% -*- Mode: TeX -*-

% POOR MAN'S BOLDFACE; TEXBOOK P.386
% USEFUL FOR BOLD GREEK

\def\bold#1{\setbox0=\hbox{#1}
 \kern-.025em\copy0\kern-\wd0
 \kern.05em\copy0\kern-\wd0
 \kern-.025em\raise.0433em\box0 }

% SCRIPT LETTERS

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

% FOR DEFINTIONS, THEOREMS, PROPOSITIONS, PROOFS

\def\theorem#1#2{{\vpar{\bf Theorem #1}\quad{\it#2\par}}}
\def\corollary#1#2{{\vpar{\bf Corollary #1}\quad{\it#2\par}}}
\def\definition#1#2{{\vpar{\bf Definition #1}\quad{\it#2\par}}}
\def\proposition#1#2{{\vpar{\bf Proposition #1}\quad{\it#2\par}}}
\def\endproof{\hbox{\hskip1pt
	\vrule width4pt height6pt depth1.5pt \hskip1pt}}
\def\proof#1{{\vpar{\bf Proof.}\quad#1\quad\endproof\par}}

% MATHEMATICAL ABBREVIATIONS

\def\noteq{\mathrel{\not=}}			 % patch not equal;  not work
\def\vec#1{{\bf#1}}		% vector
\def\mat#1{{\bf#1}}		% matrix
\def\uvec#1{\underline{\vec#1}}			% underlined vector
\def\iter#1{^{\left(#1\right)}}		 % iteration superscript (n)
\def\tpose{^\top}			 % transpose
\def\inv{^{-1}}			         % matrix inverse
\def\opt{^\ast}				 % optimum superscript
\def\op#1{\hbox{\bf#1}}				 % operator
\def\inp#1#2{\left(#1,\,#2\right)}		 % inner product (., .)
\def\ainp#1#2{a(#1,\,#2)}			 % energy inner product a(., .)
\def\ahinp#1#2{a^h(#1,\,#2)}			 % discrete  " _h(., .)
\def\lform#1{f(#1)}				 % linear form f(.)  
\def\norm#1{\left\|#1\right\|}			 % norm
\def\seminorm#1{\left|#1\right|}		 % semi-norm
\def\regionint#1{\int\int_\Omega#1\,dx\,dy}	 % double integral over omega
\def\boundaryint#1{\oint_{\partial\Omega}#1\,ds}% boundary integral
\def\level#1{^{h_{#1}}}			 % level number 
\def\interp#1#2{\mathop{\hbox{\rm I}}_{#1\Rightarrow#2}}	%interpolation operator
\def\vers{\mathop{\rm vers}\nolimits}		% versine 
\def\sgn{\mathop{\rm sgn}\nolimits}		% signum function
\def\diag{\mathop{\rm diag}\nolimits}		% diagonal matrix
\def\grad{\nabla}				 % gradient operator
\def\dotp{\cdot}				% dot product
\def\crossp{\times}				% cross product

% FOR INDEXING NODES

\def\ch#1#2{{\hbox{\rm c}_{#1\hbox to .5pt{},\hbox to .5pt{}#2}^h}}
\def\dh#1#2{{\hbox{\rm d}_{#1\hbox to .5pt{},\hbox to .5pt{}#2}^h}}
\def\eh#1#2{{\hbox{\rm e}_{#1\hbox to .5pt{},\hbox to .5pt{}#2}^h}}
\def\fh#1#2{{\hbox{\rm f}_{#1\hbox to .5pt{},\hbox to .5pt{}#2}^h}}
\def\gh#1#2{{\hbox{\rm g}_{#1\hbox to .5pt{},\hbox to .5pt{}#2}^h}}
\def\ph#1#2{{\hbox{\rm p}_{#1\hbox to .5pt{},\hbox to .5pt{}#2}^h}}
\def\qh#1#2{{\hbox{\rm q}_{#1\hbox to .5pt{},\hbox to .5pt{}#2}^h}}
\def\rh#1#2{{\hbox{\rm r}_{#1\hbox to .5pt{},\hbox to .5pt{}#2}^h}}
\def\uh#1#2{{\hbox{\rm u}_{#1\hbox to .5pt{},\hbox to .5pt{}#2}^h}}
\def\vh#1#2{{\hbox{\rm v}_{#1\hbox to .5pt{},\hbox to .5pt{}#2}^h}}

\def\c#1#2{\hbox{\rm c}_{#1\hbox to .5pt{},\hbox to .5pt{}#2}}
\def\d#1#2{\hbox{\rm d}_{#1\hbox to .5pt{},\hbox to .5pt{}#2}}
\def\e#1#2{\hbox{\rm e}_{#1\hbox to .5pt{},\hbox to .5pt{}#2}}
\def\f#1#2{\hbox{\rm f}_{#1\hbox to .5pt{},\hbox to .5pt{}#2}}
\def\g#1#2{\hbox{\rm g}_{#1\hbox to .5pt{},\hbox to .5pt{}#2}}
\def\p#1#2{\hbox{\rm p}_{#1\hbox to .5pt{},\hbox to .5pt{}#2}}
\def\q#1#2{\hbox{\rm q}_{#1\hbox to .5pt{},\hbox to .5pt{}#2}}
\def\r#1#2{\hbox{\rm r}_{#1\hbox to .5pt{},\hbox to .5pt{}#2}}
\def\u#1#2{\hbox{\rm u}_{#1\hbox to .5pt{},\hbox to .5pt{}#2}}
\def\v#1#2{\hbox{\rm v}_{#1\hbox to .5pt{},\hbox to .5pt{}#2}}
\def\uu{\hbox{\rm u}}
\def\vv{\hbox{\rm v}}

% VECTOR DYNAMICS

\def\ru{{\rm u}} \def\dru{\,d\ru}
\def\vx{{\vec x}} \def\vxdot{{\dot\vx}} \def\vxddot{{\ddot\vx}}
\def\vc{{\vec c}} \def\vcdot{{\dot\vc}} \def\vcddot{{\ddot\vc}}
\def\ve{{\vec e}} \def\vedot{{\dot\ve}} \def\veddot{{\ddot\ve}}
\def\uve{{\uvec e}} \def\uvedot{{\dot\uve}} \def\uveddot{{\ddot\uve}}
\def\uvf{{\uvec f}} \def\uvfdot{{\dot\uvf}} \def\uvfddot{{\ddot\uvf}}
\def\uvq{{\uvec q}} \def\uvqdot{{\dot\uvq}} \def\uvqddot{{\ddot\uvq}}
\def\uvx{{\uvec x}} \def\uvxdot{{\dot\uvx}} \def\uvxddot{{\ddot\uvx}}
\def\vv{{\vec v}} \def\vvdot{{\dot\vv}}
\def\vq{{\vec q}} \def\vqdot{{\dot\vq}}
\def\vr{{\vec r}}\def\vrdot{{\dot\vr}}
\def\vf{{\vec f}}
\def\valpha{{\bold{$\alpha$}}} \def\valphadot{{\dot\valpha}}
\def\vbeta{{\bold{$\beta$}}} \def\vbetadot{{\dot\vbeta}}
\def\vlambda{{\bold{$\lambda$}}} \def\vlambdadot{{\dot\vlambda}}
\def\vomega{{\bold{$\omega$}}} \def\vomegadot{{\dot\vomega}}
\def\vtheta{{\bold{$\theta$}}} \def\vthetadot{{\dot\vtheta}}
\def\vepsilon{{\bold{$\epsilon$}}} \def\vepsilondot{{\dot\vepsilon}}
\def\vsigma{{\bold{$\sigma$}}} \def\vsigmadot{{\dot\vsigma}}
\def\vgamma{{\bold{$\gamma$}}} \def\vgammadot{{\dot\vgamma}}
\def\gq{{\vec g_q}} \def\fq{{\vec f_q}}
\def\Cqtpose{{\mat C_q\tpose}} \def\Cq{{\mat C_q}} 
