\input ./mtexsis.tex
%\input /hda/t/docs/mtexsis.tex
%\input /hda/t/leabhar/qm/qmdf.doc
\texsis
%\PhysRev %Use for Phys Rev output
%\input/hda/texsis/PhysRev.txs %Use for Phys Rev output

%\draft
%%\paper
%\preprint
%%%\hoffset -0.5cm %use for printing draft
%\hoffset 0.5cm %use for printing draft
\paper\tenpoint
\superrefsfalse % Prints reference as [1], etc.
\hfuzz 2.cm
%%\hoffset 2.cm
%%\hsize 13.cm
\Eurostyletrue

\font\sstenz=cmss10 scaled \magstep0
\font\ssten=cmss10 scaled \magstep1

%\font\sstwv=cmss12 scaled \magstep1
%\font\sstentwo=cmss10 scaled \magstep2
%\font\ssiten=cmssi12 scaled \magstep1
%\font\sstwl=cmss10 scaled \magstep3
%\font\math=cmmib10 scaled \magstep

%=======================Definitions qmdef.doc=============================
\def\frac#1#2{{#1\over#2}}%Qmdef.doc macros and definitions for qm.tex Quantum mechanics notes.
%Slash vectors for QED
\def\As{A\!\!\!\slash\,}
\def\as{a\!\!\!\slash\,}
\def\bs{b\!\!\!\slash\,}
\def\cs{c\!\!\!\slash\,}
\def\ds{d\!\!\!\slash\,}
\def\gs{\gamma\!\!\!\slash\,}
\def\sls{s\!\!\!\slash\,}
\def\ps{p\!\!\!\slash\,}
\def\qs{q\!\!\!\slash\,}
\def\ss{s\!\!\!\slash\,}
\def\Ss{S\!\!\!\slash\,}
\def\dss{ds\!\!\!\slash\,}

%\def\s{\,\,\,}                                                              

%Definitions for Quantum Mechanics
\def\scp#1#2{\langle{#1}\vert{#2}\rangle}
\def\ah{{\hat{a}}}
\def\bh{{\hat{b}}}
\def\bra#1{\langle{#1}\vert}
\def\ket#1{\vert{#1}\rangle}


\def\ad{{\hat{a}}^\dagger}
\def\bd{{\hat{b}}^\dagger}  
\def\H{{\hat H}}
\def\vv{\parallel}
\def\x{{\hat x}}
\def\Ih{{\hat I}}  
\def\K{{\hat K}}  
\def\Lh{{\hat L}}  
\def\Mh{{\hat M}}  
\def\p{{\hat p}}
\def\q{{\hat q}}
\def\Q{{\hat Q}}
\def\P{{\hat P}} 
\def\N{{\hat N}}
\def\A{{\hat A}}  
\def\B{{\hat B}}
\def\C{{\hat C}}
\def\SH{{\hat S}}
\def\SHD{{\hat S}^\dagger}
\def\Y{{\hat Y}}
\def\U{{\hat U}}
%=====================================================================
%Definitions for Operators
%Definitions for TFD.doc Thermal field dynamics.
\def\OK{K(\alpha,\theta)}
\def\Kd{K^{\dagger}(\alpha,\theta)}
\def\a{a} %fix this. See \ah
\def\at{\tilde{a}}
\def\atd{\tilde{a}^{\dagger}}                                               
%=======================================================================
%Definitions for coher.doc coherent states and sqz.doc squeezed states
\def\alf{\alpha}
\def\la{\langle}
\def\ra{\rangle}
%=========================EXTRAS========================================
\def\n{\hfill\break}
\def\frac#1#2{{#1\over#2}}
\def\square{\hbox{{$\sqcup$}\llap{$\sqcap$}}}%
\def\Box{\hbox{{$\sqcup$}\llap{$\sqcap$}}}%
%=================================
%from{qmch7.doc}
\def\a{\alpha}
\def\b{\beta}
\def\de{\delta}
\def\De{\Delta}
\def\degg{^\circ\ }
\def\deggg{^\circ}
\def\fre{frequency\ }
\def\frep{frequency}
\def\e{\epsilon}
\def\g{\gamma}
\def\G{\Gamma}
\def\hb{\hfil<\break}
\def\ib{\item\bullet}

\def\itemm{\hangindent\parindent\textindent}
\def\l{\lambda}
\def\la{\langle}
\def\lbar{{\mathchar'26\mkern-9mu \lambda}}
\def\noi{\noindent}
\def\o{\omega}
\def\O{\Omega}
\def\ol{\overline}
\def\onehead#1{\vskip1pc\leftline{\bf #1}}
\def\part{\partial}
\def\ra{\rangle}
\def\rand{\mathop{ rand}}
\def\ree{\mathop{ Re}}
%\def\s{\sigma}
\def\sgn{\mathop{ sgn}}
\def\ship#1{\noalign{\vskip#1pt}}
\def\th{\theta}
\def\too{\rightarrow}
\def\twohead#1{\vskip1pc\leftline{\bf #1}}
\def\ts{\thinspace}


%======================End of Definitions=================================

%======================START OF REFERENCE LIST============================== 
\referencelist

\reference{[TGCVQT]} 
T.~Garavaglia, {\it Covariant relativistic quantum theory}, hep-th/9907059
\endreference

%\reference{[Garrod]} 
%G.~Garrod, Phys. Rev. {\bf 167}, 1143 (1968)
%G.~Garrod,"Covariant Hamiltonian Dynamics with Interactions," 
%\endreference

\reference{[HG]}
H.~Goldstein, {\it Classical Mechanics} 
(Addison Wesley, Reading Mass., 1959) p. 207
\endreference

\reference{[Fock]} 
V.~Fock, Physik Z. Sowjetunion {\bf 12}, 404 (1937) 
%Covariant wave equation.
\endreference

\reference{[Schwinger]}
J.~Schwinger, Phys. Rev. {\bf 82}, 664 (1951)
\endreference


\reference{[Dirac33]} 
P.~A.~M.~Dirac, Physikalische Zeitschrift der Sowjetunion, Band {\bf 3},
Heft {\bf 1}, 64 (1933)
\endreference

\reference{[REDUCE]} 
A.~C.~Hearn, and J.~P.~Fitch, {\it REDUCE User's Manual}, (Rand, Santa Monica, 1995)
\endreference

\endreferencelist
%============================END OF REFERENCE===================================


%================================TITLE PAGE================================  
%Start of title page.
%\nopagenumbers
%\rightline{{ hep-th/xxxxxxxxx}}
\line{{cvefp.tex\hfill dias-stp-01-04}}
%\centerline{\bf INSTITI\'UID \'ARD-L\'EINN BHAILE \'ATHA CLIATH}
%\centerline{(Dublin Institute for Advanced Studies, Dublin 4, Ireland)}
%\hrule
\n\n
\centerline{\bf Covariant Quantum Green's Function for an Accelerated Particle}
\n
\centerline{T. Garavaglia$^{*}$}
\n
\centerline{\it Institi\'uid \'Ard-l\'einn Bhaile \'Atha Cliath, Baile
\'Atha Cliath  4, \'Eire$^{\dagger}$}
%\centerline{\it and}
%\centerline{\it Institi\'uid Teicneola\'iochta Bhaile \'Atha Cliath, Baile \'Atha Cliath  2, \'Eire}
\vskip 24pt
%\centerline{\bf Abstract}
\par
\vbox{\sstenz 
\par
Covariant relativistic quantum theory is used to study the covariant 
Green's function, which can be used to determine 
the proper time evolved wave functions
that are solutions to the covariant Schr\"odinger type equation for a 
massive spin
zero particle. The concept of covariant action is used to obtain
the Green's function for an accelerated  relativistic particle. 
} 
\vskip 40pt
\noindent
PACS: {\sstenz 04.60, 03.65, 03.65P, 03.30}
%03.65P Relativistic wave equation
%03.65 Quantum Mechanics
%03.30 Relativistic mechanics
%04.60 quantization covariant
%Keywords: {\ssten quantum, relativistic, covariant}
\vskip 200pt 
%\today\n
%\centerline{20 November 2000}
\vskip 24pt
\hrule \n
\item{$^*$}{Email address: bronco@stp.dias.ie }  
\item{$^\dagger$}{Also {\it Institi\'uid Teicneola\'iochta Bhaile 
\'Atha Cliath.}}
%\vfill
%\supereject
%End of Title page.
%======================END TITLE PAGE=======================================
%\centerline{{\it Covariant relativistic quantum theory}}
%\n\n\n
%\centerline{\singlespace\qquad\qquad{\hsize 7cm\vbox{\noindent
%T. Garavaglia\n 
%School of Theoretical Physics\n
%Dublin Institute for Advanced Studies\n
%10 Burlington Road\n
%Dublin 4, Ireland\n\n
%E-Mail: bronco@dias.stp.ie\n
%Fax: 353-1-6680561}}}
\vfill\eject
%===================Start of TEXT==========================================
%\doublecolumns\tenpoint\singlespace
%\section{INTRODUCTION}
\par
Covariant relativistic quantum theory has been described in \cite{[TGCVQT]}, and the
methods that are developed  there are used to find the proper time
covariant Green's function for a relativistic spin zero particle of mass $m$
that undergoes uniform acceleration. Covariant relativistic quantum
theory is a natural extension of the concepts of classical covariant 
relativistic particle 
dynamics \cite{[HG]}. Proper time covariant methods
have been  used previously in the context of relativistic wave equations
\cite{[Fock]}, and quantum field theory \cite{[Schwinger]}. 
The Lorentz invariant parameter that is relevant for dynamical development
in classical covariant mechanics is proper distance $s$, proper time times the
speed of light, and the invariant parameter that characterizes the rest
energy of a particle is its mass. 
The evolution of
quantum states with respect to the parameter $s$ is found in terms of 
the covariant Green's function. This Green's function is found with the
aid of the concept of covariant action. The resulting Green's function  has a practical
application in the study of the quantum state proper time evolution of, for 
example, an accelerated spin zero heavy ion.
\par
The conventions used are those of \cite{[TGCVQT]}, along with the units
$\hbar=c=1$.
The space-time contravariant coordinate four-vector is defined as
$q^\mu=(q^0,q^1,q^2,q^3)=(ct,x,y,z),$
and the dimensionless form is found by dividing the components with the
fundamental units of length $q_s$. The Einstein summation convention is used
throughout, and the covariant components are found from
$q_\mu=g_{\mu\nu}q^\nu$,
with the non-zero components of the metric tensor given by
$(g_{00},g_{11},g_{22},g_{33})=(1,-1,-1,-1).$
The scalar product of two four-vectors is $q\cdot p=q_\mu p^\mu$, and
the space-time measure is
$ds=\sqrt{dq\cdot dq}$.
The four-momentum for a free particle is
$p^\mu=mu^\mu=(p^0,\vec p)=(\gamma m,\gamma{\vec \beta}m)$,
with ${\vec \beta}={{d{\vec q}}/{dq^0}}$,
$\gamma=1/\sqrt{1-{\vec \beta}\cdot{\vec \beta}}$, $p\cdot p=m^2$, and
$u^\mu=dq^\mu/ds$.


%\section{COVARIANT ACTION AND COVARIANT CLASSICAL DYNAMICS}

\par
Covariant action is defined as
$$
{\cal S}=\int {\cal L}(q,u)ds,
\EQN{ac.1}$$
where ${\cal L}(q,u)$ is a Lorentz invariant Lagrangian.
The requirement that the action be an extremum under a variation of the
coordinates $q^\mu$ leads to the covariant Euler-Lagrange equation
$$
\frac{d \frac{\partial {\cal L}}{\partial u^\mu}}{ds}
-\frac{\partial {\cal L}}{\partial q^\mu}=0.
\EQN{ac.2}$$
\par
The covariant Lagrangian for a particle of mass $m$ and charge $e$ interacting 
with a four-vector field $A^\mu(q)$ is 
$$
{\cal L}=\frac{m}{2}u^2-eA\cdot u,
\EQN{ac.3}$$
and the generalized four-momentum is
$$
p_\mu=\frac{\partial {\cal L}}{\partial u^\mu}=mu_\mu-eA_\mu.
\EQN{ac.4}$$
The equation of motion is found from \Eq{ac.2} to be
$$
\frac{dp_\mu}{ds}+\partial_\mu{eA\cdot u}=0,
\EQN{ac.5}$$
where $\partial_\mu=\partial/\partial q^\mu$.
\par
From the covariant Lagrangian \Eq{ac.3}, the covariant Hamiltonian is defined 
as 
$$
{\cal H}=p\cdot u-{\cal L}=\frac{(p+eA)^2}{2m}.
\EQN{ac.6}$$

%\section{COVARIANT QUANTUM GREEN'S FUNCTION}

\par 
The properties of the covariant action can be used to determine the
covariant quantum Green's function for an accelerated spin zero 
particle of unit mass. For the four-vector potential $eA^\mu=(-V(\vec
q),0,0,0)$, the differential equation for the covariant action is
$$
\frac{1}{2}((\frac{\partial S}{\partial q^0}-
V(\vec q))^2-\vec \nabla S\cdot\vec
\nabla S)+\frac{\partial S}{\partial s}=0.
\EQN{qef.1}$$
The four-momentum associated with the covariant action is 
$$
p_\mu=\frac{\partial S}{\partial q^\mu}.
\EQN{qef.2}$$
For a free particle of unit mass  the solution to \Eq{qef.1}  is 
$$
S=\frac{(q-q')\cdot (q-q')}{2s}.
\EQN{qef.3}$$
\par
For a time independent potential $V(z)$, $p^0$ is a constant, and the covariant action can be written as
$$
S(q,s)=S_0(z,p^0,s)-\frac{y^2}{2s}-\frac{x^2}{2s}+p^0t;
\EQN{qef.4}$$
hence, \Eq{qef.1} becomes
$$
\frac{1}{2}((p^0-V(z))^2-(\frac{\partial S_0(z,p^0,s)}{\partial z})^2)
+\frac{\partial S_0(z,p^0,s)}{\partial s}=0.
\EQN{qef.5}$$
From \Eq{ac.4} and \Eq{ac.5}, the equations of motion become
$$\eqalign{
\frac{dt}{ds}&=p^0-V(z),\quad \frac{dp^0}{ds}=0,\cr
\frac{dz}{ds}&=p^3,\quad \frac{dp^3}{ds}=-(p^0-V(z))\frac{\partial V(z)}{\partial z}.\cr
}
\EQN{qef.6}$$
A particle with constant acceleration results from the potential $V(z)=-gz$,
where $g$ is a constant.
With the replacements
$q^\mu\rightarrow q^\mu/\sqrt{g}$, $p^\mu\rightarrow p^\mu\sqrt{g}$, and $s\rightarrow
s/g$, the equations of motion become
$$
\frac{dt}{ds}=p^0+z=\xi,\quad\frac{d^2\xi}{ds^2}=\xi.
\EQN{qef.7}$$
The solutions to these equations are
$$
\eqalign{
\xi(s)&=\xi(0)\cosh(s)+b\sinh(s)\cr
t(s)&=\xi(0)\sinh(s)+b(\cosh(s)-1)+t(0).\cr
}
\EQN{qef.8}$$
The action function $S_0(\xi,s)$ is now found from
$$
S_0(\xi,s)=\int_0^s{\cal L}_0 ds,
=-\int_0^s \frac{1}{2}((\frac{d\xi}{ds})^2+\xi^2)ds.
\EQN{qef.9}$$
After integration and the substitution
$$
b=(\xi-\xi(0)\cosh(s))/\sinh(s),
\EQN{qef.10}$$
one finds
$$
S_0(\xi,s)=- (1/2)((\xi^2+\xi(0)^2)\cosh(s)-2\xi\xi(0))/\sinh(s).
\EQN{qef.11}$$
\par
The covariant Schr\"odinger type equation for a spin zero particle is
$$
{\hat{\cal H}}\ket{\Psi(s)}=\frac{(\hat p+eA)^2}{2}\ket{\Psi(s)}
=i\frac{\partial \ket{\Psi(s)}}{\partial s},
\EQN{qef.12}$$
and the proper time evolved state is found from
$$
\ket{\Psi(s)}=\hat U(s)\ket{\Psi(0)}=e^{-i\hat{\cal H}s} \ket{\Psi(0)},
\EQN{qef.13}$$
The covariant proper time Green's function is
$$
{\cal G}(\vec q,q',s)=\bra{q}\hat U(s)\ket{q'}\theta(s),
\EQN{qef.14}$$
where $\theta(s)$ is the Heaviside function. This function is a solution to
the partial differential equation
$$
(\hat{\cal H}-i\frac{\partial}{\partial s}){\cal G}(q,q',s)=
-i\delta(q-q')\delta(s),
\EQN{qef.15}$$
and it satisfies the condition
$$
\lim_{s\rightarrow 0}{\cal G}(q,q',s)=\delta(q-q').
\EQN{qef.16}$$
The covariant Hamiltonian operator for the accelerated particle is 
$$
\hat{\cal H}=((\hat p^0+z)^2-\hat {\vec p}\cdot \hat {\vec p})/2,
\EQN{qef.17}$$
with $\hat p_\mu=i\partial/\partial q^\mu$, which satisfy the commutation
relation
$$
[\hat q^\mu,\hat p^\nu]=-ig^{\mu\nu}.
\EQN{qef.18}$$
\par
The s-dependent operators are
$$
\eqalign
{
\hat\xi(s)&=\hat U(s)\hat \xi \hat U(-s)=\hat\xi \cosh(s)+{\hat p^3} \sinh(s)\cr
\hat t(s)&=\hat U(s)\hat t \hat U(-s)=t+\hat\xi \sinh(s)+{\hat p^3}(\cosh(s)-1),\cr
}
\EQN{qef.19}$$
and the solutions to the classical equations of motion \Eq{qef.7} are found
from the matrix elements $\bra{\Psi(0)}\hat\xi(s)\ket{\Psi(0)}$, and 
$\bra{\Psi(0)}\hat t(s)\ket{\Psi(0)}$, where $\ket{\Psi(0)}$ is a minimum 
uncertainty state \cite{[TGCVQT]}.
Using the identities
$$\eqalign
{
\bra{q}\hat U(s)\hat \xi \hat U(-s)\hat U(s)\ket{q'}&=(\hat p^0+\hat z')\bra{q}\hat U(s)\ket{q'}\cr
\bra{q}\hat U(s)\hat t \hat U(-s)\hat U(s)\ket{q'}&=\hat t'\bra{q}\hat U(s)\ket{q'},\cr
}
\EQN{qef.20}$$
one can show that the Green's function also satisfies the first order
partial differential equations
$$
\eqalign
{
((\hat p^0+\hat z)\cosh(s)+\hat p^3\sinh(s)){\cal G}(q,q',s)=(\hat p^0+z'){\cal G}(q,q',s)\cr
(\hat t +(\hat p^0+\hat z)\sinh(s)+\hat p^3(\cosh(s)-1)){\cal G}(q,q',s)=t'{\cal G}(q,q',s).\cr
}
\EQN{qef.21}$$
\par
The solution to the equations \Eq{qef.15} and \Eq{qef.21} can be found using a method inspired by Dirac\cite{[Dirac33]} 
for non-relativistic quantum mechanics. One
assumes a solution of the form
$$
\bra{q}\hat U(s)\ket{q'}=a_0(s)\int_{-\infty}^{+\infty}e^{i\Phi}dp^0,
\EQN{qef.22}$$
with
$$
\Phi=S_0(z,z',p0,s)-\frac{(y-y')^2}{2s}
-\frac{(x-x')^2}{2s}-p^0(t-t'),
\EQN{qef.23}$$
and $q'^\mu=q^\mu(0)$.
The evaluation of \Eq{qef.22} and substitution into \Eq{qef.15}
leads to the differential equation for $a_0(s)$,
$$
\frac{da_0(s)}{ds}=-(1/s+\coth(s/2)/2)a_0(s).
\EQN{qef.24}$$
Solving this equation and using the condition \Eq{qef.16} gives the 
final result
$$
{\cal G}(q,q',s)=\frac{-i\theta(s)e^{i(-B^2A+C)}e^{-i\frac{(x-x')^2}{2s}}
e^{-i\frac{(y-y')^2}{2s}}}{8\pi^2s\sinh(s/2)},
\EQN{qef.25}$$
with
$$
\eqalign{
A(s)&=-\tanh(s/2)\cr
B(t,t',z,z',s)&=\frac{1}{2}(z+z'+(t-t')\coth(s/2))\cr
C(z,z',s)&=(-\cosh(s)\frac{1}{2}(z^2+z'^2)+zz')\sinh^{-1}(s).\cr
}
\EQN{qef.26}$$

The evolved wave function $\Psi(q,s)$ is found from the
initial state wave function $\Psi(q,0)$ using the evolution equation
$$
\Psi(q,s)=\int{\cal G}(q,q',s) \Psi( q',0)dq'.
\EQN{qef.27}$$
\par
Examples of evolved wave functions for a free particle are found in
\cite{[TGCVQT]}. In these examples the sum of the exponents of the initial
state wave function
and the Green's function are combined by completing the square,
and the $q'$ integration is then  performed. For a Gaussian initial state, 
it is
found that the evolved free particle wave function spreads about the 
classical path
described by the coordinates $q^\mu(s)=(p^0s,\vec p s)/m$, with $s=t/\gamma$.
For plane wave,
and Gaussian initial state wave functions, the integration using \Eq{qef.25}
can be performed in a similar manner.
Normal units may be restored in \Eq{qef.25} with the replacements
$q^\mu\rightarrow {q^\mu}/{q_s}$, $p^\mu\rightarrow {p^\mu}/{p_s}$,
and $s\rightarrow {s}/{s_s}$, with $q_s=\sqrt{\hbar c/(mg)}$, $q_sp_s=\hbar$, 
and $s_s=c^2/g$. In the limit $g\rightarrow 0$, the Green's function 
\Eq{qef.25} becomes the free particle
Green's function,
$$
{\cal G}(q,q',s)\rightarrow \frac{-i(mc)^2}{4(\pi\hbar s)^2}e^{i\frac{mc(q-q')^2}{2s\hbar}}.
\EQN{qef.28}$$
Calculations have been confirmed with the aid of REDUCE \cite{[REDUCE]}.
%\section{CONCLUSIONS}
%========================List References[B=======================================
%\vfill\eject
%\leftline{REFERENCES}
\n
\hrule
\n
%\hrule \n

\item{$^*$}{Email address: bronco@stp.dias.ie }

\item{$^\dagger$}{Also {\it Institi\'uid Teicneola\'iochta Bhaile \'Atha Cliath.}}

\ListReferences
\vfill\eject
%End LIST References==============================================================================
%================END of TEXT==============================================
\bye


% file: mtexsis.tex -- TeXsis version 2.16
% $Revision: 16.2 $  :  $Date: 1994/11/12 22:32:02 $  :  $Author: myers $
%======================================================================*
%  mTeXsis - mini version of the TeX Macros for Physicists
%
%  This is mtexsis.tex, a "mini" version of the TeXsis macro package.
%  mtexsis.tex contains only the core macros of TeXsis, and there are
%  absolutely no comments (except these).  mtexsis.tex is convenient for
%  printing papers prepared with the TeXsis macros when you don't have
%  TeXsis installed on your system.  If you receive a manuscript file
%  prepared with TeXsis you can (usually) print it by inserting the line
%
%       \input mtexsis
%
%  at the begining of the manuscript file (if it's not already there)
%  and then running it through Plain TeX.
%
%  Authors who prepare papers with TeXsis for submission to physics
%  bulletin boards like hep-lat, hep-th or hep-ph may want to try
%  their manuscripts with mtexsis.tex and Plain TeX to be sure that
%  it works.  
%
%  If you want to know how a macro works you will have to look in the
%  full TeXsis source files.  Both the source and documentation for
%  TeXsis are available via anonymous ftp from lifshitz.ph.utexas.edu
%  in the /texsis subdirectory.  See the README file there for more
%  information.
%
%  Comments, suggestions, or bug reports should be directed to 
%  texsis@lifshitz.ph.utexas.edu
%
%  (C) copyright 1988, 1992, 1994 by Eric Myers and Frank Paige.
%  Permission is granted to use this software by any member the academic
%  community in conjunction with basic research.  This software may not
%  be used or distributed for profit without permission from the authors.
%======================================================================*
\def\TeXsis{\TeX sis}%                          % the TeXsis logo
\catcode`@=11                                   % @ is a letter in what follows
% file: TXSfonts.tex                                TeXsis version 2.16
%%> {TeXsis fonts:}
\catcode`@=11
\newskip\ttglue
%++ 9 pt fonts:
\def\ninefonts{%
   \global\font\ninerm=cmr9
   \global\font\ninei=cmmi9
   \global\font\ninesy=cmsy9
   \global\font\nineex=cmex10
   \global\font\ninebf=cmbx9
   \global\font\ninesl=cmsl9
   \global\font\ninett=cmtt9
   \global\font\nineit=cmti9
   \skewchar\ninei='177
   \skewchar\ninesy='60
   \hyphenchar\ninett=-1
   \moreninefonts
   \gdef\ninefonts{\relax}}
\def\moreninefonts{\relax}%
%++ 10 pt fonts:                               
\font\tenss=cmss10
\def\moretenfonts{\relax}%
%++ 11 pt fonts:
\def\elevenfonts{%
   \global\font\elevenrm=cmr10 scaled \magstephalf
   \global\font\eleveni=cmmi10 scaled \magstephalf
   \global\font\elevensy=cmsy10 scaled \magstephalf
   \global\font\elevenex=cmex10
   \global\font\elevenbf=cmbx10 scaled \magstephalf
   \global\font\elevensl=cmsl10 scaled \magstephalf
   \global\font\eleventt=cmtt10 scaled \magstephalf
   \global\font\elevenit=cmti10 scaled \magstephalf
   \global\font\elevenss=cmss10 scaled \magstephalf
   \skewchar\eleveni='177%
   \skewchar\elevensy='60%
   \hyphenchar\eleventt=-1%
   \moreelevenfonts
   \gdef\elevenfonts{\relax}}%
\def\moreelevenfonts{\relax}%
%++ 12 pt fonts:
\def\twelvefonts{%
   \global\font\twelverm=cmr10 scaled \magstep1%
   \global\font\twelvei=cmmi10 scaled \magstep1%
   \global\font\twelvesy=cmsy10 scaled \magstep1%
   \global\font\twelveex=cmex10 scaled \magstep1%
   \global\font\twelvebf=cmbx10 scaled \magstep1%
   \global\font\twelvesl=cmsl10 scaled \magstep1%
   \global\font\twelvett=cmtt10 scaled \magstep1%
   \global\font\twelveit=cmti10 scaled \magstep1%
   \global\font\twelvess=cmss10 scaled \magstep1%
   \skewchar\twelvei='177%
   \skewchar\twelvesy='60%
   \hyphenchar\twelvett=-1%
   \moretwelvefonts
   \gdef\twelvefonts{\relax}}
\def\moretwelvefonts{\relax}%
%++ 14 pt fonts:
\def\fourteenfonts{%
   \global\font\fourteenrm=cmr10 scaled \magstep2%
   \global\font\fourteeni=cmmi10 scaled \magstep2%
   \global\font\fourteensy=cmsy10 scaled \magstep2%
   \global\font\fourteenex=cmex10 scaled \magstep2%
   \global\font\fourteenbf=cmbx10 scaled \magstep2%
   \global\font\fourteensl=cmsl10 scaled \magstep2%
   \global\font\fourteenit=cmti10 scaled \magstep2%
   \global\font\fourteenss=cmss10 scaled \magstep2%
   \skewchar\fourteeni='177%
   \skewchar\fourteensy='60%
   \morefourteenfonts
   \gdef\fourteenfonts{\relax}}
\def\morefourteenfonts{\relax}%
%++ 16 pt fonts:
\def\sixteenfonts{%
   \global\font\sixteenrm=cmr10 scaled \magstep3%
   \global\font\sixteeni=cmmi10 scaled \magstep3%
   \global\font\sixteensy=cmsy10 scaled \magstep3%
   \global\font\sixteenex=cmex10 scaled \magstep3%
   \global\font\sixteenbf=cmbx10 scaled \magstep3%
   \global\font\sixteensl=cmsl10 scaled \magstep3%
   \global\font\sixteenit=cmti10 scaled \magstep3%
   \skewchar\sixteeni='177%
   \skewchar\sixteensy='60%
   \moresixteenfonts
   \gdef\sixteenfonts{\relax}}
\def\moresixteenfonts{\relax}%
%++ 20 pt fonts:
\def\twentyfonts{%
   \global\font\twentyrm=cmr10 scaled \magstep4%
   \global\font\twentyi=cmmi10 scaled \magstep4%
   \global\font\twentysy=cmsy10 scaled \magstep4%
   \global\font\twentyex=cmex10 scaled \magstep4%
   \global\font\twentybf=cmbx10 scaled \magstep4%
   \global\font\twentysl=cmsl10 scaled \magstep4%
   \global\font\twentyit=cmti10 scaled \magstep4%
   \skewchar\twentyi='177%
   \skewchar\twentysy='60%
   \moretwentyfonts
   \gdef\twentyfonts{\relax}}
\def\moretwentyfonts{\relax}%
%++ 24 pt fonts:
\def\twentyfourfonts{%
   \global\font\twentyfourrm=cmr10 scaled \magstep5%
   \global\font\twentyfouri=cmmi10 scaled \magstep5%
   \global\font\twentyfoursy=cmsy10 scaled \magstep5%
   \global\font\twentyfourex=cmex10 scaled \magstep5%
   \global\font\twentyfourbf=cmbx10 scaled \magstep5%
   \global\font\twentyfoursl=cmsl10 scaled \magstep5%
   \global\font\twentyfourit=cmti10 scaled \magstep5%
   \skewchar\twentyfouri='177%
   \skewchar\twentyfoursy='60%
   \moretwentyfourfonts
   \gdef\twentyfourfonts{\relax}}
\def\moretwentyfourfonts{\relax}%
\def\tenmibfonts{%
   \global\font\tenmib=cmmib10
   \global\font\tenbsy=cmbsy10
   \skewchar\tenmib='177%
   \skewchar\tenbsy='60%
   \gdef\tenmibfonts{\relax}}
\def\elevenmibfonts{%
   \global\font\elevenmib=cmmib10 scaled \magstephalf
   \global\font\elevenbsy=cmbsy10 scaled \magstephalf
   \skewchar\elevenmib='177%
   \skewchar\elevenbsy='60%
   \gdef\elevenmibfonts{\relax}}
\def\twelvemibfonts{%
   \global\font\twelvemib=cmmib10 scaled \magstep1%
   \global\font\twelvebsy=cmbsy10 scaled \magstep1%
   \skewchar\twelvemib='177%
   \skewchar\twelvebsy='60%
   \gdef\twelvemibfonts{\relax}}
\def\fourteenmibfonts{%
   \global\font\fourteenmib=cmmib10 scaled \magstep2%
   \global\font\fourteenbsy=cmbsy10 scaled \magstep2%
   \skewchar\fourteenmib='177%
   \skewchar\fourteenbsy='60%
   \gdef\fourteenmibfonts{\relax}}
\def\sixteenmibfonts{%
   \global\font\sixteenmib=cmmib10 scaled \magstep3%
   \global\font\sixteenbsy=cmbsy10 scaled \magstep3%
   \skewchar\sixteenmib='177%
   \skewchar\sixteenbsy='60%
   \gdef\sixteenmibfonts{\relax}}
\def\twentymibfonts{%
   \global\font\twentymib=cmmib10 scaled \magstep4%
   \global\font\twentybsy=cmbsy10 scaled \magstep4%
   \skewchar\twentymib='177%
   \skewchar\twentybsy='60%
   \gdef\twentymibfonts{\relax}}
\def\twentyfourmibfonts{%
   \global\font\twentyfourmib=cmmib10 scaled \magstep5%
   \global\font\twentyfourbsy=cmbsy10 scaled \magstep5%
   \skewchar\twentyfourmib='177%
   \skewchar\twentyfourbsy='60%
   \gdef\twentyfourmibfonts{\relax}}
%%> {\noexpand\mib,}
\def\mib{%
   \tenmibfonts
   \textfont0=\tenbf\scriptfont0=\sevenbf
   \scriptscriptfont0=\fivebf
   \textfont1=\tenmib\scriptfont1=\seveni
   \scriptscriptfont1=\fivei
   \textfont2=\tenbsy\scriptfont2=\sevensy
   \scriptscriptfont2=\fivesy}
%%> {\noexpand\scr,}
\newfam\scrfam
\def\scr{\scrfonts
   \global\textfont\scrfam=\tenscr
   \fam\scrfam\tenscr}
\def\scrfonts{%
   \global\font\twentyfourscr=rsfs10  scaled \magstep5
   \global\font\twentyscr=rsfs10  scaled \magstep4
   \global\font\sixteenscr=rsfs10  scaled \magstep3
   \global\font\fourteenscr=rsfs10  scaled \magstep2
   \global\font\twelvescr=rsfs10  scaled \magstep1
   \global\font\elevenscr=rsfs10  scaled \magstephalf
   \global\font\tenscr=rsfs10
   \global\font\sevenscr=rsfs7
   \global\font\fivescr=rsfs5
   \skewchar\tenscr='177 \skewchar\sevenscr='177 \skewchar\fivescr='177%
   \textfont\scrfam=\tenscr \scriptfont\scrfam=\sevenscr
   \scriptscriptfont\scrfam=\fivescr
   \gdef\scrfonts{\relax}}
%%> {9pt,}
\def\ninepoint{\ninefonts
   \def\rm{\fam0\ninerm}%
   \textfont0=\ninerm\scriptfont0=\sevenrm\scriptscriptfont0=\fiverm
   \textfont1=\ninei\scriptfont1=\seveni\scriptscriptfont1=\fivei
   \textfont2=\ninesy\scriptfont2=\sevensy\scriptscriptfont2=\fivesy
   \textfont3=\nineex\scriptfont3=\nineex\scriptscriptfont3=\nineex
   \textfont\itfam=\nineit\def\it{\fam\itfam\nineit}%
   \textfont\slfam=\ninesl\def\sl{\fam\slfam\ninesl}%
   \textfont\ttfam=\ninett\def\tt{\fam\ttfam\ninett}%
   \textfont\bffam=\ninebf
   \scriptfont\bffam=\sevenbf
   \scriptscriptfont\bffam=\fivebf\def\bf{\fam\bffam\ninebf}%
   \def\mib{\relax}%
   \def\scr{\relax}%
   \tt\ttglue=.5emplus.25emminus.15em
   \normalbaselineskip=11pt
   \setbox\strutbox=\hbox{\vrule height 8pt depth 3pt width 0pt}%
   \normalbaselines\rm\singlespaced}%
%%> {10pt,}
\def\tenpoint{%
   \def\rm{\fam0\tenrm}%
   \textfont0=\tenrm\scriptfont0=\sevenrm\scriptscriptfont0=\fiverm
   \textfont1=\teni\scriptfont1=\seveni\scriptscriptfont1=\fivei
   \textfont2=\tensy\scriptfont2=\sevensy\scriptscriptfont2=\fivesy
   \textfont3=\tenex\scriptfont3=\tenex\scriptscriptfont3=\tenex
   \textfont\itfam=\tenit\def\it{\fam\itfam\tenit}%
   \textfont\slfam=\tensl\def\sl{\fam\slfam\tensl}%
   \textfont\ttfam=\tentt\def\tt{\fam\ttfam\tentt}%
   \textfont\bffam=\tenbf
   \scriptfont\bffam=\sevenbf
   \scriptscriptfont\bffam=\fivebf\def\bf{\fam\bffam\tenbf}%
   \def\mib{%
      \tenmibfonts
      \textfont0=\tenbf\scriptfont0=\sevenbf
      \scriptscriptfont0=\fivebf
      \textfont1=\tenmib\scriptfont1=\seveni
      \scriptscriptfont1=\fivei
      \textfont2=\tenbsy\scriptfont2=\sevensy
      \scriptscriptfont2=\fivesy}%
   \def\scr{\scrfonts
      \global\textfont\scrfam=\tenscr\fam\scrfam\tenscr}%
   \tt\ttglue=.5emplus.25emminus.15em
   \normalbaselineskip=12pt
   \setbox\strutbox=\hbox{\vrule height 8.5pt depth 3.5pt width 0pt}%
   \normalbaselines\rm\singlespaced}%
%%> {11pt,}
\def\elevenpoint{\elevenfonts
   \def\rm{\fam0\elevenrm}%
   \textfont0=\elevenrm\scriptfont0=\sevenrm\scriptscriptfont0=\fiverm
   \textfont1=\eleveni\scriptfont1=\seveni\scriptscriptfont1=\fivei
   \textfont2=\elevensy\scriptfont2=\sevensy\scriptscriptfont2=\fivesy
   \textfont3=\elevenex\scriptfont3=\elevenex\scriptscriptfont3=\elevenex
   \textfont\itfam=\elevenit\def\it{\fam\itfam\elevenit}%
   \textfont\slfam=\elevensl\def\sl{\fam\slfam\elevensl}%
   \textfont\ttfam=\eleventt\def\tt{\fam\ttfam\eleventt}%
   \textfont\bffam=\elevenbf
   \scriptfont\bffam=\sevenbf
   \scriptscriptfont\bffam=\fivebf\def\bf{\fam\bffam\elevenbf}%
   \def\mib{%
      \elevenmibfonts
      \textfont0=\elevenbf\scriptfont0=\sevenbf
      \scriptscriptfont0=\fivebf
      \textfont1=\elevenmib\scriptfont1=\seveni
      \scriptscriptfont1=\fivei
      \textfont2=\elevenbsy\scriptfont2=\sevensy
      \scriptscriptfont2=\fivesy}%
   \def\scr{\scrfonts
      \global\textfont\scrfam=\elevenscr\fam\scrfam\elevenscr}%
   \tt\ttglue=.5emplus.25emminus.15em
   \normalbaselineskip=13pt
   \setbox\strutbox=\hbox{\vrule height 9pt depth 4pt width 0pt}%
   \normalbaselines\rm\singlespaced}%
%%> {12pt,}
\def\twelvepoint{\twelvefonts\ninefonts
   \def\rm{\fam0\twelverm}%
   \textfont0=\twelverm\scriptfont0=\ninerm\scriptscriptfont0=\sevenrm
   \textfont1=\twelvei\scriptfont1=\ninei\scriptscriptfont1=\seveni
   \textfont2=\twelvesy\scriptfont2=\ninesy\scriptscriptfont2=\sevensy
   \textfont3=\twelveex\scriptfont3=\twelveex\scriptscriptfont3=\twelveex
   \textfont\itfam=\twelveit\def\it{\fam\itfam\twelveit}%
   \textfont\slfam=\twelvesl\def\sl{\fam\slfam\twelvesl}%
   \textfont\ttfam=\twelvett\def\tt{\fam\ttfam\twelvett}%
   \textfont\bffam=\twelvebf
   \scriptfont\bffam=\ninebf
   \scriptscriptfont\bffam=\sevenbf\def\bf{\fam\bffam\twelvebf}%
   \def\mib{%
      \twelvemibfonts\tenmibfonts
      \textfont0=\twelvebf\scriptfont0=\ninebf
      \scriptscriptfont0=\sevenbf
      \textfont1=\twelvemib\scriptfont1=\ninei
      \scriptscriptfont1=\seveni
      \textfont2=\twelvebsy\scriptfont2=\ninesy
      \scriptscriptfont2=\sevensy}%
   \def\scr{\scrfonts
      \global\textfont\scrfam=\twelvescr\fam\scrfam\twelvescr}%
   \tt\ttglue=.5emplus.25emminus.15em
   \normalbaselineskip=14pt
   \setbox\strutbox=\hbox{\vrule height 10pt depth 4pt width 0pt}%
   \normalbaselines\rm\singlespaced}%
%%> {14pt,}
\def\fourteenpoint{\fourteenfonts\twelvefonts
   \def\rm{\fam0\fourteenrm}%
   \textfont0=\fourteenrm\scriptfont0=\twelverm\scriptscriptfont0=\tenrm
   \textfont1=\fourteeni\scriptfont1=\twelvei\scriptscriptfont1=\teni
   \textfont2=\fourteensy\scriptfont2=\twelvesy\scriptscriptfont2=\tensy
   \textfont3=\fourteenex\scriptfont3=\fourteenex
      \scriptscriptfont3=\fourteenex
   \textfont\itfam=\fourteenit\def\it{\fam\itfam\fourteenit}%
   \textfont\slfam=\fourteensl\def\sl{\fam\slfam\fourteensl}%
   \textfont\bffam=\fourteenbf
   \scriptfont\bffam=\twelvebf
   \scriptscriptfont\bffam=\tenbf\def\bf{\fam\bffam\fourteenbf}%
   \def\mib{%
      \fourteenmibfonts\twelvemibfonts\tenmibfonts
      \textfont0=\fourteenbf\scriptfont0=\twelvebf
      \scriptscriptfont0=\tenbf
      \textfont1=\fourteenmib\scriptfont1=\twelvemib
      \scriptscriptfont1=\tenmib
      \textfont2=\fourteenbsy\scriptfont2=\tenbsy
      \scriptscriptfont2=\tenbsy}%
   \def\scr{\scrfonts
      \global\textfont\scrfam=\fourteenscr\fam\scrfam\fourteenscr}%
   \normalbaselineskip=17pt
   \setbox\strutbox=\hbox{\vrule height 12pt depth 5pt width 0pt}%
   \normalbaselines\rm\singlespaced}%
%%> {16pt,}
\def\sixteenpoint{\sixteenfonts\fourteenfonts\twelvefonts
   \def\rm{\fam0\sixteenrm}%
   \textfont0=\sixteenrm\scriptfont0=\fourteenrm\scriptscriptfont0=\twelverm
   \textfont1=\sixteeni\scriptfont1=\fourteeni\scriptscriptfont1=\twelvei
   \textfont2=\sixteensy\scriptfont2=\fourteensy\scriptscriptfont2=\twelvesy
   \textfont3=\sixteenex\scriptfont3=\sixteenex\scriptscriptfont3=\sixteenex
   \textfont\itfam=\sixteenit\def\it{\fam\itfam\sixteenit}%
   \textfont\slfam=\sixteensl\def\sl{\fam\slfam\sixteensl}%
   \textfont\bffam=\sixteenbf
   \scriptfont\bffam=\fourteenbf
   \scriptscriptfont\bffam=\twelvebf\def\bf{\fam\bffam\sixteenbf}%
   \def\mib{%
      \sixteenmibfonts\fourteenmibfonts\twelvemibfonts
      \textfont0=\sixteenbf\scriptfont0=\fourteenbf
      \scriptscriptfont0=\twelvebf
      \textfont1=\sixteenmib\scriptfont1=\fourteenmib
      \scriptscriptfont1=\twelvemib
      \textfont2=\sixteenbsy\scriptfont2=\fourteenbsy
      \scriptscriptfont2=\twelvebsy}%
   \def\scr{\scrfonts
      \global\textfont\scrfam=\sixteenscr\fam\scrfam\sixteenscr}%
   \normalbaselineskip=20pt
   \setbox\strutbox=\hbox{\vrule height 14pt depth 6pt width 0pt}%
   \normalbaselines\rm\singlespaced}%
%%> {20pt,}
\def\twentypoint{\twentyfonts\sixteenfonts\fourteenfonts
   \def\rm{\fam0\twentyrm}%
   \textfont0=\twentyrm\scriptfont0=\sixteenrm\scriptscriptfont0=\fourteenrm
   \textfont1=\twentyi\scriptfont1=\sixteeni\scriptscriptfont1=\fourteeni
   \textfont2=\twentysy\scriptfont2=\sixteensy\scriptscriptfont2=\fourteensy
   \textfont3=\twentyex\scriptfont3=\twentyex\scriptscriptfont3=\twentyex
   \textfont\itfam=\twentyit\def\it{\fam\itfam\twentyit}%
   \textfont\slfam=\twentysl\def\sl{\fam\slfam\twentysl}%
   \textfont\bffam=\twentybf
   \scriptfont\bffam=\sixteenbf
   \scriptscriptfont\bffam=\fourteenbf\def\bf{\fam\bffam\twentybf}%
   \def\mib{%
      \twentymibfonts\sixteenmibfonts\fourteenmibfonts
      \textfont0=\twentybf\scriptfont0=\sixteenbf
      \scriptscriptfont0=\fourteenbf
      \textfont1=\twentymib\scriptfont1=\sixteenmib
      \scriptscriptfont1=\fourteenmib
      \textfont2=\twentybsy\scriptfont2=\sixteenbsy
      \scriptscriptfont2=\fourteenbsy}%
   \def\scr{\scrfonts
      \global\textfont\scrfam=\twentyscr\fam\scrfam\twentyscr}%
   \normalbaselineskip=24pt
   \setbox\strutbox=\hbox{\vrule height 17pt depth 7pt width 0pt}%
   \normalbaselines\rm\singlespaced}%
%%> {24pt.}
\def\twentyfourpoint{\twentyfourfonts\twentyfonts\sixteenfonts
   \def\rm{\fam0\twentyfourrm}%
   \textfont0=\twentyfourrm\scriptfont0=\twentyrm\scriptscriptfont0=\sixteenrm
   \textfont1=\twentyfouri\scriptfont1=\twentyi\scriptscriptfont1=\sixteeni
   \textfont2=\twentyfoursy\scriptfont2=\twentysy\scriptscriptfont2=\sixteensy
   \textfont3=\twentyfourex\scriptfont3=\twentyfourex
      \scriptscriptfont3=\twentyfourex
   \textfont\itfam=\twentyfourit\def\it{\fam\itfam\twentyfourit}%
   \textfont\slfam=\twentyfoursl\def\sl{\fam\slfam\twentyfoursl}%
   \textfont\bffam=\twentyfourbf
   \scriptfont\bffam=\twentybf
   \scriptscriptfont\bffam=\sixteenbf\def\bf{\fam\bffam\twentyfourbf}%
   \def\mib{%
      \twentyfourmibfonts\twentymibfonts\sixteenmibfonts
      \textfont0=\twentyfourbf\scriptfont0=\twentybf
      \scriptscriptfont0=\sixteenbf
      \textfont1=\twentyfourmib\scriptfont1=\twentymib
      \scriptscriptfont1=\sixteenmib
      \textfont2=\twentyfourbsy\scriptfont2=\twentybsy
      \scriptscriptfont2=\sixteenbsy}%
   \def\scr{\scrfonts
      \global\textfont\scrfam=\twentyfourscr\fam\scrfam\twentyfourscr}%
   \normalbaselineskip=28pt
   \setbox\strutbox=\hbox{\vrule height 19pt depth 9pt width 0pt}%
   \normalbaselines\rm\singlespaced}%
\def\Tbf{\fourteenpoint\bf}
\def\tbf{\twelvepoint\bf}
\def\printfont{\autoload\printfont{printfont.txs}\printfont}
% file: TXSmacs.tex  (TeXsis version 2.16)
%%> {TeXsis main macros.}
\catcode`@=11
\let\XA=\expandafter
\let\NX=\noexpand
\def\emsg#1{\relax
   \begingroup
     \def\@quote{"}%
     \def\TeX{TeX}\def\label##1{}\def\use{\string\use}%
     \def\ { }\def~{ }%
     \def\tt{\string\tt}\def\bf{}\def\Tbf{}\def\tbf{}%
     \def\break{}\def\n{\string\n}%
     \immediate\write16{#1}%
   \endgroup}
\newif\ifmarkerrors     \markerrorsfalse
\def\@errmark#1{\ifmarkerrors
   \vadjust{\vbox to 0pt{%
   \kern-\baselineskip
   \line{\hfil\rlap{{\tt\ <-#1}}}%
   \vss}}\fi}%
\def\draft{%
   \def\draftline{{\tentt Preliminary Draft \hfill
         -~\folio~- \hfill \runtime}}\footline={\draftline}%
   \eqnotracetrue
   \markerrorstrue
   \overfullrule=1em}%
\def\bye{%
    \endmode
    \par\vfill\supereject
    \checktags
    \end}
\def\endmode{\relax}%
\def\checktags{\relax}%
\def\setTableskip{\relax}%
\def\singlespaced{%
   \baselineskip=\normalbaselineskip
   \setRuledStrut
   \setTableskip}%
\def\singlespace{\singlespaced}%
\def\doublespaced{%
   \baselineskip=\normalbaselineskip
   \multiply\baselineskip by 150
   \divide\baselineskip by 100
   \setRuledStrut
   \setTableskip}%
\def\doublespace{\doublespaced}%
\def\TrueDoubleSpacing{%
   \baselineskip=\normalbaselineskip
   \multiply\baselineskip by 2
   \setRuledStrut
   \setTableskip}%
\def\truedoublespacing{\TrueDoubleSpacing}%
\def\triplespaced{%
   \baselineskip=\normalbaselineskip
   \multiply\baselineskip by 3
   \setRuledStrut
   \setTableskip}%
\def\widenspacing{%
   \multiply\baselineskip by 125
   \divide\baselineskip by 100
   \setRuledStrut
   \setTableskip}%
\def\whitespaced{\widenspacing}%
\def\whitespace{\widenspacing}%
\def\Footnote#1{%
   \let\@sf\empty
   \ifhmode\edef\@sf{\spacefactor\the\spacefactor}\/\fi
   ${}^{\scriptstyle\smash{#1}}$\@sf
   \Vfootnote{#1}}%
\def\Vfootnote#1{%
   \begingroup
     \def\@foot{\strut\egroup\endgroup}%
     \tenpoint
     \baselineskip=\normalbaselineskip
     \parskip=0pt
     \FootFont
     \vfootnote{${}^{\hbox{#1}}$}}%
\def\FootFont{\rm}%
\newcount\footnum \footnum=0
\let\footnotemark=\empty
\def\NFootnote{%
  \advance\footnum by 1
  \xdef\lab@l{\the\footnum}%
  \Footnote{\footnotemark\the\footnum}}
\def\setRuledStrut{\relax}              
\def\undertext#1{$\relax\underline{\hbox{#1}}$}
\def\n{\hfil\break}%
\def\nl{\hfil\break}%
\def\newpage{\vfill\eject}%
\def\Afour{\hsize=16.5cm \vsize=24.5cm\relax}%
\def\unobeylines{\catcode`\^^M=5}%
{\obeyspaces\gdef\unobeyspaces{\catcode`\ =10}}
\def\unraggedright{\rightskip=\z@\spaceskip=0pt\xspaceskip=0pt}
\catcode`\"=\active
\newcount\@quoteflag   \@quoteflag=\z@
\def"{\@quote}%
\def\@quote{%
   \ifnum\@quoteflag=\z@
     \@quoteflag=\@ne {``}%
   \else
     \@quoteflag=\z@ {''}%
   \fi}
\def\quoteon{\catcode`\"=\active}%
\def\quoteoff{\catcode`\"=12}%
\def\@checkquote#1{\ifnum\@quoteflag=\@ne\message{#1}\fi}
\quoteoff
\def\checkquote{{\quoteoff\@checkquote{> Unbalanced "}}}%
\def\obsolete#1#2{\def#1{\@obsolete#1#2}}
\def\@obsolete#1#2{%
   \emsg{>=========================================================}%
   \emsg{> \string#1 is now obsolete! It may soon disappear!}%
   \emsg{> Please use \string#2 instead.  But I'll try to do it anyway...}%
   \emsg{>=========================================================}%
   \let#1=#2\relax
   #2}%
\let\DUMP=\dump
\def\setcnt#1#2{%
  \edef\th@value{\the#1}%
  \aftergroup\global\aftergroup#1
  \aftergroup=\relax
  \XA\@ftergroup\th@value\endafter
  \global#1=#2\relax}%
\def\@ftergroup{\futurelet\next\@ftertoken} 
\long\def\@ftertoken#1{
   \ifx\next\endafter\relax
     \let\next=\relax
   \else\aftergroup#1\relax
     \let\next=\@ftergroup
   \fi\next}%
\def\ATlock{\catcode`@=12\relax}%
\def\ATunlock{\catcode`@=11\relax}%
\newhelp\AThelp{@: 
You've apparantly tried to use a macro which begins with ``@''.^^J
These macros are usually for internal TeXsis functions and should^^J
not be used casually.  If you really want to use the macro try first^^J
saying \string\ATunlock.  If you got this message by pure accident^^J
then something else is wrong.} 
\def\@{\begingroup
    \errhelp=\AThelp
    \newlinechar=10
    \errmessage{Are you tring to use an internal @-macro?}\relax
   \endgroup}
\def~{\ifmmode\phantom{0}\else\penalty10000\ \fi}%
\def\0{\phantom{0}}%
\def\,{\relax\ifmmode\mskip\the\thinmuskip\else\thinspace\fi}
\def\topspace{\hrule height \z@\vskip}
\long\def\comment#1/*#2*/{\relax}%
\long\def\Ignore#1\endIgnore{\relax}%
\def\endIgnore{\relax}%
{\catcode`\%=11 \gdef\@comment{% }}
\def\REV{\begingroup
   \def\endcomment{\endgroup}%
   \catcode`\|=12
   \catcode`(=12 \catcode`)=12
   \catcode`[=12 \catcode`]=12
   \comment}%
\def\begin#1{%
   \begingroup
     \let\end=\endbegin
     \expandafter\ifx\csname #1\endcsname\relax\relax
        \def\next{\beginerror{#1}}%
     \else
        \def\next{\csname #1\endcsname}%
     \fi\next}
\def\endbegin#1{%
   \endgroup
   \expandafter\ifx\csname end#1\endcsname\relax\relax
      \def\next{\begingroup\beginerror{end#1}}%
   \else
      \def\next{\csname end#1\endcsname}%
   \fi\next}
\newhelp\beginhelp{begin: 
    The \string\begin\space or \string\end\space marked above is for a
    non-existant^^J
    environment.  Check for spelling errors and such.}
\def\beginerror#1{%
   \endgroup
   \errhelp=\beginhelp
   \newlinechar=10
   \errmessage{Undefined environment for \string\begin\space or \string\end}}
\def\spine#1{\spineSetup
%   \headline={\LandscapeSpecial}%
   \setbox0=\hbox{\twentyfourpoint\bf\quad #1\quad}%
   \dimen0=\wd0
   \ifdim\wd0<15cm \dimen0=15cm\fi
   \vskip 1cm plus 2cm
   \tightboxit{\vbox to 1in{\vfill
     \hbox to \dimen0{\hfil\box0\hfil}%
     \vfill}}%
   \vskip 1cm plus 2cm}%
\def\spineSetup{%
   \LandscapeSpecial
   \vbox{\hsize=15cm
     \bigskip\bigskip
     \tenpoint\parskip=\smallskipamount
     \noindent
     How to install the spine label on a binder:
     \item{1.}
     Cut out the label around the outside of the 
     bounding ruled box.  Leave extra paper
     (about 1.5cm or so) on the RIGHT side.
     \item{2.}
     Obtain a long thin plastic ruler or similar object which can 
     slide down the pocket on the binder spine.
     \item{3.}
     Put the label along the ruler, face up, and fold the extra tab 
     of paper on the right of the label over the end of the ruler.
     \item{4.}
     Slide the ruler, with the label on it, down the spine of the 
     binder.  When the label is in place remove the ruler.  The label 
     will remain.
     \bigskip\bigskip
   \gdef\spineSetup{\relax}%
   }}
\def\\{\global\let\@stoken= }\\ 
\long\def\unexpandedwrite#1#2{%
   \def\@finwrite{\immediate\write#1}%
   \begingroup
    \aftergroup\@finwrite
    \aftergroup{\relax
    \@sanitize#2\endsanity
    \aftergroup}\relax
   \endgroup
 }
\long\def\writeNX#1#2{%
   \def\@finwrite{\write#1}%
   \begingroup
    \aftergroup\@finwrite
    \aftergroup{\relax
    \@sanitize#2\endsanity
    \aftergroup}\relax
   \endgroup}%
\def\@sanitize{\futurelet\next\@sanswitch} 
\def\@sanswitch{%
    \ifx\next\endsanity\relax
    \else\ifcat\noexpand\next\@stoken
        \aftergroup\space\let\next=\@eat
    \else\ifcat\noexpand\next\bgroup
        \aftergroup{\let\next=\@eat
    \else\ifcat\noexpand\next\egroup
        \aftergroup}\let\next=\@eat
     \else
        \let\next=\@copytoken
     \fi\fi\fi\fi 
     \next}%
\def\@eat{\afterassignment\@sanitize\let\next= } 
\long\def\@copytoken#1{%
    \ifcat\noexpand#1\relax
        \aftergroup\noexpand
    \else\ifcat\noexpand#1\noexpand~\relax
        \aftergroup\noexpand
    \fi\fi
    \aftergroup#1\relax
    \@sanitize}%
\def\endsanity\endsanity{}%
%%> {Checkpoint/Restart.}
\newwrite\checkpointout
\def\checkpoint#1{\emsg{\@comment\NX\checkpoint --> #1.chk}%
    \immediate\openout\checkpointout= #1.chk
    \@checkwrite{\pageno}%
    \@checkwrite{\chapternum}%
    \@checkwrite{\corollarynum}%
    \@checkwrite{\definitionnum}%
    \@checkwrite{\eqnum}%
    \@checkwrite{\fignum}%
    \@checkwrite{\lemmanum}
    \@checkwrite{\refnum}%
    \@checkwrite{\sectionnum}%
    \@checkwrite{\subsectionnum}%
    \@checkwrite{\tabnum}%
    \@checkwrite{\theoremnum}%
    \@checkwrite{\footnum}%
    \immediate\closeout\checkpointout}%
\def\@checkwrite#1{\edef\tnum{\the #1}%
     \immediate\write\checkpointout{\NX #1 = \tnum}}%
\def\restart#1{\relax
    \immediate\closeout\checkpointout
    \ATunlock
    \Input #1.chk \relax
    \@firstrefnum=\refnum
    \advance\@firstrefnum by \@ne
    \ATlock}%
\let\restore=\restart
\def\endstat{%
   \emsg{\@comment Last PAGE      number is \the\pageno.}%
   \emsg{\@comment Last CHAPTER   number is \the\chapternum.}%
   \emsg{\@comment Last EQUATION  number is \the\eqnum.}%
   \emsg{\@comment Last FIGURE    number is \the\fignum.}%
   \emsg{\@comment Last REFERENCE number is \the\refnum.}%
   \emsg{\@comment Last SECTION   number is \the\sectionnum.}%
   \emsg{\@comment Last TABLE     number is \the\tabnum.}%
   \tracingstats=1}%
{\catcode`\%=11 \gdef\@comment{% }}
\def\theBlank#1{\nobreak\hbox{\lower\jot\vbox{\hrule width #1\relax}}}
\def\Romannumeral#1{\uppercase\expandafter{\romannumeral #1}}
\def\monthname#1{\ifcase#1 \errmessage{0 is not a 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\else \errmessage{#1 is not a month}\fi}
\def\leftpar#1{%
    \setbox\@capbox=\vbox{\normalbaselines
    \noindent #1\par
        \global\@caplines=\prevgraf}%
    \ifnum \@ne=\@caplines
        \leftline{#1}\else
        \hbox to\hsize{\hss\box\@capbox\hss}\fi}
\def\dospecials{\do\ \do\\\do\{\do\}\do\$\do\&\do\"\do\(\do\)\do\[\do\]%
  \do\#\do\^\do\^^K\do\_\do\^^A\do\%\do\~}
\def\tightbox#1{\vbox{\hrule\hbox{\vrule\vbox{#1}\vrule}\hrule}}
\let\tightboxit=\tightbox
\def\loosebox#1{%
    \vbox{\vskip\jot
        \hbox{\hskip\jot #1\hskip\jot}%
        \vskip\jot}}
\def\eqnbox#1{\lower\jot\tightbox{\loosebox{\quad $#1$ \quad}}}
\def\gloop#1\repeat{\gdef\body{#1}\iterate}
\newif\iflastarg\lastargfalse
\def\car#1,#2;{\gdef\@arg{#1}\gdef\@args{#2}}
\def\@apply{%
    \iflastarg
    \else
        \XA\car\@args;
        \islastarg
        \XA\@fcn\XA{\@arg}%
        \@apply
    \fi}
\def\apply#1#2{%
    \gdef\@args{#2,}\let\@fcn#1
    \islastarg
    \@apply
    }
\def\islastarg{\ifx \@args\empty\lastargtrue\else\lastargfalse\fi}%
\def\@seppuku{\errmessage{Interwoven alignment preambles are not allowed.}\end}
\def\jtem#1#2{\par\hangafter0\hangindent#1
              \noindent\llap{#2\enspace}\ignorespaces}
% file: TXSinit.tex  (TeXsis version 2.16)
%%> {Initialization.}
\catcode`@=11
\uchyph=\@ne
\brokenpenalty=\@M
\widowpenalty=\@M
\clubpenalty=\@M
\long\def\texsis{%
    \quoteon
    \Contentsfalse
    \autoparens
    \ATlock
    \resetcounters
    \pageno=1
    \colwidth=\hsize
    \headline={\HeadLine}\headlineoffset=0.5cm
    \footline={\FootLine}\footlineoffset=0.5cm
    \twelvepoint
    \doublespaced
    \newlinechar=`\^^M
}
\obsolete\inittexsis\texsis     \obsolete\texsisinit\texsis    
\obsolete\initexsis\texsis      \obsolete\initTeXsis\texsis    
\def\today{\number\day\ 
    \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\
    \number\year}
\def\dated#1{\xdef\today{#1}}
\def\SetDate{%
  \xdef\adate{\monthname{\the\month}~\number\day, \number\year}%
  \xdef\edate{\number\day~\monthname{\the\month}~\number\year}%
  \count255=\time\divide\count255 by 60
  \edef\hour{\the\count255}%
  \multiply\count255 by -60 \advance\count255 by\time
  \edef\minutes{\ifnum 10>\count255 {0}\fi\the\count255}%
  \edef\runtime{\the\year/\the\month/\the\day\space\hour:\minutes}}
\def\gzero#1{\ifx#1\undefined\relax\else\global#1=\z@\fi}
\def\resetcounters{%
  \gzero\chapternum     \gzero\sectionnum
  \gzero\subsectionnum  \gzero\subsubsectionnum 
  \gzero\theoremnum     \gzero\lemmanum         
  \gzero\corollarynum   \gzero\definitionnum    
  \gzero\tabnum         \gzero\fignum        
  \gzero\@BadRefs       \gzero\@BadTags  
  \gzero\@envDepth      \gzero\enumDepth
  \gzero\enumcnt        \gzero\@quoteflag  
  \gzero\refnum         \gzero\eqnum         
  \global\@firstrefnum=1\global\@lastrefnum=1                   
}
\newread\patchfile
\def\LoadSiteFile{%
  \immediate\openin\patchfile=TXSsite.tex
  \ifeof\patchfile
     \emsg{> Trying to load the site info file TXSsite.tex...}%
  \fi
  \immediate\closein\patchfile
  \input TXSsite.tex \relax}%
\def\ReadPatches{%
    \immediate\openin\patchfile=\TXSpatches.tex
    \ifeof\patchfile
         \closein\patchfile
    \else\immediate\closein\patchfile
       \input\TXSpatches.tex \relax
    \fi
    \immediate\openin\patchfile=\TXSmods.tex \relax
    \ifeof\patchfile
       \closein\patchfile
    \else\immediate\closein\patchfile
       \input\TXSmods.tex \relax
    \fi}
\newinsert\botins 
\skip\botins=\bigskipamount
\count\botins=1000
\dimen\botins=\maxdimen
\newif\if@bot
\def\topinsert{\@midfalse\p@gefalse\@botfalse\@ins}
\def\midinsert{\@midtrue\p@gefalse\@botfalse\@ins}
\def\pageinsert{\@midfalse\p@getrue\@botfalse\@ins}
\def\bottominsert{\@midfalse\p@gefalse\@bottrue\@ins\bigskip}
\def\heavyinsert{\@midtrue\p@gefalse\@bottrue\@ins}
\def\endinsert{%
  \egroup
  \if@mid \dimen@\ht\z@ \advance\dimen@\dp\z@
    \advance\dimen@12\p@ \advance\dimen@\pagetotal
    \ifdim\dimen@>\pagegoal\@midfalse\p@gefalse\fi\fi
  \if@mid \bigskip\box\z@\bigbreak
  \else\if@bot\@insert\botins \else\@insert\topins \fi
  \fi
  \endgroup}
\def\@insert#1{%
  \insert#1{\penalty100
  \splittopskip\z@skip
  \splitmaxdepth\maxdimen \floatingpenalty\z@
  \ifp@ge \dimen@=\dp\z@
    \vbox to\vsize{\unvbox\z@\kern-\dimen@}%
  \else \box\z@ \nobreak
    \ifx #1\topins \ifp@ge\else\bigskip\fi\fi
  \fi}}
\def\pagecontents{%
  \ifvoid\topins\else\unvbox\topins
      \vskip\skip\topins\fi
  \dimen@=\dp\@cclv \unvbox\@cclv
  \ifvoid\footins\else
    \vskip\skip\footins
    \footnoterule
    \unvbox\footins\fi
  \ifvoid\botins\else\vskip\skip\botins
        \unvbox\botins\fi
  \ifr@ggedbottom \kern-\dimen@ \vfil \fi}
\newread\txsfile
\def\loadstyle#1#2{%
   \def#1{\@loaderr{#1}}%
   \ATunlock
   \immediate\openin\txsfile=#2
   \ifeof\txsfile
      \emsg{> Trying to load the style file #2...}%
   \fi
   \closein\txsfile
   \input #2 \relax
   \ATlock
   #1}%
\newhelp\@utohelp{%
loadstyle: The macro named above was supposed to be defined^^J
In the style file that was just read, but I couldn't find^^J
the definition in that file.  Maybe you can learn something^^J
from the comments in that style file, or find someone who knows^^J
something about it.}
\def\@loaderr#1{%
   \newlinechar=10
   \errhelp=\@utohelp
   \errmessage{No definition of \string#1 in the style file.}}
\def\autoload#1#2{%
   \def#1{\loadstyle#1{#2}}}
\autoload\PhysRev{PhysRev.txs}%
\autoload\PhysRevLett{PhysRev.txs}%
\autoload\PhysRevManuscript{PhysRev.txs}%
\autoload\nuclproc{nuclproc.txs}%
\autoload\NorthHolland{Elsevier.txs}%
\autoload\NorthHollandTwo{Elsevier.txs}%
\autoload\WorldScientific{WorldSci.txs}%
\autoload\IEEEproceedings{IEEE.txs}%
\autoload\IEEEreduced{IEEE.txs}%
\autoload\AIPproceedings{AIP.txs}%
\autoload\CVformat{CVformat.txs}%
\autoload\idx{index.tex}\autoload\index{index.tex}\autoload\theindex{index.tex}
\autoload\markindexfalse{index.tex}\autoload\markindextrue{index.tex}
\autoload\makeindexfalse{index.tex}\autoload\makeindextrue{index.tex}
% file: TXShead.tex                                 TeXsis version 2.16
%%> {Running Headlines.}
\newdimen\headlineoffset        \headlineoffset=0.0cm
\newdimen\footlineoffset        \footlineoffset=0.0cm
\newif\ifRunningHeads           \RunningHeadsfalse
\newif\ifbookpagenumbers        \bookpagenumbersfalse
\newif\ifrightn@m               \rightn@mtrue
\def\makeheadline{\vbox to 0pt{\vskip-22.5pt
   \vskip-\headlineoffset
   \line{\vbox to 8.5pt{}\the\headline}\vss}\nointerlineskip}
\def\makefootline{\baselineskip=24pt
   \vskip\footlineoffset
   \line{\the\footline}}
\def\HeadLine{%
   \edef\firstm{{\XA\iffalse\firstmark\fi}}%
   \edef\topm{{\XA\iffalse\topmark\fi}}%
   \ifRunningHeads
     \def\He@dText{{\HeadFont \HeadText}}%
   \else\def\He@dText{\relax}\fi
   \ifbookpagenumbers
      \ifodd\pageno\rightn@mtrue
      \else\rightn@mfalse\fi
   \else\rightn@mtrue\fi
   \ifx\topm\firstm
     \ifrightn@m
        {\hss\He@dText\hss\llap{\PageNumber}}%
     \else
        {\rlap{\PageNumber}\hss\He@dText\hss}%
      \fi
   \else \hfill \fi}%
\def\HeadText{\hfill}%
\def\He@dText{\relax}
\def\FootLine{%
   \edef\firstm{%
      {\expandafter\iffalse\firstmark\fi}}%
   \edef\topm{%
      {\expandafter\iffalse\topmark\fi}}%
   \ifx\topm\firstm \hss
    \else {\hss \FootText \hss} \fi}%
\def\FootText{\hfill}%
\def\PageNumber{{\tenrm\folio}}%
\def\HeadFont{\tenit}%
\def\nopagenumbers{\headline={\hfil}\footline={\hfil}}
\def\pagenumbers{\headline={\HeadLine}\footline={\FootLine}}
\def\bookpagenumbers{\bookpagenumberstrue}
\def\plainoutput{%
  \makeBindingMargin
  \shipout\vbox{\makeheadline\pagebody\makefootline}%
  \advancepageno
  \ifnum\outputpenalty>-\@MM \else\dosupereject\fi}
\newdimen\BindingMargin \BindingMargin=0pt
\def\makeBindingMargin{%
   \ifdim\BindingMargin>0pt
   \ifodd\pageno\hoffset=\BindingMargin\else
   \hoffset=-\BindingMargin\fi\fi}
% file: TXSeqns.tex  (TeXsis version 2.16)
%%> {Equation numbering.}
\newcount\eqnum         \eqnum=\z@
\def\@chaptID{}         \def\@sectID{}%
\newif\ifeqnotrace      \eqnotracefalse
\def\EQN{%
   \begingroup
   \quoteoff\offparens
   \@EQN}%
\def\@EQN#1$${%
   \endgroup
   \if ?#1? \EQNOparse *;;\endlist
   \else \EQNOparse#1;;\endlist\fi
   $$}%
\def\EQNOparse#1;#2;#3\endlist{%
  \if ?#3?\relax
    \global\advance\eqnum by\@ne
    \edef\tnum{\@chaptID\@sectID\the\eqnum}%
    \Eqtag{#1}{\tnum}%
    \@EQNOdisplay{#1}%
  \else\stripblanks #2\endlist
    \edef\p@rt{\tok}%
    \if a\p@rt\relax
      \global\advance\eqnum by\@ne\fi
    \edef\tnum{\@chaptID\@sectID\the\eqnum}%
    \Eqtag{#1}{\tnum}%
    \edef\tnum{\@chaptID\@sectID\the\eqnum\p@rt}%
    \Eqtag{#1;\p@rt}{\tnum}%
    \@EQNOdisplay{#1;#2}%
  \fi
  \global\let\?=\tnum
  \relax}%
\def\Eqtag#1#2{\tag{Eq.#1}{#2}} 
\def\@EQNOdisplay#1{%
   \@eqno
   \ifeqnotrace
     \rlap{\phantom{(\tnum)}%
        \quad{\tenpoint\tt["#1"]}}\fi
    (\tnum)}%
\let\@eqno=\eqno
\def\endlist{\endlist}%
\def\Eq#1{Eq.~($\use{Eq.#1}$)}%
\def\Eqs#1{Eqs.~($\use{Eq.#1}$)}%
\def\Ep#1{($\use{Eq.#1}$)}%
\def\EQNdisplaylines#1{%
   \@EQNcr
   \displ@y
   \halign{%
      \hbox to\displaywidth{%
      $\@lign\hfil\displaystyle##\hfil$}%
      &\llap{$\@lign\@@EQN{##}$}\crcr
   #1\crcr}%
   \@EQNuncr}%
\long\def\EQNalign#1{%
   \@EQNcr
   \displ@y
     \tabskip=\centering
   \halign to\displaywidth{%
   \hfil$\relax\displaystyle{##}$
     \tabskip=0pt
   &$\relax\displaystyle{{}##}$\hfil
     \tabskip=\centering
   &\llap{$\relax\@@EQN{##}$}%
     \tabskip=0pt\crcr
    #1\crcr}%
   }
\def\@@EQN#1{\if ?#1? \EQNOparse *;;\endlist
         \else \EQNOparse#1;;\endlist\fi}%
\def\@EQNcr{%
   \let\EQN=&
   \let\@eqno=\relax}%
\def\@EQNuncr{%
   \let\EQN=\@EQN
   \let\@eqno=\eqno}%
\def\EQNdoublealign#1{%
   \@EQNcr
   \displ@y
   \tabskip=\centering
   \halign to\displaywidth{%
      \hfil$\relax\displaystyle{##}$
      \tabskip=0pt
   &$\relax\displaystyle{{}##}$\hfil
      \tabskip=0pt
   &$\relax\displaystyle{{}##}$\hfil
      \tabskip=\centering
   &\llap{$\relax\@@EQN{##}$}%
      \tabskip=0pt\crcr
   #1\crcr}%
   \@EQNuncr}%
%\def\displaylines#1{%
%   \displ@y                            
%   \halign{\hbox to \displaywidth{$\hfil\displaystyle##\hfil$}%
%           &\llap{$##$}\crcr           
%    #1\crcr}}                          
\def\eqn#1$${\edef\tok\string#1
   \xdef#1{\NX\use{Eq.\tok}}%
   \EQNOparse \tok;;\endlist $$}%
\def\eqnmarker{\triangleright}%
\def\eqnmark{\quoteoff\offparens\@eqnmark}
\def\@eqnmark#1$${\@@eqnmark#1\eqno\eqno\endlist}
\def\@@eqnmark#1\eqno#2\eqno#3\endlist{\def\EQN{\relax}%
   \if ?#3? \@EQNmark#1\EQN\EQN\endlist
   \else\displaylines{\hbox to 0pt{$\eqnmarker$\hss}\hfill{#1}\hfill
                      \hbox to 0pt{\hss$#2$}}\fi$$}
\def\@EQNmark#1\EQN#2\EQN#3\endlist{%
   \if ?#3?\displaylines{\hbox to 0pt{$\eqnmarker$\hss}\hfill{#1}\hfill}%
   \else \let\@eqno=\relax
      \EQNdisplaylines{\hbox to 0pt{$\eqnmarker$\hss}\hfill{#1}\hfill
                \hbox to 0pt{\hss$\EQNOparse#2;;\endlist$}}\fi}
% file: TXSprns.tex                                 TeXsis version 2.16  
%%> {Auto-sizing of Parentheses.}
\catcode`@=11
\ifx\@left\undefined
 \let\@left=\left       \let\@right=\right
 \let\lparen=(          \let\rparen=)
 \let\lbrack=[          \let\rbrack=]
 \let\@vert=\vert
\fi
\begingroup
\catcode`\(=\active \catcode`\)=\active
\catcode`\[=\active \catcode`\]=\active
\gdef({\relax
   \ifmmode \push@delim{P}%
    \@left\lparen
   \else\lparen
   \fi}
\global\let\@lparen=(
\gdef){\relax
   \ifmmode\@right\rparen
     \pop@delim\@delim
     \if P\@delim \relax \else
       \if B\@delim\emsg{> Expecting \string] but got \string).}%
                   \@errmark{PAREN}%
       \else\emsg{> Unmatched \string).}\@errmark{PAREN}%
     \fi\fi
   \else\rparen
   \fi}
\gdef[{\relax
   \ifmmode \push@delim{B}%
     \@left\lbrack
   \else\lbrack
   \fi}
\global\let\@lbrack=[
\gdef]{\relax
   \ifmmode\@right\rbrack
     \pop@delim\@delim
     \if B\@delim \relax \else
       \if P\@delim\emsg{> Expecting \string) but got \string].}%
                   \@errmark{BRACK}%
       \else\emsg{> Unmatched \string].}\@errmark{BRACK}%
     \fi\fi
   \else\rbrack
   \fi}
\gdef\EZYleft{\futurelet\nexttok\@EZYleft}%
\gdef\@EZYleft#1{%
   \ifx\nexttok(  \let\nexttok=\lparen
   \else
   \ifx\nexttok[  \let\nexttok=\lbrack
   \fi\fi
   \@left\nexttok}%
\gdef\EZYright{\futurelet\nexttok\@EZYright}%
\gdef\@EZYright#1{%
   \ifx\nexttok)  \let\nexttok=\rparen
   \else
   \ifx\nexttok]  \let\nexttok=\rbrack
   \fi\fi
   \@right\nexttok}%
\endgroup
\toksdef\@CAR=0  \toksdef\@CDR=2
\def\push@delim#1{\@CAR={{#1}}%
     \@CDR=\XA{\@delimlist}%
    \edef\@delimlist{\the\@CAR\the\@CDR}}%
\def\pop@delim#1{\XA\pop@delimlist\@delimlist\endlist#1}%
\def\pop@delimlist#1#2\endlist#3{\def\@delimlist{#2}\def#3{#1}}    
\def\@delimlist{}%
\newif\ifEZparens   \EZparensfalse
\def\autoparens{\EZparenstrue
   \everydisplay={\@onParens}%
   }
\def\@onParens{%
   \ifEZparens
    \def\@delimlist{}%
    \let\left=\EZYleft
    \let\right=\EZYright
    \catcode`\(=\active \catcode`\)=\active
    \catcode`\[=\active \catcode`\]=\active
   \fi}
\def\offparens{%
   \EZparensfalse\@offParens
   \everymath={}\everydisplay={}}%
\def\@offParens{%
   \let\left=\@left
   \let\right=\@right
   \catcode`(=12 \catcode`)=12
   \catcode`[=12 \catcode`]=12
   }
\offparens
\def\onparens{%
   \EZparenstrue
   \everymath={\@onMathParens}%
   \everydisplay={\@onParens}%
   }
\def\easyparenson{\onparens}%
\def\@onMathParens#1{%
   \@SetRemainder#1\endlist
   \ifx#1\lparen\let\@remainder=\@lparen\fi
   \ifx#1\lbrack\let\@remainder=\@lbrack\fi
   \@onParens
   \@remainder}%
\def\@SetRemainder#1#2\endlist{%
   \ifx @#2@ \def\@remainder{#1}%
   \else  \def\@remainder{{#1#2}}%
   \fi}
\def\easyparensoff{\offparens}%
\def\pmatrix#1{\@left\lparen\matrix{#1}\@right\rparen}
\def\bordermatrix#1{\begingroup \m@th
  \setbox\z@\vbox{\def\cr{\crcr\noalign{\kern2\p@\global\let\cr\endline}}%
    \ialign{$##$\hfil\kern2\p@\kern\p@renwd&\thinspace\hfil$##$\hfil
      &&\quad\hfil$##$\hfil\crcr
      \omit\strut\hfil\crcr\noalign{\kern-\baselineskip}%
      #1\crcr\omit\strut\cr}}%
  \setbox\tw@\vbox{\unvcopy\z@\global\setbox\@ne\lastbox}%
  \setbox\tw@\hbox{\unhbox\@ne\unskip\global\setbox\@ne\lastbox}%
  \setbox\tw@\hbox{$\kern\wd\@ne\kern-\p@renwd\@left\lparen\kern-\wd\@ne
    \global\setbox\@ne\vbox{\box\@ne\kern2\p@}%
    \vcenter{\kern-\ht\@ne\unvbox\z@\kern-\baselineskip}\,\right\rparen$}%
  \;\vbox{\kern\ht\@ne\box\tw@}\endgroup}
\def\partitionmatrix#1{\,\vcenter{\offinterlineskip\m@th
   \def\tablerule{\noalign{\hrule}}
   \halign{\hfil\loosebox{$\mathstrut ##$}\hfil&&\quad\vrule##\quad&
      \hfil\loosebox{$##$}\hfil\crcr
   #1\crcr}}\,}
% file: TXSrefs.tex                                 TeXsis version 2.16
%%> {References and Citations.}
\catcode`@=11
\newcount\refnum        \refnum=\z@
\newcount\@firstrefnum  \@firstrefnum=1
\newcount\@lastrefnum   \@lastrefnum=1
\newcount\@BadRefs      \@BadRefs=0
\newif\ifrefswitch      \refswitchtrue
\newif\ifbreakrefs      \breakrefstrue
\newif\ifsuperrefs      \superrefstrue
\newif\ifmarkit         \markittrue
\newif\ifnullname       \nullnamefalse
\newif\iftagit
\newif\ifreffollows
\newif\ifrefpunct       \refpuncttrue
\def\refterminator{}%
\newdimen\refindent     \refindent=2em
\newdimen\refpar        \refpar=20pt
\newbox\tempbox
\newwrite\reflistout
\def\@refinit{\ifrefswitch
   \immediate\openout\reflistout=\jobname.ref
  \else
    \let\@refwrite=\@refwrong
    \let\@refNXwrite=\@refwrong
    \immediate\closeout\reflistout
  \fi
  \gdef\refinit{\relax}%
}%
\def\refinit{\@refinit}%
\def\@refwrite#1{\refinit
   \immediate\write\reflistout{#1}}%
\def\@refNXwrite#1{\refinit
   \unexpandedwrite\reflistout{#1}}%
\def\@refwrong#1{}%
\long\def\reference#1{%
  \markittrue
  \@tagref{#1}%
  \@GetRefText{#1}%
  }%
\long\def\addreference#1{%
  \markitfalse
  \@tagref{#1}%
  \@GetRefText{#1}%
  }%
\def\hiddenreference{\addreference}%
\def\@tagref#1{%
  \stripblanks #1\endlist
  \XA\ifstar\tok*\fi
  \ifnullname\relax\else
    \global\advance\refnum by \@ne
    \@lastrefnum=\refnum
    \edef\rnum{\the\refnum}%
    \tag{Ref.#1}{\rnum}%
    \ifnum\pageno>\z@
      \begingroup
      \quoteoff\offparens
      \immediate\write16{(\the\refnum)% write comment to .LIS and terminal
 First reference to "#1" on page \the\pageno.}%
      \endgroup
    \fi
  \fi
  }%
\def\ifstar#1#2\fi{\ifx*#1\relax\nullnametrue\else\nullnamefalse\fi}
\def\@GetRefText#1{%
  \ifnullname
    \p@nctwrite;\relax
    \begingroup\quoteoff
      \@refwrite{\@comment ... Reference text for%
      "#1" defined on page \number\pageno.}%
    \endgroup
  \else
    \ifnum\refnum>1
      \p@nctwrite.\fi
    \begingroup\quoteoff\@parensoff
      \@refwrite{\@comment }%
      \@refwrite{\@comment (\the\refnum) Reference text for%
      "#1" defined on page \number\pageno.}%
    \endgroup
    \@refwrite{\NX\@refitem{\the\refnum}}%
  \fi
  \begingroup
   \def\endreference{\NX\endreference}%
   \def\reference{\NX\reference}%
   \def\ref{\NX\ref}%
   \obeylines
   \@copyref
}%
{\obeylines\gdef\@copyref#1
   {\def\@arg{#1}\ifx\@arg\emtpy\relax\let\@nextline=\@copyref% get next line
    \else\ParseRefText#1\endreference\endreference\endlist\fi% parse line
    \@nextline}%
}%
\def\ParseRefText#1\endreference#2\endreference#3\endlist{%
   \def\@arg{#1}\ifx\@arg\empty\relax
   \else\begingroup
     \@refNXwrite{#1}%
     \endgroup
   \fi
   \def\@arg{#3}\ifx\@arg\empty
        \let\@nextline=\@copyref
   \else\let\@nextline=\@endcopyref
     \gdef\@remainder{\@endreference #2}%
   \fi}%
\def\@endcopyref{\endgroup
    \@remainder
    }%
{\catcode`\%=11 \gdef\@comment{% }}
\def\@parensoff{\catcode`\(=11 \catcode`\)=11}
\long\def\@endreference#1{%
  \reffollowsfalse
  \ifx#1\cite\reffollowstrue\fi
  \ifx#1\citerange\reffollowstrue\fi
  \ifx#1\refrange\reffollowstrue\fi
  \ifx#1\ref\reffollowstrue\fi
  \ifx#1\reference\reffollowstrue
  \else
   \ifnum\@firstrefnum>\@lastrefnum\relax
   \else\ifmarkit
    \ifnum\@firstrefnum=\@lastrefnum
      \xdef\@refmark{\the\@lastrefnum}%
    \else
      \xdef\@refmark{\the\@firstrefnum-\the\@lastrefnum}%
    \fi
    \global\@firstrefnum=\refnum
    \global\advance\@firstrefnum by \@ne
    \add@refmark
   \fi\fi
  \fi
  \flush@reflist{#1}%
  \def\@next{#1}\ifcat.\NX#1\def\@next{#1 }\fi
  \@next}%
\def\endreference{%
  \emsg{>  Whoops! \string\endreference was called without
  first calling \string\reference.}\@errmark{REF?}%
  \emsg{>  I'll just ignore it.}%
  }%
\def\@refspace{\ }
\def\citemark#1{%
   \relax\let\@sf\empty
   \ifhmode\edef\@sf{\spacefactor\the\spacefactor}\/\fi
   \ifsuperrefs
      $\relax{}^{\hbox{$\citestyle
           #1\refterminator$}}$\relax
   \else
      {}~[{#1}]\relax
   \fi
   \@sf}%
\def\citestyle{\scriptstyle}%
\def\referencelist{%
   \begingroup
   \pageno=0
   \def\citemark##1{\relax}%
   \def\@refspace{\relax}}%
\def\endreferencelist{%
   \endgroup}%
\long\def\cite#1#2{%
  \markittrue
  \reffollowsfalse
  \ifx#2\cite\reffollowstrue\fi
  \ifx#2\citerange\reffollowstrue\fi
  \ifx#2\refrange\reffollowstrue\fi
  \ifx#2\ref\reffollowstrue\fi
  \ifx#2\reference\reffollowstrue\fi
  \make@refmark{#1}%
  \add@refmark
  \flush@reflist{#2}%
  #2}%
\let\ref=\cite
\def\@refmarklist{}%
\gdef\refbef@re{F}%
\def\make@refmark#1{%
  \testtag{Ref.#1}\ifundefined
    \emsg{> UNDEFINED REFERENCE #1 ON PAGE \number\pageno.}%
    \global\advance\@BadRefs by 1
    \xdef\@refmark{{\tenbf #1}}%
    \@errmark{REF?}%
  \else
    \xdef\@refmark{\csname\tok\endcsname}%
  \fi}%
\def\add@refmark{%
  \if\refbef@re T\relax
    \xdef\@refmarklist{\@refmarklist,\@refmark}%
  \else
    \xdef\@refmarklist{\@refmark}%
    \gdef\refbef@re{T}%
  \fi}
\long\def\flush@reflist#1{%
  \ifmarkit
  \ifreffollows\else
    \citemark{\@refmarklist}%
    \gdef\refbef@re{F}%
    \gdef\@refmarklist{}%
    \ifx#1\par\else\space@head{#1}\fi
  \fi\fi}%
{\quoteon
\gdef\space@head#1{\def\next{\space}%
    \ifcat.\NX#1\relax\def\next{\relax}\fi
    \ifx)#1\def\next{\relax}\fi
    \ifx]#1\def\next{\relax}\fi
    \ifx"#1\def\next{\relax}\fi
   \next}%
}
\def\Ref#1{Ref.~\use{Ref.#1}}
\long\def\refrange#1#2#3{%
  \reffollowsfalse
  \ifx#3\cite\reffollowstrue\fi
  \ifx#3\ref\reffollowstrue\fi
  \ifx#3\reference\reffollowstrue\fi
  \ifx#3\refrange\reffollowstrue\fi
  \make@refmark{#2}%
  \xdef\@refmarktwo{\@refmark}%
  \make@refmark{#1}%
  \xdef\@refmark{\@refmark\hbox{--}\@refmarktwo}%
  \add@refmark
  \flush@reflist{#3}%
  #3}%
\let\citerange=\refrange
\def\vol#1{\undertext{#1}}
\def\booktitle#1{{\sl #1}}
\def\etal{{\it et al.}}
\def\ie{{\it i.e.}}
\def\cf{{\it cf.}}
\def\ibid{{\it ibid.}}
\def\NP{Nucl.\ Phys.}
\def\PL{Phys.\ Lett.}
\def\PR{Phys.\ Rev.}
\def\PRL{Phys.\ Rev.\ Lett.}
\def\ao{Appl.\  Opt.\ }
\def\ap{Appl.\  Phys.\ }
\def\apl{Appl.\ Phys.\ Lett.\ }
\def\apj{Astrophys.\ J.\ }
\def\bell{Bell Syst.\ Tech.\ J.\ }
\def\jqe{IEEE J.\ Quantum Electron.\ }
\def\assp{IEEE Trans.\ Acoust.\ Speech Signal Process.\ }
\def\aprop{IEEE Trans.\ Antennas Propag.\ }
\def\mtt{IEEE Trans.\ Microwave Theory Tech.\ }
\def\iovs{Invest.\ Ophthalmol.\ Vis.\ Sci.\ }
\def\jcp{J.\ Chem.\ Phys.\ }
\def\jmo{J.\ Mod.\ Opt.\ }
\def\josa{J.\ Opt.\ Soc.\ Am.\ }
\def\josaa{J.\ Opt.\ Soc.\ Am.\ A }
\def\josab{J.\ Opt.\ Soc.\ Am.\ B }
\def\jpp{J.\ Phys.\ (Paris) }
\def\nat{Nature (London) }
\def\oc{Opt.\ Commun.\ }
\def\ol{Opt.\ Lett.\ }
\def\pl{Phys.\ Lett.\ }
\def\pra{Phys.\ Rev.\ A }
\def\prb{Phys.\ Rev.\ B }
\def\prc{Phys.\ Rev.\ C }
\def\prd{Phys.\ Rev.\ D }
\def\pre{Phys.\ Rev.\ E }
\def\prl{Phys.\ Rev.\ Lett.\ }
\def\rmp{Rev.\ Mod.\ Phys.\ }
\def\pspie{Proc.\ Soc.\ Photo-Opt.\ Instrum.\ Eng.\ }
\def\sjqe{Sov.\ J.\ Quantum Electron.\ }
\def\vr{Vision Res.\ }
\def\ListReferences{\emsg{Reference List}%
  \ifnum\refnum>\z@ \p@nctwrite{.}%
    \@refwrite{\@comment>>> EOF \jobname.ref <<<}% and EOF marker comment
    \immediate\closeout\reflistout
  \fi
  \ifnum\@BadRefs>\z@
    \emsg{>}\emsg{> There were \the\@BadRefs\ undefined references.}%
    \emsg{> See the file \jobname.log for the citations, or try running}%
    \emsg{> TeXsis again to resolve forward references.}\emsg{>}%
  \fi
  \begingroup
    \offparens
    \immediate\openin\reflistout=\jobname.ref
    \ifeof\reflistout
       \closein\reflistout
       \emsg{> \string\ListReferences: no references.}%
    \else
       \catcode`@=11
       \unobeylines
       \setbox\tempbox\hbox{\the\refnum.\quad}%
       \refindent=\wd\tempbox
       \leftskip=\refindent
       \parindent=\z@
       \def\reference{\@noendref}%
       \refFormat
       \Input\jobname.ref  \relax
       \vskip 0pt
    \fi
  \endgroup
  \emsg{}%
  \refReset
  }%
\def\References{\ListReferences}%
\def\refFormat{\relax}%
\def\@noendref#1{%
   \emsg{>  Whoops! \string\reference{#1} was given before the}%
   \emsg{>  \string\endreference for the previous \string\reference.}%
   \emsg{>  I'll just ignore it and run the two together.}%
   }%
\def\@refitem#1#2{\message{#1.}%
   \refskip\noindent\hskip-\refindent
   \hbox to \refindent {\hss #1.\quad}%
   #2}
\def\refskip{\smallskip}%
\def\@refpunct#1{\unskip#1}%
\def\p@nctwrite#1{%
   \ifrefpunct
      \@refwrite{\NX\@refpunct#1\NX\@refbreak}%
   \else
      \@refwrite{\NX\@refbreak}%
   \fi}
\def\@refbreak{\ifbreakrefs\par\fi}
\def\refReset{%
   \global\refnum=\z@
   \global\@firstrefnum=1
   \global\@lastrefnum=1
   \global\@BadRefs=0
   \gdef\refinit{\@refinit}%
   }
\newif\ifEurostyle     \Eurostylefalse
{\catcode`\.=\active
   \gdef.{\hbox{\p@riod\null}}}%
\def\p@riod{.}%
\def\journal{%
  \bgroup
   \catcode`\.=\active
   \offparens
   \j@urnal}%
\offparens
 \def\j@urnal#1;#2,#3(#4){%
   \ifEurostyle
      {#1} {\vol{#2}} (\@fullyear{#4}) #3\relax
   \else
      {#1} {\vol{#2}}, #3 (\@fullyear{#4})\relax
   \fi
  \egroup}%
\def\@fullyear#1{%
  \begingroup
   \count255=\year
      \divide \count255 by 100 \multiply \count255 by 100
   \count254=\year
      \advance \count254 by -\count255 \advance \count254 by 1
   \count253=#1\relax
   \ifnum\count253<100
     \ifnum \count253>\count254
       \advance \count253 by -100\fi
      \advance \count253 by \count255
   \fi
   \number\count253
  \endgroup
}
% file: TXSsects.tex  (TeXsis version 2.16)
%%> {Section and Chapter divisions.}
\catcode`@=11
\newcount\chapternum            \chapternum=\z@
\newcount\sectionnum            \sectionnum=\z@
\newcount\subsectionnum         \subsectionnum=\z@
\newcount\subsubsectionnum      \subsubsectionnum=\z@
\newif\ifshowsectID             \showsectIDtrue
\def\@sectID{}%
\newif\ifshowchaptID            \showchaptIDtrue
\def\@chaptID{}%
\newskip\sectionskip            \sectionskip=1cm plus4pt minus4pt
\newskip\subsectionskip         \subsectionskip=0.5cm plus2pt minus2pt
\newdimen\sectionminspace       \sectionminspace = 0.25\vsize
\def\chapter#1{%
  \vfill\supereject
  \global\advance\chapternum by \@ne
  \global\sectionnum=\z@
  \global\def\@sectID{}%
  \edef\lab@l{\ChapterStyle{\the\chapternum}}%
  \ifshowchaptID
    \global\edef\@chaptID{\lab@l.}%
    \r@set
  \else\edef\@chaptID{}\fi
  \everychapter
  \ifx\Tbf\undefined\def\Tbf{\bf}\fi
  \ifshowchaptID
    \leftline{\Tbf{Chapter\ \@chaptID}}%
    \nobreak\smallskip\fi
  \begingroup
    \raggedright\pretolerance=2000\hyphenpenalty=2000
    \parindent=\z@ {\Tbf{#1}}\relax
    \bigskip
  \endgroup
  \nobreak\bigskip
  \begingroup
    \def\label##1{}%
    \xdef\ChapterTitle{#1}%
    \def\n{}\def\nl{}\def\mib{}%
    \setHeadline{#1}%
    \emsg{Chapter \@chaptID\space #1}%
    \def\@quote{\string\@quote\relax}%
    \addTOC{0}{\TOCcID{\lab@l.}#1}{\folio}%
  \endgroup
  \@Mark{#1}%
  \s@ction
  \afterchapter}%
\def\everychapter{\relax}%
\def\afterchapter{\relax}%
\def\ChapterStyle#1{#1}%
\def\setChapterID#1{\edef\@chaptID{#1.}}%
\def\r@set{%
  \global\subsectionnum=\z@
  \global\subsubsectionnum=\z@
  \ifx\eqnum\undefined\relax
    \else\global\eqnum=\z@\fi
  \ifx\theoremnum\undefined\relax
  \else
    \global\theoremnum=\z@
    \global\lemmanum=\z@
    \global\corollarynum=\z@
    \global\definitionnum=\z@
    \global\fignum=\z@
    \ifRomanTables\relax
    \else\global\tabnum=\z@\fi
  \fi}
\long\def\s@ction{%
  \checkquote
  \checkenv
  \nobreak\noindent}
\def\@Mark#1{%
   \begingroup
     \def\label##1{}%
     \def\goodbreak{}%
     \def\mib{}\def\n{}%
     \mark{#1\NX\else\lab@l}%
   \endgroup}%
\def\@noMark#1{\relax}%
\def\setHeadline#1{\@setHeadline#1\n\endlist}%
\def\@setHeadline#1\n#2\endlist{%
   \def\@arg{#2}\ifx\@arg\empty
      \global\edef\HeadText{#1}%
   \else
      \global\edef\HeadText{#1\dots}%
   \fi
}
\def\section#1{%
   \vskip\sectionskip
   \goodbreak\pagecheck\sectionminspace
   \global\advance\sectionnum by \@ne
   \edef\lab@l{\@chaptID\SectionStyle{\the\sectionnum}}%
   \ifshowsectID
     \global\edef\@sectID{\SectionStyle{\the\sectionnum}.}%
     \global\edef\@fullID{\lab@l.\space\space}%
     \r@set
   \else\gdef\@fullID{}\fi
   \everysection
   \ifx\tbf\undefined\def\tbf{\bf}\fi
   \vbox{%
     {\raggedright\pretolerance=2000\hyphenpenalty=2000
     \setbox0=\hbox{\noindent\tbf\@fullID}%
     \hangindent=\wd0 \hangafter=1
     \noindent\unhbox0{\tbf{#1}}\relax
     \medskip}}%
   \nobreak
   \begingroup
     \def\label##1{}%
     \global\edef\SectionTitle{#1}%
     \def\n{}\def\nl{}\def\mib{}%
     \ifnum\chapternum=0\setHeadline{#1}\fi
     \emsg{Section \@fullID #1}%
     \def\@quote{\string\@quote\relax}%
     \addTOC{1}{\TOCsID{\lab@l.}#1}{\folio}%
   \endgroup
   \s@ction
   \aftersection}%
\def\everysection{\relax}%
\def\aftersection{\relax}%
\def\setSectionID#1{\edef\@sectID{#1.}}%
\def\SectionStyle#1{#1}%
\def\subsection#1{%
   \vskip\subsectionskip
   \goodbreak\pagecheck\sectionminspace
   \global\advance\subsectionnum by \@ne
   \subsubsectionnum=\z@
   \edef\lab@l{\@chaptID\@sectID\SubsectionStyle{\the\subsectionnum}}%
   \ifshowsectID
     \global\edef\@fullID{\lab@l.\space}%
   \else\gdef\@fullID{}\fi
   \everysubsection
   \vbox{%
     {\raggedright\pretolerance=2000\hyphenpenalty=2000
     \setbox0=\hbox{\noindent\bf\@fullID}%
     \hangindent=\wd0 \hangafter=1
     \noindent\unhbox0{\bf{#1}}\relax
     \medskip}}%
   \nobreak
   \begingroup
     \def\label##1{}%
     \global\edef\SubsectionTitle{#1}%
     \def\n{}\def\nl{}\def\mib{}%
     \emsg{\@fullID #1}%
     \def\@quote{\string\@quote\relax}%
     \addTOC{2}{\TOCsID{\lab@l.}#1}{\folio}%
   \endgroup
   \s@ction
   \aftersubsection}%
\def\everysubsection{\relax}%
\def\aftersubsection{\relax}%
\def\SubsectionStyle#1{#1}%
\def\subsubsection#1{%
   \vskip\subsectionskip
   \goodbreak\pagecheck\sectionminspace
   \global\advance\subsubsectionnum by \@ne
   \edef\lab@l{\@chaptID\@sectID\SubsectionStyle{\the\subsectionnum}.%
           \SubsubsectionStyle{\the\subsubsectionnum}}%
   \ifshowsectID
     \global\edef\@fullID{\lab@l.\space\space}%
   \else\gdef\@fullID{}\fi
   \everysubsubsection
   \vbox{%
     {\raggedright\bf
     \setbox0=\hbox{\noindent\@fullID}%
     \hangindent=\wd0 \hangafter=1
     \noindent\@fullID\relax
     #1\relax}}%
   \nobreak\medskip
   \begingroup
     \def\label##1{}%
     \global\edef\SubsectionTitle{#1}%
     \def\n{}\def\nl{}\def\mib{}%
     \emsg{\@fullID #1}%
     \def\@quote{\string\@quote\relax}%
     \addTOC{3}{\TOCsID{\lab@l.}#1}{\folio}%
   \endgroup
   \s@ction
   \aftersubsection}%
\def\everysubsubsection{\relax}%
\def\aftersubsubsection{\relax}%
\def\SubsubsectionStyle#1{#1}%
\def\Appendix#1#2{%
  \vfill\supereject
  \global\sectionnum=\z@
  \def\@arg{#1}%
  \gdef\@sectID{}%
  \edef\lab@l{#1}%
  \ifshowchaptID
    \ifx\@arg\empty\else
       \global\edef\@chaptID{\lab@l.}\fi
    \r@set
  \else\def\@chaptID{}\fi
  \everychapter
  \ifx\Tbf\undefined\def\Tbf{\bf}\fi
  \leftline{\Tbf{Appendix\ \@chaptID}}%
  \begingroup
    \nobreak\smallskip
    \parindent=\z@\raggedright
    {\Tbf{#2}}\relax
    \nobreak\bigskip
  \endgroup
  \nobreak\bigskip
  \begingroup
    \def\label##1{}%
    \global\edef\ChapterTitle{#2}%
    \def\n{}\def\nl{}\def\mib{}%
    \setHeadline{#2}%
    \emsg{Appendix \@chaptID\space #2}%
    \def\@quote{\string\@quote\relax}%
    \addTOC{0}{\TOCcID{\lab@l.}#2}{\folio}%
  \endgroup
  \@Mark{#2}%
  \s@ction
  \afterchapter}%
\def\appendix#1#2{%
   \vskip\sectionskip
   \goodbreak\pagecheck\sectionminspace
           \global\advance\sectionnum by \@ne
   \def\@arg{#1}%
   \gdef\@sectID{}%
   \edef\lab@l{#1}%
   \ifshowsectID
     \r@set
     \ifx\@arg\empty\else
       \global\edef\@sectID{\lab@l.}%
       \global\edef\@fullID{\lab@l.\space\space}\fi
   \else\gdef\@fullID{}\fi
   \everysection
   \ifx\tbf\undefined\def\tbf{\bf}\fi
   \vbox{%
     {\raggedright\tbf
     \setbox0=\hbox{\tbf\@fullID}%
     \hangindent=\wd0 \hangafter=1
     \noindent\@fullID
     {#2}}}\relax
   \nobreak\medskip
   \begingroup
     \def\label##1{}%
     \global\edef\SectionTitle{#2}%
     \def\n{}\def\nl{}\def\mib{}%
     \ifnum\chapternum=0\setHeadline{#2}\fi
     \emsg{appendix \@fullID #2}%
     \def\@quote{\string\@quote\relax}%
     \addTOC{1}{\TOCsID{\lab@l.}#2}{\folio}%
   \endgroup
   \s@ction
   \aftersection}%
\def\pagecheck#1{%
   \dimen@=\pagegoal
   \advance\dimen@ by -\pagetotal
   \ifdim\dimen@>0pt
   \ifdim\dimen@< #1\relax
      \vfil\break \fi\fi
   }
\def\nosechead#1{%
   \vskip\subsectionskip
   \goodbreak\pagecheck\sectionminspace
   \checkquote\checkenv
   \vbox{%
     {\raggedright\bf\noindent
     {#1}%
     \nobreak\medskip}}%
   }
\def\checkenv{%
   \ifx\@envdepth\undefined\relax
   \else\ifnum\@envdepth=\z@
      \else\emsg{> Unclosed environment \@envname in the last section!}\fi 
   \fi}%
% file: TXStags.tex  (TeXsis version 2.16)
%%> {Labels and tags.}
\newread\auxfilein
\newwrite\auxfileout
\newif\ifauxswitch      \auxswitchtrue
\let\XA=\expandafter    \let\NX=\noexpand
\catcode`"=12
\catcode`@=11
\newcount\@BadTags   \@BadTags= 0
\def\auxinit{%
  \ifauxswitch
    \immediate\openout\auxfileout=\jobname.aux
    \immediate\write\auxfileout{\string\let\string\XA=\string\expandafter}%
  \else
    \gdef\auxout##1##2{}%
  \fi
  \gdef\auxinit{\relax}}%
\def\auxout#1#2{\auxinit
   \immediate\write\auxfileout{%
   \string\XA\string\gdef\string\csname\space
     #1\string\endcsname{#2}}%
   }       
\def\ReadAUX{%
   \openin\auxfilein=\jobname.aux
   \ifeof\auxfilein\closein\auxfilein
   \else\closein\auxfilein
     \begingroup
      \unSpecial
      \input\jobname.aux \relax
     \endgroup
   \fi}%
\def\tag{%
   \begingroup\unSpecial
    \@tag}%
\def\@tag#1#2{%
   \endgroup
   \edef\@@temp{#2}%
   \stripblanks @#1@\endlist
   \XA\let\csname\tok\endcsname=\z@%   
   \XA\xdef\csname\tok\endcsname{\@@temp}%
   \auxout{\tok}{\@@temp}%
   }
\def\label{%
   \begingroup\unSpecial
    \@label}
\def\@label#1{%
   \endgroup
   \tag{#1}{\lab@l}}%
\def\lab@l{\relax}%
\def\use{%
   \begingroup
    \unSpecial
    \@use}%
\def\@use#1{%
   \endgroup
   \stripblanks @#1@\endlist
   \XA\ifx\csname\tok\endcsname\relax\relax
     \emsg{> UNDEFINED TAG #1 ON PAGE \folio.}%
     \global\advance\@BadTags by 1
     \@errmark{UNDEF}%
     \edef\tok{{\bf\tok}}%
   \else
     \edef\tok{\csname\tok\endcsname}%
   \fi
   \tok}%
\def\unSpecial{%
   \catcode`@=11\catcode`"=12
   \catcode`(=12\catcode`)=12
   \catcode`[=12\catcode`]=12
   \catcode`\&=12\catcode`\#=12
   }
\def\stripblanks{%
   \let\tok=\empty\@stripblanks}
\def\@stripblanks#1{\def\next{#1}\@striplist}
\def\@striplist{%
   \ifx\next\stripblanks\message{>\NX\@striplist: Oops!}\next=\endlist\fi
   \ifx\next\endlist\let\next=\relax
   \else\@stripspace\let\next=\@stripblanks\fi
   \next}
\def\@stripspace{\XA\if\space\next\else\edef\tok{\tok\next}\fi}
\def\endlist{\endlist}%
\def\tok{}
\newif\ifundefined      \undefinedfalse
\def\testtag#1{\stripblanks @#1@\endlist   
   \XA\ifx\csname\tok\endcsname\relax\undefinedtrue
   \else\undefinedfalse\fi}
\def\checktags{%
  \ifnum\@BadTags>\z@
    \emsg{>}\emsg{> There were \the\@BadTags\ undefined tags.}%
    \emsg{> See the file \jobname.log for the citations, or try running}%
    \emsg{> TeXsis again to resolve forward references.}\emsg{>}%
  \fi}
\def\LabelParse#1;#2;#3\endlist{%
  \if ?#3?\relax
    \global\advance\@count by\@ne
    \xdef\@ID{\@chaptID\@sectID\the\@count}%
    \tag{\@prefix#1}{\@ID}%
  \else
    \stripblanks #2\endlist
    \edef\p@rt{\tok}%
    \if a\p@rt\relax
      \global\advance\@count by\@ne\fi
    \xdef\@ID{\@chaptID\@sectID\the\@count}%
    \tag{\@prefix#1}{\@ID}%
    \xdef\@ID{\@chaptID\@sectID\the\@count\p@rt}%
    \tag{\@prefix#1;\p@rt}{\@ID}%
  \fi
}%
\def\@ID{}%
% file: TXStitle.tex                                TeXsis version 2.16  
%%> {Title Page macros.}
\catcode`@=11
\def\pubcode#1{\gdef\@DOCcode{#1}}
\def\PUBcode#1{\gdef\@DOCcode{#1}}%
\def\DOCcode#1{\PUBcode{#1}}%
\def\BNLcode#1{\PUBcode{#1}\banner}%
\def\@DOCcode{\TeXsis~\fmtversion}%
\def\pubdate#1{\gdef\@PUBdate{#1}}
\def\PUBdate#1{\gdef\@PUBdate{#1}}%
\def\@PUBdate{\monthname{\month},~\number\year}%
\def\ORGANIZATION{BROOKHAVEN\ NATIONAL\ LABORATORY}%
\def\banner{%
   \line{\hfil
      \vbox to 0pt{\vss \hbox{\twelvess \ORGANIZATION}}%
      \hfil}%
   \vskip 12pt
   \hrule height 0.6pt \vskip 1pt \hrule height 0.6pt
   \vskip 4pt \relax
   \line{\twelvepoint\rm\@PUBdate \hfil \@DOCcode}%
   \vskip 3pt
   \hrule height 0.6pt \vskip 1pt \hrule height 0.6pt
   \vskip 0pt plus 1fil
   \vskip 1.0cm minus 1.0cm
   \relax}
\def\titlepage{%
   \bgroup
   \pageno=1
   \hbox{\space}%
   \let\title=\Title
   \let\endmode=\relax
   }
\def\endtitlepage{%
   \endmode
   \vfil\eject
   \egroup}%
\def\Title{%
   \endmode
   \vskip 0pt
   \mark{Title Page\NX\else Title Page}% mark page so no \HeadLine
   \bgroup
   \let\endmode=\endTitle
   \center\Tbf}%
\let\title=\Title
\def\endTitle{%
   \endcenter
   \bigskip
   \gdef\title{%
      \emsg{> Please use \NX\booktitle instead of \NX\title.}%
      \@errmark{OLD!}%
      \booktitle}%
   \egroup}%
\def\endtitle{\endTitle}%
\def\Tbf{\sixteenpoint\bf}%
\def\author{%
  \endmode
  \bgroup
   \let\endmode=\endauthor
   \singlespaced\parskip=0pt
   \obeylines\def\\{\par}%
   \@getauthor}%
{\obeylines\gdef\@getauthor#1
  #2
  {#1\bigskip\def\n{\egroup\centerline\bgroup\bf}%
   \centerline{\bf #2}%
   \medskip\center}%
}
\def\endauthor{\endcenter\egroup\bigskip}
\def\authors{%
   \endmode
   \bigskip
   \bgroup
    \let\endmode=\endauthors
    \let\@uthorskip=\medskip
    \raggedcenter\singlespaced}%
\def\endauthors{%
   \endraggedcenter
   \egroup
   \bigskip}%
\def\note#1#2{%
  ${}^{\hbox{#1}}\ $
  \space@head#2
  #2}%
\def\institution#1#2{%
   \@uthorskip\let\@uthorskip=\relax
   \raggedcenter
      ${}^{\rm #1}$\space #2%                  
   \endraggedcenter
   }
\let\@uthorskip=\medskip
\long\def\titlenote#1#2{%
   \footnote{}{%
   \llap{\hbox to \parindent{\hfil
   ${}^{\rm #1}$\space}}#2}}%
\def\and{\centerline{and}\medskip}
\def\abstract{%
   \endmode
   \bigskip\bigskip
    \centerline{ABSTRACT}%
    \medskip
    \bgroup
    \let\endmode=\endabstract
    \narrower\narrower
    \singlespaced}%
\def\endabstract{\smallskip\egroup}
\def\pacs#1{\medskip\centerline{PACS numbers: #1}\smallskip}
\def\submit#1{\bigskip\centerline{Submitted to {\sl #1}}}
\def\submitted#1{\submit{#1}}%
\def\toappear#1{\bigskip\raggedcenter
     To appear in {\sl #1}
     \endraggedcenter}
\def\disclaimer#1{\footnote{}\bgroup\tenrm\singlespaced
   This manuscript has been authored under contract number #1
   \@disclaimer\par}
\def\disclaimers#1{\footnote{}\bgroup\tenrm\singlespaced
   This manuscript has been authored under contract numbers #1
   \@disclaimer\par}
\def\@disclaimer{%
with the U.S. Department of Energy.  Accordingly, the U.S.
Government retains a non-exclusive, royalty-free license to publish
or reproduce the published form of this contribution,
or allow others to do so, for U.S. Government purposes.
\egroup}
% file: TXSenvmt.tex  (TeXsis version 2.16)
%%> {Environments.}
\catcode`@=11
\chardef\other=12
\def\center{%
   \flushenv
   \advance\leftskip \z@ plus 1fil
   \advance\rightskip \z@ plus 1fil
   \obeylines\@eatpar}%
\def\flushright{%
    \flushenv
    \advance\leftskip \z@ plus 1fil
    \obeylines\@eatpar}%
\def\flushleft{%
   \flushenv
   \advance\rightskip \z@ plus 1fil
   \obeylines\@eatpar}%
\def\flushenv{%
    \vskip \z@
    \bgroup
     \def\flushhmode{F}%
     \parindent=\z@  \parfillskip=\z@}%
\def\endcenter{\endflushenv}
\def\endflushleft{\endflushenv}
\def\endflushright{\endflushenv}
\def\@eatpar{\futurelet\next\@testpar}
\def\@testpar{\ifx\next\par\let\@next=\@@eatpar\else\let\@next=\relax\fi\@next}
\long\def\@@eatpar#1{\relax}
\def\raggedcenter{%
    \flushenv
    \advance\leftskip\z@ plus4em
    \advance\rightskip\z@ plus 4em
    \spaceskip=.3333em \xspaceskip=.5em
    \pretolerance=9999 \tolerance=9999
    \hyphenpenalty=9999 \exhyphenpenalty=9999
    \@eatpar}%
\def\endraggedcenter{\endflushenv}%
\def\hcenter{\hflushenv
   \advance\leftskip \z@ plus 1fil
   \advance\rightskip \z@ plus 1fil
   \obeylines\@eatpar}%
\def\hflushright{\hflushenv
    \advance\leftskip \z@ plus 1fil
    \obeylines\@eatpar}%
\def\hflushleft{\hflushenv
    \advance\rightskip \z@ plus 1fil
    \obeylines\@eatpar}%
\def\hflushenv{%
   \def\par{\endgraf\indent}%
   \hbox to \z@ \bgroup\hss\vtop
   \flushenv\def\flushhmode{T}}%
\def\endflushenv{%
   \ifhmode\endgraf\fi
   \if T\flushhmode \egroup\hss\fi
   \egroup}%
\def\endhcenter{\endflushenv}
\def\endhflushleft{\endflushenv}
\def\endhflushright{\endflushenv}
\newskip\EnvTopskip     \EnvTopskip=\medskipamount
\newskip\EnvBottomskip  \EnvBottomskip=\medskipamount
\newskip\EnvLeftskip    \EnvLeftskip=2\parindent
\newskip\EnvRightskip   \EnvRightskip=\parindent
\newskip\EnvDelt@skip   \EnvDelt@skip=0pt
\newcount\@envDepth     \@envDepth=\z@
\def\beginEnv#1{%
   \begingroup
   \def\@envname{#1}%
   \ifvmode\def\@isVmode{T}%
   \else\def\@isVmode{F}\vskip 0pt\fi
   \ifnum\@envDepth=\@ne\parindent=\z@\fi
   \global\advance\@envDepth by \@ne
   \EnvDelt@skip=\baselineskip
   \advance\EnvDelt@skip by-\normalbaselineskip
   \@setenvmargins\EnvLeftskip\EnvRightskip
   \setenvskip{\EnvTopskip}%
   \vskip\skip@\penalty-500
   }
\def\endEnv#1{%
   \ifnum\@envDepth<1
      \emsg{> Tried to close ``#1'' environment, but no environment open!}%
      \begingroup
   \else
      \def\test{#1}%
      \ifx\test\@envname\else
         \emsg{> Miss-matched environments!}%
         \emsg{> Should be closing ``\@envname'' instead of ``\test''}%
      \fi
   \fi
   \vskip 0pt
   \setenvskip\EnvBottomskip
   \vskip\skip@\penalty-500
   \xdef\@envtemp{\@isVmode}%
   \endgroup
   \global\advance\@envDepth by -\@ne
   \if F\@envtemp\vskip-\parskip\noindent\fi
   }
\def\setenvskip#1{\skip@=#1 \divide\skip@ by \@envDepth}
\def\@setenvmargins#1#2{%
   \advance \leftskip  by #1    \advance \displaywidth by -#1
   \advance \rightskip by #2    \advance \displaywidth by -#2
   \advance \displayindent by #1}%
\def\itemize{\beginEnv{itemize}%
   \let\itm=\itemizeitem
   \if F\@isVmode\vskip-\parskip\fi
   }
\def\itemizeitem{%
   \par\noindent
   \hbox to 0pt{\hss\itemmark\space}}%
\def\enditemize{\endEnv{itemize}}%
\def\itemmark{$\bullet$}%
\newcount\enumDepth     \enumDepth=\z@
\newcount\enumcnt
\def\enumerate{\beginEnv{enumerate}%
   \global\advance\enumDepth by \@ne
   \setenumlead
   \enumcnt=\z@
   \let\itm=\enumerateitem
   \if F\@isVmode\vskip-\parskip\fi
   }
\def\enumerateitem{%
    \par\noindent                 
    \advance\enumcnt by \@ne
    \edef\lab@l{\enumlead \enumcur}%
    \hbox to \z@{\hss \lab@l \enummark
       \hskip .5em\relax}%
    \ignorespaces}%
\def\endenumerate{%
   \global\advance\enumDepth by -\@ne
   \endEnv{enumerate}}%
\def\enumPoints{%
   \def\setenumlead{\ifnum\enumDepth>1
          \edef\enumlead{\enumlead\enumcur.}%
      \else\def\enumlead{}\fi}%
   \def\enumcur{\number\enumcnt}%
   }
\def\enumpoints{\enumPoints}%
\def\enumOutline{%
   \def\setenumlead{\def\enumlead{}}%
   \def\enumcur{\ifcase\enumDepth
     \or\uppercase{\XA\romannumeral\number\enumcnt}%
     \or\LetterN{\the\enumcnt}%
     \or\XA\romannumeral\number\enumcnt
     \or\letterN{\the\enumcnt}%
     \or{\the\enumcnt}%
     \else $\bullet$\space\fi}%
   }
\def\enumoutline{\enumOutline}%
\def\enumNumOutline{%
   \def\setenumlead{\def\enumlead{}}%
   \def\enumcur{\ifcase\enumDepth
      \or{\XA\number\enumcnt}%
      \or\letterN{\the\enumcnt}%
      \or{\XA\romannumeral\number\enumcnt}%
      \else $\bullet$\space\fi}%
   }
\def\enumnumoutline{\enumNumOutline}%
\def\LetterN#1{\count@=#1 \advance\count@ 64 \XA\char\count@}
\def\letterN#1{\count@=#1 \advance\count@ 96 \XA\char\count@}
\def\enummark{.}%
\def\enumlead{}%
\enumpoints
\newbox\@desbox
\newbox\@desline
\newdimen\@glodeswd
\newcount\@deslines
\newif\ifsingleline \singlelinefalse
\def\description#1{\beginEnv{description}%
   \setbox\@desbox=\hbox{#1}%
   \@glodeswd=\wd\@desbox
   \@setenvmargins{\@glodeswd}{0pt}%
   \let\itm=\descriptionitem
   \if F\@isVmode\vskip-\parskip\fi
  }%
\def\descriptionitem#1{%
   \goodbreak\noindent
   \setbox\@desline=\vtop\bgroup
      \hfuzz=100cm\hsize=\@glodeswd
      \rightskip=\z@ \leftskip=\z@
      \raggedright
      \noindent{#1}\par
      \global\@deslines=\prevgraf
      \egroup
   \ifsingleline
     \ifnum\@deslines>1
        \@deslineitm{#1}%
     \else
        \setbox\@desline=\hbox{#1}%
        \ifdim \wd\@desline>\wd\@desbox
            \@deslineitm{#1}%
        \else\@desitm\fi
     \fi
   \else
     \@desitm
   \fi
   \ignorespaces}
\def\@desitm{%
   \noindent
   \hbox to \z@{\hskip-\@glodeswd
     \hbox to \@glodeswd{\vtop to \z@{\box\@desline\vss}%
     \hss}\hss}}%
\def\@deslineitm#1{%
   \hbox{\hskip-\@glodeswd {#1}\hss}%
   \vskip-\parskip\nobreak\noindent
   }
\def\enddescription{\ifhmode\par\fi
   \@setenvmargins{-\wd\@desbox}{0pt}%
   \endEnv{description}}
\def\example{\beginEnv{example}%
   \parskip=\z@ \parindent=\z@
   \baselineskip=\normalbaselineskip
   }%
\def\endexample{\endEnv{example}%
   \noindent}%
\let\blockquote=\example
\let\endblockquote=\endexample
\def\Listing{%
   \beginEnv{Listing}%
   \vskip\EnvDelt@skip
   \baselineskip=\normalbaselineskip
   \parskip=\z@ \parindent=\z@
   \def\\##1{\char92##1}%
   \catcode`\{=\other \catcode`\}=\other
   \catcode`\(=\other \catcode`\)=\other
   \catcode`\"=\other \catcode`\|=\other
   \catcode`\%=\other \catcode`\&=\other        
   \catcode`\-=\other \catcode`\==\other
   \catcode`\$=\other \catcode`\#=\other
   \catcode`\_=\other \catcode`\^=\other
   \catcode`\~=\other
   \obeylines
   \tt\Listingtabs
   \everyListing}%
\def\endListing{\endEnv{Listing}}%
\def\everyListing{\relax}
\def\ListCodeFile#1{%
   \Listing
   \hsize=2\hsize\raggedright
   \catcode`\\=\other
   \input #1\relax
   \endListing}
{\catcode`\^^I=\active\catcode`\ =\active
\gdef\Listingtabs{\catcode`\^^I=\active\let^^I\@listingtab
\catcode`\ =\active\let \@listingspace}%
}%
\def\@listingspace{\hskip 0.5em\relax}%
\def\@listingtab{\hskip 4em\relax}%
\def\TeXexample{\beginEnv{TeXexample}%
   \vskip\EnvDelt@skip
   \parskip=\z@ \parindent=\z@
   \baselineskip=\normalbaselineskip
   \def\par{\leavevmode\endgraf}%
   \obeylines
   \catcode`|=\z@
   \ttverbatim
   \@eatpar}%
\def\endTeXexample{%
   \vskip 0pt
   \endgroup
   \endEnv{TeXexample}}%
\def\ttverbatim{\begingroup
   \catcode`\(=\other \catcode`\)=\other
   \catcode`\"=\other \catcode`\[=\other
   \catcode`\]=\other
   \let\do=\uncatcode \dospecials
   \obeyspaces\obeylines
   \def\n{\vskip\baselineskip}%
   \tt}%
\def\uncatcode#1{\catcode`#1=\other}%
{\obeyspaces\gdef {\ }}%
\def\TeXquoteon{\catcode`\|=\active}%
\let\TeXquoteson=\TeXquoteon
\def\TeXquoteoff{\catcode`\|=\other}%
\let\TeXquotesoff=\TeXquoteoff
{\TeXquoteon\obeylines% active "|" calls \ttverbatim
   \gdef|{\ifmmode\vert\else% | is \vert in math mode, but
     \ttverbatim\spaceskip=\ttglue% to use \tt type
     \let^^M=\ \relax% and to ignore ^^M
     \let|=\endgroup\fi}%
}     
\def\ttvert{\hbox{\tt\char`\|}}
\outer\def\begintt{$$\let\par=\endgraf \ttverbatim \parskip=0pt
   \catcode`\|=0 \rightskip=-5pc \ttfinish}
{\catcode`\|=0 |catcode`|\=\other% | is temporary escape character
   |obeylines% end of line is active
   |gdef|ttfinish#1^^M#2\endtt{#1|vbox{#2}|endgroup$$}%
}
\def\beginlines{\par\begingroup\nobreak\medskip\parindent=0pt
   \hrule\kern1pt\nobreak \obeylines \everypar{\strut}}
\def\endlines{\kern1pt\hrule\endgroup\medbreak\noindent}
\def\beginproclaim#1#2#3#4#5{\medbreak\vskip-\parskip
   \global\XA\advance\csname #2\endcsname by \@ne
   \edef\lab@l{\@chaptID\@sectID
      \number\csname #2\endcsname}%
   \tag{#4#5}{\lab@l}%
   \noindent{\bf #1 \lab@l.\space}%
   \begingroup #3}%
\def\endproclaim{%
   \par\endgroup\ifdim\lastskip<\medskipamount
   \removelastskip\penalty55\medskip\fi}%
\newcount\theoremnum           \theoremnum=\z@
\def\theorem#1{\beginproclaim{Theorem}{theoremnum}{\sl}{Thm.}{#1}}
\let\endtheorem=\endproclaim
\def\Theorem#1{Theorem~\use{Thm.#1}}
\newcount\lemmanum             \lemmanum=\z@
\def\lemma#1{\beginproclaim{Lemma}{lemmanum}{\sl}{Lem.}{#1}}
\let\endlemma=\endproclaim
\def\Lemma#1{Lemma~\use{Lem.#1}}
\newcount\corollarynum         \corollarynum=\z@
\def\corollary#1{\beginproclaim{Corollary}{corollarynum}{\sl}{Cor.}{#1}}
\let\endcorollary=\endproclaim
\def\Corollary#1{Corollary~\use{Cor.#1}}
\newcount\definitionnum        \definitionnum=\z@
\def\definition#1{\beginproclaim{Definition}{definitionnum}{\rm}{Def.}{#1}}
\let\enddefinition=\endproclaim
\def\Definition#1{Definition~\use{Def.#1}}
\def\proof{\medbreak\vskip-\parskip\noindent{\it Proof. }}
\def\blackslug{%
   \setbox0\hbox{(}%
   \vrule width.5em height\ht0 depth\dp0}%
\def\QED{\blackslug}%
\def\endproof{\quad\blackslug\par\medskip}
% file: TXSfmts.tex                                 TeXsis version 2.16
%%> {Layout macros.}
\catcode`@=11
\def\paper{%
   \auxswitchtrue
   \refswitchtrue
   \texsis
   \def\titlepage{%
      \bgroup
      \let\title=\Title
      \let\endmode=\relax
      \pageno=1}%
   \def\endtitlepage{%
      \endmode
      \goodbreak\bigskip
      \egroup}%
   \autoparens
   \quoteon
   }
\def\Tbf{\fourteenpoint\bf}%
\def\tbf{\twelvepoint\bf}%
\def\preprint{%
   \auxswitchtrue
   \refswitchtrue
   \texsis
   \def\titlepage{%
      \bgroup
      \pageno=1
      \let\title=\Title
      \let\endmode=\relax
      \banner}%
   \def\endtitlepage{%
      \endmode
      \vfil\eject
      \egroup}%
   \autoparens
   \quoteon
   }
\def\Manuscript{%
   \preprint
   \showsectIDfalse
   \showchaptIDfalse
   \def\SectionStyle##1{\uppercase
         \expandafter{\romannumeral ##1}}%
   \RomanTablestrue
   \TablesLast
   \FiguresLast
   \TrueDoubleSpacing
   }
\autoload\PhysRevManuscript{PhysRev.txs}%
\def\book{%
   \ContentsSwitchtrue
   \refswitchtrue
   \auxswitchtrue
   \texsis
   \RunningHeadstrue
   \bookpagenumbers
   \def\titlepage{%
      \bgroup
      \pageno=-1
      \let\title=\Title
      \let\endmode=\relax
      \def\FootText{\relax}}%
   \def\endtitlepage{%
      \endmode
      \vfil\eject
      \egroup
      \pageno=1}%
   \def\abstract{%
      \endmode
      \bigskip\bigskip\medskip
      \bgroup\singlespaced
         \let\endmode=\endabstract
         \narrower\narrower}%
   \def\endabstract{%
      \medskip\egroup\bigskip}%
   \def\FootText{--\ \tenrm\folio\ --}%
   \def\Tbf{\sixteenpoint\bf}%
   \def\tbf{\fourteenpoint\bf}%
   \twelvepoint
   \doublespaced
   \autoparens
   \quoteon
   }%
\autoload\thesis{thesis.txs}
\autoload\UTthesis{thesis.txs}
\autoload\YaleThesis{thesis.txs}
\def\Letter{%
   \ContentsSwitchfalse
   \refswitchfalse
   \auxswitchfalse
   \texsis
   \singlespaced
   \LetterFormat}%
\def\letter{\Letter}%
\def\Memo{%
   \ContentsSwitchfalse
   \refswitchfalse
   \auxswitchfalse
   \texsis
   \singlespaced
   \MemoFormat}%
\def\memo{\Memo}%
\def\Referee{%
   \ContentsSwitchfalse
   \auxswitchfalse
   \refswitchfalse
   \texsis
   \RefReptFormat}%
\def\referee{\Referee}%
\def\Landscape{%
   \texsis
   \hsize=9in
   \vsize=6.5in
   \voffset=.5in
   \nopagenumbers
   \LandscapeSpecial
}
\def\landscape{\Landscape}%
\def\LandscapeSpecial{\special{papersize=11in,8.5in}}
\def\slides{%
   \quoteon
   \autoparens
   \ATlock
   \pageno=1
   \twentyfourpoint
   \doublespaced
   \raggedright\tolerance=2000
   \hyphenpenalty=500
   \raggedbottom
   \nopagenumbers
   \hoffset=-.25in \hsize=7.0in
   \voffset=-.25in \vsize=9.0in
   \parindent=30pt
   \def\bl{\vskip\normalbaselineskip}%
   \def\np{\vfill\eject}%
   \def\nospace{\nulldelimiterspace=0pt
      \mathsurround=0pt}%
   \def\big##1{{\hbox{$\left##1
      \vbox to2ex{}\right.\nospace$}}}%
   \def\Big##1{{\hbox{$\left##1
      \vbox to2.5ex{}\right.\nospace$}}}%
   \def\bigg##1{{\hbox{$\left##1
       \vbox to3ex{}\right.\nospace$}}}%
   \def\Bigg##1{{\hbox{$\left##1
      \vbox to4ex{}\right.\nospace$}}}%
  }
\autoload\twinout{twin.txs}%
\def\twinprint{%
   \preprint
   \let\t@tl@=\title
   \def\title{\vskip-1.5in\t@tl@}%
   \let\endt@tlep@ge=\endtitlepage
   \def\endtitlepage{\endt@tlep@ge
       \twinformat}%
}
\def\twinformat{%
   \tenpoint\doublespaced
   \def\Tbf{\twelvebf}\def\tbf{\tenbf}%
   \headlineoffset=0pt
   \twinout}%
% file: TXSfigs.tex (TeXsis version 2.16)
%%> {Figures and Tables.}
\catcode`\@=11
\let\NX=\noexpand\let\XA=\expandafter
\offparens
\newcount\tabnum        \tabnum=\z@
\newcount\fignum        \fignum=\z@
\newif\ifRomanTables    \RomanTablesfalse
\long\def\figure{\@figure\topinsert}
\long\def\topfigure{\@figure\topinsert}%
\long\def\midfigure{\@figure\midinsert}
\long\def\fullfigure{\@figure\pageinsert}
\long\def\bottomfigure{\@figure\bottominsert}
\long\def\heavyfigure{\@figure\heavyinsert}
\long\def\widefigure{\@figure\widetopinsert}
\long\def\widetopfigure{\@figure\widetopinsert}
\long\def\widefullfigure{\@figure\widepageinsert}
\obsolete\topFigure\figure   \obsolete\midFigure\midfigure 
\obsolete\fullFigure\fullfigure \obsolete\TOPFIGURE\figure              
\obsolete\MIDFIGURE\midfigure   \obsolete\FULLFIGURE\fullfigure            
\obsolete\endFigure\endfigure   \obsolete\ENDFIGURE\endfigure
\def\@figure#1#2{%
  \ifvmode\else\vskip 0pt\fi
  \begingroup
   \let\@count=\fignum
   \def\@prefix{Fg.}%
   \let\@FigInsert=#1\relax
   \if ?#2?\relax \def\@ID{}%
   \else\LabelParse #2;;\endlist\fi
   \def\CaptionName{Figure}%
   \ifFigsLast
     \emsg{\CaptionName\space\@ID. {#2} [storing in \jobname.fg]}%
     \@fgwrite{\@comment> \CaptionName\space\@ID.\space{#2}}%
     \@fgwrite{\NX\@FigureItem{\CaptionName}{\@ID}{\NX#1}}%
     \newlinechar=`\^^M
     \obeylines
     \let\@next=\@copyfig
   \else
     \@FigInsert
     \setbox\@capbox\vbox to 0pt{}%
     \def\@whereCap{N}%
     \emsg{\CaptionName\ \@ID.\ {#2}}%
     \let\endfigure=\@endfigure
     \let\@next=\@findcap
   \fi
   \@next}
\long\def\@findcap#1{%
   \ifx #1\Caption \def\@whereCap{T}\fi
   \ifx #1\caption \def\@whereCap{T}\fi
   #1}%
\def\@whereCap{N}%
\def\@endfigure{\relax
   \if B\@whereCap\relax
     \vskip\baselineskip\medskip
     \centerline{\box\@capbox}%
   \fi
   \endinsert \endgroup}%
\def\endfigure{\emsg{> \NX\endfigure before \NX\figure!}}
\def\figuresize#1{\vglue #1}%
\newbox\@capbox
\newcount\@caplines
\def\CaptionName{}%
\def\@ID{}%
\def\caption#1{%
   \def\lab@l{\@ID}%
   \global\setbox\@capbox=\vbox\bgroup
     \def\@inCaption{T}%
     \captionspacing
     \dimen@=20\parindent
     \ifdim\colwidth>\dimen@\narrower\narrower\fi
     \noindent{\bf \CaptionName~\@ID:\space}%
     #1\relax
     \vskip0pt
     \global\@caplines=\prevgraf
   \egroup
   \ifnum\@ne=\@caplines
    \global\setbox\@capbox=\vbox\bgroup
       \noindent
       \hfil{\bf \CaptionName~\@ID:\space}%
       #1\hfil\egroup
   \fi
   \def\@inCaption{F}%
   \if N\@whereCap\def\@whereCap{B}\fi
   \if T\@whereCap
     \centerline{\box\@capbox}%
     \vskip\baselineskip\medskip
   \fi}
\def\captionspacing{\normalbaselines}%
\def\@inCaption{F}%
\long\def\Caption#1\endCaption{\caption{#1}}
\def\endCaption{\emsg{> \NX\endCaption called before \NX\Caption.}}
\def\endcaption{\emsg{> try using \NX\caption{ text... }}}
\long\def\table{\@table\topinsert}
\long\def\toptable{\@table\topinsert}%
\long\def\midtable{\@table\midinsert}
\long\def\fulltable{\@table\pageinsert}
\long\def\bottomtable{\@table\bottominsert}
\long\def\heavytable{\@table\heavyinsert}
\long\def\widetable{\@table\widetopinsert}
\long\def\widetoptable{\@table\widetopinsert}
\long\def\widefulltable{\@table\widepageinsert}
\let\topTable=\toptable
\let\midTable=\midtable
\let\fullTable=\fulltable
\let\TOPTABLE=\toptable
\let\MIDTABLE=\midtable
\let\FULLTABLE=\fulltable
\def\@table#1#2{%
  \vskip 0pt
  \begingroup
   \def\CaptionName{Table}%
   \def\@prefix{Tb.}%
   \let\@count=\tabnum
   \if ?#2?\relax \def\@ID{}%
   \else
     \ifRomanTables
      \global\advance\@count by\@ne
      \edef\@ID{\uppercase\expandafter
         {\romannumeral\the\@count}}%
      \tag{\@prefix#2}{\@ID}%
     \else
       \LabelParse #2;;\endlist\fi
   \fi
   \ifTabsLast
    \emsg{\CaptionName\space\@ID. {#2} [storing in \jobname.tb]}%
    \@tbwrite{\@comment> \CaptionName\space\@ID.\space{#2}}%
    \@tbwrite{\NX\@FigureItem{\CaptionName}{\@ID}{\NX#1}}%
    \newlinechar=`\^^M
    \obeylines
    \let\@next=\@copytab
   \else
    #1\relax
    \setbox\@capbox\vbox to 0pt{}%
    \def\@whereCap{N}%
    \emsg{\CaptionName\ \@ID.\ {#2}}%
    \let\endtable=\@endfigure
    \let\endTable=\@endfigure
    \let\ENDTABLE=\@endfigure
    \let\@next=\@findcap
   \fi
   \@next}                                      
\def\endtable{\emsg{> \NX\endtable before \NX\table!}}
\def\endTable{\endtable}%
\def\ENDTABLE{\endtable}%
\autoload\Tablebody{Tablebod.txs}
\autoload\Tablebodyleft{Tablebod.txs}          
\autoload\tablebody{Tablebod.txs}
\def\Fig#1{Fig.~\use{Fg.#1}}
\def\Figs#1{Figs.~\use{Fg.#1}}
\def\Fg#1{\use{Fg.#1}}
\def\Tab#1{Table~\use{Tb.#1}}
\def\Tbl#1{Table~\use{Tb.#1}}
\def\FIG{\@obsolete\FIG\Fig\Fig}%
\def\TBL{\@obsolete\TBL\Tbl\Tbl}%
\newif\ifFigsLast       \FigsLastfalse
\def\FiguresLast{\FigsLasttrue}
\def\FiguresNow{\FigsLastfalse}
\newwrite\fgout
\def\@fginit{%
   \immediate\openout\fgout=\jobname.fg \relax
   \gdef\@fginit{\relax}%
   \immediate\write\fgout{\@comment FIGURES for job \jobname}%
   \immediate\write\fgout{\@comment ====================================}%
}
\def\@fgwrite#1{%
  \@fginit
  \immediate\write\fgout{#1}%
  }
\long\def\@fgNXwrite#1{%
  \@fginit
  \unexpandedwrite\fgout{#1}%
  }
{\obeylines\long\gdef\@copyfig#1
  {\@ParseFigText#1\endfigure\endfigure\endlist% Parse line
    \@nextline}%
}%
\long\def\@ParseFigText#1\endfigure#2\endfigure#3\endlist{%
   \ifx?#1?\relax
   \else\@fgNXwrite{#1}\fi
   \ifx?#3?\let\@nextline=\@copyfig
   \else
     \gdef\@remainder{#2}%
     \let\@nextline=\@endcopyfig
   \fi
   }
\def\@endcopyfig{\@fgNXwrite{\@endfigure}%
   \endgroup
   \@remainder
   }
\def\PrintFigures{%
  \ifFigsLast\@PrintFigures\fi}
\def\@PrintFigures{%
   \@fgwrite{\@comment>>> EOF \jobname.fg <<<}%
   \immediate\closeout\fgout
   \begingroup
      \FigsLastfalse
      \vbox to 0pt{\hbox to 0pt{\ \hss}\vss}%
      \ATunlock
      \offparens
      \catcode`@=11
      \unobeylines
      \emsg{[Getting figures from file \jobname.fg]}%
      \Input\jobname.fg \relax
   \endgroup
}
\def\@FigureItem#1#2#3{%
   \begingroup
    #3\relax
    \def\@ID{#2}%
    \def\CaptionName{#1}%
    \setbox\@capbox\vbox to 0pt{}%
    \def\@whereCap{N}%
    \@findcap
    }
\newif\ifTabsLast       \TabsLastfalse
\def\TablesLast{\TabsLasttrue}
\def\TablesNow{\TabsLastfalse}
\newwrite\tbout
\def\@TBinit{%
   \immediate\openout\tbout=\jobname.tb \relax
   \gdef\@TBinit{\relax}%
   \immediate\write\tbout{\@comment TABLES FOR \jobname.tex}%
   \immediate\write\tbout{\@comment ====================================}%
}
\def\@tbwrite#1{%
  \@TBinit
  \immediate\write\tbout{#1}%
  }
\long\def\@tbNXwrite#1{%
  \@TBinit
  \unexpandedwrite\tbout{#1}%
  }
{\obeylines\long\gdef\@copytab#1
   {\@ParseTabText#1\endtable\endtable\endlist% PARSE line
    \@nextline}%
}%
\long\def\@ParseTabText#1\endtable#2\endtable#3\endlist{%
   \ifx?#1?\relax
   \else\@tbNXwrite{#1}\fi
   \ifx?#3?\let\@nextline=\@copytab
   \else
     \gdef\@remainder{#2}%
     \let\@nextline=\@endcopytab
   \fi
   }
\def\@endcopytab{\@tbNXwrite{\@endfigure}%
   \endgroup
   \@remainder
   }
\def\PrintTables{%
  \ifTabsLast\@PrintTables\fi}
\def\@PrintTables{%
   \@tbwrite{\@comment>>> EOF \jobname.tb <<<}%
   \immediate\closeout\tbout
   \TabsLastfalse
   \begingroup
     \catcode`@=11
     \offparens
     \unobeylines
     \emsg{[Getting tables from file.]}%
     \Input\jobname.tb \relax
   \endgroup
}
\newwrite\figlist
\newwrite\tablelist
\def\FigListInit{\relax
   \immediate\openout\figlist=\jobname.fgl\relax
   \immediate\write\figlist{\@comment List of Figures for job `\jobname'
                                -- Created at \runtime}%
   \immediate\write\figlist{\@comment ============================}%
   \gdef\FigListInit{\relax}%
 }
\def\TabListInit{\relax
   \immediate\openout\tablelist=\jobname.tbl\relax
   \immediate\write\tablelist{\@comment List of Tables for job `\jobname'
                                -- Created: \runtime}%
   \immediate\write\tablelist{\@comment ===========================}%
   \gdef\TabListInit{\relax}%
 }
\def\FigListWrite#1#2{\relax
  \ifx#1\figlist\relax   \FigListInit\fi
  \ifx#1\tablelist\relax \TabListInit\fi
  \edef\@line@{{#2}}%
  \write#1\@line@}%
\def\FigListWriteNX#1#2{\relax
  \ifx#1\figlist\relax\FigListInit\fi
  \ifx#1\tablelist\relax\TabListInit\fi
  \writeNX#1{#2}%
  }
\def\infiglist{%
   \begingroup\obeylines
   \newlinechar=`\^^M
     \@infiglist\figlist}%
\def\intablelist{%
   \begingroup\obeylines
   \newlinechar=`\^^M
     \@infiglist\tablelist}                               
\def\@infiglist#1#2{%
   \FigListWrite#1{\@comment -- \CaptionName\space\@ID:}%
   \FigListWrite#1{\string\FIGLitem{\CaptionName} {\@ID.\space}}%
   \FigListWriteNX#1{{#2}}%
   \FigListWrite#1{{\folio}}%
   \endgroup}%
\def\FIGLitem#1#2#3#4{%
   \medskip
   \begingroup
     \raggedright\tolerance=1700
     \advance\rightskip by \TOCmargin
     \parfillskip=-\TOCmargin
     \hangindent=1.41\parindent\hangafter=1
     \noindent \ifshowsectID #1\ \fi #2
        #3 \hskip 0pt plus 10pt
     \leaddots
     \hbox to 2em{\hss #4}%
     \vskip 0pt
   \endgroup
   }
\def\ListFigures{%
   \emsg{\@comment List of Figures:}%
   \immediate\closeout\figlist
   \openin\figlist=\jobname.fgl
   \ifeof\figlist\closein\figlist
      \emsg{> \NX\ListFigures: no list of figures.}%
   \else\closein\figlist
     \begingroup
      \ATunlock\quoteoff\offparens
      \Input\jobname.fgl \relax
     \endgroup
   \fi}%
\def\ListTables{%
   \emsg{\@comment List of Tables}%
   \immediate\closeout\tablelist
   \openin\tablelist=\jobname.tbl
   \ifeof\tablelist\closein\tablelist
      \emsg{> \NX\ListTables: no list of tables.}%
   \else\closein\tablelist
     \begingroup
      \ATunlock\quoteoff\offparens
      \Input\jobname.tbl \relax
     \endgroup
   \fi}%
\def\ListFigureCaptions{%
   \showsectIDtrue
   \emsg{\@comment List of Figure Captions:}%
   \immediate\closeout\figlist
   \openin\figlist=\jobname.fgl
   \ifeof\figlist\closein\figlist
      \emsg{> \NX\ListFigureCaptions: no list of figures.}%
   \else\closein\figlist
     \begingroup
      \ATunlock\quoteoff\offparens
      \let\FIGLitem=\CAPLitem
      \Input\jobname.fgl \relax
     \endgroup
   \fi}%
\def\ListTableCaptions{%
   \showsectIDtrue
   \emsg{\@comment List of Table Captions:}%
   \immediate\closeout\figlist
   \openin\figlist=\jobname.tbl
   \ifeof\figlist\closein\figlist
      \emsg{> \NX\ListFigureCaptions: no list of figures.}%
   \else\closein\figlist
     \begingroup
      \ATunlock\quoteoff\offparens
      \let\FIGLitem=\CAPLitem
      \Input\jobname.tbl \relax
     \endgroup
   \fi}%
\def\CAPLitem#1#2#3#4{%
   \medskip
   \begingroup
     \raggedright\tolerance=1700
     \advance\rightskip by \TOCmargin
     \parfillskip=-\TOCmargin
     \hangindent=1.41\parindent\hangafter=1
     \noindent \ifshowsectID #1\ \fi #2
        #3 \hskip 0pt plus 10pt
     \vskip 0pt
   \endgroup}%
\autoload\epsffile{epsf.tex}
\autoload\epsfbox{epsf.tex}
\autoload\epsfxsize{epsf.tex}
\autoload\epsfysize{epsf.tex}   
\autoload\epsfverbosetrue{epsf.tex}
\autoload\epsfverbosefalse{epsf.tex}
% file: TXSruled.tex -- TeXsis 2.16
\catcode`@=11
\catcode`\|=12
\catcode`\&=4
\newcount\ncols         \ncols=\z@
\newcount\nrows         \nrows=\z@
\newcount\curcol        \curcol=\z@
\let\currow=\nrows
\newdimen\thinsize      \thinsize=0.6pt
\newdimen\thicksize     \thicksize=1.5pt
\newdimen\tablewidth    \tablewidth=-\maxdimen
\newdimen\parasize      \parasize=4in
\newif\iftableinfo      \tableinfotrue
\newif\ifcentertables   \centertablestrue
\def\centeredtables{\centertablestrue}%
\def\noncenteredtables{\centertablesfalse}%
\def\nocenteredtables{\centertablesfalse}%
\let\plaincr=\cr
\let\plainspan=\span
\let\plaintab=&
\def\ampersand{\char`\&}%
\let\lparen=(
\let\NX=\noexpand
\def\ruledtable{\relax
    \@BeginRuledTable
    \@RuledTable}%
\def\@BeginRuledTable{%
   \ncols=0\nrows=0
   \begingroup
    \offinterlineskip
    \def~{\phantom{0}}%
    \def\span{\plainspan\omit\relax\colcount\plainspan}%
    \let\cr=\crrule
    \let\CR=\crthick
    \let\nr=\crnorule
    \let\|=\Vb
    \def\hfill{\hskip0pt plus1fill\hbox{}}%
    \ifx\tablestrut\undefined\relax
    \else\let\tstrut=\tablestrut\fi
    \catcode`\|=13 \catcode`\&=13\relax
    \TableActive
    \curcol=1
    \ifdim\tablewidth>-\maxdimen\relax
      \edef\@Halign{\NX\halign to \NX\tablewidth\NX\bgroup\TablePreamble}%
      \tabskip=0pt plus 1fil
    \else
      \edef\@Halign{\NX\halign\NX\bgroup\TablePreamble}%
      \tabskip=0pt
    \fi
    \ifcentertables
       \ifhmode\vskip 0pt\fi
       \line\bgroup\hss
    \else\hbox\bgroup
    \fi}%
\long\def\@RuledTable#1\endruledtable{%
   \vrule width\thicksize
     \vbox{\@Halign
       \thickrule
       #1\killspace
       \tstrut
       \linecount
       \plaincr\thickrule
     \egroup}%
   \vrule width\thicksize
   \ifcentertables\hss\fi\egroup
  \endgroup
  \global\tablewidth=-\maxdimen
  \iftableinfo
      \immediate\write16{[Nrows=\the\nrows, Ncols=\the\ncols]}%
   \fi}%
\def\TablePreamble{%
   \TableItem{####}%
   \plaintab\plaintab
   \TableItem{####}%
   \plaincr}%
\def\@TableItem#1{%
   \hfil\tablespace
   #1\killspace
   \tablespace\hfil
    }%
\def\@tableright#1{%
   \hfil\tablespace\relax
   #1\killspace
   \tablespace\relax}%
\def\@tableleft#1{%
   \tablespace\relax
   #1\killspace
   \tablespace\hfil}%
\let\TableItem=\@TableItem
\def\RightJustifyTables{\let\TableItem=\@tableright}%
\def\LeftJustifyTables{\let\TableItem=\@tableleft}%
\def\NoJustifyTables{\let\TableItem=\@TableItem}%
\def\LooseTables{\let\tablespace=\quad}%
\def\TightTables{\let\tablespace=\space}%
\LooseTables
\def\TrailingSpaces{\let\killspace=\relax}%
\def\NoTrailingSpaces{\let\killspace=\unskip}%
\TrailingSpaces
\def\setRuledStrut{%
   \dimen@=\baselineskip
   \advance\dimen@ by-\normalbaselineskip
   \ifdim\dimen@<.5ex \dimen@=.5ex\fi
   \setbox0=\hbox{\lparen}%
   \dimen1=\dimen@ \advance\dimen1 by \ht0% space above line
   \dimen2=\dimen@ \advance\dimen2 by \dp0% space below line
   \def\tstrut{\vrule height\dimen1 depth\dimen2 width\z@}%
   }%
\def\tstrut{\vrule height 3.1ex depth 1.2ex width 0pt}%
\def\bigitem#1{%
   \dimen@=\baselineskip
   \advance\dimen@ by-\normalbaselineskip
   \ifdim\dimen@<.5ex \dimen@=.5ex\fi
   \setbox0=\hbox{#1}%
   \dimen1=\dimen@ \advance\dimen1 by \ht0
   \dimen2=\dimen@ \advance\dimen2 by \dp0
   \vrule height\dimen1 depth\dimen2 width\z@
   \copy0}%
\def\vctr#1{\hfil\vbox to 0pt{\vss\hbox{#1}\vss}\hfil}%
\def\nextcolumn#1{%
   \plaintab\omit#1\relax\colcount
   \plaintab}%
\def\tab{%
   \nextcolumn{\relax}}%
\let\novb=\tab
\def\vb{%
   \nextcolumn{\vrule width\thinsize}}%
\def\Vb{%
   \nextcolumn{\vrule width\thicksize}}%
\def\dbl{%
   \nextcolumn{\vrule width\thinsize
   \hskip\thinsize\vrule width\thinsize}}%
{\catcode`\|=13 \let|0
 \catcode`\&=13 \let&0
 \gdef\TableActive{\let|=\vb \let&=\tab}%
}%
\def\crrule{\killspace
   \tstrut
   \linecount
   \plaincr\tablerule
  }%
\def\crthick{\killspace
   \tstrut
   \linecount
   \plaincr\thickrule
  }%
\def\crnorule{\killspace
   \tstrut
   \linecount
   \plaincr
   }%
\def\crpart{\killspace
   \linecount
   \plaincr}%
\def\tablerule{\noalign{\hrule height\thinsize depth 0pt}}%
\def\thickrule{\noalign{\hrule height\thicksize depth 0pt}}%
\def\cskip{\omit\relax}%
\def\crule{\omit\leaders\hrule height\thinsize depth0pt\hfill}%
\def\Crule{\omit\leaders\hrule height\thicksize depth0pt\hfill}%
\def\linecount{%
   \global\advance\nrows by1
   \ifnum\ncols>0
      \ifnum\curcol=\ncols\relax\else
      \immediate\write16
      {\NX\ruledtable warning: Ncols=\the\curcol\space for Nrow=\the\nrows}%
      \fi\fi
   \global\ncols=\curcol
   \global\curcol=1}%
\def\colcount{\relax
   \global\advance\curcol by 1\relax}%
\long\def\para#1{%
   \vtop{\hsize=\parasize
   \normalbaselines
   \noindent #1\relax
   \vrule width 0pt depth 1.1ex}%
}%
\def\begintable{\relax
    \@BeginRuledTable
    \@begintable}%
\long\def\@begintable#1\endtable{%
   \@RuledTable#1\endruledtable}%
% file: TXSsymb.tex (TeXsis version 2.16)
%%> {Extended math/physics symbols,}
\def\E#1{\hbox{$\times 10^{#1}$}}
\def\square{\hbox{{$\sqcup$}\llap{$\sqcap$}}}%
\def\grad{\nabla}%
\def\del{\partial}%
\def\frac#1#2{{#1\over#2}}
\def\smallfrac#1#2{{\scriptstyle {#1 \over #2}}}
\def\half{\ifinner {\scriptstyle {1 \over 2}}%
          \else {\textstyle {1 \over 2}}\fi}
\def\bra#1{\langle#1\vert}%
\def\ket#1{\vert#1\/\rangle}%
\def\vev#1{\langle{#1}\rangle}%
\def\simge{%
    \mathrel{\rlap{\raise 0.511ex 
        \hbox{$>$}}{\lower 0.511ex \hbox{$\sim$}}}}
\def\simle{%
    \mathrel{\rlap{\raise 0.511ex 
        \hbox{$<$}}{\lower 0.511ex \hbox{$\sim$}}}}
\def\gtsim{\simge}%
\def\ltsim{\simle}%
\def\therefore{%
   \setbox0=\hbox{$.\kern.2em.$}\dimen0=\wd0
   \mathrel{\rlap{\raise.25ex\hbox to\dimen0{\hfil$\cdotp$\hfil}}%
   \copy0}}
\def\|{\ifmmode\Vert\else \char`\|\fi}          
\def\sterling{{\hbox{\it\char'44}}}     
\def\degrees{\hbox{$^\circ$}}%
\def\degree{\degrees}%
\def\real{\mathop{\rm Re}\nolimits}%
\def\imag{\mathop{\rm Im}\nolimits}%
\def\tr{\mathop{\rm tr}\nolimits}%
\def\Tr{\mathop{\rm Tr}\nolimits}%
\def\Det{\mathop{\rm Det}\nolimits}%
\def\mod{\mathop{\rm mod}\nolimits}%
\def\wrt{\mathop{\rm wrt}\nolimits}%
\def\TeV{{\rm TeV}}%
\def\GeV{{\rm GeV}}%
\def\MeV{{\rm MeV}}%
\def\KeV{{\rm KeV}}%
\def\eV{{\rm eV}}%
\def\Ry{{\rm Ry}}%
\def\mb{{\rm mb}}%
\def\mub{\hbox{\rm $\mu$b}}%
\def\nb{{\rm nb}}%
\def\pb{{\rm pb}}%
\def\cmsec{{\rm cm^{-2}s^{-1}}}%
\def\units#1{\hbox{\rm #1}} 
\let\unit=\units
\def\dimensions#1#2{\hbox{$[\hbox{\rm #1}]^{#2}$}}
\def\parenbar#1{{\null\!
   \mathop{\smash#1}\limits
   ^{\hbox{\fiverm(--)}}%
   \!\null}}%
\def\nunubar{\parenbar{\nu}}
\def\ppbar{\parenbar{p}}
\def\buildchar#1#2#3{{\null\!
   \mathop{\vphantom{#1}\smash#1}\limits
   ^{#2}_{#3}%
   \!\null}}%
\def\overcirc#1{\buildchar{#1}{\circ}{}}
\def\slashchar#1{\setbox0=\hbox{$#1$}%
   \dimen0=\wd0
   \setbox1=\hbox{/} \dimen1=\wd1
   \ifdim\dimen0>\dimen1
      \rlap{\hbox to \dimen0{\hfil/\hfil}}%
      #1
   \else
      \rlap{\hbox to \dimen1{\hfil$#1$\hfil}}%
      /
   \fi}%
\def\subrightarrow#1{%
  \setbox0=\hbox{%
    $\displaystyle\mathop{}%
    \limits_{#1}$}%
  \dimen0=\wd0
  \advance \dimen0 by .5em
  \mathrel{%
    \mathop{\hbox to \dimen0{\rightarrowfill}}%
       \limits_{#1}}}%
\newdimen\vbigd@men
\def\vbigl{\mathopen\vbig}
\def\vbigm{\mathrel\vbig}
\def\vbigr{\mathclose\vbig}
\def\vbig#1#2{{\vbigd@men=#2\divide\vbigd@men by 2
   \hbox{$\left#1\vbox to \vbigd@men{}\right.\n@space$}}}
\def\Leftcases#1{\smash{\vbigl\{{#1}}}
\def\Rightcases#1{\smash{\vbigr\}{#1}}}
%% $Revision: 16.2 $  :  $Date: 1994/11/12 22:32:02 $  :  $Author: myers $
%======================================================================*
% First, null definitions for ``missing'' things from other parts of TeXsis
%
% Make double column stuff do nothing nicely:
%
\def\doublecolumns{\relax}
\def\enddoublecolumns{\relax}
\def\leftcolrule{\relax}
\def\rightcolrule{\relax}
\def\longequation{\relax}
\def\endlongequation{\relax}
\def\newcolumn{\relax}
\def\widetopinsert{\topinsert}
\def\widepageinsert{\pageinsert}
\def\forceleft{\relax}\def\forceright{\relax}   
\def\SetDoubleColumns#1{\relax}

% ...and other stuff that's not in mTeXsis:

\def\addTOC#1#2#3{\relax}\def\Contents{\relax}  % disable table of contents
\newif\ifContents                               % disable table of contents
\def\ContentsSwitchtrue{\Contentstrue}\def\ContentsSwitchfalse{\Contentsfalse}

\def\obsolete#1#2{\let#1=#2\relax #2}		% \obsolete is silent here

\let\Input=\input                               % TeXsis synonym
\newdimen\colwidth      \colwidth=\hsize        % default column width
\def\ORGANIZATION{}%                            % default is empty

% You shouldn't use style files that might not be around when using
% mTeXsis.  But we will try to be friendly about it...

\newhelp\@utohelp{%
loadstyle: The definition of the macro named above is actually contained^^J%
in a style file, and so it cannot be used with mTeXsis.  If you really^^J%
need to load the definition from that file, you should do so explicitly^^J%
at the begining of your manuscript file, with %
'\string\input\space filename.txs',^^J%
and that still may not give you what you want.}

\def\loadstyle#1#2{% disable \loadstyle in mTeXsis
   \newlinechar=10                              % ^^J is line break
   \errhelp=\@utohelp                           % longer help message
   \emsg{> Whoops! Trying to load \string#1\space from style file #2.}%
   \errmessage{You cannot use macro definitions from style files in mTeXsis}}

 
% -- These make mtexsis more friendly than TeX or TeXsis when printing
%    e-prints, but you won't find your errors as easily.

\hbadness=10000         % don't complain about overfull hboxes!
\overfullrule=0pt       % and don't mark them in the output!
\vbadness=10000         % and don't complain about vboxes either.

% -- Run time setup:
\ATunlock
\SetDate				% sets \adate and \edate
\ReadAUX				% reads .aux file, if it exists
\def\fmtname{TeXsis}\def\fmtversion{2.16}%
\def\revdate{12 November 1994}%
\def\imsg#1{\emsg{\@comment #1}}%
\imsg{================================================== \@comment}
\imsg{This is m\TeXsis, containing the core macros from \TeXsis, the \TeX}
\imsg{macro package for physicists.  Complete source code and documentation}
\imsg{for \TeXsis\space can be obtained via anonymous ftp from %
lifshitz.ph.utexas.edu.}
\imsg{See the README file there for more information.}
\imsg{================================================== \@comment}
\emsg{m\fmtname\space version \fmtversion\space (\revdate)  loaded.}%
\ATlock					% lock internal @ macros
\texsis					% assumed, since they asked for it
%%>>> EOF mtexsis.tex <<<

