% This version: ROME 14 June 1986

% An ampersand tells TeX to ignore the rest of the line so you
% include comments.  This "macro" file grew from Bill Press's macro file
% at CFA Harvard and was modified to suit the needs of Bob Jantzen
%  dept of math sciences, villanova university, villanova, PA 19085 USA.
%  tel:(215)645-4850

% For PLAIN TeX margins of 1 inch on American size paper
% you need the following commands:
% \hoffset=1.0 true in
% \voffset=1.0 true in

% For centered PLAIN TeX output on the VAXROM QMS LASER PRINTER
% (European size paper: A4)
% one needs  the following command:
 \hoffset=-.85truecm
% For a 1 inch (2.54cm) left margin one needs instead:
% \hoffset=-.6truein
% This shifts to the right enough for stapling on the left.

%Definitions to use math symbols even in text
\let\Malpha=\alpha
\def\alpha{\relax\ifmmode{\Malpha}\else{$\Malpha$}\fi}
\let\Mbeta=\beta
\def\beta{\relax\ifmmode{\Mbeta}\else{$\Mbeta$}\fi}
\let\Mgamma=\gamma
\def\gamma{\relax\ifmmode{\Mgamma}\else{$\Mgamma$}\fi}
\let\Msection=\section
\def\section{\relax\ifmmode{\Msection}\else{$\Msection$}\fi}
\let\Mdollar=\$
\def\${\relax\ifmmode{\Mdollar}\else{$\Mdollar$}\fi}
\let\Ldots=\ldots
\def\ldots{\relax\ifmmode{\Ldots}\else{$\Ldots$}\fi}

% Miscellaneous spacing macros
\def\lft#1{#1\hfill}
\def\ctr#1{\hfill#1\hfill}
\def\rt#1{\hfill#1}
\def\lftl#1{\leftline#1}
\def\ctrl#1{\centerline#1}
\def\rtl#1{\rightline#1}
\def\lftb#1{\leftline{\bf#1}}
\def\ctrlb#1{\centerline{\bf #1}}

\def\newline{\hfil\break}
\def\indent{\hbox to 20pt{}}
\def\singlespace{\baselineskip 12 pt}
\def\doublespace{\baselineskip 24 pt}
\def\triplespace{\baselineskip 36 pt}
\def\oneandahalfspace{\baselineskip 18pt}  % scientific manuscripts which should
                                           % be doublespaced look much better at
                                           % one and a half space; also use
                                           % \magnification=\magstep1
\def\blankline{\par\vskip 12 pt\noindent}
\def\thsp{\thinspace}

% see p357 top of The TeXbook:
\def\noarrowfill{$\mathsurround=0pt \mathord- \mkern-6mu
  \cleaders\hbox{$\mkern-2mu \mathord- \mkern-2mu$}\hfill
  \mkern-6mu \mathord-$}
\def\clinefill{\noarrowfill}

% Automatic list with count starting at 1 for bibliography (correct indenting).
\newcount\listno
\def\beginlist{\listno=0}
  \beginlist
\def\list{\par\noindent\hangindent 20pt\advance\listno by 1 
  \hbox to 20pt{\hfil\relax\the\listno.\ }}

% Automatic list with count starting at 1 for bibliography (correct indenting).
% (superscript style numbering of references)
\newcount\listsno
\def\beginlists{\listsno=0}
  \beginlists
\def\lists{\par\noindent\hangindent 20pt\advance\listsno by 1 
  $^{\relax\the\listsno}$}

% For unnumbered bibliography just use `\ref'.
\def\ref{\par\noindent\hangindent 20pt}

% Title page or sectioning commands
\def\nobreak{\penalty1000}
\def\titl#1\endtitl{\par\vfil\eject
     \par\vbox to 2in {}{\bf #1}\par\vskip 1in\nobreak}
\def\sect#1\endsect{\par\vfil\eject{\bf #1}\par\vskip 12pt\nobreak}
\def\subsect#1\endsubsect{\par
      \vskip 0in plus 1in\penalty -5\vskip 12pt plus -1in
      {\bf #1}\par\nobreak}
\def\Received{\par\vskip 12 pt
	\centerline{\it Received 1985 \vrule height -1 pt width 1.5 in
	depth 1.8 pt ; accepted \vrule height -1 pt width 1.5 in depth 1.8pt
	.}\par}
\def\ABSTRACT{\par\vfil\eject\vskip 1 in \centerline{\bf ABSTRACT }
	\par\vskip .5in }
\def\REFERENCES{\par\vfil\eject\vskip 1 in \centerline{\bf REFERENCES}
         \par\vskip .5in }


% bob's useful definitions

% old version of \textunderline:
%\def\textunderline#1{\setbox0=\hbox{#1}\hbox
%    {\vrule height -1pt depth 1.8pt width \wd0 \hskip -1\wd0 \box0}}
% new version:
\def\textunderline#1{$\underline{\smash{\hbox{#1}}}$}
% This only works if the underlined text is on a single line.

\def\boxit#1{\vbox{\hrule height .8pt\hbox{\vrule width .8pt\hskip 3pt
  \vbox{\vskip 3pt #1 \vskip 3pt}\hskip 3pt\vrule width .8pt}
  \hrule height .8pt}}
% This puts a slightly larger ruled box around the box which is the argument.
\newdimen\boxmarg 
\def\boxitto#1#2{\relax\boxmarg=#1
\vbox{\hrule height .8pt\hbox{\vrule width .8pt\hskip \boxmarg
  \vbox{\vskip \boxmarg #2 \vskip \boxmarg}\hskip \boxmarg\vrule width .8pt}
  \hrule height .8pt}}
% This accepts a margin dimension parameter. The following is a useful test
% sample of \boxitto:
%  $$\vcenter{\boxitto{10pt}{\halign{#\cr ONE\cr TWO\cr THREE\cr}}} \rightarrow
%    \vcenter{\boxitto{12pt}{\halign{#\cr FOUR\cr FIVE\cr}}}$$

% This defines a version of \matrix with options for horizontal and vertical
% lines separating some rows and columns; just use a \vline in a column to get
% a vertical line and replace a whole row by \hline for a horizontal line.
\def\vline{\hbox{\strut\vrule}}
\def\hline{\noalign{\hrule}}
\def\matrixtable#1{\,\vcenter{\normalbaselines\mathsurround=0pt
   \tabskip=2.5pt\offinterlineskip
   \halign{\hfil$##$\hfil &&\hfil$##$\hfil\crcr
      \mathstrut\crcr\noalign{\kern-12pt}
      #1\crcr\mathstrut\crcr\noalign{\kern-12pt}}}\,}
% This is an example:
% $$\left(\matrixtable{A&\vline&B\cr \hline C&\vline&D\cr}\right)$$

\def\bivec#1{\vbox{\ialign{##\crcr $\leftrightarrow$\crcr\noalign{
   \kern-1pt \nointerlineskip}$\hfil\displaystyle{#1}\hfil$\crcr}}}
% This puts a double arrow over a symbol.

\def\dal{\rlap{\sqcap}\sqcup}    % the relativistic d'Alembertian operator

\let\ovl=\overline

\def\ut#1{\mathop{\vtop{\ialign{##\crcr
     $\hfil\displaystyle{#1}\hfil$\crcr\noalign
     {\kern1pt\nointerlineskip}\hbox{$\hfil\sim\hfil$}\crcr
     \noalign{\kern1pt}}}}}
\def\undersim{\ut}
% This puts a \sim under a symbol.
% This is the model for putting a symbol under another symbol
% without shrinkage:
\def\undersymbol#1#2{\mathop{\vtop{\ialign{##\crcr
     $\hfil\displaystyle{#2}\hfil$\crcr\noalign
     {\kern1pt\nointerlineskip}\hbox{$\hfil#1\hfil$}\crcr
     \noalign{\kern1pt}}}}}

\def\expo#1{e^{\hbox{$#1$}}}
% This is for exponentiating an expression without shrinkage.

\def\leftcontract{\hbox{\vrule height0.7pt width6pt \vrule width0.7pt 
   height4.5pt}\hskip 2pt}
% This is for contraction of a vector against a covariant tensor in
% index free notation.

% These are various subscript and superscript abbreviations.
\def\p{^{\prime}\null}
\def\pp{^{\prime\prime}\null}
\def\pprime{\prime\prime}
\def\ps{_{\bot}}
\def\sast{^{\ast}}

% These are definitions for textstyle fractions in display mode.
\def\half{\textstyle {1\over2}\displaystyle}
\def\fraction#1#2{\textstyle{#1\over#2}\displaystyle}
\def\hhalf{1/2}

% These are roman abbreviations for math mode.
\def\Tr{\mathop{\rm Tr}\nolimits}
\def\diag{\mathop{\rm diag}\nolimits}
\def\sgn{\mathop{\rm sgn}\nolimits}
\def\ad{\mathop{\rm ad}\nolimits}
\def\Ad{\mathop{\rm Ad}\nolimits}
\def\aut{\mathop{\it aut}\nolimits}
\def\Aut{\mathop{\rm Aut}\nolimits}
\def\SAut{\mathop{\rm SAut}\nolimits}
\def\span{\mathop{\rm span}\nolimits}
\def\ker{\mathop{\rm ker}\nolimits}
\def\rank{\mathop{\rm rank}\nolimits}
\def\sech{\mathop{\rm sech}\nolimits}


% style abbreviations
\def\ds{\dispstyle}
\def\st{\scriptstyle}
\def\sst{\scriptscriptstyle}

% BOLDFACE Definitions

% From the TeXbook, a poor man's boldface in math mode:
\def\pmb#1{\setbox0=\hbox{$#1$}%
  \kern-.025em\copy0\kern-\wd0
  \kern.05em\copy0\kern-\wd0
  \kern-.025em\raise.0433em\box0}
% and reducing by a factor of .7 for \scriptstyle:
\def\pmbs#1{\setbox0=\hbox{$\st #1$}%
  \kern-.0175em\copy0\kern-\wd0
  \kern.035em\copy0\kern-\wd0
  \kern-.0175em\raise.0303em\box0}

%\def\bff#1{\hbox to .00385in{$#1$\hss}\hbox to .00385in{$#1$\hss}#1}
\def\bfs#1{\hbox to .0035in{$\st#1$\hss}\hbox to .0035in{$\st#1$\hss}\st#1}
%\def\bfk#1{\hbox to .00385in{$#1$\hss}\textstyle #1}
%These are old definitions for boldface Greek displaystyle, scriptstyle 
% and kappa (which doesn't look good the first way).

% boldface greek
\def\bfalpha{\pmb{\alpha}}
\def\bfsalpha{\pmbs{\alpha}}
\def\bfbeta{\pmb{\beta}}
\def\bfsbeta{\pmbs{\beta}}
\def\bfdelta{\pmb{\delta}}
\def\bfkappa{\pmb{\kappa}}
\def\bfskappa{\pmbs{\kappa}}
\def\bfomega{\pmb{\omega}}
\def\bfrho{\pmb{\rho}}
\def\bfsigma{\pmb{\sigma}}
\def\bfpi{\pmb{\pi}}

% miscellaneous boldface
\def\bfone{\hbox{\bf 1}}
\def\bfsone{\pmbs{1}}
\def\bfg{\hbox{\bf g}}
\def\bfn{\hbox{\bf n}}
\def\bfA{\hbox{\bf A}}
\def\bfB{\hbox{\bf B}}
\def\bfH{\hbox{\bf H}}
\def\bfS{\hbox{\bf S}}
\def\bfI{\hbox{\bf I}}
\def\bfk{\hbox{\bf k}}
\def\bfK{\hbox{\bf K}}
\def\bfe{\hbox{\bf e}}

% Italic Greek Capitals
\def\Gammait{{\mit\Gamma}}
\def\Deltait{{\mit\Delta}}
\def\Thetait{{\mit\Theta}}
\def\Lambdait{{\mit\Lambda}}
\def\Xiit{{\mit\Xi}}
\def\Piit{{\mit\Pi}}
\def\Sigmait{{\mit\Sigma}}
\def\Upsilonit{{\mit\Upsilon}}
\def\Phiit{{\mit\Phi}}
\def\Psiit{{\mit\Psi}}
\def\Omegait{{\mit\Omega}}

% Script Capital Macros
\def\Ascr{{\cal A}}
\def\Bscr{{\cal B}}
\def\Cscr{{\cal C}}
\def\Dscr{{\cal D}}
\def\Escr{{\cal E}}
\def\Fscr{{\cal F}}
\def\Gscr{{\cal G}}
\def\Hscr{{\cal H}}
\def\Iscr{{\cal I}}
\def\Jscr{{\cal J}}
\def\Kscr{{\cal K}}
\def\Lscr{{\cal L}}
\def\Mscr{{\cal M}}
\def\Nscr{{\cal N}}
\def\Oscr{{\cal O}}
\def\Pscr{{\cal P}}
\def\Qscr{{\cal Q}}
\def\Rscr{{\cal R}}
\def\Sscr{{\cal S}}
\def\Tscr{{\cal T}}
\def\Uscr{{\cal U}}
\def\Vscr{{\cal V}}
\def\Wscr{{\cal W}}
\def\Xscr{{\cal X}}
\def\Yscr{{\cal Y}}
\def\Zscr{{\cal Z}}

% Miscellaneous

\def\xc{\hbox{\rlap{\hskip 1.5pt\raise .75pt\hbox{--}}$\Xscr$}}
%This is the symbol used for the space of vector fields on a manifold.

\def\partialslash{\rlap{\hbox{/}}\partial}
\def\deltaslash{\rlap{\hbox{/}}\delta}
% These are slashed symbols for divergences and variational derivatives
% in a frame.

\def\del{\nabla}
\def\ketl{\langle}
\def\ketr{\rangle}
\def\larrow{\leftarrow}
\def\rarrow{\rightarrow}
\def\relv{\bigm|}

\def\Lie{\hbox{\it\char'44}}
\def\Lied#1{\Lie_{\hbox{$#1$}}\thsp}

\def\sterling{\hbox{\it\char'44}}
\def\tb{\overline{t}\null}
\def\inm{\rlap{$\hskip 1.3pt -$}\supset}
\def\inr{\rlap{$\hskip 2.55pt\scriptstyle{\vert}\displaystyle$}\cap}
\let\hold=\null
\def\fcaption#1{\parshape=1 .75cm 12.2cm {#1} \parshape=0}

\def\twov#1#2{\pmatrix{#1\cr#2\cr}}
\def\threev#1#2#3{\pmatrix{#1\cr#2\cr#3\cr}}
\let\mtx=\pmatrix

\def\et{\tilde{e}\null}
\def\zd{_{(0)}}

% These are old definitions for raised dots:
\def\du{\rlap{\raise 6.75pt\hbox{\hskip 3pt$\cdot$}}}
\def\dl{\rlap{\raise 4.5pt\hbox{\hskip 2pt$\cdot$}}}
\def\odu{\rlap{\raise 4pt\hbox{\hskip 3pt$^{\circ}$}}}
\def\odl{\rlap{\raise 1.75pt\hbox{\hskip 2pt$^{\circ}$}}}
\def\dott#1{\vbox{\baselineskip-1pt\lineskip 1pt\halign{\ctr{##}\cr
     .\cr $#1$\cr}}}
\def\ddott#1{\vbox{\baselineskip-1pt\lineskip 1pt\halign{\ctr{##}\cr
    ..\cr/$#1$\cr}}}

\def\Wd{\dot{\tilde{W}}\null}
\def\wedget{\scriptstyle{\wedge}\displaystyle}
\def\A#1{\hat{#1}}
%\def\As#1{\rlap{\raise 1pt\hbox{\hskip 1pt\char'017}}#1}
\def\As#1{\hat#1}
\def\bfbbeta{\bfs{\beta}}

% some journal abbreviations
\def\jmp{{\it J. Math. Phys.}\ }
\def\pr{{\it Phys. Rev.}\ }
\def\prl{{\it Phys. Rev. Lett.}\ }
\def\pl{{\it Phys. Lett.}\ }
\def\cmp{{\it Commun. Math. Phys.}\ }
\def\cqg{{\it Class. Quantum Grav.}\ }
\def\ap{{\it Ann. Phys. (N.Y.)}\ }
\def\spj{{\it Sov. Phys. JETP}\ }
\def\grg{{\it Gen. Relativ. Grav.}\ }
\def\nat{{\it Nature}\ }
\def\apj{{\it Ap. J.}\ }
\def\aaa{{\it Astron. Astrophys.}\ }
\def\ncim{{\it Nuovo Cim.}\ }
\def\ptp{{\it Prog. Theor. Phys.}\ }
\def\aip{{\it Adv. Phys.}\ }
\def\jpamg{{\it J. Phys. A: Math. Gen.}\ }
\def\mnras{{\it Mon. Not. R. ast. Soc.}\ }
\def\prep{{\it Phys. Rep.}\ }
\def\ncb{{\it Il Nuovo Cimento ``B''}}
\def\ssr{{\it Space Sci. Rev.}\ }
\def\pasp{{\it Pub. A. S. P.}\ }
\def\araa{{\it Ann. Rev. Astr. Ap.}\ }
\def\asr{{\it Adv. Space Res.}\ }