% Abbreviate symbols for bold-face letters: note you need defs.tex first
\newcommand{\Ba}{{\bfm a}}
\newcommand{\Bb}{{\bfm b}}
\newcommand{\Bc}{{\bfm c}}
\newcommand{\Bd}{{\bfm d}}
\newcommand{\Be}{{\bfm e}}
\newcommand{\Bf}{{\bfm f}}
\newcommand{\Bg}{{\bfm g}}
\newcommand{\Bh}{{\bfm h}}
\newcommand{\Bi}{{\bfm i}}
\newcommand{\Bj}{{\bfm j}}
\newcommand{\Bk}{{\bfm k}}
\newcommand{\Bl}{{\bfm l}}
\newcommand{\Bm}{{\bfm m}}
\newcommand{\Bn}{{\bfm n}}
\newcommand{\Bo}{{\bfm o}}
\newcommand{\Bp}{{\bfm p}}
\newcommand{\Bq}{{\bfm q}}
\newcommand{\Br}{{\bfm r}}
\newcommand{\Bs}{{\bfm s}}
\newcommand{\Bt}{{\bfm t}}
\newcommand{\Bu}{{\bfm u}}
\newcommand{\Bv}{{\bfm v}}
\newcommand{\Bw}{{\bfm w}}
\newcommand{\Bx}{{\bfm x}}
\newcommand{\By}{{\bfm y}}
\newcommand{\Bz}{{\bfm z}}
\newcommand{\BA}{{\bfm A}}
\newcommand{\BB}{{\bfm B}}
\newcommand{\BC}{{\bfm C}}
\newcommand{\BD}{{\bfm D}}
\newcommand{\BE}{{\bfm E}}
\newcommand{\BF}{{\bfm F}}
\newcommand{\BG}{{\bfm G}}
\newcommand{\BH}{{\bfm H}}
\newcommand{\BI}{{\bfm I}}
\newcommand{\BJ}{{\bfm J}}
\newcommand{\BK}{{\bfm K}}
\newcommand{\BL}{{\bfm L}}
\newcommand{\BM}{{\bfm M}}
\newcommand{\BN}{{\bfm N}}
\newcommand{\BO}{{\bfm O}}
\newcommand{\BP}{{\bfm P}}
\newcommand{\BQ}{{\bfm Q}}
\newcommand{\BR}{{\bfm R}}
\newcommand{\BS}{{\bfm S}}
\newcommand{\BT}{{\bfm T}}
\newcommand{\BU}{{\bfm U}}
\newcommand{\BV}{{\bfm V}}
\newcommand{\BW}{{\bfm W}}
\newcommand{\BX}{{\bfm X}}
\newcommand{\BY}{{\bfm Y}}
\newcommand{\BZ}{{\bfm Z}}

% Abbreviate symbols for caligraphic letters
\newcommand{\Ca}{{\cal a}}
\newcommand{\Cb}{{\cal b}}
\newcommand{\Cc}{{\cal c}}
\newcommand{\Cd}{{\cal d}}
\newcommand{\Ce}{{\cal e}}
\newcommand{\Cf}{{\cal f}}
\newcommand{\Cg}{{\cal g}}
\newcommand{\Ch}{{\cal h}}
\newcommand{\Ci}{{\cal i}}
\newcommand{\Cj}{{\cal j}}
\newcommand{\Ck}{{\cal k}}
\newcommand{\Cl}{{\cal l}}
\newcommand{\Cm}{{\cal m}}
\newcommand{\Cn}{{\cal n}}
\newcommand{\Co}{{\cal o}}
\newcommand{\Cp}{{\cal p}}
\newcommand{\Cq}{{\cal q}}
\newcommand{\Cr}{{\cal r}}
\newcommand{\Cs}{{\cal s}}
\newcommand{\Ct}{{\cal t}}
\newcommand{\Cu}{{\cal u}}
\newcommand{\Cv}{{\cal v}}
\newcommand{\Cx}{{\cal x}}
\newcommand{\Cy}{{\cal y}}
\newcommand{\Cz}{{\cal z}}
\newcommand{\CA}{{\cal A}}
\newcommand{\CB}{{\cal B}}
\newcommand{\CC}{{\cal C}}
\newcommand{\CD}{{\cal D}}
\newcommand{\CE}{{\cal E}}
\newcommand{\CF}{{\cal F}}
\newcommand{\CG}{{\cal G}}
\newcommand{\CH}{{\cal H}}
\newcommand{\CI}{{\cal I}}
\newcommand{\CJ}{{\cal J}}
\newcommand{\CK}{{\cal K}}
\newcommand{\CL}{{\cal L}}
\newcommand{\CM}{{\cal M}}
\newcommand{\CN}{{\cal N}}
\newcommand{\CO}{{\cal O}}
\newcommand{\CP}{{\cal P}}
\newcommand{\CQ}{{\cal Q}}
\newcommand{\CR}{{\cal R}}
\newcommand{\CS}{{\cal S}}
\newcommand{\CT}{{\cal T}}
\newcommand{\CU}{{\cal U}}
\newcommand{\CV}{{\cal V}}
\newcommand{\CW}{{\cal W}}
\newcommand{\CX}{{\cal X}}
\newcommand{\CY}{{\cal Y}}
\newcommand{\CZ}{{\cal Z}}

% Reduce space surrounding equal signs (=) in equation arrays.
\setlength{\arraycolsep}{2pt}
% Set up counter for list environments
\newcounter{itemnbr}
% Handy abbreviations for Latex commands.
\newcommand\eq[1] {(\ref{#1})}
\newcommand\eqp[1] {(\ref{eq:#1})}
\newcommand\defn[1] {\ref{def:#1}}
\newcommand\thm[1] {\ref{thm:#1}}
\newcommand\sect[1] {\ref{sec:#1}}
\newcommand\fig[1] {\ref{fig:#1}}
\newcommand\labeq[1] {\label{eq:#1}}
\newcommand\labdefn[1] {\label{def:#1}}
\newcommand\labthm[1] {\label{thm:#1}}
\newcommand\labsect[1] {\label{sec:#1}}
\newcommand\labfig[1] {\label{fig:#1}}
\newcommand\etal{{\it et al.}}
\newcommand\pd[2] {{\partial{#1} \over \partial{#2}  }}
\newcommand\od[2] {{d{#1} \over d{#2}  }}
\newcommand\f[2] {{\frac{#1}{#2} }}
% Math environments
\newtheorem{definition}{Definition}[section]
\newtheorem{lemma}{Lemma}[section]
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}{Corollary}[section]
\newtheorem{remark}{Remark}[section]
\newtheorem{example}{Example}[section]
\newcommand\proof{{\it Proof:}\quad}
%%\newcommand\remark{{\it Remark:}\quad}
\newcommand\qed{\ \rule[-0.2ex]{0.3em}{1.5ex}}
% De-verbose the LaTeX math environment
\newcommand{\bfm}[1]{\mbox{\boldmath ${#1}$}}
\newcommand{\nonum}{\nonumber \\}
\newcommand{\beqa}{\begin{eqnarray}}
\newcommand{\eeqa}[1]{\label{#1}\end{eqnarray}}
\newcommand{\beqan}{\begin{eqnarray*}}
\newcommand{\eeqan}{\end{eqnarray*}}
\newcommand{\beq}{\begin{equation}}
\newcommand{\eeq}[1]{\label{#1}\end{equation}}
\newcommand{\bay}{\begin{array}}
\newcommand{\eay}{\end{array}}

% abbreviations for symbols
\newcommand{\sign}{\mbox{sign\,}}
\newcommand{\hf}{\frac{1}{2}}
\newcommand{\Grad}{\nabla}
\newcommand{\Ink}{\mbox{Ink~}}
\newcommand{\Def}{\mbox{Def~}}
\newcommand{\Div}{\nabla \cdot}
\newcommand{\Curl}{\nabla \times}
\newcommand{\Md}{\partial}
\newcommand{\Tr}{\mbox{ \rm{Tr\,}}}
\newcommand{\In}{\mbox{ \rm{in }}}
\newcommand{\On}{\mbox{ \rm{on }}}
\newcommand{\And}{\mbox{ \rm{and }}}
\newcommand{\Or}{\mbox{ \rm{or }}}
\newcommand{\If}{\mbox{ \rm{if }}}
\newcommand{\Cnst}{\mbox{ \rm{constant}}}
%\newcommand{\inf}{\mbox{\rm{inf}}\;}
\newcommand{\sub}[1]{_{\mbox{\footnotesize{\rm{#1}}}}}
%\newcommand{\sup}[1]{^{\mbox{\footnotesize{\rm{#1}}}}}
%\newcommand{\Than\mbox{ \rm{than} }}
%%\newcommand{\In}{\quad \mbox{\rm{in} }}
%%\newcommand{\On}{\quad \mbox{\rm{on} }}



\newcommand{\xfgr}[5] {%
\begin{figure}
    %
    \centerline{\epsfxsize=#5\textwidth
                \epsfxsize=1.25\epsfxsize %% Final book production: enlarge figures by 25%
                \epsffile{#1.eps}}%
    \caption[{#3}]{#2}%
    \label{#4}%
\end{figure}
}
\newcommand{\X}[1]{#1\index{#1}}




% Abbreviate definitions of bold Greek symbols: note that defs.tex is
% needed first
\newcommand{\BGa}{\bfm\alpha}
\newcommand{\BGb}{\bfm\beta}
\newcommand{\BGd}{\bfm\delta}
\newcommand{\BGe}{\bfm\epsilon}
\newcommand{\BGve}{\bfm\varepsilon}
\newcommand{\BGf}{\bfm\phi}
\newcommand{\BGvf}{\bfm\varphi}
\newcommand{\BGg}{\bfm\gamma}
\newcommand{\BGc}{\bfm\chi}
\newcommand{\BGi}{\bfm\iota}
\newcommand{\BGk}{\bfm\kappa}
\newcommand{\BGl}{\bfm\lambda}
\newcommand{\BGn}{\bfm\eta}
\newcommand{\BGm}{\bfm\mu}
\newcommand{\BGv}{\bfm\nu}
\newcommand{\BGp}{\bfm\pi}
\newcommand{\BGt}{\bfm\theta}
\newcommand{\BGvt}{\bfm\vartheta}
\newcommand{\BGr}{\bfm\rho}
\newcommand{\BGvr}{\bfm\varrho}
\newcommand{\BGs}{\bfm\sigma}
\newcommand{\BGj}{\bfm\tau}
\newcommand{\BGu}{\bfm\upsilon}
\newcommand{\BGo}{\bfm\omega}
\newcommand{\BGx}{\bfm\xi}
\newcommand{\BGy}{\bfm\psi}
\newcommand{\BGz}{\bfm\zeta}
\newcommand{\BGD}{\bfm\Delta}
\newcommand{\BGF}{\bfm\Phi}
\newcommand{\BGG}{\bfm\Gamma}
\newcommand{\BGL}{\bfm\Lambda}
\newcommand{\BGP}{\bfm\Pi}
\newcommand{\BGT}{\bfm\Theta}
\newcommand{\BGS}{\bfm\Sigma}
\newcommand{\BGU}{\bfm\Upsilon}
\newcommand{\BGO}{\bfm\Omega}
\newcommand{\BGX}{\bfm\Xi}
\newcommand{\BGY}{\bfm\Psi}

% Abbreviate definitions of greek symbols
\newcommand{\Ga}{\alpha}
\newcommand{\Gb}{\beta}
\newcommand{\Gd}{\delta}
\newcommand{\Ge}{\epsilon}
\newcommand{\Gve}{\varepsilon}
\newcommand{\Gf}{\phi}
\newcommand{\Gvf}{\varphi}
\newcommand{\Gg}{\gamma}
\newcommand{\Gc}{\chi}
\newcommand{\Gi}{\iota}
\newcommand{\Gk}{\kappa}
\newcommand{\Gl}{\lambda}
\newcommand{\Gn}{\eta}
\newcommand{\Gm}{\mu}
\newcommand{\Gv}{\nu}
\newcommand{\Gp}{\pi}
\newcommand{\Gt}{\theta}
\newcommand{\Gvt}{\vartheta}
\newcommand{\Gr}{\rho}
\newcommand{\Gvr}{\varrho}
\newcommand{\Gs}{\sigma}
\newcommand{\Gj}{\tau}
\newcommand{\Gu}{\upsilon}
\newcommand{\Go}{\omega}
\newcommand{\Gx}{\xi}
\newcommand{\Gy}{\psi}
\newcommand{\Gz}{\zeta}
\newcommand{\GD}{\Delta}
\newcommand{\GF}{\Phi}
\newcommand{\GG}{\Gamma}
\newcommand{\GL}{\Lambda}
\newcommand{\GP}{\Pi}
\newcommand{\GT}{\Theta}
\newcommand{\GS}{\Sigma}
\newcommand{\GU}{\Upsilon}
\newcommand{\GO}{\Omega}
\newcommand{\GX}{\Xi}
\newcommand{\GY}{\Psi}
