diff options
Diffstat (limited to 'macros/plain/contrib/jns')
-rw-r--r-- | macros/plain/contrib/jns/index | 59 | ||||
-rw-r--r-- | macros/plain/contrib/jns/jns.amm | 540 | ||||
-rw-r--r-- | macros/plain/contrib/jns/jns.cmm | 556 | ||||
-rw-r--r-- | macros/plain/contrib/jns/jns.dem | 331 | ||||
-rw-r--r-- | macros/plain/contrib/jns/jns.doc | 1188 | ||||
-rw-r--r-- | macros/plain/contrib/jns/jns.sty | 801 | ||||
-rw-r--r-- | macros/plain/contrib/jns/jnsl.dem | 354 | ||||
-rw-r--r-- | macros/plain/contrib/jns/jnsl.doc | 1162 | ||||
-rw-r--r-- | macros/plain/contrib/jns/jnsldoc.sty | 39 |
9 files changed, 5030 insertions, 0 deletions
diff --git a/macros/plain/contrib/jns/index b/macros/plain/contrib/jns/index new file mode 100644 index 0000000000..fc58a7d2ba --- /dev/null +++ b/macros/plain/contrib/jns/index @@ -0,0 +1,59 @@ +# ....Plain TeX.... +# +# jns.doc general instructions, this is the TeX source +# for the documentation. Please TeX it if you +# have the paper version not at hand +# jns.dem an example showing how to code the front matter +# jns.amm the macro package with am-fonts (the old \TeX{} fonts) +# jns.cmm the macro package with cm-fonts (newer and preferable) +# (these are both macro files and should not be changed) +# +# Include the macros and the cm-fonts by inserting the command +# \input jns.cmm +# at the beginning of your text file +# (also called input or source file) +# +# If you do not have the cm-fonts which are preferable, +# please insert at the beginning of your text file +# \input jns.amm +# +# +# If you use PC \TeX +# +# In PC TeX default memory capacity is not sufficient to accommodate our +# fonts. To cope with this problem, invoke TeX with the following +# command: +# tex file.tex /f=26000 /m=65000 +# +# +# +# +# ....LaTeX.... +# +# jnsl.dem an example showing how to code +# jnsl.doc general instructions +# jnsldoc.sty documentstyle +# +# +# +# +# ....AmSTeX.... +# +# jnsa.doc general instructions, this is the AmSTeX source +# for the documentation. Please TeX it if you +# have the paper version not at hand +# jnsa.dem an example showing how to code +# jnsams.cmm the macro package +# +# Include the macros and the cm-fonts by inserting the command +# \input jnsams.cmm +# at the beginning of your text file +# (also called input or source file) +# +# If you use PC \TeX +# +# In PC TeX default memory capacity is not sufficient to accommodate our +# fonts. To cope with this problem, invoke TeX with the following +# command: +# tex file.tex /f=26000 /m=65000 +# diff --git a/macros/plain/contrib/jns/jns.amm b/macros/plain/contrib/jns/jns.amm new file mode 100644 index 0000000000..09af01d2de --- /dev/null +++ b/macros/plain/contrib/jns/jns.amm @@ -0,0 +1,540 @@ +% This is JNS.AMM the plain TeX macro package +% (AM version) from Springer-Verlag +% for the Journal of Nonlinear Science +% version of 16 July 1990 +\font \tbfontt = ambx10 scaled\magstep1 +\font \tafontt = ambx10 scaled\magstep2 +\font \tbfontss = ambx5 scaled\magstep1 +\font \tafontss = ambx5 scaled\magstep2 +\font \sixbf = ambx6 +\font \tbfonts = ambx7 scaled\magstep1 +\font \tafonts = ambx7 scaled\magstep2 +\font \ninebf = ambx9 +\font \tasys = amex10 scaled\magstep1 +\font \tasyt = amex10 scaled\magstep2 +\font \sixi = ammi6 +\font \ninei = ammi9 +\font \tams = ambi10 +\font \tbmss = ambi10 scaled 600 +\font \tamss = ambi10 scaled 700 +\font \tbms = ambi10 scaled 833 +\font \tbmt = ambi10 scaled\magstep1 +\font \tamt = ambi10 scaled\magstep2 +\font \smallescriptscriptfont = amr5 +\font \smalletextfont = amr5 at 10pt +\font \smallescriptfont = amr5 at 7pt +\font \sixrm = amr6 +\font \ninerm = amr9 +\font \ninesl = amsl9 +\font \tensans = amss10 +\font \fivesans = amss10 at 5pt +\font \sixsans = amss10 at 6pt +\font \sevensans = amss10 at 7pt +\font \ninesans = amss10 at 9pt +\font \tbst = amsy10 scaled\magstep1 +\font \tast = amsy10 scaled\magstep2 +\font \tbsss = amsy5 scaled\magstep1 +\font \tasss = amsy5 scaled\magstep2 +\font \sixsy = amsy6 +\font \tbss = amsy7 scaled\magstep1 +\font \tass = amsy7 scaled\magstep2 +\font \ninesy = amsy9 +\font \markfont = amti10 at 11pt +\font \nineit = amti9 +\font \ninett = amtt9 +%----------------------------------------------------------------------- +\magnification=\magstep0 +\hsize=12.2truecm +\vsize=19.4truecm +\hfuzz=2pt +\tolerance=500 +\abovedisplayskip=3 mm plus6pt minus 4pt +\belowdisplayskip=3 mm plus6pt minus 4pt +\abovedisplayshortskip=0mm plus6pt minus 2pt +\belowdisplayshortskip=2 mm plus4pt minus 4pt +\predisplaypenalty=0 +\clubpenalty=10000 +\widowpenalty=10000 +\frenchspacing +\newdimen\oldparindent\oldparindent=1.5em +\parindent=1.5em +%----------------------------------------------------------------------- +\def\getsto{\mathrel{\mathchoice {\vcenter{\offinterlineskip +\halign{\hfil +$\displaystyle##$\hfil\cr\gets\cr\to\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr\gets +\cr\to\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr\gets +\cr\to\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +\gets\cr\to\cr}}}}} +\def\lid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil +$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr +\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr +\noalign{\vskip1pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +<\cr +\noalign{\vskip0.9pt}=\cr}}}}} +\def\gid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil +$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr +\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr +\noalign{\vskip1pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +>\cr +\noalign{\vskip0.9pt}=\cr}}}}} +\def\grole{\mathrel{\mathchoice {\vcenter{\offinterlineskip +\halign{\hfil +$\displaystyle##$\hfil\cr>\cr\noalign{\vskip-1pt}<\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr +>\cr\noalign{\vskip-1pt}<\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr +>\cr\noalign{\vskip-0.8pt}<\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +>\cr\noalign{\vskip-0.3pt}<\cr}}}}} +\def\bbbr{{\rm I\!R}} %reelle Zahlen +\def\bbbm{{\rm I\!M}} +\def\bbbn{{\rm I\!N}} %natuerliche Zahlen +\def\bbbf{{\rm I\!F}} +\def\bbbh{{\rm I\!H}} +\def\bbbk{{\rm I\!K}} +\def\bbbp{{\rm I\!P}} +\def\bbbone{{\mathchoice {\rm 1\mskip-4mu l} {\rm 1\mskip-4mu l} +{\rm 1\mskip-4.5mu l} {\rm 1\mskip-5mu l}}} +\def\bbbc{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}}} +\def\bbbe{{\mathchoice {\setbox0=\hbox{\smalletextfont e}\hbox{\raise +0.1\ht0\hbox to0pt{\kern0.4\wd0\vrule width0.3pt height0.7\ht0\hss}\box0}} +{\setbox0=\hbox{\smalletextfont e}\hbox{\raise +0.1\ht0\hbox to0pt{\kern0.4\wd0\vrule width0.3pt height0.7\ht0\hss}\box0}} +{\setbox0=\hbox{\smallescriptfont e}\hbox{\raise +0.1\ht0\hbox to0pt{\kern0.5\wd0\vrule width0.2pt height0.7\ht0\hss}\box0}} +{\setbox0=\hbox{\smallescriptscriptfont e}\hbox{\raise +0.1\ht0\hbox to0pt{\kern0.4\wd0\vrule width0.2pt height0.7\ht0\hss}\box0}}}} +\def\bbbq{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle\rm Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle\rm Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}}} +\def\bbbt{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm +T$}\hbox{\hbox to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle\rm T$}\hbox{\hbox +to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle\rm T$}\hbox{\hbox +to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm T$}\hbox{\hbox +to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}}} +\def\bbbs{{\mathchoice +{\setbox0=\hbox{$\displaystyle \rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox +to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle \rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox +to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle \rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox +to0pt{\kern0.5\wd0\vrule height0.45\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.4\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox +to0pt{\kern0.55\wd0\vrule height0.45\ht0\hss}\box0}}}} +\def\bbbz{{\mathchoice {\hbox{$\sans\textstyle Z\kern-0.4em Z$}} +{\hbox{$\sans\textstyle Z\kern-0.4em Z$}} +{\hbox{$\sans\scriptstyle Z\kern-0.3em Z$}} +{\hbox{$\sans\scriptscriptstyle Z\kern-0.2em Z$}}}} +%-------------------------------------------------------------------------- +% petit-fonts +\skewchar\ninei='177 \skewchar\sixi='177 +\skewchar\ninesy='60 \skewchar\sixsy='60 +\hyphenchar\ninett=-1 +\def\newline{\hfil\break}% +%-------------------------------------------------------------------------- +\catcode`@=11 +\def\folio{\ifnum\pageno<\z@ +\uppercase\expandafter{\romannumeral-\pageno}% +\else\number\pageno \fi} +\catcode`@=12 % at signs are no longer letters +%------------------------------------------------------- +% Definition der versal griechischen Buchstaben +%=============================================================================== + \mathchardef\Gamma="0100 + \mathchardef\Delta="0101 + \mathchardef\Theta="0102 + \mathchardef\Lambda="0103 + \mathchardef\Xi="0104 + \mathchardef\Pi="0105 + \mathchardef\Sigma="0106 + \mathchardef\Upsilon="0107 + \mathchardef\Phi="0108 + \mathchardef\Psi="0109 + \mathchardef\Omega="010A +%------------------------------------------------------------------------------- +\def\squareforqed{\hbox{\rlap{$\sqcap$}$\sqcup$}} +\def\qed{\ifmmode\squareforqed\else{\unskip\nobreak\hfil +\penalty50\hskip1em\null\nobreak\hfil\squareforqed +\parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi} +%--------------------------------------------------------------------------- +\newfam\sansfam +\textfont\sansfam=\tensans\scriptfont\sansfam=\sevensans +\scriptscriptfont\sansfam=\fivesans +\def\sans{\fam\sansfam\tensans} +%--------------------------------------------------------------------------- +\def\stackfigbox{\if +Y\FIG\global\setbox\figbox=\vbox{\unvbox\figbox\box1}% +\else\global\setbox\figbox=\vbox{\box1}\global\let\FIG=Y\fi} +% +\def\placefigure{\dimen0=\ht1\advance\dimen0by\dp1 +\advance\dimen0by5\baselineskip +\advance\dimen0by0.4true cm +\ifdim\dimen0>\vsize\pageinsert\box1\vfill\endinsert +\else%keine seitenhohe Abbildung +\if Y\FIG\stackfigbox\else +\dimen0=\pagetotal\ifdim\dimen0<\pagegoal%aktuelle Seite ist noch nicht voll +\advance\dimen0by\ht1\advance\dimen0by\dp1\advance\dimen0by1.7true cm +\ifdim\dimen0>\pagegoal\stackfigbox +\else\box1\vskip7true mm\fi +\else\box1\vskip7true mm\fi\fi\fi\let\firstleg=Y} +% +% Abbildungen +\def\begfig#1cm#2\endfig{\par +\setbox1=\vbox{\dimen0=#1true cm\advance\dimen0 +by1true cm\kern\dimen0\vskip-.8333\baselineskip#2}\placefigure} +% +\def\begdoublefig#1cm #2 #3 \enddoublefig{\begfig#1cm% +\line{\vtop{\hsize=0.46\hsize#2}\hfill +\vtop{\hsize=0.46\hsize#3}}\endfig} +%------------------------------------------------------------------- +\let\firstleg=Y +% Abbildungslegenden +% Falls Text kleiner als eine volle Zeile, zentriert. +\def\figure#1#2{\if Y\firstleg\vskip1true cm\else\vskip1.7true mm\fi +\let\firstleg=N\setbox0=\vbox{\noindent\petit{\bf +Fig.\ts#1\unskip.\ }\ignorespaces #2\smallskip +\count255=0\global\advance\count255by\prevgraf}% +\ifnum\count255>1\box0\else +\centerline{\petit{\bf Fig.\ts#1\unskip.\ +}\ignorespaces#2}\smallskip\fi} +%----------------------------------------------------------------- +% Tabellenkoepfe +\def\tabcap#1#2{\smallskip\vbox{\noindent\petit{\bf Table\ts#1\unskip.\ +}\ignorespaces #2\medskip}} +%------------------------------------------------------------------- +\def\begtab#1cm#2\endtab{\par + \ifvoid\topins\midinsert\medskip\vbox{#2\kern#1true cm}\endinsert + \else\topinsert\vbox{#2\kern#1true cm}\endinsert\fi} +%------------------------------------------------------------------- +\def\begpet{\vskip6pt\bgroup\petit} +\def\endpet{\vskip6pt\egroup} +%------------------------------------------------------------------- +% Referenzen +\newdimen\refindent +\newlinechar=`\| +\def\begref#1#2{\titlea{}{#1}% +\bgroup\petit +\setbox0=\hbox{#2\enspace}\refindent=\wd0\relax +\if!#2!\else +\ifdim\refindent>0.5em\else +\message{|Something may be wrong with your references;}% +\message{probably you missed the second argument of \string\begref.}% +\fi\fi} +\def\ref{\goodbreak +\hangindent\oldparindent\hangafter=1 +\noindent\ignorespaces} +\def\refno#1{\goodbreak +\setbox0=\hbox{#1\enspace}\ifdim\refindent<\wd0\relax +\message{|Your reference `#1' is wider than you pretended in using +\string\begref.}\fi +\hangindent\refindent\hangafter=1 +\noindent\kern\refindent\llap{#1\enspace}\ignorespaces} +\def\refmark#1{\goodbreak +\setbox0=\hbox{#1\enspace}\ifdim\refindent<\wd0\relax +\message{|Your reference `#1' is wider than you pretended in using +\string\begref.}\fi +\hangindent\refindent\hangafter=1 +\noindent\hbox to\refindent{#1\hss}\ignorespaces} +\def\endref{\goodbreak\endpet}% Ende der Referenzen +%------------------------------------------------------------------- +\def\vec#1{{\textfont1=\tenbf\scriptfont1=\sevenbf +\textfont0=\tenbf\scriptfont0=\sevenbf +\mathchoice{\hbox{$\displaystyle#1$}}{\hbox{$\textstyle#1$}} +{\hbox{$\scriptstyle#1$}}{\hbox{$\scriptscriptstyle#1$}}}} +%--------------------------------------------------------------------- +\def\petit{\def\rm{\fam0\ninerm}% +\textfont0=\ninerm \scriptfont0=\sixrm \scriptscriptfont0=\fiverm + \textfont1=\ninei \scriptfont1=\sixi \scriptscriptfont1=\fivei + \textfont2=\ninesy \scriptfont2=\sixsy \scriptscriptfont2=\fivesy + \def\it{\fam\itfam\nineit}% + \textfont\itfam=\nineit + \def\sl{\fam\slfam\ninesl}% + \textfont\slfam=\ninesl + \def\bf{\fam\bffam\ninebf}% + \textfont\bffam=\ninebf \scriptfont\bffam=\sixbf + \scriptscriptfont\bffam=\fivebf + \def\sans{\fam\sansfam\ninesans}% + \textfont\sansfam=\ninesans \scriptfont\sansfam=\sixsans + \scriptscriptfont\sansfam=\fivesans + \def\tt{\fam\ttfam\ninett}% + \textfont\ttfam=\ninett + \normalbaselineskip=11pt + \setbox\strutbox=\hbox{\vrule height7pt depth2pt width0pt}% + \normalbaselines\rm +\def\vec##1{{\textfont1=\tbms\scriptfont1=\tbmss +\textfont0=\ninebf\scriptfont0=\sixbf +\mathchoice{\hbox{$\displaystyle##1$}}{\hbox{$\textstyle##1$}} +{\hbox{$\scriptstyle##1$}}{\hbox{$\scriptscriptstyle##1$}}}}} +%------------------------------------------------------------------- +\nopagenumbers +% +% Der Schalter \header gibt an, ob ein "running head" gedruckt werden +% soll; wenn er nicht auf "N" steht kommt ein solcher. +\let\header=Y +\let\FIG=N +\newbox\figbox +\output={\if N\header\headline={\hfil}\fi\plainoutput\global\let\header=Y +\if Y\FIG\topinsert\unvbox\figbox\endinsert\global\let\FIG=N\fi} +%------------------------------------------------------ +\let\lasttitle=N +%--------------------------------------------------------------- +\catcode`\@=\active +\def\author#1{\bgroup +\baselineskip=13.2pt +\lineskip=0pt +\pretolerance=10000 +\markfont +\ignorespaces#1\bigskip\egroup +{\def@##1{}% +\setbox0=\hbox{\petit\kern2.5true cc\ignorespaces#1\unskip}% +\ifdim\wd0>\hsize +\message{The names of the authors exceed the headline, please use a }% +\message{short form with AUTHORRUNNING}\gdef\leftheadline{% +\hbox to2.5true cc{\folio\hfil}\hfil AUTHORS suppressed due to excessive +length}% +\else +\xdef\leftheadline{\hbox to2.5true +cc{\noexpand\folio\hfil}\hfill\ignorespaces#1\unskip}% +\fi +}\let\INS=E} +\def\address#1{\bgroup\petit +\ignorespaces#1\bigskip\egroup +\catcode`\@=12 +\vskip2cm\noindent\ignorespaces} +%--------------------------------------------------------------------- +\let\INS=N% +% Aktionen, die bei Antreffen des @-Zeichens zu machen sind; +% drei Faelle a) @ bei AUTHOR, b) 1.@ bei ADDRESS, c) alle weiteren @'s +\def@#1{\if N\INS\unskip$\,^{#1}$\else\global\footcount=#1\relax +\if E\INS\hangindent0.5\parindent\noindent\hbox +to0.5\parindent{$^{#1}$\hfil}\let\INS=Y\ignorespaces +\else\par\hangindent0.5\parindent\noindent\hbox +to0.5\parindent{$^{#1}$\hfil}\ignorespaces\fi\fi}% +\catcode`\@=12 +%------------------------------------------------------------------- +% "running head" +\headline={\petit\def\newline{ }\def\fonote#1{}\ifodd\pageno +\rightheadline\else\leftheadline\fi} +\def\rightheadline{Missing CONTRIBUTION +title\hfil\hbox to2.5true cc{\hfil\folio}} +\def\leftheadline{\hbox to2.5true cc{\folio\hfil}\hfil Missing name(s) of the +author(s)} +\nopagenumbers +% +\let\header=Y +%------------------------------------------------------ +\def\contributionrunning#1{\message{Running head on right hand sides +(CONTRIBUTION) +has been changed}\gdef\rightheadline{\ignorespaces#1\unskip\hfil +\hbox to2.5true cc{\hfil\folio}}} +\def\authorrunning#1{\message{Running head on left hand sides (AUTHOR) +has been changed}\gdef\leftheadline{\hbox to2.5true cc{\folio +\hfil}\hfil\ignorespaces#1\unskip}} +%------------------------------------------------------ +\let\lasttitle=N + \def\contribution#1{\vfill\eject + \let\header=N\bgroup + \textfont0=\tafontt \scriptfont0=\tafonts \scriptscriptfont0=\tafontss + \textfont1=\tamt \scriptfont1=\tams \scriptscriptfont1=\tams + \textfont2=\tast \scriptfont2=\tass \scriptscriptfont2=\tasss + \par\baselineskip=16pt + \lineskip=16pt + \tafontt + \raggedright + \pretolerance=10000 + \noindent + \ignorespaces#1 + \vskip17pt\egroup + \nobreak + \parindent=0pt + \everypar={\global\parindent=1.5em + \global\let\lasttitle=N\global\everypar={}}% + \global\let\lasttitle=A% + \setbox0=\hbox{\petit\def\newline{ }\def\fonote##1{}\kern2.5true + cc\ignorespaces#1}\ifdim\wd0>\hsize + \message{Your CONTRIBUTIONtitle exceeds the headline, +please use a short form +with CONTRIBUTIONRUNNING}\gdef\rightheadline{CONTRIBUTION title +suppressed due to excessive length\hfil\hbox to2.5true cc{\hfil\folio}}% +\else +\gdef\rightheadline{\ignorespaces#1\unskip\hfil\hbox to2.5true +cc{\hfil\folio}}\fi +\catcode`\@=\active + \ignorespaces} +%------------------------------------------------------ +% Beginn Ueberschrift 1. Ordnung +\def\titlea#1#2{\if N\lasttitle\else\vskip-28pt + \fi + \vskip18pt plus 4pt minus4pt + \bgroup +\textfont0=\tbfontt \scriptfont0=\tbfonts \scriptscriptfont0=\tbfontss +\textfont1=\tbmt \scriptfont1=\tbms \scriptscriptfont1=\tbmss +\textfont2=\tbst \scriptfont2=\tbss \scriptscriptfont2=\tbsss +\textfont3=\tasys \scriptfont3=\tenex \scriptscriptfont3=\tenex + \baselineskip=16pt + \lineskip=0pt + \pretolerance=10000 + \noindent + \tbfontt + \rightskip 0pt plus 6em + \setbox0=\vbox{\vskip23pt\def\fonote##1{}% + \noindent + \if!#1!\ignorespaces#2 + \else\ignorespaces#1\unskip\enspace\ignorespaces#2\fi + \vskip18pt}% + \dimen0=\pagetotal\advance\dimen0 by-\pageshrink + \ifdim\dimen0<\pagegoal + \dimen0=\ht0\advance\dimen0 by\dp0\advance\dimen0 by + 3\normalbaselineskip + \advance\dimen0 by\pagetotal + \ifdim\dimen0>\pagegoal\eject\fi\fi + \noindent + \if!#1!\ignorespaces#2 + \else\ignorespaces#1\unskip\enspace\ignorespaces#2\fi + \vskip12pt plus4pt minus4pt\egroup + \nobreak + \parindent=0pt + \everypar={\global\parindent=\oldparindent + \global\let\lasttitle=N\global\everypar={}}% + \global\let\lasttitle=A% + \ignorespaces} +%------------------------------------------------------ + % Beginn Ueberschrift 2. Ordnung + \def\titleb#1#2{\if N\lasttitle\else\vskip-22pt + \fi + \vskip18pt plus 4pt minus4pt + \bgroup +\textfont0=\tenbf \scriptfont0=\sevenbf \scriptscriptfont0=\fivebf +\textfont1=\tams \scriptfont1=\tamss \scriptscriptfont1=\tbmss + \lineskip=0pt + \pretolerance=10000 + \noindent + \bf + \rightskip 0pt plus 6em + \setbox0=\vbox{\vskip23pt\def\fonote##1{}% + \noindent + \if!#1!\ignorespaces#2 + \else\ignorespaces#1\unskip\enspace\ignorespaces#2\fi + \vskip10pt}% + \dimen0=\pagetotal\advance\dimen0 by-\pageshrink + \ifdim\dimen0<\pagegoal + \dimen0=\ht0\advance\dimen0 by\dp0\advance\dimen0 by + 3\normalbaselineskip + \advance\dimen0 by\pagetotal + \ifdim\dimen0>\pagegoal\eject\fi\fi + \noindent + \if!#1!\ignorespaces#2 + \else\ignorespaces#1\unskip\enspace\ignorespaces#2\fi + \vskip8pt plus4pt minus4pt\egroup + \nobreak + \parindent=0pt + \everypar={\global\parindent=\oldparindent + \global\let\lasttitle=N\global\everypar={}}% + \global\let\lasttitle=B% + \ignorespaces} +%------------------------------------------------------ + % Beginn Ueberschrift 3. Ordnung + \def\titlec#1{\if N\lasttitle\else\vskip-\baselineskip + \fi + \vskip18pt plus 4pt minus4pt + \bgroup +\textfont0=\tenbf \scriptfont0=\sevenbf \scriptscriptfont0=\fivebf +\textfont1=\tams \scriptfont1=\tamss \scriptscriptfont1=\tbmss + \bf + \noindent + \ignorespaces#1\unskip\ \egroup + \ignorespaces} +%------------------------------------------------------------------- + % Beginn Ueberschrift 4. Ordnung + \def\titled#1{\if N\lasttitle\else\vskip-\baselineskip + \fi + \vskip12pt plus 4pt minus 4pt + \bgroup + \it + \noindent + \ignorespaces#1\unskip\ \egroup + \ignorespaces} +%------------------------------------------------------------------- +\let\ts=\thinspace +\def\footnoterule{\kern-3pt\hrule width 2true cm\kern2.6pt} +% Fussnoten-macros +\newcount\footcount \footcount=0 +\def\advftncnt{\advance\footcount by1\global\footcount=\footcount} +% Automatisch numerierte Fussnote, Fussnotentex in petit +\def\fonote#1{\advftncnt$^{\the\footcount}$\begingroup\petit +\parfillskip=0pt plus 1fil +\def\textindent##1{\hangindent0.5\oldparindent\noindent\hbox +to0.5\oldparindent{##1\hss}\ignorespaces}% +\vfootnote{$^{\the\footcount}$}{#1\vskip-9.69pt}\endgroup} +%------------------------------------------------------------------- +\def\item#1{\par\noindent +\hangindent6.5 mm\hangafter=0 +\llap{#1\enspace}\ignorespaces} +%------------------------------------------------------------------- +\def\itemitem#1{\par\noindent +\hangindent11.5 mm\hangafter=0 +\llap{#1\enspace}\ignorespaces} +%------------------------------------------------------------------- +\def\newenvironment#1#2#3#4{\long\def#1##1##2{\removelastskip +\vskip\baselineskip\noindent{#3#2\if!##1!.\else\unskip\ \ignorespaces +##1\unskip\fi\ }{#4\ignorespaces##2}\vskip\baselineskip}} +% Lemma, Proposition, Theorem, Corollary +\newenvironment\lemma{Lemma}{\bf}{\it} +\newenvironment\proposition{Proposition}{\bf}{\it} +\newenvironment\theorem{Theorem}{\bf}{\it} +\newenvironment\corollary{Corollary}{\bf}{\it} +%--------------------------------------------------------------------- +% Example, Exercise, Problem, Solution, Definition +\newenvironment\example{Example}{\it}{\rm} +\newenvironment\exercise{Exercise}{\bf}{\rm} +\newenvironment\problem{Problem}{\bf}{\rm} +\newenvironment\solution{Solution}{\bf}{\rm} +\newenvironment\definition{Definition}{\bf}{\rm} +%--------------------------------------------------------------------- +%Note, Question +\newenvironment\note{Note}{\it}{\rm} +\newenvironment\question{Question}{\it}{\rm} +%--------------------------------------------------------------------- +%Proof, Remark +\long\def\remark#1{\removelastskip\vskip\baselineskip\noindent{\it +Remark.\ }\ignorespaces} +\long\def\proof#1{\removelastskip\vskip\baselineskip\noindent{\it +Proof\if!#1!\else\ \ignorespaces#1\fi.\ }\ignorespaces} +%------------------------------------------------------------------ +\def\typeset{\petit\noindent This article was processed by the author +using the \TeX\ macro package from Springer-Verlag.\par} +\outer\def\byebye{\bigskip\bigskip\typeset +\footcount=1\ifx\speciali\undefined\else +\loop\smallskip\noindent special character No\number\footcount: +\csname special\romannumeral\footcount\endcsname +\advance\footcount by 1\global\footcount=\footcount +\ifnum\footcount<11\repeat\fi +\vfill\supereject\end} diff --git a/macros/plain/contrib/jns/jns.cmm b/macros/plain/contrib/jns/jns.cmm new file mode 100644 index 0000000000..0842e27a92 --- /dev/null +++ b/macros/plain/contrib/jns/jns.cmm @@ -0,0 +1,556 @@ +% This is JNS.CMM the plain TeX macro package +% (CM version) from Springer-Verlag +% for the Journal of Nonlinear Science +% version of 16 July 1990 +\font \tafontt = cmbx10 scaled\magstep2 +\font \tafontss = cmbx5 scaled\magstep2 +\font \sixbf = cmbx6 +\font \tafonts = cmbx7 scaled\magstep2 +\font \eightbf = cmbx8 +\font \sixi = cmmi6 +\font \eighti = cmmi8 +\font \tams = cmmib10 +\font \tbmss = cmmib10 scaled 600 +\font \tamss = cmmib10 scaled 700 +\font \tbms = cmmib10 scaled 833 +\font \tamt = cmmib10 scaled\magstep2 +\font \smallescriptscriptfont = cmr5 +\font \smalletextfont = cmr5 at 10pt +\font \smallescriptfont = cmr5 at 7pt +\font \sixrm = cmr6 +\font \eightrm = cmr8 +\font \tensans = cmss10 +\font \fivesans = cmss10 at 5pt +\font \sixsans = cmss10 at 6pt +\font \sevensans = cmss10 at 7pt +\font \eightsans = cmss10 at 8pt +\font \tast = cmsy10 scaled\magstep2 +\font \tasss = cmsy5 scaled\magstep2 +\font \sixsy = cmsy6 +\font \tass = cmsy7 scaled\magstep2 +\font \eightsy = cmsy8 +\font \eightit = cmti8 +\font \eighttt = cmtt8 +%----------------------------------------------------------------------- +\magnification=\magstep0 +\hsize=12.2cm +\vsize=19.4cm +\hfuzz=2pt +\tolerance=500 +\abovedisplayskip=3 mm plus6pt minus 4pt +\belowdisplayskip=3 mm plus6pt minus 4pt +\abovedisplayshortskip=0mm plus6pt minus 2pt +\belowdisplayshortskip=2 mm plus4pt minus 4pt +\predisplaypenalty=0 +\clubpenalty=10000 +\widowpenalty=10000 +\frenchspacing +\newdimen\oldparindent\oldparindent=1.5em +\parindent=1.5em +%----------------------------------------------------------------------- +\def\getsto{\mathrel{\mathchoice {\vcenter{\offinterlineskip +\halign{\hfil +$\displaystyle##$\hfil\cr\gets\cr\to\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr\gets +\cr\to\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr\gets +\cr\to\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +\gets\cr\to\cr}}}}} +\def\lid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil +$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr +\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr +\noalign{\vskip1pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +<\cr +\noalign{\vskip0.9pt}=\cr}}}}} +\def\gid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil +$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr +\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr +\noalign{\vskip1pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +>\cr +\noalign{\vskip0.9pt}=\cr}}}}} +\def\grole{\mathrel{\mathchoice {\vcenter{\offinterlineskip +\halign{\hfil +$\displaystyle##$\hfil\cr>\cr\noalign{\vskip-1pt}<\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr +>\cr\noalign{\vskip-1pt}<\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr +>\cr\noalign{\vskip-0.8pt}<\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +>\cr\noalign{\vskip-0.3pt}<\cr}}}}} +\def\bbbr{{\rm I\!R}} %reelle Zahlen +\def\bbbm{{\rm I\!M}} +\def\bbbn{{\rm I\!N}} %natuerliche Zahlen +\def\bbbf{{\rm I\!F}} +\def\bbbh{{\rm I\!H}} +\def\bbbk{{\rm I\!K}} +\def\bbbp{{\rm I\!P}} +\def\bbbone{{\mathchoice {\rm 1\mskip-4mu l} {\rm 1\mskip-4mu l} +{\rm 1\mskip-4.5mu l} {\rm 1\mskip-5mu l}}} +\def\bbbc{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}}} +\def\bbbe{{\mathchoice {\setbox0=\hbox{\smalletextfont e}\hbox{\raise +0.1\ht0\hbox to0pt{\kern0.4\wd0\vrule width0.3pt height0.7\ht0\hss}\box0}} +{\setbox0=\hbox{\smalletextfont e}\hbox{\raise +0.1\ht0\hbox to0pt{\kern0.4\wd0\vrule width0.3pt height0.7\ht0\hss}\box0}} +{\setbox0=\hbox{\smallescriptfont e}\hbox{\raise +0.1\ht0\hbox to0pt{\kern0.5\wd0\vrule width0.2pt height0.7\ht0\hss}\box0}} +{\setbox0=\hbox{\smallescriptscriptfont e}\hbox{\raise +0.1\ht0\hbox to0pt{\kern0.4\wd0\vrule width0.2pt height0.7\ht0\hss}\box0}}}} +\def\bbbq{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle\rm Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle\rm Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}}} +\def\bbbt{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm +T$}\hbox{\hbox to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle\rm T$}\hbox{\hbox +to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle\rm T$}\hbox{\hbox +to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm T$}\hbox{\hbox +to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}}} +\def\bbbs{{\mathchoice +{\setbox0=\hbox{$\displaystyle \rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox +to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle \rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox +to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle \rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox +to0pt{\kern0.5\wd0\vrule height0.45\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.4\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox +to0pt{\kern0.55\wd0\vrule height0.45\ht0\hss}\box0}}}} +\def\bbbz{{\mathchoice {\hbox{$\sans\textstyle Z\kern-0.4em Z$}} +{\hbox{$\sans\textstyle Z\kern-0.4em Z$}} +{\hbox{$\sans\scriptstyle Z\kern-0.3em Z$}} +{\hbox{$\sans\scriptscriptstyle Z\kern-0.2em Z$}}}} +%-------------------------------------------------------------------------- +% petit-fonts +\skewchar\eighti='177 \skewchar\sixi='177 +\skewchar\eightsy='60 \skewchar\sixsy='60 +\hyphenchar\eighttt=-1 +\def\newline{\hfil\break}% +%-------------------------------------------------------------------------- +\catcode`@=11 +\def\folio{\ifnum\pageno<\z@ +\uppercase\expandafter{\romannumeral-\pageno}% +\else\number\pageno\fi} +\catcode`@=12 % at signs are no longer letters +%------------------------------------------------------- +% Definition der versal griechischen Buchstaben +%=============================================================================== + \mathchardef\Gamma="0100 + \mathchardef\Delta="0101 + \mathchardef\Theta="0102 + \mathchardef\Lambda="0103 + \mathchardef\Xi="0104 + \mathchardef\Pi="0105 + \mathchardef\Sigma="0106 + \mathchardef\Upsilon="0107 + \mathchardef\Phi="0108 + \mathchardef\Psi="0109 + \mathchardef\Omega="010A +%------------------------------------------------------------------------------- +\def\squareforqed{\hbox{\rlap{$\sqcap$}$\sqcup$}} +\def\qed{\ifmmode\squareforqed\else{\unskip\nobreak\hfil +\penalty50\hskip1em\null\nobreak\hfil\squareforqed +\parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi} +%--------------------------------------------------------------------------- +\newfam\sansfam +\textfont\sansfam=\tensans\scriptfont\sansfam=\sevensans +\scriptscriptfont\sansfam=\fivesans +\def\sans{\fam\sansfam\tensans} +%--------------------------------------------------------------------------- +\def\stackfigbox{\if +Y\FIG\global\setbox\figbox=\vbox{\unvbox\figbox\box1}% +\else\global\setbox\figbox=\vbox{\box1}\global\let\FIG=Y\fi} +% +\def\placefigure{\dimen0=\ht1\advance\dimen0by\dp1 +\advance\dimen0by5\baselineskip +\advance\dimen0by0.4true cm +\ifdim\dimen0>\vsize\pageinsert\box1\vfill\endinsert +\else%keine seitenhohe Abbildung +\if Y\FIG\stackfigbox\else +\dimen0=\pagetotal\ifdim\dimen0<\pagegoal%aktuelle Seite ist noch nicht voll +\advance\dimen0by\ht1\advance\dimen0by\dp1\advance\dimen0by1.7true cm +\ifdim\dimen0>\pagegoal\stackfigbox +\else\box1\vskip7true mm\fi +\else\box1\vskip7true mm\fi\fi\fi\let\firstleg=Y} +% +% Abbildungen +\def\begfig#1cm#2\endfig{\par +\setbox1=\vbox{\dimen0=#1true cm\advance\dimen0 +by1true cm\kern\dimen0\vskip-.8333\baselineskip#2}\placefigure} +% +\def\begdoublefig#1cm #2 #3 \enddoublefig{\begfig#1cm% +\line{\vtop{\hsize=0.46\hsize#2}\hfill +\vtop{\hsize=0.46\hsize#3}}\endfig} +%------------------------------------------------------------------- +\let\firstleg=Y +% Abbildungslegenden +% Falls Text kleiner als eine volle Zeile, zentriert. +\def\figure#1#2{\if Y\firstleg\vskip1true cm\else\vskip1.7true mm\fi +\let\firstleg=N\setbox0=\vbox{\noindent\petit{\bf +Fig.\ts#1\unskip.\ }\ignorespaces #2\smallskip +\count255=0\global\advance\count255by\prevgraf}% +\ifnum\count255>1\box0\else +\centerline{\petit{\bf Fig.\ts#1\unskip.\ +}\ignorespaces#2}\smallskip\fi} +%----------------------------------------------------------------- +% Tabellenkoepfe +\def\tabcap#1#2{\smallskip\vbox{\noindent\petit{\bf Table\ts#1\unskip.\ +}\ignorespaces #2\medskip}} +%------------------------------------------------------------------- +\def\begtab#1cm#2\endtab{\par + \ifvoid\topins\midinsert\medskip\vbox{#2\kern#1true cm}\endinsert + \else\topinsert\vbox{#2\kern#1true cm}\endinsert\fi} +%------------------------------------------------------------------- +\def\begpet{\vskip6pt\bgroup\petit} +\def\endpet{\vskip6pt\egroup} +%------------------------------------------------------------------- +% Referenzen +\newdimen\refindent +\newlinechar=`\| +\def\begref#1#2{\titlea{}{#1}% +\bgroup\petit +\setbox0=\hbox{#2\enspace}\refindent=\wd0\relax +\if!#2!\else +\ifdim\refindent>0.5em\else +\message{|Something may be wrong with your references;}% +\message{probably you missed the second argument of \string\begref.}% +\fi\fi} +\def\ref{\goodbreak +\hangindent\oldparindent\hangafter=1 +\noindent\ignorespaces} +\def\refno#1{\goodbreak +\setbox0=\hbox{#1\enspace}\ifdim\refindent<\wd0\relax +\message{|Your reference `#1' is wider than you pretended in using +\string\begref.}\fi +\hangindent\refindent\hangafter=1 +\noindent\kern\refindent\llap{#1\enspace}\ignorespaces} +\def\refmark#1{\goodbreak +\setbox0=\hbox{#1\enspace}\ifdim\refindent<\wd0\relax +\message{|Your reference `#1' is wider than you pretended in using +\string\begref.}\fi +\hangindent\refindent\hangafter=1 +\noindent\hbox to\refindent{#1\hss}\ignorespaces} +\def\endref{\goodbreak\endpet}% Ende der Referenzen +%------------------------------------------------------------------- +\def\vec#1{{\textfont1=\tenbf\scriptfont1=\sevenbf +\textfont0=\tenbf\scriptfont0=\sevenbf +\mathchoice{\hbox{$\displaystyle#1$}}{\hbox{$\textstyle#1$}} +{\hbox{$\scriptstyle#1$}}{\hbox{$\scriptscriptstyle#1$}}}} +%--------------------------------------------------------------------- +\def\petit{\def\rm{\fam0\eightrm}% +\textfont0=\eightrm \scriptfont0=\sixrm \scriptscriptfont0=\fiverm + \textfont1=\eighti \scriptfont1=\sixi \scriptscriptfont1=\fivei + \textfont2=\eightsy \scriptfont2=\sixsy \scriptscriptfont2=\fivesy + \def\it{\fam\itfam\eightit}% + \textfont\itfam=\eightit + \def\bf{\fam\bffam\eightbf}% + \textfont\bffam=\eightbf \scriptfont\bffam=\sixbf + \scriptscriptfont\bffam=\fivebf + \def\sans{\fam\sansfam\eightsans}% + \textfont\sansfam=\eightsans \scriptfont\sansfam=\sixsans + \scriptscriptfont\sansfam=\fivesans + \def\tt{\fam\ttfam\eighttt}% + \textfont\ttfam=\eighttt + \normalbaselineskip=10pt + \setbox\strutbox=\hbox{\vrule height7pt depth2pt width0pt}% + \normalbaselines\rm +\def\vec##1{{\textfont1=\tbms\scriptfont1=\tbmss +\textfont0=\eightbf\scriptfont0=\sixbf +\mathchoice{\hbox{$\displaystyle##1$}}{\hbox{$\textstyle##1$}} +{\hbox{$\scriptstyle##1$}}{\hbox{$\scriptscriptstyle##1$}}}}} +%------------------------------------------------------------------- +\nopagenumbers +% +% Der Schalter \header gibt an, ob ein "running head" gedruckt werden +% soll; wenn er nicht auf "N" steht kommt ein solcher. +\let\header=Y +\let\FIG=N +\newbox\figbox +\output={\if N\header\headline={\hfil}\fi\plainoutput +\global\let\header=Y +\if Y\FIG\topinsert\unvbox\figbox\endinsert\global\let\FIG=N\fi} +%------------------------------------------------------ +\let\lasttitle=N +%------------------------------------------------------ +% "running head" +\headline={\petit\def\newline{ }\def\fonote#1{}\ifodd\pageno +\rightheadline\else\leftheadline\fi} +\def\rightheadline{Missing MAINTITLE\hfil\hbox to2.5true +cc{\hfil\folio}} +\def\leftheadline{\hbox to2.5true cc{\folio\hfil}\hfil Missing name(s) +of the author(s)} +\nopagenumbers +% +\let\header=Y +%------------------------------------------------------ +\def\Logo{\setbox254=\hbox{ THE JOURNAL OF }% +\vbox{\hrule\hbox{\vrule\vbox{\kern3pt +\copy254 +\hbox to\wd254{\hfil NONLINEAR\hfil} +\hbox to\wd254{\hfil SCIENCE\hfil} +\hbox to\wd254{\hfil\number\day.\number\month.\number\year\hfil} +\kern3pt}\vrule}\hrule}} +%------------------------------------------------------ +\def\makelogo{\hbox to\hsize{\hfil +\Logo}\vskip2.1cm} +%------------------------------------------------------ + \def\maintitle#1{\vfill\eject + \makelogo + \let\header=N\bgroup + \textfont0=\tafontt \scriptfont0=\tafonts \scriptscriptfont0=\tafontss + \textfont1=\tamt \scriptfont1=\tams \scriptscriptfont1=\tamss + \textfont2=\tast \scriptfont2=\tass \scriptscriptfont2=\tasss + \par\baselineskip=16pt + \lineskip=0pt + \tafontt + \raggedright + \pretolerance=10000 + \noindent + \ignorespaces#1 + \vskip10.8pt\egroup + \nobreak + \parindent=0pt + \everypar={\global\parindent=1.5em + \global\let\lasttitle=N\global\everypar={}}% + \global\let\lasttitle=A% + \setbox0=\hbox{\petit\def\newline{ }\def\fonote##1{}\kern2.5true + cc\ignorespaces#1}\ifdim\wd0>\hsize + \message{Your MAINTITLE exceeds the headline, +please use a short form +with MAINRUNNING}\gdef\rightheadline{MAIN title +suppressed due to excessive length\hfil\hbox to2.5true cc{\hfil\folio}}% +\else +\gdef\rightheadline{\ignorespaces#1\unskip\hfil\hbox to2.5true +cc{\hfil\folio}}\fi +\catcode`\@=\active + \ignorespaces} +%------------------------------------------------------ +\def\mainrunning#1{\message{Running head on right hand sides +(MAINTITLE) +has been changed}\gdef\rightheadline{\ignorespaces#1\unskip\hfil +\hbox to2.5true cc{\hfil\folio}}} +\def\authorrunning#1{\message{Running head on left hand sides (AUTHOR) +has been changed}\gdef\leftheadline{\hbox to2.5true cc{\folio +\hfil}\hfil\ignorespaces#1\unskip}} +%------------------------------------------------------ +\def\subtitle#1{\vskip-5.7pt + \bgroup +\textfont0=\tenbf \scriptfont0=\sevenbf \scriptscriptfont0=\fivebf +\textfont1=\tams \scriptfont1=\tamss \scriptscriptfont1=\tbmss + \pretolerance=10000 + \noindent + \bf + \rightskip 0pt plus 6em + \ignorespaces#1 + \vskip10.8pt\egroup + \nobreak + \parindent=0pt + \everypar={\global\parindent=1.5em + \global\let\lasttitle=N\global\everypar={}}% + \global\let\lasttitle=A% + \ignorespaces} +%------------------------------------------------------ +\catcode`\@=\active +\def\author#1{\bgroup +\pretolerance=10000 +\bf +\noindent +\ignorespaces#1\vskip.1cm\egroup +{\def@##1{}% +\setbox0=\hbox{\petit\kern2.5true cc\ignorespaces#1\unskip}% +\ifdim\wd0>\hsize +\message{The names of the authors exceed the headline, please use a }% +\message{short form with AUTHORRUNNING}\gdef\leftheadline{% +\hbox to2.5true cc{\folio\hfil}\hfil AUTHORS suppressed due to excessive +length}% +\else +\xdef\leftheadline{\hbox to2.5true +cc{\noexpand\folio\hfil}\hfill\ignorespaces#1\unskip}% +\fi +}\let\INS=E} +\def\address#1{\bgroup\petit +\ignorespaces#1\vskip8pt\egroup +\catcode`\@=12} +%--------------------------------------------------------------------- +\let\INS=N% +% Aktionen, die bei Antreffen des @-Zeichens zu machen sind; +% drei Faelle a) @ bei AUTHOR, b) 1.@ bei ADDRESS, c) alle weiteren @'s +\def@#1{\if N\INS\unskip$\,^{#1}$\else\global\footcount=#1\relax +\if E\INS\hangindent0.5\parindent\noindent\hbox +to0.5\parindent{$^{#1}$\hfil}\let\INS=Y\ignorespaces +\else\par\hangindent0.5\parindent\noindent\hbox +to0.5\parindent{$^{#1}$\hfil}\ignorespaces\fi\fi}% +\catcode`\@=12 +%------------------------------------------------------------------- +\def\received#1{\bgroup\petit\noindent Received #1 +\vskip24pt\egroup} +%--------------------------------------------------------------- +\long\def\summary#1{\noindent{\bf Summary. }\ignorespaces#1 +\vskip12pt} +%--------------------------------------------------------------- +\def\keywords#1{\noindent{\bf Key words. }\ignorespaces#1 +\par} +%--------------------------------------------------------------- +% Beginn Ueberschrift 1. Ordnung +\def\titlea#1#2{\if N\lasttitle\else\vskip-28pt + \fi + \vskip18pt plus 4pt minus4pt + \bgroup +\textfont0=\tenbf \scriptfont0=\sevenbf \scriptscriptfont0=\fivebf +\textfont1=\tams \scriptfont1=\tamss \scriptscriptfont1=\tbmss + \pretolerance=10000 + \noindent + \bf + \rightskip 0pt plus 6em + \setbox0=\vbox{\vskip23pt\def\fonote##1{}% + \noindent + \if!#1!\ignorespaces#2 + \else\ignorespaces#1\unskip\enspace\ignorespaces#2\fi + \vskip18pt}% + \dimen0=\pagetotal\advance\dimen0 by-\pageshrink + \ifdim\dimen0<\pagegoal + \dimen0=\ht0\advance\dimen0 by\dp0\advance\dimen0 by + 3\normalbaselineskip + \advance\dimen0 by\pagetotal + \ifdim\dimen0>\pagegoal\eject\fi\fi + \noindent + \if!#1!\ignorespaces#2 + \else\ignorespaces#1\unskip\enspace\ignorespaces#2\fi + \vskip14pt plus4pt minus4pt\egroup + \nobreak + \parindent=0pt + \everypar={\global\parindent=\oldparindent + \global\let\lasttitle=N\global\everypar={}}% + \global\let\lasttitle=A% + \ignorespaces} +%------------------------------------------------------ + % Beginn Ueberschrift 2. Ordnung + \def\titleb#1#2{\if N\lasttitle\else\vskip-20pt + \fi + \vskip18pt plus 4pt minus4pt + \bgroup + \pretolerance=10000 + \noindent + \it + \rightskip 0pt plus 6em + \setbox0=\vbox{\vskip23pt\def\fonote##1{}% + \noindent + \if!#1!\ignorespaces#2 + \else\ignorespaces#1\unskip\enspace\ignorespaces#2\fi + \vskip10pt}% + \dimen0=\pagetotal\advance\dimen0 by-\pageshrink + \ifdim\dimen0<\pagegoal + \dimen0=\ht0\advance\dimen0 by\dp0\advance\dimen0 by + 3\normalbaselineskip + \advance\dimen0 by\pagetotal + \ifdim\dimen0>\pagegoal\eject\fi\fi + \noindent + \if!#1!\ignorespaces#2 + \else\ignorespaces#1\unskip\enspace\ignorespaces#2\fi + \vskip8pt plus4pt minus4pt\egroup + \nobreak + \parindent=0pt + \everypar={\global\parindent=\oldparindent + \global\let\lasttitle=N\global\everypar={}}% + \global\let\lasttitle=B% + \ignorespaces} +%------------------------------------------------------ + % Beginn Ueberschrift 3. Ordnung + \def\titlec#1{\if N\lasttitle\else\vskip-\baselineskip + \fi + \vskip18pt plus 4pt minus4pt + \bgroup +\textfont0=\tenbf \scriptfont0=\sevenbf \scriptscriptfont0=\fivebf +\textfont1=\tams \scriptfont1=\tamss \scriptscriptfont1=\tbmss + \bf + \noindent + \ignorespaces#1\unskip\ \egroup + \ignorespaces} +%------------------------------------------------------------------- + % Beginn Ueberschrift 4. Ordnung + \def\titled#1{\if N\lasttitle\else\vskip-\baselineskip + \fi + \vskip12pt plus 4pt minus 4pt + \bgroup + \it + \noindent + \ignorespaces#1\unskip\ \egroup + \ignorespaces} +%------------------------------------------------------------------- +\let\ts=\thinspace +\def\footnoterule{\kern-3pt\hrule width 2true cm\kern2.6pt} +% Fussnoten-macros +\newcount\footcount \footcount=0 +\def\advftncnt{\advance\footcount by1\global\footcount=\footcount} +% Automatisch numerierte Fussnote, Fussnotentex in petit +\def\fonote#1{\advftncnt$^{\the\footcount}$\begingroup\petit +\parfillskip=0pt plus 1fil +\def\textindent##1{\hangindent0.5\oldparindent\noindent\hbox +to0.5\oldparindent{##1\hss}\ignorespaces}% +\vfootnote{$^{\the\footcount}$}{#1\vskip-9.69pt}\endgroup} +%------------------------------------------------------------------- +\def\item#1{\par\noindent +\hangindent6.5 mm\hangafter=0 +\llap{#1\enspace}\ignorespaces} +%------------------------------------------------------------------- +\def\itemitem#1{\par\noindent +\hangindent11.5 mm\hangafter=0 +\llap{#1\enspace}\ignorespaces} +%------------------------------------------------------------------- +\def\newenvironment#1#2#3#4{\long\def#1##1##2{\removelastskip +\vskip\baselineskip\noindent{#3#2\if!##1!.\else\unskip\ \ignorespaces +##1\unskip\fi\ }{#4\ignorespaces##2}\vskip\baselineskip}} +% Lemma, Proposition, Theorem, Corollary +\newenvironment\lemma{Lemma}{\bf}{\it} +\newenvironment\proposition{Proposition}{\bf}{\it} +\newenvironment\theorem{Theorem}{\bf}{\it} +\newenvironment\corollary{Corollary}{\bf}{\it} +%--------------------------------------------------------------------- +% Example, Exercise, Problem, Solution, Definition +\newenvironment\example{Example}{\it}{\rm} +\newenvironment\exercise{Exercise}{\bf}{\rm} +\newenvironment\problem{Problem}{\bf}{\rm} +\newenvironment\solution{Solution}{\bf}{\rm} +\newenvironment\definition{Definition}{\bf}{\rm} +%--------------------------------------------------------------------- +%Note, Question +\newenvironment\note{Note}{\it}{\rm} +\newenvironment\question{Question}{\it}{\rm} +%--------------------------------------------------------------------- +%Proof, Remark +\long\def\remark#1{\removelastskip\vskip\baselineskip\noindent{\it +Remark.\ }\ignorespaces} +\long\def\proof#1{\removelastskip\vskip\baselineskip\noindent{\it +Proof\if!#1!\else\ \ignorespaces#1\fi.\ }\ignorespaces} +%------------------------------------------------------------------ +\def\typeset{\petit\noindent This article was processed by the author +using the \TeX\ macro package from Springer-Verlag.\par} +\outer\def\byebye{\bigskip\bigskip\typeset +\footcount=1\ifx\speciali\undefined\else +\loop\smallskip\noindent special character No\number\footcount: +\csname special\romannumeral\footcount\endcsname +\advance\footcount by 1\global\footcount=\footcount +\ifnum\footcount<11\repeat\fi +\vfill\supereject\end} diff --git a/macros/plain/contrib/jns/jns.dem b/macros/plain/contrib/jns/jns.dem new file mode 100644 index 0000000000..a989acf3a8 --- /dev/null +++ b/macros/plain/contrib/jns/jns.dem @@ -0,0 +1,331 @@ +% This is JNS.DEM the demonstration file of +% the plain TeX macro package from Springer-Verlag +% for the Journal of Nonlinear Science +% version of 16 July 1990 +\def\12{{1\ov 2}} +\def\al{\alpha} +\def\Aun{A_\un} +\def\aun{a_\un} +\def\bullet{\cdot} +\def\Bun{B_\un} +\def\bun{b_\un} +\def\de{\delta} +\def\dx{\dot x} +\def\ep{\epsilon} +\def\fa{\forall} +\def\for{{\rm for}} +\def\Lai{\Lambda} +\def\lb{\left[} +\def\lg{\left\{} +\def\degr{\hbox{$^\circ$}} +\def\arcmin{\hbox{$^\prime$}} +\def\arcsec{\hbox{$^{\prime\prime}$}} +\def\liminfuu{{\rm lim inf}$\,$} +\def\liminfu{\mathop{\vphantom{\tst\sum}\hbox{\liminfuu}}} +\def\limsupuu{{\rm lim sup}$\,$} +\def\limsupu{\mathop{\vphantom{\tst\sum}\hbox{\limsupuu}}} +\def\lr{\left(} +\def\lss{\left\|} +\def\Min{{\rm Min\,}} +\def\NN{\bbbn} +\def\ol{\overline} +\def\om{\omega} +\def\ov{\over} +\def\rb{\right]} +\def\rg{\right\}} +\def\RRn{\bbbr^{2n}} +\def\RR{\bbbr} +\def\rr{\right)} +\def\rss{\right\|} +\def\sm{\setminus} +\def\tst{\textstyle} +\def\tx{\wt x} +\def\un{\infty} +\def\wt{\widetilde} +\def\ZZ{\bbbz} +\ifx\BlankIsSpace\undefined % <| Is this file +\input jns.cmm %<---| called by +\else\vfill\eject\pageno=26\relax %<---| +\def\ident{Macro Package for Authors %<---| JNS.DOC +Coding with Plain\TeX{} -- %<---| +Demonstration File}\let\INS=N %<---| or +\let\speciali=\undefined\fi %<| standalone? +% +\maintitle{Haupttitel 14pt halbfett/Title boldface -- 14/16} +\mainrunning{Expression of Cellular Oncogenes} +\subtitle{Untertitel 10pt halbfett/Subtitle boldface -- 10/11} + +\author{Ivar Ekeland@{1} and Roger Temam@{2}} +\authorrunning{R. M\"uller} + +\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. It +uses multiple coarse-grid corrections with particularly associated +prolongations and restrictions. In this paper the robustness with +respect to anisotropic problems is considered.} + +\keywords{multi-grid method -- coarse--grid correction -- +singular perturbation -- robustness.} + +\titlea{1.}{The Anisotropic Equation and Standard Multi-Grid Methods} +\titleb{1.1.}{Introduction} +Multi-grid methods are known as very fast solvers of a large class of +discretised partial differential equations. However, the multi-grid +method cannot be understood as a fixed algorithm. Usually, the +components of the multi-grid iteration have to be adapted to the given +problem and sometimes the problems are modified in order to make them +acceptable for multi-grid methods. In particular, the smoothing +iteration is the most delicated part of the multi-grid process. + +An iteration is called a {\it robust} one, if it works for a sufficient +large class of problems. Attempts have been made to construct robust +multi-grid iterations by means of sophisticated smoothing processes\dots +\vfil\eject +With this chapter, the preliminaries are over, and we begin the search +for periodic solutions to Hamiltonian systems. All this will be done in +the convex case; that is, we shall study the boundary-value problem +$$\eqalign{\dot x &= JH' (t,x)\cr x(0) &= x(T)\cr}$$ +with $H(t,\bullet )$ a convex function of $x$, going to $+\un$ when +$\lss x\rss \to \un$. + +\titleb{1.2.}{Autonomous Systems} +In this section, we will consider the case when the Hamiltonian $H(x)$ +is autonomous. For the sake of simplicity, we shall also assume that it +is $C^1$. + +We shall first consider the question of nontriviality, within the +general framework of $\lr \Aun , \Bun\rr$-subquadratic Hamiltonians. In +the second subsection, we shall look into the special case when $H$ is +$\lr 0,\bun\rr$-subquadratic, and we shall try to derive additional +information. +\titlec{ The General Case: Nontriviality.} +We assume that $H$ is $\lr \Aun , \Bun \rr$-sub\-qua\-dra\-tic at infinity, +for some constant symmetric matrices $\Aun$ and $\Bun$, with $\Bun +-\Aun$ positive definite. Set: +$$\eqalignno{ +\gamma :& = {\rm smallest\ eigenvalue\ of}\ \ \Bun - \Aun & (1)\cr +\lambda : & = {\rm largest\ negative\ eigenvalue\ of}\ \ J {d\ov dt} +\Aun\ +. & (2)\cr}$$ + +Theorem 21 tells us that if $\lambda +\gamma < 0$, the boundary-value +problem: +$$\eqalign{ \dx &= JH' (x)\cr +x(0) &= x (T)\cr}\eqno(3)$$ +has at least one solution $\ol x$, which is found by minimizing the dual +action functional: +$$ \psi (u) = \int_o^T \lb \12 \lr \Lai_o^{-1} u,u\rr + N^\ast (-u)\rb +dt\eqno(4)$$ +on the range of $\Lai$, which is a subspace $R (\Lai )\sb L^2$ with +finite codimension. Here +$$ N(x) := H(x) - \12 \lr \Aun x,x\rr\eqno(5)$$ +is a convex function, and +$$ N(x) \le \12 \lr \lr \Bun - \Aun\rr x,x\rr + c\ \ \ \fa x\ +.\eqno(6)$$ + +\proposition{ 1.} { Assume $H'(0)=0$ and $ H(0)=0$. Set: +$$ \de := \liminfu_{x\to 0} 2 N (x) \lss x\rss^{-2}\ .\eqno(7)$$ + +If $\gamma < - \lambda < \de$, the solution $\ol u$ is non-zero: +$$ \ol x (t) \ne 0\ \ \ \fa t\ .\eqno(8)$$} +\proof{} Condition (7) means that, for every $\de ' > \de$, there is +some $\ep > 0$ such that +$$ \lss x\rss \le \ep \Rightarrow N (x) \le {\de '\ov 2} \lss x\rss^2\ +.\eqno(9)$$ + +It is an exercise in convex analysis, into which we shall not go, to +show that this implies that there is an $\eta > 0$ such that +$$ f\lss x\rss \le \eta \Rightarrow N^\ast (y) \le {1\ov 2\de '} \lss +y\rss^2\ .\eqno(10)$$ + +\begfig 1.5cm +\figure{1}{This is the caption of the figure displaying a white eagle +and a white horse on a snow field} +\endfig + +Since $u_1$ is a smooth function, we will have $\lss hu_1\rss_\un \le +\eta$ for $h$ small enough, and inequality (10) will hold, yielding +thereby: +$$ \psi (hu_1) \le {h^2\ov 2} {1\ov \lambda} \lss u_1 \rss_2^2 + {h^2\ov 2} +{1\ov \de '} \lss u_1\rss^2\ .\eqno(11)$$ + +If we choose $\de '$ close enough to $\de$, the quantity $\lr {1\ov \lambda} ++ {1\ov \de '}\rr$ will be negative, and we end up with +$$ \psi (hu_1) < 0\ \ \ \ \ \for\ \ h\ne 0\ \ {\rm small}\ .\eqno(12)$$ + +On the other hand, we check directly that $\psi (0) = 0$. This shows +that 0 cannot be a minimizer of $\psi$, not even a local one. So $\ol u +\ne 0$ and $\ol u \ne \Lai_o^{-1} (0) = 0$. \qed + +\corollary{ 2.} { Assume $H$ is $C^2$ and $\lr \aun +,\bun\rr$-subquadratic at infinity. Let +$\xi_1,\allowbreak\dots,\allowbreak\xi_N$ be the +equilibria, that is, the solutions of $H' (\xi ) = 0$. Denote by $\om_k$ +the smallest eigenvalue of $H'' \lr \xi_k\rr$, and set: +$$ \om : = \Min \lg \om_1 , \dots , \om_k\rg\ .\eqno(13)$$ +If: +$$ {T\ov 2\pi} \bun < - E \lb - {T\ov 2\pi}\aun\rb < {T\ov +2\pi}\om\eqno(14)$$ +then minimization of $\psi$ yields a non-constant $T$-periodic solution +$\ol x$.} +We recall once more that by the integer part $E [\al ]$ of $\al \in +\RR$, we mean the $a\in \ZZ$ such that $a< \al \le a+1$. For instance, +if we take $\aun = 0$, Corollary 2 tells us that $\ol x$ exists and is +non-constant provided that: +$$ {T\ov 2\pi} \bun < 1 < {T\ov 2\pi}\eqno(15)$$ +or +$$ T\in \lr {2\pi\ov \om},{2\pi\ov \bun}\rr\ .\eqno(16)$$ +\proof{} The spectrum of $\Lai$ is ${2\pi\ov T} \ZZ +\aun$. The +largest negative eigenvalue $\lambda$ is given by ${2\pi\ov T}k_o +\aun$, +where +$$ {2\pi\ov T}k_o + \aun < 0\le {2\pi\ov T} (k_o +1) + \aun\ +.\eqno(17)$$ +Hence: +$$ k_o = E \lb - {T\ov 2\pi} \aun\rb \ .\eqno(18)$$ + +The condition $\gamma < -\lambda < \de$ now becomes: +$$ \bun - \aun < - {2\pi\ov T} k_o -\aun < \om -\aun\eqno(19)$$ +which is precisely condition (14).\qed + +\lemma {3.} { Assume that $H$ is $C^2$ on $\RRn \sm \{ 0\}$ and +that $H'' (x)$ is non-degenerate for any $x\ne 0$. Then any local +minimizer $\tx$ of $\psi$ has minimal period $T$.} +\proof{} We know that $\tx$, or $\tx + \xi$ for some constant $\xi +\in \RRn$, is a $T$-periodic solution of the Hamiltonian system: +$$ \dx = JH' (x)\ .\eqno(20)$$ + +There is no loss of generality in taking $\xi = 0$. So $\psi (x) \ge +\psi (\tx )$ for all $\tx$ in some neighbourhood of $x$ in $W^{1,2} \lr +\RR / T\ZZ ; \RRn\rr$. + +But this index is precisely the index $i_T (\tx )$ of the $T$-periodic +solution $\tx$ over the interval $(0,T)$, as defined in Sect.~2.6. So +$$ i_T (\tx ) = 0\ .\eqno(21)$$ + +Now if $\tx$ has a lower period, $T/k$ say, we would have, by Corollary +31: +$$ i_T (\tx ) = i_{kT/k}(\tx ) \ge ki_{T/k} (\tx ) + k-1 \ge k-1 \ge +1\ .\eqno(22)$$ + +This would contradict (21), and thus cannot happen.\qed +\titled{Notes and Comments.} The results in this section are a +refined +version of [CE1]; the minimality result of Proposition 14 was the first +of its kind. + +To understand the nontriviality conditions, such as the one in formula +(16), one may think of a one-parameter family $x_T$, $T\in \lr +2\pi\om^{-1}, 2\pi \bun^{-1}\rr$ of periodic solutions, $x_T (0) = x_T +(T)$, with $x_T$ going away to infinity when $T\to 2\pi \om^{-1}$, which +is the period of the linearized system at 0. +\vskip8 true mm +\tabcap{1}{Observational results from NGC 4827} +\vbox{\petit\hrule\smallskip +\vbox{\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 + +\theorem{4 (Ghoussoub-Preiss).} { Assume $H(t,x)$ is +$(0,\ep )$-subquadratic at +infinity for all $\ep > 0$, and $T$-periodic in $t$ +$$ H (t,\bullet )\ \ \ \ \ {\rm is\ convex}\ \ \fa t\eqno(23)$$ +$$ H (\bullet ,x)\ \ \ \ \ {\rm is}\ \ T{\rm -periodic}\ \ \fa x +\eqno(24)$$ +$$ H (t,x)\ge n\lr \lss x\rss\rr\ \ \ \ \ {\rm with}\ \ n (s)s^{-1}\to +\un\ \ {\rm as}\ \ s\to \un\eqno(25)$$ +$$ \fa \ep > 0\ ,\ \ \ \exists c\ :\ H(t,x) \le {\ep\ov 2}\lss x\rss^2 + +c\ .\eqno(26)$$ + +Assume also that $H$ is $C^2$, and $H'' (t,x)$ is positive definite +everywhere. Then there is a sequence $x_k$, $k\in \NN$, of $kT$-periodic +solutions of the system +$$ \dx = JH' (t,x)\eqno(27)$$ +such that, for every $k\in \NN$, there is some $p_o\in\NN$ with: +$$ p\ge p_o\Rightarrow x_{pk} \ne x_k\ .\eqno(28)$$\qed} +\example {1 {\rm(External forcing).}}{ Consider the system: +$$ \dx = JH' (x) + f(t)\eqno(29)$$ +where the Hamiltonian $H$ is $\lr 0,\bun\rr$-subquadratic, and the +forcing term is a distribution on the circle: +$$ f = {d\ov dt} F + f_o\ \ \ \ \ {\rm with}\ \ F\in L^2 \lr \RR / T\ZZ +; \RRn\rr\ ,\eqno(30)$$ +where $f_o : = T^{-1}\int_o^T f (t) dt$. For instance, +$$ f (t) = \sum_{k\in \NN} \de_k \xi\ ,\eqno(31)$$ +where $\de_k$ is the Dirac mass at $t= k$ and $\xi \in \RRn$ is a +constant, fits the prescription. This means that the system $\dx = JH' +(x)$ is being excited by a series of identical shocks at interval $T$.} + +\definition{5.}{Let $A_\un (t)$ and $B_\un (t)$ be symmetric +operators in $\RRn$, depending continuously on $t\in [0,T]$, such that +$A_\un (t) \le B_\un (t)$ for all $t$. + +A Borelian function $H: [0,T]\times \RRn \to \RR$ is called $\lr A_\un +,B_\un\rr$-{\it subquadratic at infinity} if there exists a function +$N(t,x)$ such that: +$$ H (t,x) = \12 \lr A_\un (t) x,x\rr + N(t,x)\eqno(32)$$ +$$ \fa t\ ,\ \ \ N(t,x)\ \ \ \ \ {\rm is\ convex\ with\ respect\ to}\ +\ x\eqno(33)$$ +$$ N(t,x) \ge n\lr \lss x\rss\rr\ \ \ \ \ {\rm with}\ \ n(s)s^{-1}\to ++\un\ \ {\rm as}\ \ s\to +\un\eqno(34)$$ +$$ \exists c\in \RR\ :\ \ \ H (t,x) \le \12 \lr B_\un (t) x,x\rr + c\ \ +\ \fa x\ .\eqno(35)$$ +} +If $A_\un (t) = a_\un I$ and $B_\un (t) = b_\un I$, with $a_\un \le +b_\un \in \RR$, we shall say that $H$ is $\lr a_\un +,b_\un\rr$-subquadratic at infinity. As an example, the function $\lss x +\rss^\al$, with $1\le \al < 2$, is $(0,\ep )$-subquadratic at infinity +for every $\ep > 0$. Similarly, the Hamiltonian +$$ H (t,x) = \12 k \lss k\rss^2 +\lss x\rss^\al\eqno(36)$$ +is $(k,k+\ep )$-subquadratic for every $\ep > 0$. Note that, if $k<0$, +it is not convex. + +\titled{Notes and Comments.} The first results on subharmonics were +obtained by Rabinowitz in [Ra1], who showed the existence of infinitely +many subharmonics both in the subquadratic and superquadratic case, with +suitable growth conditions on $H'$. Again the duality approach enabled +Clarke and Ekeland in [CE2] to treat the same problem in the +convex-subquadratic case, with growth conditions on $H$ only. + +Recently, Michalek and Tarantello (see [MT1] and [Ta1]) have obtained +lower bound on the number of subharmonics of period $kT$, based on +symmetry considerations and on pinching estimates, as in Sect.~5.2 of +this article. +\begref{References}{[MT1]} +\refmark{[CE1]} Clarke, F., Ekeland, I.: Nonlinear oscillations and +boundary-value problems for Hamiltonian systems. Arch. Rat. Mech. Anal. +{\bf 78} (1982) 315--333 +\refmark{[CE2]} Clarke, F., Ekeland, I.: Solutions p\'eriodiques, du +p\'eriode donn\'ee, des \'equations hamiltoiennes. Note CRAS Paris {\bf +287} (1978) 1013--1015 +\refmark{[MT1]} Michalek, R., Tarantello, G.: Subharmonic solutions with +prescribed minimal period for nonautonomous Hamiltonian systems. J. +Diff. Eq. {\bf 72} (1988) 28--55 +\refmark{[Ta1]} Tarantello, G.: Subharmonic solutions for Hamiltonian +systems via a $\bbbz_p$ pseudoindex theory. Annali di Mathematica Pura +(to appear) +\refmark{[Ra1]} Rabinowitz, P.: On subharmonic solutions of a Hamiltonian +system. Comm. Pure Appl. Math. {\bf 33} (1980) 609--633 +\endref +\byebye diff --git a/macros/plain/contrib/jns/jns.doc b/macros/plain/contrib/jns/jns.doc new file mode 100644 index 0000000000..1ea5a58cfe --- /dev/null +++ b/macros/plain/contrib/jns/jns.doc @@ -0,0 +1,1188 @@ +% 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{<Your contribution title>}| +\verb|\subtitle{<Your subtitle>}|, it is optional +\verb|\author{<Your name including forename(s)|$^1$\verb| and surname>}| +\verb|\address{<Your address including street name and postal code>}| +\verb|\received{<Date of receipt of your manuscript>}| +\verb|\summary{<The summary of your article>}| +\verb|\keywords{<Key words for your contribution>}| +\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 + + diff --git a/macros/plain/contrib/jns/jns.sty b/macros/plain/contrib/jns/jns.sty new file mode 100644 index 0000000000..dc116ac792 --- /dev/null +++ b/macros/plain/contrib/jns/jns.sty @@ -0,0 +1,801 @@ +% JNS DOCUMENT STYLE -- Released 16 July 1990 +% i.e. Journal of Nonlinear Science document style +% for LaTeX version 2.09 + +% This style file is an adaptation of +% the original LaTeX article.sty, by: +% Frank Holzwarth, Springer-Verlag Heidelberg, +% Tiergartenstrasse 17, D-6900 Heidelberg. + +\typeout{Document Style `jns' <16 Jul 90>.} + +\frenchspacing +\def~{\penalty\@M\kern3pt} + +\def\thebibliography#1{\section*{References}\small\list + {\arabic{enumi}.}{\settowidth\labelwidth{[#1]}\leftmargin\labelwidth + \advance\leftmargin\labelsep + \usecounter{enumi}} + \def\newblock{\hskip .11em plus .33em minus -.07em} + \sloppy + \sfcode`\.=1000\relax} + +\def\ds@citeauthoryear{\def\thebibliography##1{\section*{References}% + \small\list{}{\settowidth\labelwidth{}\leftmargin\parindent + \itemindent=-\parindent + \labelsep=\z@ + \usecounter{enumi}}% + \def\newblock{\hskip .11em plus .33em minus -.07em}% + \sloppy + \sfcode`\.=1000\relax}% + \def\@cite##1{##1}% + \def\@lbibitem[##1]##2{\item[]\if@filesw + {\def\protect####1{\string ####1\space}\immediate + \write\@auxout{\string\bibcite{##2}{##1}}}\fi\ignorespaces}}% + +\newif\if@envcountreset\@envcountresetfalse +\def\ds@envcountreset{\@envcountresettrue} + +\def\@mbi{cmmib10} +\def\@ptsize{0} \@namedef{ds@11pt}{\def\@ptsize{1}} +\@namedef{ds@12pt}{\def\@ptsize{2}} +\def\ds@twoside{\@twosidetrue \@mparswitchtrue} +\def\ds@draft{\overfullrule +5pt} +\@options + +\ds@twoside + +\lineskip 1pt \normallineskip 1pt +\def\baselinestretch{1} + +\def\@normalsize{\@setsize\normalsize{12pt}\xpt\@xpt +\abovedisplayskip=3 mm plus6pt minus 4pt +\belowdisplayskip=3 mm plus6pt minus 4pt +\abovedisplayshortskip=0mm plus6pt minus 2pt +\belowdisplayshortskip=2 mm plus4pt minus 4pt} + +\mathchardef\Gamma="0100 +\mathchardef\Delta="0101 +\mathchardef\Theta="0102 +\mathchardef\Lambda="0103 +\mathchardef\Xi="0104 +\mathchardef\Pi="0105 +\mathchardef\Sigma="0106 +\mathchardef\Upsilon="0107 +\mathchardef\Phi="0108 +\mathchardef\Psi="0109 +\mathchardef\Omega="010A + +\def\small{\@setsize\small{10pt}\viiipt\@viiipt +\abovedisplayskip=2.5 mm plus5pt minus 3pt +\belowdisplayskip=2.5 mm plus5pt minus 3pt +\abovedisplayshortskip=0mm plus6pt minus 2pt +\belowdisplayshortskip=2 mm plus4pt minus 4pt +\def\@listi{\topsep 4pt plus 2pt minus 2pt}} + +\def\footnotesize{\@setsize\footnotesize{10pt}\viiipt\@viiipt +\abovedisplayskip=2.5 mm plus5pt minus 3pt +\belowdisplayskip=2.5 mm plus5pt minus 3pt +\abovedisplayshortskip=0mm plus6pt minus 2pt +\belowdisplayshortskip=2 mm plus4pt minus 4pt +\def\@listi{\topsep 4pt plus 2pt minus 2pt}} + +\def\scriptsize{\@setsize\scriptsize{8.4pt}\viipt\@viipt} + +\def\tiny{\@setsize\tiny{6pt}\vpt\@vpt} +\def\large{\@setsize\large{13.2pt}\xipt\@xipt} +\def\Large{\@setsize\Large{14.4pt}\xiipt\@xiipt} +\def\LARGE{\@setsize\LARGE{16pt}\xivpt\@xivpt} +\def\huge{\@setsize\huge{22pt}\xxpt\@xxpt} +\def\Huge{\@setsize\Huge{30pt}\xxvpt\@xxvpt} +\@normalsize + +\if@twoside + \oddsidemargin 44pt + \evensidemargin 82pt + \marginparwidth 107pt +\else \oddsidemargin 63pt \evensidemargin 63pt + \marginparwidth 90pt +\fi +\marginparsep 11pt +\topmargin 11pt \headheight 12pt \headsep 13.66pt +\footheight 12pt \footskip 30pt +\textwidth 12.2cm +\textheight 19.4cm +\columnsep 1cc \columnseprule 0pt + +\footnotesep 7.7pt +\skip\footins 9pt plus 4pt minus 2pt +\floatsep 12pt plus 2pt minus 2pt +\textfloatsep 8mm plus 2pt minus 4pt +\intextsep 8mm plus 2pt minus 2pt +\@maxsep 8mm + +\dblfloatsep 12pt plus 2pt minus 2pt +\dbltextfloatsep 20pt plus 2pt minus 4pt +\@dblmaxsep 20pt + +\@fptop 0pt plus 1fil \@fpsep 8pt plus 2fil \@fpbot 0pt plus 1fil +\@dblfptop0pt plus1fil \@dblfpsep8pt plus2fil\@dblfpbot 0pt plus1fil +\marginparpush 5pt + +\parskip 0pt plus 1pt \parindent 1.5em \topsep 8pt plus 2pt minus 4pt +\partopsep 2pt plus 1pt minus 1pt \itemsep \z@ +\@lowpenalty 51 \@medpenalty 151 \@highpenalty 301 +\@beginparpenalty-\@lowpenalty\@endparpenalty -\@lowpenalty\@itempenalty +-\@lowpenalty + +\def\vec#1{\mathchoice{\mbox{\boldmath$\displaystyle\bf#1$}} +{\mbox{\boldmath$\textstyle\bf#1$}} +{\mbox{\boldmath$\scriptstyle\bf#1$}} +{\mbox{\boldmath$\scriptscriptstyle\bf#1$}}} + +\def\@sect#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth + \def\@svsec{}\else + \refstepcounter{#1}\edef\@svsec{\csname the#1\endcsname. }\fi + \@tempskipa #5\relax + \ifdim \@tempskipa>\z@ + \begingroup #6\relax + \noindent{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par} + \endgroup + \csname #1mark\endcsname{#7}\addcontentsline + {toc}{#1}{\ifnum #2>\c@secnumdepth \else + \protect\numberline{\csname the#1\endcsname}\fi + #7}\else + \def\@svsechd{#6\hskip #3\@svsec #8\csname #1mark\endcsname + {#7}\addcontentsline + {toc}{#1}{\ifnum #2>\c@secnumdepth \else + \protect\numberline{\csname the#1\endcsname}\fi + #7}}\fi + \@xsect{#5}} + +\def\part{\par \addvspace{4ex} \@afterindentfalse \secdef\@part\@spart} + +\def\@part[#1]#2{\ifnum \c@secnumdepth >\m@ne \refstepcounter{part} +\addcontentsline{toc}{part}{\thepart \hspace{1em}#1}\else +\addcontentsline{toc}{part}{#1}\fi { \parindent 0pt \raggedright + \ifnum \c@secnumdepth >\m@ne \Large \bf + Part\thepart\par\nobreak\fi\huge +\bf #2\markboth{}{}\par } \nobreak \vskip 3ex \@afterheading } + +\def\@spart#1{{\parindent 0pt \raggedright + \huge \bf + #1\par} \nobreak \vskip 3ex \@afterheading } + +\def\section{\@startsection {section}{1}{\z@}{-18pt plus -4pt minus +-4pt}{12pt plus 4pt minus 4pt}{\normalsize\bf\boldmath +\pretolerance=10000\relax\rightskip=0pt plus8em}} +\def\subsection{\@startsection{subsection}{2}{\z@}{-18pt plus-4pt minus + -4pt}{8pt plus 4pt minus 4pt}{\normalsize\it +\pretolerance=10000\relax\rightskip=0pt plus8em}} +\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-18pt plus-4pt + minus -4pt}{-0.5em plus -.22em minus -0.1em}{\normalsize\bf\boldmath}} +\def\paragraph{\@startsection{paragraph}{4}{\z@}{-12pt plus -4pt minus + -4pt}{-0.5em plus -.22em minus -0.1em}{\normalsize\it}} +\def\subparagraph#1{\typeout{JNS Warning: You should not use +\protect\subparagraph \space in this style.}\vskip0.5cm +You should not use $\backslash${\tt subparagraph} in this +style.\vskip0.5cm} + +\setcounter{secnumdepth}{2} + +\def\appendix{\par + \setcounter{section}{0} + \setcounter{subsection}{0} + \def\thesection{\Alph{section}}} + +% Define \keywords +\def\keywords{\par\vspace{12pt}\noindent{\bf Key words: }\ignorespaces} + +% Define \acknowledgements +\def\acknowledgements{\vspace{12pt}\noindent{\em Acknowledgements.\/ }} + +% The `abstract' environment has been renamed to `abstr' so a new environment +% `abstract' can be defined in terms of the old one. +\def\abstr{{\noindent \bf Summary. }% +\ignorespaces} +\def\endabstr{\relax} + +\newenvironment{abstract}{\begin{abstr}}{\end{abstr}} + +\leftmargini 17pt \leftmarginii 17pt +\leftmarginiii 17pt \leftmarginiv 17pt +\leftmarginv 10pt \leftmarginvi 10pt +\leftmargin\leftmargini \labelwidth\leftmargini +\advance\labelwidth-\labelsep +\labelsep 5pt +\parsep 0pt plus 1pt +\def\@listi{\leftmargin\leftmargini} +\def\@listii{\leftmargin\leftmarginii + \labelwidth\leftmarginii\advance\labelwidth-\labelsep + \topsep 0pt plus 1pt} +\def\@listiii{\leftmargin\leftmarginiii + \labelwidth\leftmarginiii\advance\labelwidth-\labelsep + \topsep 0pt plus 1pt} +\def\@listiv{\leftmargin\leftmarginiv + \labelwidth\leftmarginiv\advance\labelwidth-\labelsep + \topsep 0pt plus 1pt} +\def\@listv{\leftmargin\leftmarginv + \labelwidth\leftmarginv\advance\labelwidth-\labelsep + \topsep 0pt plus 1pt} +\def\@listvi{\leftmargin\leftmarginvi + \labelwidth\leftmarginvi\advance\labelwidth-\labelsep + \topsep 0pt plus 1pt} + +\def\labelenumi{\arabic{enumi}.} +\def\theenumi{\arabic{enumi}} +\def\labelenumii{(\alph{enumii})} +\def\theenumii{\alph{enumii}} +\def\p@enumii{\theenumi} +\def\labelenumiii{\roman{enumiii}.} +\def\theenumiii{\roman{enumiii}} +\def\p@enumiii{\theenumi(\theenumii)} +\def\labelenumiv{\Alph{enumiv}.} +\def\theenumiv{\Alph{enumiv}} +\def\p@enumiv{\p@enumiii\theenumiii} + +\def\labelitemi{\bf --} +\def\labelitemii{$\bullet$} +\def\labelitemiii{$\ast$} +\def\labelitemiv{$\cdot$} + +\def\verse{\let\\=\@centercr + \list{}{\itemsep\z@ \itemindent -1.5em\listparindent \itemindent + \rightmargin\leftmargin\advance\leftmargin 1.5em}\item[]} +\let\endverse\endlist +\def\quotation{\list{}{\listparindent 1.5em + \itemindent\listparindent + \rightmargin\leftmargin}\item[]} +\let\endquotation=\endlist +\def\quote{\list{}{\rightmargin\leftmargin}\item[]} +\let\endquote=\endlist + +\def\descriptionlabel#1{\hspace\labelsep \bf #1} +\def\description{\list{}{\labelwidth\z@ \itemindent-\leftmargin + \let\makelabel\descriptionlabel}} +\let\enddescription\endlist + +\def\theequation{\arabic{equation}} + +\def\titlepage{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn + \else \newpage \fi \thispagestyle{empty}\c@page\z@} +\def\endtitlepage{\if@restonecol\twocolumn \else \newpage \fi} + +\arraycolsep 1.4pt \tabcolsep 1.4pt \arrayrulewidth .4pt \doublerulesep +2pt +\tabbingsep \labelsep + +\skip\@mpfootins = \skip\footins +\fboxsep = 3pt \fboxrule = .4pt + +\newcounter{part} +\newcounter {section} +\newcounter {subsection}[section] +\newcounter {subsubsection}[subsection] +\newcounter {paragraph}[subsubsection] + +\def\thepart{\Roman{part}} +\def\thesection {\arabic{section}} +\def\thesubsection {\thesection.\arabic{subsection}} +\def\thesubsubsection {\thesubsection.\arabic{subsubsection}} +\def\theparagraph {\thesubsubsection.\arabic{paragraph}} + +\def\@pnumwidth{1.55em} +\def\@tocrmarg {2.55em} +\def\@dotsep{4.5} +\setcounter{tocdepth}{3} + +\def\tableofcontents{\section*{Table of Contents} + \@starttoc{toc}} +\def\l@part#1#2{\addpenalty{\@secpenalty} + \addvspace{2.25em plus 1pt} \begingroup + \@tempdima 3em \parindent \z@ \rightskip \@pnumwidth \parfillskip +-\@pnumwidth + {\Large \bf \leavevmode #1\hfil \hbox to\@pnumwidth{\hss #2}}\par + \nobreak \endgroup} +% +\def\numberline#1{\advance\hangindent by\@tempdima% +\hbox to\@tempdima{\hss#1\enspace}} +% +\def\bf@dottedtocline#1#2#3#4#5{\ifnum #1>\c@tocdepth \else + \vskip \z@ plus .2pt + {\leftskip #2\relax \rightskip \@tocrmarg \parfillskip -\rightskip + \parindent #2\relax\@afterindenttrue + \interlinepenalty\@M + \leavevmode + \@tempdima #3\relax \advance\leftskip \@tempdima \hbox{}\hskip -\leftskip +{\bf#4}\nobreak\leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern \@dotsep + mu$}\hfill \nobreak \hbox to\@pnumwidth{\hfil\rm #5}\par}\fi} +% +\def\l@section{\vskip2mm\bf@dottedtocline{1}{0em}{1.7em}} +\def\l@subsection{\@dottedtocline{2}{1.7em}{2.3em}} +\def\l@subsubsection{\@dottedtocline{3}{4em}{2em}} +\def\l@paragraph{\@dottedtocline{4}{6em}{2em}} +\def\l@subparagraph{\@dottedtocline{5}{8em}{2em}} +\def\listoffigures{\section*{List of Figures\markboth + {List of Figures}{List of Figures}}\@starttoc{lof}} +\def\l@figure{\@dottedtocline{1}{1.5em}{2.3em}} +\def\listoftables{\section*{List of Tables\markboth + {List of Tables}{List of Tables}}\@starttoc{lot}} +\let\l@table\l@figure + +\def\endthebibliography{\endlist\normalsize} + +\newif\if@restonecol +\def\theindex{\@restonecoltrue\if@twocolumn\@restonecolfalse\fi +\columnseprule \z@ +\columnsep 35pt\twocolumn[\section*{Index}] + \markboth{Index}{Index}\thispagestyle{plain}\parindent\z@ + \parskip\z@ plus .3pt\relax\let\item\@idxitem} +\def\@idxitem{\par\hangindent 40pt} +\def\subitem{\par\hangindent 40pt \hspace*{20pt}} +\def\subsubitem{\par\hangindent 40pt \hspace*{30pt}} +\def\endtheindex{\if@restonecol\onecolumn\else\clearpage\fi} +\def\indexspace{\par \vskip 10pt plus 5pt minus 3pt\relax} + +\def\footnoterule{\kern-3\p@\hrule width 2 true cm\kern 2.6\p@} + +\long\def\@makefntext#1{\@setpar{\@@par\@tempdima \hsize + \advance\@tempdima-1em\parshape \@ne 1em\@tempdima}\par + \parindent 1em\noindent \hbox to \z@{\hss$^{\@thefnmark}$\ }#1} + +\setcounter{topnumber}{2} +\def\topfraction{.9} +\setcounter{bottomnumber}{1} +\def\bottomfraction{.3} +\setcounter{totalnumber}{3} +\def\textfraction{.15} +\def\floatpagefraction{.85} +\setcounter{dbltopnumber}{2} +\def\dbltopfraction{.85} +\def\dblfloatpagefraction{.85} + +\long\def\@makecaption#1#2{ + \vskip 10pt + \setbox\@tempboxa\hbox{{\bf #1} #2} + \ifdim \wd\@tempboxa >\hsize \unhbox\@tempboxa\par \else \hbox +to\hsize{\box\@tempboxa\hfil} + \fi\vskip5pt} + +\long\def\@caption#1[#2]#3{\addcontentsline{\csname + ext@#1\endcsname}{#1}{\protect\numberline{\csname + the#1\endcsname}{\ignorespaces #2}}\par + \begingroup + \@parboxrestore + \@makecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par + \endgroup} + +\newcounter{figure} +\def\thefigure{\@arabic\c@figure} + +\def\fps@figure{htbp} +\def\ftype@figure{1} +\def\ext@figure{lof} +\def\fnum@figure{Fig.\thinspace\thefigure.} +\def\figure{\@float{figure}\small\rm} +\def\endfigure{\vskip-5pt\end@float} +\@namedef{figure*}{\@dblfloat{figure}} +\@namedef{endfigure*}{\end@dblfloat} + +\newcounter{table} +\def\thetable{\@arabic\c@table} +\def\fps@table{htbp} +\def\ftype@table{2} +\def\ext@table{lot} +\def\fnum@table{Table \thetable.} +\def\table{\@float{table}\small\rm} +\let\endtable\end@float +\@namedef{table*}{\@dblfloat{table}} +\@namedef{endtable*}{\end@dblfloat} + +% LaTeX does not provide a command to enter the authors institute +% addresses. The \institute command is defined here. + +\newcounter{@inst} +\newcounter{@auth} +\newdimen\instindent + +\def\institute#1{\gdef\@institute{#1}} + +\def\institutename{\par + \begingroup + \parskip=0pt + \setcounter{@inst}{1}% + \def\and{\par\stepcounter{@inst}% + \hangindent\instindent\hangafter=0\noindent + \llap{$^{\the@inst}$\enspace}\ignorespaces}% + \setbox0=\vbox{\def\thanks##1{}\@institute}% + \ifnum\c@@inst>9\relax\setbox0=\hbox{$^{88}$\enspace}% + \else\setbox0=\hbox{$^{8}$\enspace}\fi + \instindent=\wd0\relax + \ifnum\c@@inst=1\relax\else + \setcounter{footnote}{\c@@inst}% + \setcounter{@inst}{1}% + \hangindent\instindent\hangafter=0\noindent + \llap{$^{\the@inst}$\enspace}\fi\ignorespaces + \@institute\par + \endgroup} + +\def\@thanks{} + +\def\@fnsymbol#1{\ifcase#1\or\star\or{\star\star}\or{\star\star\star}% + \or \dagger\or \ddagger\or + \mathchar "278\or \mathchar "27B\or \|\or **\or \dagger\dagger + \or \ddagger\ddagger\else\@ctrerr\fi\relax} + +\def\inst#1{\unskip\/$^{#1}$} + +\def\subtitle#1{\gdef\@subtitle{#1}} +\def\@subtitle{} + +\def\titlerunning#1{\gdef\@titlerunning{#1}} +\def\@titlerunning{} + +\def\authorrunning#1{\gdef\@authorrunning{#1}} +\def\@authorrunning{} + +\def\Logo{\setbox254=\hbox{ THE JOURNAL OF }% +\vbox{\hrule\hbox{\vrule\vbox{\kern3pt +\copy254 +\hbox to\wd254{\hfil NONLINEAR\hfil} +\hbox to\wd254{\hfil SCIENCE\hfil} +\hbox to\wd254{\hfil\number\day.\number\month.\number\year\hfil} +\kern3pt}\vrule}\hrule}} +\def\makeheadbox{\hbox to\hsize{\hfil +\Logo}} + +\def\maketitle{\par + \begingroup + \parindent=\z@ + \def\thefootnote{\fnsymbol{footnote}} + \if@twocolumn + \twocolumn[\@maketitle] + \else \newpage + \global\@topnum\z@ \@maketitle \fi\thispagestyle{empty}\@thanks + \endgroup + \let\maketitle\relax + \let\@maketitle\relax + \gdef\@thanks{}\gdef\@author{}\gdef\@title{}\gdef\@subtitle{}% + \let\thanks\relax} + +\def\@maketitle{\newpage + \rm + \makeheadbox + {\LARGE \bf\boldmath + \pretolerance=10000 + \rightskip=0pt plus 4cm + \vskip2.1cm + \@title \par}\vskip .4cm +\if!\@subtitle!\else {\bf\boldmath + \vskip -.2cm + \pretolerance=10000 + \rightskip=0pt plus 3cm + \@subtitle \par}\vskip .4cm\fi +{\bf\@author\vskip.1cm +\def\\{ }\def\inst##1{}\def\thanks##1{}\def\and{}% +\setcounter{@auth}{1}% +\if!\@titlerunning!\else\def\@title{\@titlerunning}\fi +\if!\@authorrunning!\else\def\@author{\@authorrunning}\fi +\xdef\@author{\@author\unskip\unskip}% +\xdef\@title{\ignorespaces\@title}% +\instindent=\hsize\advance\instindent by-1cm\relax +\setbox0=\hbox{\small\@author}\ifdim\wd0>\instindent +\typeout{Warning: The running head produced by the +\protect\author \space command}\typeout{exceeds the pagewidth, +please supply a short form with \protect\authorrunning.}% +\def\@author{Author(s) suppressed due to excessive length, +please use {\tt$\backslash$authorrunning}.}\fi +\setbox0=\hbox{\small\@title}\ifdim\wd0>\instindent +\typeout{Warning: The running head produced by the +\protect\title \space command}\typeout{exceeds the pagewidth, +please supply a short form with \protect\titlerunning.}% +\def\@title{Title suppressed due to excessive length, +please use {\tt$\backslash$titlerunning}.}\fi +\markboth{\@author}{\@title}} + {\small\rm\institutename + \par + \vskip 0.3cm + \@date + \par} + \vskip 0.8cm} + +\mark{{}{}} + +\if@twoside +\def\ps@headings{\def\@oddfoot{}\def\@evenfoot{}% +\def\@evenhead{\small\rm +\thepage\hfil\leftmark}\def\@oddhead{\hbox{}\small\rm\rightmark \hfil +\thepage}\def\sectionmark##1{}% +\def\subsectionmark##1{}} +\else \def\ps@headings{\def\@oddfoot{}\def\@evenfoot{}\def +\@oddhead{\hbox +{}\sl \rightmark \hfil \rm\thepage}\def\sectionmark##1{\markright +{\uppercase{\ifnum \c@secnumdepth >\z@ + \thesection\hskip 1em\relax \fi ##1}}}} +\fi +\def\ps@myheadings{\def\@oddhead{\hbox{}\sl\rightmark \hfil +\rm\thepage}\def\@oddfoot{}\def\@evenhead{\rm \thepage\hfil\sl +\leftmark\hbox +{}}\def\@evenfoot{}\def\sectionmark##1{}\def\subsectionmark##1{}} + +\def\today{\ifcase\month\or + January\or February\or March\or April\or May\or June\or + July\or August\or September\or October\or November\or December\fi + \space\number\day, \number\year} + +\ps@headings \pagenumbering{arabic} \onecolumn +\if@twoside\else\raggedbottom\fi + +% new environments and theorems +% borrowed form the LTMP-style of Springer-Verlag +% designed by Dr. Christoph Ender +% +% define the new theorem like environments +% define a new style of environments where it is possible to define +% the font % used as the theorem name and the fontfamily for the text. +% +% \newstytheorem{name}{thefont}{txtfont}{Text}[Counter] +% \newstytheorem{name}{thefont}{txtfont}[oldname]{Text} +% +% #1 - name of theorem +% #2 - theorem font +% #3 - text font +% +\def\newstytheorem#1#2#3{% +\@ifnextchar[{\che@othm{#1}{#2}{#3}}{\che@nthm{#1}{#2}{#3}}} +% +% #1 - name of theorem +% #2 - theorem font +% #3 - text font +% #4 - text string of theorem name +% +\def\che@nthm#1#2#3#4{% +\@ifnextchar[{\che@xnthm{#1}{#2}{#3}{#4}}{\che@ynthm{#1}{#2}{#3}{#4}}} +% +% #1 - name of theorem +% #2 - theorem font +% #3 - text font +% #4 - text string of thorem name +% #5 - add theorem counter to reset list of another counter +% +\def\che@xnthm#1#2#3#4[#5]{\expandafter +\@ifdefinable\csname #1\endcsname +{\@definecounter{#1}\if@envcountreset\@addtoreset{#1}{#5}\fi +\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}% +\global\@namedef{#1}{\che@thm{#1}{#4}{#2}{#3}}\global +\@namedef{end#1}{\@endtheorem}}} +% +% #1 - name of theorem +% #2 - theorem font +% #3 - text font +% #4 - text string of thorem name +% +\def\che@ynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname +{\@definecounter{#1}% +\expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}% +\global\@namedef{#1}{\che@thm{#1}{#2}{#3}{#4}}\global +\@namedef{end#1}{\@endtheorem}}} +% +% change oldthm if oldname in specification is '*' +% then don't use a counter +% #1 - countername +% #2 - theorem font +% #3 - text font +% #4 - counter used +% #5 - string containing theorem name to print +% +\def\che@othm#1#2#3[#4]#5{\expandafter\@ifdefinable +\csname#1\endcsname% +{\@@othm@{#1}{#2}{#3}{#4}{#5}\global\@namedef{end#1}{\@endtheorem}}} +% +\def\@@othm@#1#2#3#4#5{\if *#4{\global\@namedef{the#1}{\relax} +\global\@namedef{#1}{\@bthm@{}{#5}{#2}{#3}}}\else +{\global\@namedef{the#1}{\@nameuse{the#4}}% define the counter +\global\@namedef{#1}{\che@thm{#4}{#5}{#2}{#3}}}\fi} +% +% new defs for theorem environment che 17-MAR-1989 +% it improves the option possible +% +% #1 - countername = theorem name +% #2 - string containing theorem name to print +% #3 - theorem font +% #4 - text font +\def\che@thm#1#2#3#4{\@ifnextchar({\@athm{#1}{#2}{#3}{#4}}{% +\@ifnextchar *{\@bthm{#1}{#2}{#3}{#4}}% +{\@@thm{#1}{#2}{#3}{#4}}}} +% +% \begin{thm}(A.1)[test] results in: +% \end{thm} thm A.1 (test) .... +% #1 - theorem +% #2 - string of theorem name +% #3 - font for theorem name and label +% #4 - Text font +% #5 - is the new label +% #6 - optional string +% +\def\@athm#1#2#3#4(#5){\@ifnextchar[{% +\@aythm{#1}{#2}{#3}{#4}{#5}}{\@axthm{#1}{#2}{#3}{#4}{#5}}} +\def\@axthm#1#2#3#4#5{\@@locthmlab{#1}{#5}% +\@begintheorem{#2}{#5}{#3}{#4}\ignorespaces} +\def\@aythm#1#2#3#4#5[#6]{\@@locthmlab{#1}{#5}% +\fuh@opargbegintheorem{#2}{#5}{#6}{#3}{#4}\ignorespaces} +% +% \begin{thm}*[xytest] results in: +% \end{thm} thm (xytest) .... +% #1 - theorem +% #2 - string of theorem name +% #3 - font for theorem name and label +% #4 - Text font +% #5 - optional string +% +\def\@bthm@#1#2#3#4{\@ifnextchar[{\@bythm{#1}{#2}{#3}{#4}}{% +\@bxthm{#1}{#2}{#3}{#4}}} +\def\@bthm#1#2#3#4*{\@ifnextchar[{\@bythm{#1}{#2}{#3}{#4}}{% +\@bxthm{#1}{#2}{#3}{#4}}} +\def\@bxthm#1#2#3#4{\if !#1!\relax\else\@@locthmlab{#1}{}\fi +\@@begintheorem{#2}{#3}{#4}\ignorespaces} +\def\@bythm#1#2#3#4[#5]{% +\@@opargbegintheorem{#2}{#3}{#4}{#5}\ignorespaces} +% +% define local label +% if no number or a user specified label occured +% +\def\@@locthmlab#1#2{\expandafter\def\csname the#1\endcsname{#2} +\let\@chetempa\protect\def\protect{\noexpand\protect\noexpand}% +\edef\@currentlabel{\csname p@#1\endcsname\csname the#1\endcsname}% +\let\protect\@chetempa} +% +% #1 - counter = theorem name +% #2 - string with name +% #3 - font for theorem name and label +% #4 - font for text +\def\@@thm#1#2#3#4{\refstepcounter + {#1}\@ifnextchar[{\che@ythm{#1}{#2}{#3}{#4}}{% + \che@xthm{#1}{#2}{#3}{#4}}} +% +\def\che@xthm#1#2#3#4{\che@begintheorem{#2}{\csname +the#1\endcsname}{#3}{#4}\ignorespaces} +\def\che@ythm#1#2#3#4[#5]{\che@opargbegintheorem{#2}{\csname + the#1\endcsname}{#5}{#3}{#4}\ignorespaces} +% +% #1 - name of theorem +% #2 - label string +% #3 - font for name and lable +% #4 - text fomt +% +\def\che@begintheorem#1#2#3#4{#4\trivlist\item[#3 #1\ts #2.]} +% +% #1 - name of theorem +% #2 - label string +% #3 - additonal text +% #4 - font for name and lable +% #5 - text fomt +% +\def\che@opargbegintheorem#1#2#3#4#5{#5 \trivlist +\item[#4 #1\ts #2\ #3.]} +% +\def\fuh@opargbegintheorem#1#2#3{\it \trivlist + \item[\hskip \labelsep{\bf #1\ #2\ (#3).}]} +% +\def\@@begintheorem#1#2#3{#3\trivlist\item[#2 #1.]} +\def\@@opargbegintheorem#1#2#3#4{#3\trivlist\item[#2 #1 #4.]} + +\newstytheorem{theorem}{\bf}{\it}{Theorem}[section] +\newstytheorem{example}{\it}{\rm}{Example}[section] +\newstytheorem{proposition}{\bf}{\it}[theorem]{Proposition} +\newstytheorem{corollary}{\bf}{\it}[theorem]{Corollary} +\newstytheorem{lemma}{\bf}{\it}[theorem]{Lemma} +\newstytheorem{proof}{\it}{\rm}[*]{Proof} +\newstytheorem{definition}{\bf}{\rm}[theorem]{Definition} +\newstytheorem{remark}{\it}{\rm}[*]{Remark} +\newstytheorem{exercise}{\it}{\rm}[theorem]{Exercise} +\newstytheorem{problem}{\it}{\rm}[theorem]{Problem} +\newstytheorem{solution}{\it}{\rm}[theorem]{Solution} +\newstytheorem{note}{\it}{\rm}[theorem]{Note} +\newstytheorem{question}{\it}{\rm}[theorem]{Question} + +\def\squareforqed{\hbox{\rlap{$\sqcap$}$\sqcup$}} +\def\qed{\ifmmode\squareforqed\else{\unskip\nobreak\hfil +\penalty50\hskip1em\null\nobreak\hfil\squareforqed +\parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi} + +\def\getsto{\mathrel{\mathchoice {\vcenter{\offinterlineskip +\halign{\hfil +$\displaystyle##$\hfil\cr\gets\cr\to\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr\gets +\cr\to\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr\gets +\cr\to\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +\gets\cr\to\cr}}}}} +\def\lid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil +$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr +\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr +\noalign{\vskip1pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +<\cr +\noalign{\vskip0.9pt}=\cr}}}}} +\def\gid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil +$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr +\noalign{\vskip1.2pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr +\noalign{\vskip1pt}=\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +>\cr +\noalign{\vskip0.9pt}=\cr}}}}} +\def\grole{\mathrel{\mathchoice {\vcenter{\offinterlineskip +\halign{\hfil +$\displaystyle##$\hfil\cr>\cr\noalign{\vskip-1pt}<\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr +>\cr\noalign{\vskip-1pt}<\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr +>\cr\noalign{\vskip-0.8pt}<\cr}}} +{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr +>\cr\noalign{\vskip-0.3pt}<\cr}}}}} +\def\bbbr{{\rm I\!R}} %reelle Zahlen +\def\bbbm{{\rm I\!M}} +\def\bbbn{{\rm I\!N}} %natuerliche Zahlen +\def\bbbf{{\rm I\!F}} +\def\bbbh{{\rm I\!H}} +\def\bbbk{{\rm I\!K}} +\def\bbbp{{\rm I\!P}} +\def\bbbone{{\mathchoice {\rm 1\mskip-4mu l} {\rm 1\mskip-4mu l} +{\rm 1\mskip-4.5mu l} {\rm 1\mskip-5mu l}}} +\def\bbbc{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm C$}\hbox{\hbox +to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}}} +\def\bbbq{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm +Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle\rm Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle\rm Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm Q$}\hbox{\raise +0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}}} +\def\bbbt{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm +T$}\hbox{\hbox to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle\rm T$}\hbox{\hbox +to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle\rm T$}\hbox{\hbox +to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm T$}\hbox{\hbox +to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}}} +\def\bbbs{{\mathchoice +{\setbox0=\hbox{$\displaystyle \rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox +to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}} +{\setbox0=\hbox{$\textstyle \rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox +to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptstyle \rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox +to0pt{\kern0.5\wd0\vrule height0.45\ht0\hss}\box0}} +{\setbox0=\hbox{$\scriptscriptstyle\rm S$}\hbox{\raise0.5\ht0\hbox +to0pt{\kern0.4\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox +to0pt{\kern0.55\wd0\vrule height0.45\ht0\hss}\box0}}}} +\def\bbbz{{\mathchoice {\hbox{$\sf\textstyle Z\kern-0.4em Z$}} +{\hbox{$\sf\textstyle Z\kern-0.4em Z$}} +{\hbox{$\sf\scriptstyle Z\kern-0.3em Z$}} +{\hbox{$\sf\scriptscriptstyle Z\kern-0.2em Z$}}}} +\def\ts{\thinspace} + +\def\typeset{\vfill\small\noindent This article was processed using +the \LaTeX{} macro package with JNS style\par} + +\def\enddocument{\par\typeset +\@checkend{document}\clearpage\begingroup +\if@filesw \immediate\closeout\@mainaux +\def\global\@namedef##1##2{}\def\newlabel{\@testdef r}% +\def\bibcite{\@testdef b}\@tempswafalse\makeatletter\input \jobname.aux +\if@tempswa \@warning{Label(s) may have changed. Rerun to get +cross-references right}\fi\fi\endgroup\deadcycles\z@\@@end} diff --git a/macros/plain/contrib/jns/jnsl.dem b/macros/plain/contrib/jns/jnsl.dem new file mode 100644 index 0000000000..2bdea91d07 --- /dev/null +++ b/macros/plain/contrib/jns/jnsl.dem @@ -0,0 +1,354 @@ +% This is JNSL.DEM the demonstration file of +% the LaTeX macro package from Springer-Verlag +% for the Journal of Nonlinear Science +% version of 16 July 1990 +\def\12{{1\ov 2}} +\def\al{\alpha} +\def\Aun{A_\un} +\def\aun{a_\un} +\def\bullet{\cdot} +\def\Bun{B_\un} +\def\bun{b_\un} +\def\de{\delta} +\def\dx{\dot x} +\def\ep{\varepsilon} +\def\fa{\forall} +\def\for{{\rm for}} +\def\Lai{\Lambda} +\def\lb{\left[} +\def\lg{\left\{} +\def\degr{\hbox{$^\circ$}} +\def\arcmin{\hbox{$^\prime$}} +\def\arcsec{\hbox{$^{\prime\prime}$}} +\def\liminfuu{{\rm lim inf}\,} +\def\liminfu{\mathop{\vphantom{\tst\sum}\hbox{\liminfuu}}} +\def\limsupuu{{\rm lim sup}\,} +\def\limsupu{\mathop{\vphantom{\tst\sum}\hbox{\limsupuu}}} +\def\lr{\left(} +\def\lss{\left\|} +\def\Min{{\rm Min\,}} +\def\NN{\bbbn} +\def\ol{\overline} +\def\om{\omega} +\def\ov{\over} +\def\rb{\right]} +\def\rg{\right\}} +\def\RRn{\bbbr^{2n}} +\def\RR{\bbbr} +\def\rr{\right)} +\def\rss{\right\|} +\def\sm{\setminus} +\def\tst{\textstyle} +\def\tx{\wt x} +\def\un{\infty} +\def\wt{\widetilde} +\def\ZZ{\bbbz} +\documentstyle{jns} +\begin{document} + +\title{Haupttitel 14 pt halbfett/Title boldface -- 14/16} +\titlerunning{Expression of Cellular Oncogenes} +\subtitle{Untertitel 10 pt halbfett/Subtitle boldface -- 10/11} + +\author{Ivar Ekeland\inst{1} and Roger Temam\inst{2}} +\authorrunning{R. M\"uller} + +\institute{Princeton University, Princeton NJ 08544, USA +\and +Universit\'e de Paris-Sud, +Laboratoire d'Analyse Num\'erique, B\^atiment 425,\\ +F-91405 Orsay Cedex, France} + +\date{Received June 5, 1989} + +\maketitle + +\begin{abstract} +A new variant of the multi-grid algorithms is presented. It uses +multiple coarse-grid corrections with particularly associated +prolongations and restrictions. In this paper the robustness with +respect to anisotropic problems is considered. + +\keywords multi-grid method -- coarse--grid correction -- +singular perturbation -- robustness. +\end{abstract} + +\section{The Anisotropic Equation and Standard Multi-Grid Methods} +\subsection{Introduction} +Multi-grid methods are known as very fast solvers of a large class of +discretised partial differential equations. However, the multi-grid +method cannot be understood as a fixed algorithm. Usually, the +components of the multi-grid iteration have to be adapted to the given +problem and sometimes the problems are modified in order to make them +acceptable for multi-grid methods. In particular, the smoothing +iteration is the most delicated part of the multi-grid process. + +An iteration is called a {\em robust} one, if it works for a sufficient +large class of problems. Attempts have been made to construct robust +multi-grid iterations by means of sophisticated smoothing processes\dots +\newpage +With this chapter, the preliminaries are over, and we begin the search +for periodic solutions to Hamiltonian systems. All this will be done in +the convex case; that is, we shall study the boundary-value problem +\begin{eqnarray*}\dot x&=&JH' (t,x)\\ x(0) &=& x(T) +\end{eqnarray*} +with $H(t,\bullet )$ a convex function of $x$, going to $+\un$ when +$\lss x\rss \to \un$. + +\subsection{Autonomous Systems} +In this section, we will consider the case when the Hamiltonian $H(x)$ +is autonomous. For the sake of simplicity, we shall also assume that it +is $C^1$. + +We shall first consider the question of nontriviality, within the +general framework of $\lr \Aun , \Bun\rr$-subquadratic Hamiltonians. In +the second subsection, we shall look into the special case when $H$ is +$\lr 0,\bun\rr$-subquadratic, and we shall try to derive additional +information. +\subsubsection{ The General Case: Nontriviality.} +We assume that $H$ is $\lr \Aun , \Bun \rr$-sub\-qua\-dra\-tic at infinity, +for some constant symmetric matrices $\Aun$ and $\Bun$, with $\Bun +-\Aun$ positive definite. Set: +\begin{eqnarray} +\gamma :&=&{\rm smallest\ eigenvalue\ of}\ \ \Bun - \Aun \\ +\lambda : &=& {\rm largest\ negative\ eigenvalue\ of}\ \ J {d\ov dt} ++\Aun\ . \end{eqnarray} + +Theorem 21 tells us that if $\lambda +\gamma < 0$, the boundary-value +problem: +\begin{equation}\begin{array}{rcl} \dx&=&JH' (x)\\ +x(0)&=&x (T)\end{array}\end{equation} +has at least one solution $\ol x$, which is found by minimizing the dual +action functional: +\begin{equation} \psi (u) = \int_o^T \lb \12 \lr \Lai_o^{-1} u,u\rr + N^\ast (-u)\rb +dt\end{equation} + +\noindent on the range of $\Lai$, which is a subspace $R (\Lai )\sb L^2$ with +finite codimension. Here +\begin{equation} N(x) := H(x) - \12 \lr \Aun x,x\rr\end{equation} +is a convex function, and +\begin{equation} N(x) \le \12 \lr \lr \Bun - \Aun\rr x,x\rr + c\ \ \ \fa x\ +.\end{equation} + +\begin{proposition} Assume $H'(0)=0$ and $ H(0)=0$. Set: +\begin{equation} \de := \liminfu_{x\to 0} 2 N (x) \lss x\rss^{-2}\ . +\label{eq:one} +\end{equation} + +If $\gamma < - \lambda < \de$, the solution $\ol u$ is non-zero: +\begin{equation} \ol x (t) \ne 0\ \ \ \fa t\ .\end{equation} +\end{proposition} +\begin{proof} Condition (\ref{eq:one}) means that, for every $\de ' > +\de$, there is some $\ep > 0$ such that +\begin{equation} \lss x\rss \le \ep \Rightarrow N (x) \le {\de '\ov 2} \lss x\rss^2\ +.\end{equation} + +It is an exercise in convex analysis, into which we shall not go, to +show that this implies that there is an $\eta > 0$ such that +\begin{equation} f\lss x\rss \le \eta \Rightarrow N^\ast (y) \le {1\ov 2\de '} \lss +y\rss^2\ .\label{eq:two}\end{equation} + +\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} + +Since $u_1$ is a smooth function, we will have $\lss hu_1\rss_\un \le +\eta$ for $h$ small enough, and inequality (\ref{eq:two}) will hold, +yielding thereby: +\begin{equation} \psi (hu_1) \le {h^2\ov 2} {1\ov \lambda} \lss u_1 \rss_2^2 + {h^2\ov 2} +{1\ov \de '} \lss u_1\rss^2\ .\end{equation} + +If we choose $\de '$ close enough to $\de$, the quantity $\lr {1\ov \lambda} ++ {1\ov \de '}\rr$ will be negative, and we end up with +\begin{equation} \psi (hu_1) < 0\ \ \ \ \ \for\ +\ h\ne 0\ \ {\rm small}\ .\end{equation} + +On the other hand, we check directly that $\psi (0) = 0$. This shows +that 0 cannot be a minimizer of $\psi$, not even a local one. So $\ol u +\ne 0$ and $\ol u \ne \Lai_o^{-1} (0) = 0$. \qed +\end{proof} +\begin{corollary} Assume $H$ is $C^2$ and $\lr \aun +,\bun\rr$-subquadratic at infinity. Let +$\xi_1,\allowbreak\dots,\allowbreak\xi_N$ be the +equilibria, that is, the solutions of $H' (\xi ) = 0$. Denote by $\om_k$ +the smallest eigenvalue of $H'' \lr \xi_k\rr$, and set: +\begin{equation} \om : = \Min \lg \om_1 , \dots , \om_k\rg\ .\end{equation} +If: +\begin{equation} {T\ov 2\pi} \bun < - E \lb - {T\ov 2\pi}\aun\rb < {T\ov +2\pi}\om\label{eq:three}\end{equation} +then minimization of $\psi$ yields a non-constant $T$-periodic solution +$\ol x$.\end{corollary} + +We recall once more that by the integer part $E [\al ]$ of $\al \in +\RR$, we mean the $a\in \ZZ$ such that $a< \al \le a+1$. For instance, +if we take $\aun = 0$, Corollary 2 tells us that $\ol x$ exists and is +non-constant provided that: + +\begin{equation} {T\ov 2\pi} \bun < 1 < {T\ov 2\pi}\end{equation} +or +\begin{equation} T\in \lr {2\pi\ov \om},{2\pi\ov \bun}\rr\ . +\label{eq:four}\end{equation} + +\begin{proof} The spectrum of $\Lai$ is ${2\pi\ov T} \ZZ +\aun$. The +largest negative eigenvalue $\lambda$ is given by ${2\pi\ov T}k_o +\aun$, +where +\begin{equation} {2\pi\ov T}k_o + \aun < 0\le {2\pi\ov T} (k_o +1) + \aun\ +.\end{equation} +Hence: +\begin{equation} k_o = E \lb - {T\ov 2\pi} \aun\rb \ .\end{equation} + +The condition $\gamma < -\lambda < \de$ now becomes: +\begin{equation} \bun - \aun < - {2\pi\ov T} k_o -\aun < \om -\aun\end{equation} +which is precisely condition (\ref{eq:three}).\qed +\end{proof} + +\begin{lemma} Assume that $H$ is $C^2$ on $\RRn \sm \{ 0\}$ and +that $H'' (x)$ is non-de\-gen\-er\-ate for any $x\ne 0$. Then any local +minimizer $\tx$ of $\psi$ has minimal period $T$.\end{lemma} +\begin{proof} We know that $\tx$, or $\tx + \xi$ for some constant $\xi +\in \RRn$, is a $T$-periodic solution of the Hamiltonian system: +\begin{equation} \dx = JH' (x)\ .\end{equation} + +There is no loss of generality in taking $\xi = 0$. So $\psi (x) \ge +\psi (\tx )$ for all $\tx$ in some neighbourhood of $x$ in $W^{1,2} \lr +\RR / T\ZZ ; \RRn\rr$. + +But this index is precisely the index $i_T (\tx )$ of the $T$-periodic +solution $\tx$ over the interval $(0,T)$, as defined in Sect.~2.6. So +\begin{equation} i_T (\tx ) = 0\ .\label{eq:five}\end{equation} + +Now if $\tx$ has a lower period, $T/k$ say, we would have, by Corollary +31: +\begin{equation} i_T (\tx ) = i_{kT/k}(\tx ) \ge ki_{T/k} (\tx ) + k-1 \ge k-1 \ge +1\ .\end{equation} + +This would contradict (\ref{eq:five}), and thus cannot happen.\qed +\end{proof} +\paragraph{Notes and Comments.} 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. + +To understand the nontriviality conditions, such as the one in formula +(\ref{eq:four}), one may think of a one-parameter family $x_T$, $T\in +\lr 2\pi\om^{-1}, 2\pi \bun^{-1}\rr$ of periodic solutions, $x_T (0) = +x_T (T)$, with $x_T$ going away to infinity when $T\to 2\pi \om^{-1}$, +which is the period of the linearized system at 0. + +\begin{table} +\caption[ ]{Observational results from NGC 4827} +\begin{flushleft} +\renewcommand{\arraystretch}{1.2} +\begin{tabular}{llllllllllllll} +\hline + & & \multicolumn{3}{l}{RA (1950)} &\ & \multicolumn{3}{l}{Dec (1950)} + & $S$ & Pol & \% & $\log P$\\ +\cline{3-5}\cline{7-9} + & &(h) &(m) & (s) & & (\degr) & (\arcmin) & (\arcsec) + & (mJy) & (mJy) & & (W Hz$^{-1}$)\\ +\hline +Core & (5 GHz) & 12 & 54 & 18.0 & & 27 & 26 & 56.2 + & 8 & & & 21.64 \\ +Total&(327 MHz)& & & & & & & + & 210 & & & 23.13 \\ + &(1.4 GHz)& & & & & & & + & 57 & 1.3 & 2 & 22.49 \\ + & (5 GHz) & & & & & & & + & 26 & 0.73 & 3 & 22.15 \\ +\hline +\end{tabular} +\renewcommand{\arraystretch}{1} +\end{flushleft} +\end{table} +\begin{theorem} [(Ghoussoub-Preiss)] Assume $H(t,x)$ is +$(0,\ep )$-subquadratic at +infinity for all $\ep > 0$, and $T$-periodic in $t$ +\begin{equation} H (t,\bullet )\ \ \ \ \ {\rm is\ convex}\ \ \fa t\end{equation} +\begin{equation} H (\bullet ,x)\ \ \ \ \ {\rm is}\ \ T{\rm -periodic}\ \ \fa x +\end{equation} +\begin{equation} H (t,x)\ge n\lr \lss x\rss\rr\ \ \ \ \ {\rm with}\ \ n (s)s^{-1}\to +\un\ \ {\rm as}\ \ s\to \un\end{equation} +\begin{equation} \fa \ep > 0\ ,\ \ \ \exists c\ :\ H(t,x) \le {\ep\ov 2}\lss x\rss^2 + +c\ .\end{equation} + +Assume also that $H$ is $C^2$, and $H'' (t,x)$ is positive definite +everywhere. Then there is a sequence $x_k$, $k\in \NN$, of $kT$-periodic +solutions of the system +\begin{equation} \dx = JH' (t,x)\end{equation} +such that, for every $k\in \NN$, there is some $p_o\in\NN$ with: +\begin{equation} p\ge p_o\Rightarrow x_{pk} \ne x_k\ . +\end{equation} +\qed +\end{theorem} +\begin{example} [{\rm(External forcing)}] Consider the system: +\begin{equation} \dx = JH' (x) + f(t)\end{equation} +where the Hamiltonian $H$ is $\lr 0,\bun\rr$-subquadratic, and the +forcing term is a distribution on the circle: +\begin{equation} f = {d\ov dt} F + f_o\ \ \ \ \ {\rm with}\ \ F\in L^2 \lr \RR / T\ZZ +; \RRn\rr\ ,\end{equation} +where $f_o : = T^{-1}\int_o^T f (t) dt$. For instance, +\begin{equation} f (t) = \sum_{k\in \NN} \de_k \xi\ ,\end{equation} +where $\de_k$ is the Dirac mass at $t= k$ and $\xi \in \RRn$ is a +constant, fits the prescription. This means that the system $\dx = JH' +(x)$ is being excited by a series of identical shocks at interval $T$. +\end{example} +\begin{definition} Let $A_\un (t)$ and $B_\un (t)$ be symmetric +operators in $\RRn$, depending continuously on $t\in [0,T]$, such that +$A_\un (t) \le B_\un (t)$ for all $t$. + +A Borelian function $H: [0,T]\times \RRn \to \RR$ is called $\lr A_\un +,B_\un\rr$-{\it subquadratic at infinity} if there exists a function +$N(t,x)$ such that: +\begin{equation} H (t,x) = \12 \lr A_\un (t) x,x\rr + N(t,x)\end{equation} +\begin{equation} \fa t\ ,\ \ \ N(t,x)\ \ \ \ \ {\rm is\ convex\ with\ respect\ to}\ +\ x\end{equation} +\begin{equation} N(t,x) \ge n\lr \lss x\rss\rr\ \ \ \ \ {\rm with}\ \ n(s)s^{-1}\to ++\un\ \ {\rm as}\ \ s\to +\un\end{equation} +\begin{equation} \exists c\in \RR\ :\ \ \ H (t,x) \le \12 \lr B_\un (t) x,x\rr + c\ \ +\ \fa x\ .\end{equation} + +If $A_\un (t) = a_\un I$ and $B_\un (t) = b_\un I$, with $a_\un \le +b_\un \in \RR$, we shall say that $H$ is $\lr a_\un +,b_\un\rr$-subquadratic at infinity. As an example, the function $\lss x +\rss^\al$, with $1\le \al < 2$, is $(0,\ep )$-subquadratic at infinity +for every $\ep > 0$. Similarly, the Hamiltonian +\begin{equation} H (t,x) = \12 k \lss k\rss^2 +\lss x\rss^\al\end{equation} +is $(k,k+\ep )$-subquadratic for every $\ep > 0$. Note that, if $k<0$, +it is not convex. +\end{definition} + +\paragraph{Notes and Comments.} The first results on subharmonics were +obtained by Rabinowitz in \cite{rab}, who showed the existence of +infinitely many subharmonics both in the subquadratic and superquadratic +case, with suitable growth conditions on $H'$. Again the duality +approach enabled Clarke and Ekeland in \cite{clar:eke:2} to treat the +same problem in the convex-subquadratic case, with growth conditions on +$H$ only. + +Recently, Michalek and Tarantello (see \cite{mich:tar} and \cite{tar}) +have obtained lower bound on the number of subharmonics of period $kT$, +based on symmetry considerations and on pinching estimates, as in +Sect.~5.2 of this article. + +\begin{thebibliography}{MT1} +\bibitem[CE1]{clar:eke} Clarke, F., Ekeland, I.: Nonlinear oscillations +and +boundary-value problems for Hamiltonian systems. Arch. Rat. Mech. Anal. +{\bf 78} (1982) 315--333 +\bibitem[CE2]{clar:eke:2} Clarke, F., Ekeland, I.: Solutions +p\'eriodiques, du +p\'eriode donn\'ee, des \'equations hamiltoniennes. Note CRAS Paris {\bf +287} (1978) 1013--1015 +\bibitem[MT1]{mich:tar} Michalek, R., Tarantello, G.: Subharmonic +solutions with +prescribed minimal period for nonautonomous Hamiltonian systems. J. +Diff. Eq. {\bf 72} (1988) 28--55 +\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. {\bf 33} (1980) 609--633 +\end{thebibliography} +\end{document} diff --git a/macros/plain/contrib/jns/jnsl.doc b/macros/plain/contrib/jns/jnsl.doc new file mode 100644 index 0000000000..0e4e7801b9 --- /dev/null +++ b/macros/plain/contrib/jns/jnsl.doc @@ -0,0 +1,1162 @@ +% This is JNSL.DOC the documentation file of +% the LaTeX macro package from Springer-Verlag +% for the Journal of Nonlinear Science +% version of 16 July 1990 +\documentstyle[jnsldoc]{jns} +% +\newfont{\titelfont}{cmr10 scaled 1728} +\newfont{\titelbffont}{cmbx10 scaled 2074} +\newfont{\titelbigfont}{cmr10 scaled 2488} +\markboth{Style File for Authors Coding with \LaTeX{}}{Style File +for Authors Coding with \LaTeX{}} +% +\begin{document} +\thispagestyle{empty} +\begin{flushleft} +{\titelbffont Style File}\\[6pt] +{\titelbffont for Authors Coding with \LaTex{}}\\[2cm] +\end{flushleft} +\rule{\textwidth}{1pt} +\vspace{2pt} +\begin{flushright} +\begin{tabular}{@{}l} +{\titelbigfont The Journal of}\\[9pt] +{\titelbigfont Nonlinear Science}\\[10pt] +\end{tabular} +\end{flushright} +\rule{\textwidth}{1pt} +\vfill +\begin{flushright} +\begin{tabular}{@{}l} +{\titelfont Springer-Verlag}\\[5pt] +{\titelfont New \kern-4pt York Berlin Heidelberg Tokyo}\\[5pt] +{\titelfont London Paris Hong \kern-3pt Kong} +\end{tabular} +\end{flushright} +\newpage +% +\section*{For further information please contact us:} +% +\begin{flushleft} +\begin{tabular}{l@{\quad}l@{\hspace{3mm}}l} +$\bullet$ & \multicolumn{2}{l}{\bf Springer-Verlag New \kern-3pt +York}\\[0.5mm] + & \multicolumn{2}{l}{Springer-Verlag New \kern-2pt York, 175 Fifth + Avenue,}\\ + & & New \kern-2pt York, New \kern-2pt York 10010 + USA\\[0.5mm] + & Telex: & 232235\\ + & Fax: & (212)437-6272\\ + & Editorial: & (Mon--Fr; preferably between 9 a.m. + and 4 p.m. --\\ + & & Eastern Standard Time)\\ + & & Telephone (212)460-1565\\ + & net-address: & TROWBRIDGE@COMPUSERVE.COM\\[1mm] +$\bullet$ & \multicolumn{2}{l}{\bf Springer-Verlag Heidelberg}\\[1mm] + & \multicolumn{2}{l}{Springer-Verlag, Postfach 105280, D-6900 Heidelberg + 1, FRG}\\[0.5mm] + & 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\\ + & Telex: & 461723\\ + & Telefax: & (06221)43982\\ + & Editorial: & (Mon--Fr; preferably between 9 a.m.\\ + & & and 4 p.m. -- European local time)\\ + & & Telephone (0049)(0)6221-487534\\ + & \multicolumn{2}{l}{\TeX{}nical and \LaTeX{}nical information + (Mon--Fri; preferably between}\\ + & & 9 a.m. and 1 p.m. -- European local time):\\ + & & Telephone (0049)(0)6221-487478\\ + &bitnet/EARN:& SPRINGER@DHDSPRI6 +\end{tabular} +\end{flushleft} +\rule{\textwidth}{1pt} +% +\section*{Mailing address for your disk/magnetic tape and output:} +% +\begin{quote} +Springer-Verlag New \kern-2pt York, Inc.\\ +175 Fifth Avenue\\ +New \kern-2pt York, New \kern-2pt York 10010 USA +\end{quote} +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 +\LaTeX{} input (source) file und the final DVI-file and make sure +that the text is {\it identical in both cases.} + +Contributions coded with \LaTeX{} but not with the JNS style, cannot be +accepted for electronic processing; they will be typeset in the +conventional way. +% +\newpage +\tableofcontents +\newpage +% +\section{Introduction} +% +Authors wishing to code their contribution +for the +\begin{center} +{\it Journal of Nonlinear Science,} +\end{center} +with \LaTeX{}, as well as those who have already coded with \LaTeX{}, +will be provided with a style file that will give the text the +desired layout. Authors are requested to +adhere strictly to these instructions; {\it the style +file must not be changed}. + +The text output area is automatically set within an area of +12.2\,cm horizontally and 19.4\,cm vertically, excluding +running heads. + +If you are already familiar with \LaTeX{}, then the +JNS style file should not give you any major difficulties. +This style file will change the layout to the required JNS 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'' style. +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 JNS 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 JNS; 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} +% +Please insert the enclosed diskette or tape into your computer. You will +find the following files: +\begin{flushleft} +\begin{tabular}{@{}p{2.5cm}l} +{\it jnsl.doc} & General instructions (this document),\\ + & {\it jnsl.doc} means jns latex.documentation\\ +{\it jnsl.dem} & An example showing how to code the text\\ +{\it jns.sty} & Style file to invoke \LaTeX{} +\end{tabular} +\end{flushleft} +You have to run each file twice with: \verb|latex file.name|. +% +\subsection{How to Invoke the JNS Style File} +% +The JNS style file is an adaptation of the \LaTeX{} ``article'' style. +Therefore you may use all ``article'' style commands to prepare your +manuscript. +JNS style is invoked by replacing ``article'' by ``jns'' in the first +line of your document: +\begin{verbatim} +\documentstyle{jns}| +% +\begin{document} + <Your contribution> +\end{document} +\end{verbatim} +% +\subsection{Contributions Already Coded with \protect\LaTeX{} without +the JNS Style File} +% +If your file is already coded with \LaTeX{} you can easily +adapt it a posteriori to JNS style. Contributions submitted +to us in \LaTeX{} but not adapted to JNS style, +cannot be accepted for electronic processing; they will be typeset +in the conventional way. + +Please refrain from using any \LaTeX{} or \TeX{} commands +that affect the layout or formatting of your document (i.e. commands +like \verb|\textheight|, \verb|\vspace|, \verb|\hoffset| etc.). +There may nevertheless be exceptional occasions on which to +use some of them. + +The JNS style 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.\/} +% +\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 (1986), Addison-Wesley Publishing +Company, Reading, Mass. + +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} +{\it Sample Input} +\end{flushleft} +\begin{verbatim} +\begin{equation} + \left(\frac{a^{2} + b^{2}}{c^{3}} \right) = 1 \quad + \mbox{ if } c\neq 0 \mbox{ and if } a,b,c\in \bbbr \enspace . +\end{equation} +\end{verbatim} +{\it 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. Titles have no end punctuation. + +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 \TeX{} and \LaTeX{} treat 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 +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 +{\it abbreviations} such as Ord, Var, GL, SL, sgn, const.\ +are always set in roman type. To ensure +this use the \verb|\rm| command: \verb|{\rm Hz}|. +On p.\ 46 of the {\em \LaTeX{} User's Guide \& Reference +Manual\/} by Leslie Lamport you will find the names of +common mathe\-matical functions, such as log, sin, exp, max and sup. +These should be coded as \verb|\log|, +\verb|\sin|, \verb|\exp|, \verb|\max|, \verb|\sup| +and will appear in roman. +\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} +% +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.\,4.1) +\item +Abbreviations and expressions +in the text such as Fig(s)., Table(s), Sect(s)., Chap(s)., +Theorem, Corollary, Definition etc. when used with numbers, e.g.\ +Fig.\,3, Table\,1, Theorem 2. +\end{itemize} +Please follow the special rules in Sect.\,4.3 for referring to equations. +\item +The following should {\it not\/} be capitalized: +\begin{itemize} +\item +The words figure(s), table(s), equation(s), +theorem(s) in the text when used without an accompanying number +\item +Figure legends and table captions except for names and +abbreviations. +\end{itemize} +\end{alpherate} +% +\subsection{Abbreviation of Words} +% +\begin{alpherate} +\item +The following {\it should} be abbreviated +when they appear in running text {\it +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 .\\ +{\it 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 your contribution should be coded as follows: +\begin{verbatim} +\title{<Your contribution 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).\\[6mm] +Now the name(s) of the authors(s) must be given: +\begin{verbatim} +\author{<author(s) name(s)>} +\end{verbatim} +Numbers referring to different addresses are +to be attached to each author. +If you have done this correctly, the 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. + +If there is more than one author, the order is up to you. +However, if there are more than two authors, you must separate the names +by commas. If the authors have different affiliations, +each name has to be followed by: +\begin{verbatim} +\inst{no} +\end{verbatim} +\newpage +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. +\begin{verbatim} +\institute{<name of an institute> +\and <name of the next institute> +\and <name of the next institute>} +\end{verbatim} +Unlike usual \LaTeX{} the \verb|\and| command is used with the +\verb|\institute| and not with the \verb|\author| command. + +\medskip +If footnotes are needed in \verb|\title| please code +(immediately after the word where the footnote +indicator should be placed): +\begin{verbatim} +\thanks{<text>} +\end{verbatim} +\verb|\thanks| may only appear in \verb|\title|, \verb|\author| +and \verb|\institute| (see below) to footnote anything. + +\medskip\noindent +The command +\begin{verbatim} +\maketitle +\end{verbatim} +formats the complete heading of your article. If you leave +it out the work done so far will produce {\bf no} text, +see {\it Sample Input} on p.~\pageref{samppage}. +% +\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] +{\it 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. + +Note that \verb|\title| 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|\title| +or \verb|\author|. +\begin{verbatim} +\titlerunning{Abbreviated contribution title} +\authorrunning{Abbreviated authors} +\end{verbatim} +\newpage +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 file. +If you call lemma once, this 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 this counter at 1 in each section, +please give the document style option \verb|envcountreset|: +\begin{verbatim} +\documentstyle[envcountreset]{jns} +\end{verbatim} + +\vspace{.5cm}\noindent +The following possibilities for run-in headings are available: +\begin{flushleft} +\verb|\begin{lemma} Text of the lemma \end{lemma}|\quad (see Output +Sample 1)\\[2mm] +% +\verb|\begin{lemma}[additional explanation of lemma] Text of +lemma \end{lemma}| \quad (see Output Sample 2)\\[2mm] +% +\verb|\begin{lemma}(overriding automatic numbering.) Text of the lemma +\end{lemma}| \quad (see Output Sample 3)\\[2mm] +% +\verb|\begin{lemma}(x)[additional explanation of lemma] Text of +lemma\end{lemma}| \quad (see Output Sample 4)\\[2mm] +% +\verb|\begin{lemma}* Text of lemma \end{lemma}| \quad (see Output +Sample 5)\\[2mm] +% +\verb|\begin{lemma}*[additional explanation of lemma] Text of +lemma\end{lemma}| \quad (see Output Sample 6) +\end{flushleft} +% +\begin{flushleft} +{\it Output Sample 1} +\begin{lemma}Text of lemma\end{lemma} +% +{\it Output Sample 2} +\begin{lemma}[additional explanation of lemma] Text of lemma\end{lemma} +% +{\it Output Sample 3} +\begin{lemma}(overriding automatic numbering.) Text of lemma\end{lemma} +% +{\it Output Sample 4} +\begin{lemma}(x)[additional explanation of lemma] Text of lemma\end{lemma} +% +{\it Output Sample 5} +\begin{lemma}* Text of lemma\end{lemma} +% +{\it Output Sample 6} +\begin{lemma}*[additional explanation of lemma] Text of lemma\end{lemma} +\end{flushleft} +\newpage +\noindent +The following variety of run-in headings are at your disposal: +\begin{alpherate} +\item +{\bf Bold} run-in headings with italicized text +as built-in environments: +\begin{verbatim} +\begin{proposition} <text> \end{proposition} +\begin{corollary} <text> \end{corollary} +\begin{lemma} <text> \end{lemma} +\begin{theorem} <text> \end{theorem} +\end{verbatim} +\item +The following must generally appear as {\it italic} run-in heading: +\begin{verbatim} +\begin{proof} <text> \qed \end{proof} +\end{verbatim} +\item +Further {\it italic} or {\bf bold} run-in headings may also occur: +\begin{verbatim} +\begin{definition} <text> \end{definition} +\begin{example} <text> \end{example} +\begin{remark} <text> \end{remark} +\begin{exercise} <text> \end{exercise} +\begin{problem} <text> \end{problem} +\begin{solution} <text> \end{solution} +\begin{note} <text> \end{note} +\begin{question} <text> \end{question} +\end{verbatim} +\end{alpherate} +% +\subsubsection*{Defining Your Own Environments.} +% +You can define additional environments using the command +\verb|\newstytheorem| which has five parameters. The first is the name +your environment should have (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) and the font family to use for the text of +this new environment (e.g.\ \verb|\it| or \verb|\rm|). Then the name of +an already known environment should be given in brackets (e.g.\ +\verb|[theorem]|). Your new environment will be numbered like the old +one. Finally comes the real text of the new run-in heading (e.g.\ +\verb|Conjecture|).\\ +Sample definition: +\begin{verbatim} +\newstytheorem{conjecture}{\bf}{\it}[theorem]{Conjecture} +\end{verbatim} +\newstytheorem{conjecture}{\bf}{\it}[theorem]{Conjecture} +Use of that definition: +\begin{verbatim} +\begin{conjecture} <text> \end{conjecture} +\end{verbatim} +e.g. +\begin{verbatim} +\begin{conjecture} It is clear that ...\end{conjecture} +\end{verbatim} +Its output: +\begin{conjecture} +It is clear that \dots +\end{conjecture} +\newpage +% +\noindent +{\it Sample Input} +\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 +% +\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}[\rm (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} +{\it Sample Output\/} (follows on the next page together with +examples of the above run-in headings) +% +\setcounter{theorem}{0} +\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 +% +\section*{1 \ Fixed-Period Problems: The Sublinear Case} +% +With this chapter, the preliminaries are over, and we begin the search +for periodic solutions \dots +% +\subsection*{1.1 \ 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}[\rm (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} +\newpage +% +\markboth{Style File for Authors Coding with \LaTeX{}}{Style File +for Authors Coding with \LaTeX{}} +\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) need not be coded. {\it Italic} +(not {\sl slanted}) or, if necessary, {\bf boldface} +should be used for emphasis in the text. +\begin{flushleft} +\begin{tabular}{@{}p{.19\textwidth}p{.79\textwidth}} +\verb|{\it Text}| & {\it Italicized Text}\\ +\verb|{\em Text}| & {\em Emphasized Text}\\ + & {\it 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|.\\ +\verb|{\bf Text}| & {\bf Important Text}\\ +\verb|\vec{Symbol}| & Vectors may only appear in math mode. The default + \LaTeX{} vector symbol has been adapted to JNS conventions.\\ + & \verb|$\vec{A times B\cdot C}| yields $\vec{A\times B\cdot C}$\\ + & \verb|$\vec{A}^{T} \otimes \vec{B} \otimes \vec{\hat{D}}$|\\ + & yields $\vec{A}^{T} \otimes \vec{B} \otimes \vec{\hat{D}}$ +\end{tabular} +\end{flushleft} +\newpage +% +\section {Footnotes} +% +Footnotes within the text should be coded: +\begin{verbatim} +\footnote{Text} +\end{verbatim} +{\it Sample Input} +\begin{flushleft} +Text with a footnote\verb|\footnote{The footnote is automatically +numbered.}| and text continues \dots +\end{flushleft} +{\it 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] +{\it 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} +{\it 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} +\newpage +% +\section {Figures} +% +Figure legends should be inserted after (not in) +the paragraph in which the figure is first mentioned. +They will be numbered automatically. + +{\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 +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} +{\it 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} +{\it 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 {\it above} the tables. The tables +will be numbered automatically. +% +\subsection{Tables Coded with \protect\LaTeX{}} +% +Please use the following coding:\\[2mm] +{\it Sample Input} +\begin{verbatim} +\begin{table} +\caption[ ]{Observational results from NGC 4827} +\begin{flushleft} +\begin{tabular}{llllllllllllll} +\hline + & & \multicolumn{3}{l}{RA (1950)} &\ + & \multicolumn{3}{l}{Dec (1950)} + & $S$ & Pol & \% & $\log P$\\ +\cline{3-5}\cline{7-9} + & &(h) &(m) & (s) & & (\degr) + & (\arcmin) & (\arcsec) + & (mJy) & (mJy) & & (W Hz$^{-1}$)\\ +\hline +Core & (5 GHz) & 12 & 54 & 18.0 & & 27 & 26 & 56.2 + & 8 & & & 21.64 \\ +Total&(327 MHz)& & & & & & & + & 210 & & & 23.13 \\ + &(1.4 GHz)& & & & & & & + & 57 & 1.3 & 2 & 22.49 \\ + & (5 GHz) & & & & & & & + & 26 & 0.73 & 3 & 22.15 \\ +\hline +\end{tabular} +\end{flushleft} +\end{table} + +Before continuing your text you need an empty line. \dots +\end{verbatim} + +\begin{table} +\caption[ ]{Observational results from NGC 4827} +\begin{flushleft} +\renewcommand{\arraystretch}{1.2} +\begin{tabular}{llllllllllllll} +\hline + & & \multicolumn{3}{l}{RA (1950)} &\ & \multicolumn{3}{l}{Dec (1950)} + & $S$ & Pol & \% & $\log P$\\ +\cline{3-5}\cline{7-9} + & &(h) &(m) & (s) & & (\degr) & (\arcmin) & (\arcsec) + & (mJy) & (mJy) & & (W Hz$^{-1}$)\\ +\hline +Core & (5 GHz) & 12 & 54 & 18.0 & & 27 & 26 & 56.2 + & 8 & & & 21.64 \\ +Total&(327 MHz)& & & & & & & + & 210 & & & 23.13 \\ + &(1.4 GHz)& & & & & & & + & 57 & 1.3 & 2 & 22.49 \\ + & (5 GHz) & & & & & & & + & 26 & 0.73 & 3 & 22.15 \\ +\hline +\end{tabular} +\renewcommand{\arraystretch}{1} +\end{flushleft} +\end{table} + +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.~63~ff. and p.~182 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] +{\it Sample Input} +\begin{verbatim} +\begin{table} +\caption{text of your caption} +\vspace{x cm} % the actual height needed for your table +\end{table} +\end{verbatim} +% +\subsection{Signs and Characters} +% +\subsubsection*{Special Signs.} +% +You may need to use special signs. The available ones are listed in the +{\em \LaTeX{} User's Guide \& Reference Manual\/} by Leslie Lamport, +pp.~44\,ff. +We have created further symbols for math mode (enclosed in \$): +\begin{center} +\begin{tabular}{l@{\hspace{1em}yields\hspace{1em}} +c@{\hspace{3em}}l@{\hspace{1em}yields\hspace{1em}}c} +\verb|\grole| & $\grole$ & \verb|\getsto| & $\getsto$\\ +\verb|\lid| & $\lid$ & \verb|\gid| & $\gid$ +\end{tabular} +\end{center} +% +\subsubsection*{Gothic (Fraktur).} +% +If gothic letters are {\it necessary}, please use those of the +relevant \AmSTeX{} alphabet which are available from the +American Mathematical Society. + +In \LaTeX{} only the following gothic letters are +available: \verb|$\Re$| yields $\Re$ and \verb|$\Im$| yields $\Im$. +These should {\it not\/} be used when you need gothic letters for your +contribution. Use \AmSTeX{} gothic as explained above. +For the real and the 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). +% +\subsubsection*{Script.} +% +For script capitals use the coding +\begin{center} +\begin{tabular}{l@{\hspace{1em}which yields\hspace{1em}}c} +\verb|$\cal AB$| & $\cal AB$ +\end{tabular} +\end{center} +(see p.~43 of the \LaTeX{} book). +% +\subsubsection*{Special Roman.} +% +If you need other symbols than those below, you could 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. +\begin{flushleft} +\begin{tabular}{@{}ll@{ yields } +c@{\hspace{1.1em}}ll@{ yields }c} +\verb|\bbbc| & (complex numbers) & $\bbbc$ + & \verb|\bbbf| & (blackboard bold F) & $\bbbf$\\ +\verb|\bbbh| & (blackboard bold H) & $\bbbh$ + & \verb|\bbbk| & (blackboard bold K) & $\bbbk$\\ +\verb|\bbbm| & (blackboard bold M) & $\bbbm$ + & \verb|\bbbn| & (natural numbers N) & $\bbbn$\\ +\verb|\bbbp| & (blackboard bold P) & $\bbbp$ + & \verb|\bbbq| & (rational numbers) & $\bbbq$\\ +\verb|\bbbr| & (real numbers) & $\bbbr$ + & \verb|\bbbs| & (blackboard bold S) & $\bbbs$\\ +\verb|\bbbt| & (blackboard bold T) & $\bbbt$ + & \verb|\bbbz| & (whole numbers) & $\bbbz$\\ +\verb|\bbbone| & (symbol one) & $\bbbone$ +\end{tabular} +\end{flushleft} +\begin{displaymath} +\begin{array}{c} +\bbbc^{\bbbc^{\bbbc}} \otimes +\bbbf_{\bbbf_{\bbbf}} \otimes +\bbbh_{\bbbh_{\bbbh}} \otimes +\bbbk_{\bbbk_{\bbbk}} \otimes +\bbbm^{\bbbm^{\bbbm}} \otimes +\bbbn_{\bbbn_{\bbbn}} \otimes +\bbbp^{\bbbp^{\bbbp}}\\[2mm] +\otimes +\bbbq_{\bbbq_{\bbbq}} \otimes +\bbbr^{\bbbr^{\bbbr}} \otimes +\bbbs^{\bbbs_{\bbbs}} \otimes +\bbbt^{\bbbt^{\bbbt}} \otimes +\bbbz \otimes +\bbbone^{\bbbone_{\bbbone}} +\end{array} +\end{displaymath} +% +\subsubsection*{Sans Serif.} +% +Using our macros you can also choose this font family; +use the command \verb|\sf| for {\sf sans serif} +(like \verb|\it| for {\it italic style}). +% +\section{References} +\label{refer} +% +There are three reference systems available; only one, of course, +should be used for your contribution. With each system (by author-year, +by number only or by letter-number) a reference list +containing all citations in the +text, should be included at the end of your 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.~73. +% +\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} +\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 in \verb|documentstyle| +the option \verb|[citeauthoryear]|, like: +\begin{verbatim} +\documentstyle[citeauthoryear]{jns} +\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] +{\it 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 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. {\bf 78} (1982) 315--333 +.. +.. +\end{thebibliography} +\end{verbatim} +{\it Sample Output} +\bibauthoryear +% +\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. +\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. {\bf 78} (1982) 315--333 +.. +.. +\end{thebibliography} +\end{verbatim} +The complete bibliography looks like this: +% +\begin{thebibliography}{MT1} +% +\bibitem[CE1]{clar:eke} +Clarke, F., Ekeland, I.: +Nonlinear oscillations and +boundary-value problems for Hamiltonian systems. +Arch. Rat. Mech. Anal. {\bf 78} (1982) 315--333 +% +\bibitem[CE2]{clar:eke:2} +Clarke, F., Ekeland, I.: +Solutions p\'{e}riodiques, du +p\'{e}riode donn\'{e}e, des \'{e}quations hamiltoniennes. +Note CRAS Paris {\bf 287} (1978) 1013--1015 +% +\bibitem[MT1]{mich:tar} +Michalek, R., Tarantello, G.: +Subharmonic solutions with prescribed minimal +period for nonautonomous Hamiltonian systems. +J. Diff. Eq. {\bf 72} (1988) 28--55 +% +\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. {\bf 33} (1980) 609--633 +\end{thebibliography} +% +\subsubsection*{Number-Only System.} +% +For this 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). +\begin{verbatim} +\begin{thebibliography}{1} +\bibitem[CE1]{clar:eke} +Clarke, F., Ekeland, I.: +Nonlinear oscillations and boundary-value problems for +Hamiltonian systems. +Arch. Rat. Mech. Anal. {\bf 78} (1982) 315--333 +\end{thebibliography} +\end{verbatim} +% +\end{document} diff --git a/macros/plain/contrib/jns/jnsldoc.sty b/macros/plain/contrib/jns/jnsldoc.sty new file mode 100644 index 0000000000..a925c7d774 --- /dev/null +++ b/macros/plain/contrib/jns/jnsldoc.sty @@ -0,0 +1,39 @@ +% This is JNSLDOC.STY the modification of the +% JNS style file for the documentation of +% the LaTeX macro package from Springer-Verlag +% for the Journal of Nonlinear Science +% version of 16 July 1990 +\def\LaTex{{\xxvpt +\def\psc{\@getfont\psc\scfam\@xxvpt{\@mcsc\@magscale5}}\LaTeX}} +\def\textfontii{\the\textfont\tw@} +\def\AmSTeX{{\textfontii A}\kern-.1667em\lower.5ex\hbox + {\textfontii M}\kern-.125em{\textfontii S}-\TeX} +% +\def\degr{\hbox{$^\circ$}} +\def\arcmin{\hbox{$^\prime$}} +\def\arcsec{\hbox{$^{\prime\prime}$}} +% +\renewcommand{\labelitemi}{--} +\newenvironment{alpherate}% +{\renewcommand{\labelenumi}{\alph{enumi})}\begin{enumerate}}% +{\end{enumerate}\renewcommand{\labelenumi}{enumi}} +% +\def\bibauthoryear{\begingroup +\def\thebibliography##1{\section*{References}% + \small\list{}{\settowidth\labelwidth{}\leftmargin\parindent + \itemindent=-\parindent + \labelsep=\z@ + \usecounter{enumi}}% + \def\newblock{\hskip .11em plus .33em minus -.07em}% + \sloppy + \sfcode`\.=1000\relax}% + \def\@cite##1{##1}% + \def\@lbibitem[##1]##2{\item[]\if@filesw + {\def\protect####1{\string ####1\space}\immediate + \write\@auxout{\string\bibcite{##2}{##1}}}\fi\ignorespaces}% +\begin{thebibliography}{} +\bibitem[1982]{clar:eke} Clarke, F., Ekeland, I.: Nonlinear +oscillations and boundary-value problems for Hamiltonian systems. +Arch. Rat. Mech. Anal. {\bf 78} (1982) 315--333 +\end{thebibliography} +\endgroup} |