using this macro package, please submit your own printout of the {\it final version together with the disk or magnetic tape}, containing your \TeX{} input (source) file and the final DVI-file and make sure that the text is {\it identical in both cases.} Contributions coded with \TeX{} but not with the JNS style, cannot be accepted for electronic processing; they will be typeset in the conventional way. \vfill\eject \titlea{}{Table of Contents} \conttitlea{1}{Introduction}{4} \conttitlea{2}{General Remarks}{4} \vskip2truept \conttitleb{2.1}{How to Proceed}{4} \conttitleb{2.2}{Contributions Coded with Plain\TeX{} without the}{} \conttitleb{}{Springer-Verlag \TeX{} Macro Package}{4} \conttitleb{2.3}{Problems with PC \TeX}{5} \conttitleb{2.4}{General Rules for Coding Mathematics}{5} \conttitlec{2.4.1}{Italic and Roman in Math Mode}{6} \conttitleb{2.5}{Capitalization and Non-capitalization in the}{} \conttitleb{}{Input (Source) File}{6} \conttitleb{2.6}{Abbreviations of Words in the Input (Source) File}{6} \conttitlea{3}{How to Handle Your Contribution}{7} \conttitlea{4}{How to Code}{7} \vskip2truept \conttitleb{4.1}{Headings}{7} \conttitlec{4.1.1}{Defining Your Own Environments}{9} \conttitleb{4.2}{Text}{13} \conttitleb{4.3}{Special Typefaces}{13} \conttitleb{4.4}{Footnotes}{14} \conttitleb{4.5}{Lists}{14} \conttitleb{4.6}{Figures}{15} \conttitlec{4.6.1}{Two Figures Next to Each Other}{16} \conttitlec{4.6.2}{Modified Legend Arrangements}{17} \conttitleb{4.7}{Tables}{18} \conttitlec{4.7.1}{Tables Coded with \TeX{}}{18} \conttitlec{4.7.2}{Tables Not Coded with \TeX{}}{19} \conttitleb{4.8}{Signs and Special Characters}{19} \conttitlec{4.8.1}{Special Signs}{19} \conttitlec{4.8.2}{Gothic (Fraktur)}{20} \conttitlec{4.8.3}{Script}{20} \conttitlec{4.8.4}{Special Roman}{20} \conttitlec{4.8.5}{Sans Serif}{20} \conttitlec{4.8.6}{Invented Characters}{20} \conttitlea{5}{How to Code References}{21} \vskip2truept \conttitleb{5.1}{Author--Year System}{21} \conttitleb{5.2}{References by Number Only and by Letter--Number}{22} \conttitleb{5.3}{Examples}{22} \conttitlea{6}{Demonstration File}{26} \vfill\eject \titlea{1.}{Introduction} Authors wishing to code their contribution for the \medskip \centerline{\it Journal of Nonlinear Science,} \medskip\noindent with \TeX{}, as well as those who have already coded with \TeX{}, will be provided with macros that will give the text the desired layout. Using the macros will ease considerably your coding with \TeX.{} Authors are requested to adhere strictly to these instructions; {\it the macros must not be changed}. The text output area is 12.2\ts cm horizontal and 19.4\ts cm vertical; excluding running heads. \titlea {2.}{General Remarks} \titleb {2.1.}{How to Proceed} Please insert the enclosed diskette or tape into your computer. You will find the following files: \medskip \settabs \+xxxxxxxxxxx&xxxxxxxxxxxxxxxxxxxxxxxxxxx &xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx \cr \+{\it jns.doc}&general instructions (this document)\cr \+{\it jns.amm}&the macro package with am-fonts (the old \TeX{} fonts)\cr \+{\it jns.cmm}&the macro package with cm-fonts (newer and preferable)\cr \+&(these are both macro files and should not be changed)\cr \+{\it jns.dem}&an example showing how to code the text\cr \smallskip Please insert at the beginning of your text file (also called input or source file) the macro file with: \medskip\noindent \verb|\input jns.amm| or \newline \verb|\input jns.cmm| (preferable). \medskip Now some settings will be carried out automatically: for example, the horizontal and vertical sizes, the page layout, the running heads and other features. Some of \TeX's internal variables are changed. \titleb{2.2.}{Contributions Already Coded with Plain\TeX{} without the \newline Springer-Verlag \TeX{} Macro Package} If your file already contains \TeX\ coding, then: \item{--\kern2.5true mm} you will need to replace some of {\it your\/} \TeX{} commands by {\it our\/} codes listed in section {\it 4 How to Code}; \item{--\kern2.5true mm} you need only to insert \verb|\input jns.cmm| to get the desired page layout and fonts if your layout is close to the one you can see in our demonstration file. It is most important to change your macros for the headings (see \verb|\titlea| \dots). Making further improvements by using more of our macros is still better. \titled{Very important:} If your text or your own macros contain layout codes such as \verb|\hsize|, \verb|\goodbreak|, \verb|\eject| and \verb|\magnification|, or special fonts, these should be taken out. (There may nevertheless be exceptional occasions on which to use some of them.) If you have your {\it own macros\/} or definitions, insert them {\it before\/} the call \verb|\input jns.cmm|, so that some of them may be replaced or tailored according to Springer style. Please put in sufficient comments with your macros to help us understand them. \titleb {2.3.}{Problems with PC \TeX{} } In PC \TeX{} the default memory capacity is not sufficient to accommodate our fonts. To cope with this problem, invoke \TeX{} with the following command:\newline {\tt tex myfile.tex /f=26000 /m=65000} \titleb {2.4.}{General Rules for Coding Mathematics} For mathematical expressions and tables please follow Plain\TeX\ from {\it The \TeX{}book\/} by Donald E. Knuth (1986), Addison-Wesley Publishing Company (a comprehensive general reference). In the case of long equations in the text (enclosed in single $\$ $) that extend beyond the type area (12.2\ts cm), insert an \verb|\allowbreak| where the equation can be divided. For displayed equations (enclosed in \verb|$$|) please refer to Section {\it 3.\ts Long Formulas\/} in Chap.\ts 19, p. 195 of {\it The \TeX{}book}. Equations should be numbered consecutively throughout your contribution e.g. (1), (2) etc., on the right-hand side. Place e.g. \verb|\eqno(1)| etc. as the last item in a displayed (\verb|$$|) equation. If you include elements of ordinary text in math mode, please enclose them in \verb|\hbox{\rm text}|, e.g. \medskip\noindent {\it Input } \begintt $$\left({a^2 + b^2 \over c^2}\right)^2 = 1 \quad\hbox{\rm only when}\quad c\neq 0\enspace .\eqno (1)$$ \endtt \medskip\noindent {\it Output } $$\left({a^2 + b^2 \over c^2}\right)^2 = 1 \quad\hbox{\rm only when}\quad c\neq 0\enspace .\eqno (1)$$ Please note that the sizes of the parentheses or other so-called delimiter symbols used in equations should ideally match the formulas they enclose (see p.\ts 145\ts ff. of {\it The \TeX{}book}). After a displayed equation you have to insert a blank line or to give the command \verb|\par| if you want a new paragraph with an indention. 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 the same way as any other written statement but with an \verb|\enspace| before end punctuation. \vfill\eject \titlec{2.4.1.\enspace Italic and Roman in Math Mode} \vskip0.5\baselineskip \item{a)}In math mode \TeX{} treats all letters as though they were mathematical or physical variables, hence they are typeset 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 {\it in formulas\/} where these are merely labels and not in themselves variables, e.g.\ $T_{\rm eff}$ \ not \ $T_{eff}$, $T_{\rm K}$ \ not \ $T_K$ (K = Kelvin), $m_{\rm e}$ \ 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{b)}Please ensure that {\it physical units\/} (e.g.\ pc, erg s$^{-1}$ K, cm$^{-3}$, W m$^{-2}$ Hz$^{-1}$, m kg s$^{-2}$ A$^{-2}$) and {\it abbreviations\/} such as Ord, Var, GL, SL, Aut, Ker, sgn, const.\ are always set in roman type. To ensure this use the \verb|\rm| command: \verb|{\rm Hz}|. On p.\ts 162 of {\it The \TeX{}book\/} by Donald E.~Knuth 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. \item{c)} Chemical symbols and formulas should be coded for roman, e.g.\ Fe not $Fe$, H$_2$O not {\it H$_2$O\/}. \item{d)} Familiar foreign words and phrases, e.g. et al., a priori, in situ, brems\-strah\-lung, eigenvalues should appear also in roman. \titleb {2.5.}{Capitalization and Non-capitalization in the Input (Source) File} \item {a)} The following should always be capitalized: \itemitem {--} Headings [see {\it 4.1 Headings}] \itemitem {--} 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, Table\ts 1, Theorem 2. \item{} Please see below the special rules for referring to equations. \item {b)} The following should {\it not\/} be capitalized: \itemitem {--} The words figure(s), table(s), equation(s), theorem(s) in the text when used without an accompanying number \itemitem {--} Figure legends and table captions except for names and abbreviations. \titleb {2.6.} {Abbreviation of Words in the Input (Source) File} \item{a)} The following should be abbreviated in the text {\it unless\/} they come at the beginning of a sentence: Chap., Sect., Fig.; e.g. The results are shown in Fig.\ts 5. Figure 9 reveals that \dots . \newline {\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 mention, e.g. Plurisubharmonic (PSH) Functions, Strong Optimization (SOPT) Problem. \titlea {3.}{How to Handle Your Contribution} Once you have completed your work using this macro package, you should send your printout {\it together\/} with the disk or magnetic tape (concerning the acceptable formats see remark on p. 2) to the editorial (see address on p.2). Please make sure that the text of your printout and the disk or magnetic tape is {\it identical}. Your contribution should begin with the following coding (see {\it 4 How to Code}), and please adhere strictly to this sequence: \medskip \settabs \+xxxxxxxxxxxxxxxxxxxxxxxxxx &xxxxxxxxxxxxxxxxxxxxxxxxx \cr \+\verb|\input ...|&your own macros if you have any \cr \medskip \+\verb|\input jns.cmm|&call for the macros and fonts\cr \medskip \+\verb|\maintitle{...}|&the title of your article\cr \medskip \+\verb|\subtitle{...}|&the subtitle of your article (it is optional)\cr \medskip \+\verb|\author{...}|&author(s) name(s)\cr \medskip \+\verb|\address{...}|&address(es) of the author(s)\cr \medskip \+\verb|\received{...}|&date of receipt of your article \cr \medskip \+\verb|\summary{...}| &text of the summary \cr \medskip \+\verb|\keywords{...}| &appropriate keywords \cr \medskip \+\verb|\titlea{...}{...}|&see {\it 4 How to Code} \cr \+\quad\vdots&\raise 1mm\hbox{(here goes the body of your article)}\cr \+\verb|\begref{...}{...}|&see {\it 5 How to Code References}\cr \titlea{4.}{How to Code} \titleb{4.1.} {Headings} No blank line should be left in the input between titles or headings and the following text. Otherwise you will get an indentation which is not allowed after a heading. If you want to structure the source text for easier reading please use lines that begin with a percent sign (\verb|%|) at such places. If a long title must be divided please use the code: \verb|\newline|. \begingroup\petit \parfillskip=0pt plus 1fil \def\textindent#1{\hangindent0.5\oldparindent\noindent\hbox to0.5\oldparindent{#1\hss}\ignorespaces}% \vfootnote{$^1$}{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.}\endgroup 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. \smallskip{\parindent=0pt\obeylines \verb|\maintitle{}| \verb|\subtitle{}|, it is optional \verb|\author{}| \verb|\address{}| \verb|\received{}| \verb|\summary{}| \verb|\keywords{}| \verb|\titlea{no.}{Text of first-order heading}| \verb|\titleb{no.}{Text of second-order heading}| \verb|\titlec{Text of third-order or bold run-in heading.}| \verb|\titled{Text of fourth-order or italic run-in heading.}| \verb|\begref{Your heading of References}{widest mark therein}|} \titled{In general:} If you need a heading without numbering, suppress the first argument (the number) by coding an empty pair of braces: \smallskip\noindent \verb|\title|$n$\verb|{}{Another title}|\qquad $n$ means {\tt a} or {\tt b} here. \smallskip The text elements of \verb|\titlea| and \verb|\titleb| have no end punctuation, but their preceding number as any other numbering of a section must be completed by a period. The text elements of \verb|\titlec|\enspace and \verb|\titled|\enspace require end punctuation. \titled{More than one author:} If there are more than one author, and the address of each is different, the following coding may be used to indicate by a small superscript number which author has which address (see also {\it jns.dem}): \begintt \author{Ivar Ekeland@1 and Roger Temam@2} \address{@1Princeton University, Princeton, NJ 08544, USA @2Universit\'e de Paris-Sud, Laboratoire d'Analyse Num\'erique, B\^atiment 425, F-91405 Orsay Cedex, France} \endtt Note that \verb|\maintitle| and \verb|\author| will create the page header (running head), but it may happen that you need to shorten your title for the page header, because only one line is allowed (our macro will produce an error message whereupon you must provide a shortened version of the title for the page header). In this case you should use the following coding directly after the coding of \verb|\maintitle| or \verb|\author|. \smallskip \noindent\verb|\mainrunning{Abbreviated contribution title}|\newline \verb|\authorrunning{Abbreviated author}| \bigskip\noindent The following bold run-in headings with italicized text are available as built-in environments: \begintt \proposition{no.}{Text} \corollary{no.}{Text} \lemma{no.}{Text} \theorem{no.}{Text} |medskip |bgroup|rm The following will generally appear as italic run-in heading:|egroup|smallskip \proof{additional Text} Text \qed|vfill|eject |bgroup|rm Further italic or bold run-in headings may also occur:|egroup|smallskip \definition{no.}{Text} \example{no.}{Text} \remark{Text} \exercise{no.}{Text} \problem{no.}{Text} \solution{no.}{Text} \note{no.}{Text} \question{no.}{Text}\endtt\removelastskip \titlec{4.1.1.\enspace Defining Your Own Environments.} You can define additional environments like these using the command \verb|\newenvironment| which has four parameters. The first is the name your environment should have (e.g. \verb|\conjecture|). Then the run-in heading is to be given (e.g. \verb|Conjecture|). After this follows the font family used for this heading (please use only \verb|\bf| for bold or \verb|\it| for italic). Finally comes the font family to use for the text of this new environment (e.g. \verb|\it| or \verb|\rm|). \noindent Sample definition: \smallskip \verb|\newenvironment\conjecture {Conjecture} {\bf} {\it}| \newenvironment\conjecture {Conjecture} {\bf} {\it} \smallskip \noindent Use of that definition: \smallskip \verb|\conjecture{no.}{Text}| e.g. \verb|\conjecture{17.}{It is clear that...}| \smallskip \noindent It's output: \conjecture{17.}{It is clear that\dots} \noindent {\it Sample Input:} \begintt \maintitle{Hamiltonian Mechanics} \author{Ivar Ekeland@{1} and Roger Temam@{2}} \address{@1Princeton University, Princeton NJ 08544, USA @2Universit\'e de Paris-Sud, Laboratoire d'Analyse Num\'erique, B\^atiment 425,\newline F-91405 Orsay Cedex, France} \received{June 5, 1989} \summary{A new variant of the multi-grid algorithms is presented. \dots\ to anisotropic problems is considered.} \keywords{multi-grid method -- coarse-grid correction -- singular perturbation -- robustness.} \titlea{1.}{Fixed-Period Problems: The Sublinear Case} With this chapter, the preliminaries are over, and we begin the search for periodic solutions \dots \titleb{1.1.}{Autonomous Systems} In this section we will consider the case when the Hamiltonian $H(x)$ \dots \titlec{The General Case: Nontriviality.} We assume that $H$ is $(A_\infty, B_\infty)$-subqua\-dra\-tic at infinity, for some constant \dots \titled{Notes and Comments.} The chronology is as follows. Palais and Smale introduced their celebrated condition (PS) to extend \dots \proposition{1.}{Assume $H'(0)=0$ and $ H(0)=0$. Set \dots} \proof{of proposition.} Condition (8) means that, for every $\delta'>\delta$, there is some $\varepsilon>0$ such that \dots \qed \example{1}{(External forcing). Consider the system \dots} \corollary{2.}{Assume $H$ is $C^2$ and $(a_\infty, b_\infty)$-subquadratic at infinity. Let \dots} \lemma{3.}{Assume that $H$ is $C^2$ on $\bbbr^{2n}\backslash\{0\}$ and that $H''(x)$ is non-degenerate \dots} \theorem{4 \rm(Ghoussoub-Preiss).}{Let $X$ be a Banach Space and $\Phi:X\to\bbbr$ \dots} \definition{5.}{We shall say that a $C^1$ function $\Phi:X\to\bbbr$ satisfies \dots} \endtt \bigskip \noindent {\it Sample Output\/} (follows on the next two pages together with examples of the above run-in headings) \maintitle{Hamiltonian Mechanics} \author{Ivar Ekeland@{1} and Roger Temam@{2}} \address{@1Princeton University, Princeton NJ 08544, USA @2Universit\'e de Paris-Sud, Laboratoire d'Analyse Num\'erique, B\^atiment 425,\newline F-91405 Orsay Cedex, France} \received{June 5, 1989} \summary{A new variant of the multi-grid algorithms is presented. \dots\ to anisotropic problems is considered.} \keywords{multi-grid method -- coarse-grid correction -- singular perturbation -- robustness.} \titlea{1.}{Fixed-Period Problems: The Sublinear Case} With this chapter, the preliminaries are over, and we begin the search for periodic solutions \dots \titleb{1.1.}{Autonomous Systems} In this section we will consider the case when the Hamiltonian $H(x)$ \dots \titlec{The General Case: Nontriviality.} We assume that $H$ is $(A_\infty, B_\infty)$-subqua\-dra\-tic at infinity, for some constant \dots \titled{Notes and Comments.} The chronology is as follows. Palais and Smale introduced their celebrated condition (PS) to extend \dots \proposition{1.}{Assume $H'(0)=0$ and $ H(0)=0$. Set \dots} \proof{of proposition.} Condition (8) means that, for every $\delta'>\delta$, there is some $\varepsilon>0$ such that \dots \qed \example{1}{(External forcing). Consider the system \dots} \corollary{2.}{Assume $H$ is $C^2$ and $(a_\infty, b_\infty)$-subquadratic at infinity. Let \dots} \lemma{3.}{Assume that $H$ is $C^2$ on $\bbbr^{2n}\backslash\{0\}$ and that $H''(x)$ is non-degenerate \dots} \theorem{4 \rm(Ghoussoub-Preiss).}{Let $X$ be a Banach Space and $\Phi:X\to\bbbr$ \dots} \definition{5.}{We shall say that a $C^1$ function $\Phi:X\to\bbbr$ satisfies \dots} \bigskip\hrule\bigskip \noindent{\it This completes the demonstration output. We go on with the instructions.} \vfill\eject \titleb {4.2.}{Text} The following should be used to improve the readability of the text:\smallskip \settabs \+xxxxxxxxxxxx &xxxxxxxxxxxxxxxxxxx &xxxxxxxxxxxxxx \cr \+\verb|\ts|&a thin space, e.g. between numbers or between \cr \+&units and numbers; furthermore, a line division will\cr \+¬ be made following this space\cr \smallskip \+{\tt -}&hyphen: one stroke, no space at either end\cr\smallskip \+{\tt --} & en-dash: two strokes ({\it without\/} a space at either end)\cr\smallskip \+&Please note: in \TeX{}, {\tt ---} gives an em-dash ``---'';\cr \+&Springer does not use this.\cr \+& Instead, please use the following:\cr \+{\tt\char'40 --\char'40} & en-dash: two strokes ({\it with\/} a space at either end)\cr\smallskip \+{\tt \$-\$}& minus: in the text {\it only}\cr \smallskip \bigskip\noindent \+{\it Input} & \verb|21\ts $^{\circ}$C etc.,|\cr \+ & \verb|Dr h.\ts c.\ts Rockefellar-Smith \dots|\cr \+ & \verb|20,000\ts km and Prof.\ts Dr Mallory \dots|\cr \+ & \verb|1950--1985 \dots|\cr \+ & \verb|this -- written on a computer -- is now printed|\cr \+ & \verb|$-30$\ts K \dots|\cr \bigskip \+{\it Output} & 21\ts $^{\circ}$C etc., Dr h.\ts c.\ts Rockefellar-Smith \dots\cr \+ & 20,000\ts km and Prof.\ts Dr Mallory \dots\cr \+ & 1950--1985 \dots\cr \+ & this -- written on a computer -- is now printed\cr \+ & $-30$\ts K \dots\cr \titleb{4.3.}{Special Typefaces} Normal type (roman) need not be marked. Preferably {\it italic\/} (not {\sl slanted}) or, if necessary, {\bf boldface} should be used to emphasize words and expressions. \smallskip\noindent \settabs \+xxxxxxxxxxxxxxxxxxxxxxxxxx &xxxxxxxxxxxxxxxxxxx &xxxxxxxxxxxxxx \cr \+\verb|{\it Text}|&{\it Text}\ \ \ (preferable)\cr \smallskip \+\verb|{\bf Text}|&{\bf Text}\cr\smallskip \+\verb|\begpet ...text...\endpet|& \vtop{\hbox to.6\hsize{\hsize=.6\hsize\vtop{\noindent \petit Paragraph in small print (petit) for passages in the text that the reader may skip on first reading or for exercises or sections of similar importance.}}}\cr \medskip \+\verb|\vec{Symbol}|& Vectors may only appear in math mode\cr \+&\verb|$\vec{A\times B\cdot C}$| yields $\vec{A\times B\cdot C}$\cr \+&or\quad \verb|$\vec{A^a B\hat D\tilde S}$|\quad yields\cr \+&$\vec{A^a B\hat D\tilde S}$ \cr \titleb {4.4.}{Footnotes} \line{\verb|\fonote{...text...}|\hfil Footnote within text ({\it no\/} blank before \verb|\fonote|)} \smallskip\smallskip\noindent {\it Input}\smallskip\noindent Text with a footnote\verb|\fonote{The footnote is automatically numbered.}| and the text continues. You will find the footnote below. \smallskip\smallskip\noindent {\it Output} \smallskip\noindent Text with a footnote\fonote{The footnote is automatically numbered.} and the text continues. You will find the footnote below. \smallskip \noindent {\it Remark\/}: Please avoid using footnotes in headings. \smallskip \smallskip \noindent \titleb{4.5.}{Lists} {{\it Input}} \begintt This is ordinary text extending over several lines and interrupted by a list. The text continues ... \medskip |bgroup|rm Do not forget to type |egroup\medskip \item {1.} |bgroup|rm Start of list and first item|egroup \item {2.} |bgroup|rm Second item in list|egroup \itemitem {a)} |bgroup|rm Start of subdivision and its first item|egroup \itemitem {b)} |bgroup|rm Second item in subdivision|egroup \item {n.} |bgroup|rm Item |it n |rm in list|egroup \medskip |bgroup|rm Do not forget to type |egroup\medskip The text continues... \endtt \noindent {\it Output}\medskip \smallskip\noindent This is ordinary text extending over several lines and interrupted by a list. The text continues \dots \medskip \item{1.}Start of list and first item \item{2.}Second item in list \itemitem{a)}Start of subdivision and its first item \itemitem{b)}Second item in subdivision \item{{\it n.}}Item {\it n\/} in list \medskip The text continues \dots \titleb{4.6.}{ Figures} Figure legends should be inserted at the end of (not in) the paragraph in which the figure is first mentioned. They should be numbered (using arabic numerals) sequentially throughout your contribution, as shown below. Figures should {\it never\/} be surrounded by text. {\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\ts mm and not more than 2.5\ts 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. \smallskip \settabs \+xxxxxxxxxxxxxxxxxxxxxxxxxx &xxxxxxxxxxxxxxxxxxxx \cr \+\verb|\begfig x cm|&Begin space of {\it x\/} cm (use only cm)\cr \+\verb|\figure{no.}{...text...}|&Figure legend\ \ (no capitalization, see Sect. 2.5)\cr \+\verb|\endfig|&End space\cr \bigskip\noindent {\it Sample Input} \smallskip \+\verbb|\begfig 1.5 cm|&(This is the space required for your figure)\cr \+\verb|\figure{1}{This is a figure legend}| \cr \+\verb|\endfig |\cr \bigskip\noindent {\it Output} \begfig 1.5 cm \figure{1}{This is a figure legend} \endfig The text continues \dots \vfill\eject \titlec {4.6.1.\enspace Two Figures Next to Each Other.} If you have two narrow figures that you want to insert side by side in one ``paragraph", and if the total width is sufficient (type area 12.2\ts cm), then, giving the height of the larger figure, please code: \settabs \+xxxxxxxxxxxxxxxxxxxxxxxx &xxxxxxxxxxxxxxxxxxxx \cr \bigskip\medskip\noindent {\it Sample Input} \smallskip\smallskip\smallskip \+\verbb|\begdoublefig 6.5 cm|&(This is the space required for the larger figure)\cr \+\verbb|\figure{1}{...text...} | &First figure legend (no capitalization, see Sect. 2.5)\cr \+\verbb|\figure{2}{...text...} |&Second figure legend\cr \+\verb|\enddoublefig|\cr \medskip\bigskip\medskip\noindent \settabs \+xxxxxxxxxxxxxxxxxxxxxxxxxx &xxxxxxxxxxxxxxxxxxxx \cr \noindent {\it Sample Output} \begdoublefig 6.5 cm \figure{1}{This is the first figure legend. The width of this legend is the same as for the second figure} \figure{2}{This is the legend of the second figure. At the present stage of macro development it is not possible for two figures side by side to have legends occupying different line widths} \enddoublefig The text continues \dots \vfill\eject \titlec {4.6.2.\enspace Modified Legend Arrangements.} If the amount of text in the legends of two figures (to be placed side by side) is quite different, please use the following coding: \bigskip\noindent {\it Sample Input} \bigskip \+\verbb|\begfig 5.3 cm |\qquad(This is the space required for the larger figure)\cr \+\verb|\figure{1}{This is the first short figure legend}|\cr \+\verb|\figure{2}{This is the extremely long legend of the second...}|\cr \+\verb|\endfig|\cr \medskip\bigskip\noindent {\it Sample Output} \begfig 5.3 cm \figure{1}{This is the first short figure legend} \figure{2}{This is the extremely long legend of the second figure and should therefore be typeset using the full width of the type area. For typographical and aesthetic reasons it would be unacceptable if these legends were set next to one another in two columns, with a legend of 2 lines for the first figure and a legend of 16 lines for the second. Therefore we suggest that the legends for the two figures should be placed one below the other. It is not necessary to place the figure numbers below or beside the two figures because it should be clear that the left one is the first figure and the right one the second } \endfig The text continues \dots \vfill\eject \settabs \+xxxxxxxxxxxxxxxxxxxxxxxxx &xxxxxxxxxxxxxxxxxxx &xxxxxxxxxxxxxx \cr \titleb {4.7.}{Tables} Table captions should be treated in the same way as figure legends, except that the table captions appear above the tables. The tables should also be numbered (using arabic numerals) sequentially, throughout your contribution. \titlec{4.7.1.\enspace Tables Coded with \TeX.} The comand \smallskip\noindent\verb|\tabcap{no}{text of the table caption}| \smallskip\noindent will produce a table caption. Thereafter you should code your table with \TeX{}. Leave 8 mm (not more) additional space before the table caption and at the end of your table (\verb|\vskip 8 true mm|). Please make sure that all the material of your table will be set in small print by using the command \verb|\petit| inside a box or a group. \medskip\noindent{\it Sample Input} \begintt \vskip8 true mm \vbox{\tabcap{1}{Observational results from NGC 4827} \vbox{\petit\hrule\smallskip \halign{\enspace#\hfil\enspace&&#\hfil\enspace\cr &&\multispan3{RA (1950)}\hfil&\ &\multispan3{Dec (1950)}\hfil & $S$ & Pol & \% & $\log P$\cr \noalign{\vskip-2mm} &&\multispan3\hrulefill\quad&&\multispan3\hrulefill\quad&&\cr \noalign{\vskip-0.5mm} & &(h) &(m) & (s) & & (\degr) & (\arcmin) & (\arcsec) & (mJy) & (mJy) & & (W Hz$^{-1}$)\cr \noalign{\smallskip} \noalign{\hrule} \noalign{\smallskip} Core & (5 GHz) & 12 & 54 & 18.0 & & 27 & 26 & 56.2 & 8 & & & 21.64 \cr Total&(327 MHz)& & & & & & & & 210 & & & 23.13 \cr &(1.4 GHz)& & & & & & & & 57 & 1.3 & 2 & 22.49 \cr & (5 GHz) & & & & & & & & 26 & 0.73 & 3 & 22.15 \cr} \smallskip\hrule}} \vskip 8 true mm \endtt \vfill\eject\noindent {\it Sample Output}\vskip8 true mm \vbox{\tabcap{1}{Observational results from NGC 4827} \vbox{\petit\hrule\smallskip \halign{\enspace#\hfil\enspace&&#\hfil\enspace\cr &&\multispan3{RA (1950)}\hfil&\ &\multispan3{Dec (1950)}\hfil & $S$ & Pol & \% & $\log P$\cr \noalign{\vskip-2mm} &&\multispan3\hrulefill\quad&&\multispan3\hrulefill\quad&&\cr \noalign{\vskip-0.5mm} & &(h) &(m) & (s) & & (\degr) & (\arcmin) & (\arcsec) & (mJy) & (mJy) & & (W Hz$^{-1}$)\cr \noalign{\smallskip} \noalign{\hrule} \noalign{\smallskip} Core & (5 GHz) & 12 & 54 & 18.0 & & 27 & 26 & 56.2 & 8 & & & 21.64 \cr Total&(327 MHz)& & & & & & & & 210 & & & 23.13 \cr &(1.4 GHz)& & & & & & & & 57 & 1.3 & 2 & 22.49 \cr & (5 GHz) & & & & & & & & 26 & 0.73 & 3 & 22.15 \cr} \smallskip\hrule}} \vskip 8 true mm Here your text continues \dots \titlec {4.7.2.\enspace Tables Not Coded with \TeX.} If you do not wish to code your table using \TeX{} but prefer to have it reproduced separately, proceed as for figures and use the following coding: \smallskip \settabs \+xxxxxxxxxxxxxxxxxxxxxxxxxx &xxxxxxxxxxxxxxxxxxxx \cr \+\verb|\begtab x cm|&{Begin table of {\it x\/} cm (please use cm only)}\cr \+\verb|\tabcap{no}{text}| &Table caption (no capitalization, see Sect. 2.5) \cr \+\verb|\endtab|&End table\cr \noindent{\it Input}\smallskip \+\verbb|\begtab 2.5 cm|&(This is the space required for your table)\cr \+\verb|\tabcap{2}{This is another table caption}|\cr \+\verb|\endtab|\cr \smallskip\smallskip\smallskip \noindent {\it Output}\vskip1 true cm \vbox{\tabcap{2}{This is another table caption}\vbox to 2.5true cm{\hrule width2truecm\vfil\vbox{\noindent The distance between these two lines indicates the height of your table. In this case 2.5 true cm}% \vfil\hrule width 2truecm}} \titleb {4.8.}{Signs and Characters} \titlec{4.8.1.\enspace Special Signs.} You may need to use special signs. The available ones are listed in {\it The \TeX{}book}, by Donald E. Knuth (1986), Addison-Wesley Publishing Company, pp. 434\ts ff. We have created further symbols for math mode (enclosed in \$): \medskip {\tabskip=0pt\openup1\jot \centerline{\hbox{\vbox{\halign{{$\backslash$\tt #}\quad\hfil &yields $#$\hfil\qquad\qquad\qquad &\quad{$\backslash$\tt #}\quad\hfil &yields $#$\hfil\cr grole&\grole&getsto&\getsto\cr lid&\lid&gid&\gid\cr}}}}} \titlec{4.8.2.\enspace Gothic (Fraktur).} If gothic letters are {\it necessary}, please use those of the relevant \AmSTeX{} (American Mathematical Society) alphabet. The \AmSTeX{} gothic alphabet is available from the American Mathematical Society. In Plain\TeX{} 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 imaginary parts of a complex number within math mode you should use instead: \verb|$\rm Re$| (which yields Re) or \verb|$\rm Im$| (which yields Im). \titlec{4.8.3.\enspace Script.} For script capitals use the coding \newline {\tt $\$\backslash$cal AB$\$$,}\ \ which yields\ \ $\cal AB$\ \ \ \ (see p. 164 of {\it The \TeX{}book\/}). \titlec{4.8.4.\enspace Special Roman.} If you need other or more than the symbols below please use throughout the blackboard bold characters of \AmSTeX. The following characters are built up by the use of combined symbols and signs: \smallskip \smallskip % \tabskip=0pt \halign to\hsize{{$\backslash$\tt #}\ \hfil &#\hfil&\ yields \hfil$#$\hfil\tabskip=0pt plus1fil &\tabskip=0pt{$\backslash$\tt #}\ \hfil &#\hfil&\ yields \hfil$#$\hfil\cr bbbc&(complex numbers)&\bbbc& bbbf&(blackboard bold F)&\bbbf\cr bbbh&(blackboard bold H)&\bbbh& bbbk&(blackboard bold K)&\bbbk\cr bbbm&(blackboard bold M)&\bbbm& bbbn&(natural numbers N)&\bbbn\cr bbbp&(blackboard bold P)&\bbbp& bbbq&(rational numbers)&\bbbq\cr bbbr&(real numbers)&\bbbr& bbbs&(blackboard bold S)&\bbbs\cr bbbt&(blackboard bold T)&\bbbt& bbbz&(whole numbers)&\bbbz\cr bbbone&(symbol one)&\bbbone& bbbe&(e symbol)&\bbbe\cr} \bigskip \noindent \line{\rlap{e.g.}\hfil$\displaystyle\bbbc^{\bbbc^\bbbc}\otimes \bbbf_{\bbbf_\bbbf} \otimes \bbbh_{\bbbh_\bbbh} \otimes \bbbk_{\bbbk_\bbbk} \otimes \bbbm^{\bbbm^\bbbm} \otimes \bbbn_{\bbbn_\bbbn} \otimes \bbbp^{\bbbp^\bbbp}$\hfil} \vskip0.5\baselineskip \centerline{$\displaystyle \otimes \bbbq_{\bbbq_\bbbq} \otimes \bbbr^{\bbbr^\bbbr} \otimes \bbbs^{\bbbs_\bbbs} \otimes \bbbt^{\bbbt^\bbbt} \otimes \bbbz^{\bbbz_\bbbz} \otimes \bbbone^{\bbbone_\bbbone} \otimes \bbbe^{\bbbe_\bbbe}$} \titlec{4.8.5.\enspace Sans Serif.} Using our macros you will also be able to choose the font family of this style; use the command \verb|\sans| for \ \ {\sans sans serif}\ \ (like \verb|\it| for {\it italic style}). \titlec{4.8.6.\enspace Invented Characters.} If you need to invent a special character not available in this list, please start your coding as shown below. Be sure your coding works without math mode; the characters invented should be numbered using lower-case roman numerals. \smallskip \smallskip \def\speciali{\hbox{$ = \!\!\! > $ }} {\tt \+$\backslash$def$\backslash$speciali$\{$ $\backslash$hbox$\{ \$ $= $\backslash$!$\backslash$!$\backslash$! $> \$ $ $\} \}$\ \ \ \ {\rm yields} \ \ \ \ \speciali \cr \+$\backslash$def$\backslash$specialii$\{$ Your definition of special ii $\}$ \cr \+$\backslash$def$\backslash$specialiii$\{$ Your definition of special iii $\}$ \cr \+$\backslash$def$\backslash$specialiv$\{$ Your definition of special iv $\}$ \ \ \ \ {\rm etc.} \cr } \vfill\eject \titlea {5.}{How to Code References} There are three reference systems available; only one, of course, should be used for your contribution. With each system (by author--year, by number only or by letter--number) a reference list, preferably headed ``References" and containing all citations in the text, should be included at the end of the your contribution. \smallskip \settabs \+xxxxxxxxxxxxxxxxxxxx&xxxxxxxxxxxxxxxxxxxx \cr \+\verb|\begref{name}{mark}|&Beginning of reference list: the heading;\cr \+&the argument {\tt name} stands for the chosen heading:\cr \+&References (preferable), Literature or Bibliography;\cr \+&the argument {\tt mark} stands for the largest number or\cr \+&widest mark of your list, it is used for references\cr \+&by number only and by letter--number by the\cr \+¯os \verb|\refno| and \verb|\refmark|. In the\cr \+&author--year system it is not used but you have to\cr \+&code at least an empty pair of braces yet.\cr \medskip\noindent Use only one of the following three codings throughout your reference list: \smallskip \+\verb|\ref text|&The coding in author--year system\cr \+\verb|\refno{no.} text|&The coding in number only system\cr \+\verb|\refmark{mark} text|&The coding in letter--number system\cr \medskip \+\verb|\endref|&End of reference list\cr \bigskip For detailed examples please see below, and also refer to the demo-file ({\it jns.dem}). {\it Very important\/}: For each entry in the reference list please follow {\it exactly\/} the order shown in the examples. \titleb {5.1.}{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 \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. \medskip 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). \vfill\eject \settabs \+xxxxxxxxxxxxxxxxxxx&xxxxxxxxxxxxxxxxxxxx \cr \+\verb|\begref{name}{}|&Do not forget to code at least an empty pair of braces\cr \+&otherwise the first entry is not correctly indented\cr \+\verb|\ref text|&First entry in reference list\cr \+\verb|\ref text|&Second entry in reference list\cr \+\quad$\vdots$\cr \+\verb|\ref text|&{\it n\/}-th entry in reference list\cr \+\verb|\endref|&End of reference list\cr \titleb {5.2.}{References by Number Only or by Letter--Number} The author--year system is probably of more help to the reader. However, refer\-en{}ces may instead be cited in the text by numbers in square brackets, e.g. [1], [2] etc. used sequentially throughout your contribution 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. The coding is as follows: \medskip \settabs \+xxxxxxxxxxxxxxxxxxxx &xxxxxxxxxxxxxxxx &xxxxxxxxxxxxxx \cr \+\verb|\begref{name}{mark}|\cr \+\verb|\refno{no.} text|\cr \+\verb|\refno{no.} text|\cr \+\quad$\vdots$\cr \+\verb|\refno{no.} text|\cr \+\verb|\endref|\cr \medskip\noindent Instead of \verb|\refno| in the number--only system use the coding \verb|\refmark| for the letter--number system (e.g.: \verb|\refmark{[MB1]} this is the text of your reference|, then you should have coded the start of your references with \verb|\begref{References}{[MB1]}|, supposed ``[MB1]'' is your widest mark). \bigskip\noindent {\it Important\/}: You must ensure that the references cited in the text (name--year, number or letter--number) correspond exactly with the entries in the reference list. \titleb{5.3.}{Examples} The following examples show the three ways of organizing a reference list. Naturally, you will choose only one for your contribution. \bigskip\noindent {\it Examples of Typical Text Containing Reference Citations} \medskip\noindent This is implicit in recent work of Arnold (1968) and Lerch et al. (1983) \dots\newline Consider as an example the following theorem [1].\newline We refer now to the hypothesis as given in [S1]. \vfill\eject \noindent {\it Input of Coding for Author--Year Reference List} \begintt \begref{References}{here is no mark at all} \ref Arnold, V.I. (1968): Singularities of smooth mappings. Usp. Mat. Nauk {\bf 23}, 3--44 (Russian). [English transl.: Russ. Math. Surv. {\bf 23} (1968) 1--43] \ref Dirac, P.A.M. (1950): On generalized Hamiltonian dynamics. Can. J. Math. {\bf 2}(2), 129--148 \ref Gr\"otschel, M., Lov\'asz, L., Schrijver, A. (1988): Geometric algorithms and combinatorial optimization. (Algorithms and Combinatorics, vol.2.) Springer, Berlin Heidelberg \ref Lerch, F.J., Klosko, S.M., Patel, G.B. (1983): A refined gravity model from LAGEOS (GEM-L2). NASA, Tech. Memo. TM 84986 \ref Rham, G. de (1931): Sur l'analysis situs de vari\'et\'es \`a $n$ dimensions. J. Math. Pures Appl. {\bf 10}, 115--200 \endref \endtt \bigskip\noindent {\it Output for Author--Year Reference List} \begref{References}{here is no mark at all} \ref Arnold, V.I. (1968): Singularities of smooth mappings. Usp. Mat. Nauk {\bf 23}, 3--44 (Russian). [English transl.: Russ. Math. Surv. {\bf 23} (1968) 1--43] \ref Dirac, P.A.M. (1950): On generalized Hamiltonian dynamics. Can. J. Math. {\bf 2}(2), 129--148 \ref Gr\"otschel, M., Lov\'asz, L., Schrijver, A. (1988): Geometric algorithms and combinatorial optimization. (Algorithms and Combinatorics, vol.2.) Springer, Berlin Heidelberg \ref Lerch, F.J., Klosko, S.M., Patel, G.B. (1983): A refined gravity model from LAGEOS (GEM-L2). NASA, Tech. Memo. TM 84986 \ref Rham, G. de (1931): Sur l'analysis situs de vari\'et\'es \`a $n$ dimensions. J. Math. Pures Appl. {\bf 10}, 115--200 \endref \vfill\eject\noindent {\it Input of Coding for Number-Only Reference List} \begintt \begref{References}{5.} \refno {1.} Dieck, T. tom: Bordism of $G$-manifolds and integrality theorems. Topology {\bf 9} (1970) 345--358 \refno{2.} Gantmacher, F.R., Krein, M.G.: Oscillation matrices and kernels and small vibrations of mechanical systems. State Press for Technical Literature, Moscow Leningrad, 1950 (Russian). [German transl.: Oszillationsmatrizen, Oszillations\-kerne und kleine Schwingungen mechanischer Systeme. Akademie-Verlag, Berlin, 1960] \refno{3.} Hoare, C.A.R.: Procedures and parameters: An axiomatic approach. In: Engeler, E. (ed.) Symposium on Semantics of Algorithmic Languages. (Lecture Notes in Mathematics, vol.188.) Springer, New York Berlin Heidelberg, 1971, pp.102--116 \refno{4.} Peitgen, H.-O., Walther, H.-O. (eds.): Functional differential equations and approximation of fixed points. (Lecture Notes in Mathematics, vol.730.) Springer, New York Berlin Heidelberg, 1979 \refno {5.} Redwood, R.: Personal communication, 1986 \endref \endtt \noindent {\it Output for Number-Only Reference List} \begref{References}{5.} \refno {1.} Dieck, T. tom: Bordism of $G$-manifolds and integrality theorems. Topology {\bf 9} (1970) 345--358 \refno{2.} Gantmacher, F.R., Krein, M.G.: Oscillation matrices and kernels and small vibrations of mechanical systems. State Press for Technical Literature, Moscow Leningrad, 1950 (Russian). [German transl.: Oszillationsmatrizen, Oszillations\-kerne und kleine Schwingungen mechanischer Systeme. Akademie-Verlag, Berlin, 1960] \refno{3.} Hoare, C.A.R.: Procedures and parameters: An axiomatic approach. In: Engeler, E. (ed.) Symposium on Semantics of Algorithmic Languages. (Lecture Notes in Mathematics, vol.188.) Springer, New York Berlin Heidelberg, 1971, pp.102--116 \refno{4.} Peitgen, H.-O., Walther, H.-O. (eds.): Functional differential equations and approximation of fixed points. (Lecture Notes in Mathematics, vol.730.) Springer, New York Berlin Heidelberg, 1979 \refno {5.} Redwood, R.: Personal communication, 1986 \endref \vfill\eject\noindent {\it Input of Coding for Letter--Number List} \begintt \begref{References}{[GP1]} \refmark{[B1]} Brooks, M.: Automatic generation of test data for recursive programs having simple errors. PhD thesis, Stanford University, 1980 \refmark{[GP1]} Griswold, R.E., Poage, J.F., Polonsky, I.P.: The SNOBOL4 programming language, 2nd edn. Prentice-Hall, Englewood Cliffs, NJ, 1971 \refmark{[R1]} Rapp, R.H.: The development of the January 1983 $1^\circ\times1^\circ$ mean free-air anamoly data tape. Dept. of Geod. Sci. and Surv., Ohio State University, Columbus, OH. Internal report, 1983 \refmark{[T1]} Thompson, d'A.: On growth and form. (Abriged edition: J.T. Bonner, ed.) Cambridge University Press, 1961 \refmark{[T2]} Thompson, d'A.: Personal communication, 1963 \endref \endtt \noindent {\it Output of Coding for Letter--Number List} \begref{References}{[GP1]} \refmark{[B1]} Brooks, M.: Automatic generation of test data for recursive programs having simple errors. PhD thesis, Stanford University, 1980 \refmark{[GP1]} Griswold, R.E., Poage, J.F., Polonsky, I.P.: The SNOBOL4 programming language, 2nd edn. Prentice-Hall, Englewood Cliffs, NJ, 1971 \refmark{[R1]} Rapp, R.H.: The development of the January 1983 $1^\circ\times1^\circ$ mean free-air anamoly data tape. Dept. of Geod. Sci. and Surv., Ohio State University, Columbus, OH. Internal report, 1983 \refmark{[T1]} Thompson, d'A.: On growth and form. (Abriged edition: J.T. Bonner, ed.) Cambridge University Press, 1961 \refmark{[T2]} Thompson, d'A.: Personal communication, 1963 \endref \bigskip\bigskip\bigskip\bigskip \centerline{\vbox{\hrule\hbox{\vrule\vbox{\kern5pt \hbox{\enspace \bf To end your text you must use the \TeX{} command {\tt\bs byebye}\enspace}\kern5pt}\vrule}\hrule}} \input jns.dem \bye