%Version dated 7 February 1990

\def\tfor{.\,^{\displaystyle\cdot}\,.}

\def\predefine#1#2{\let#1#2}

\def\a{\alpha}

\def\up#1#2{\mathrel{\mathop{#1}\limits^{#2}}}

\predefine\barunder{\b}
\def\b{\beta}

\predefine\cedilla{\c}
\def\c{\gamma}
\def\C{\Gamma}

\predefine\dotunder{\d}
\def\d{\delta}
\def\D{\Delta}

\def\e{\varepsilon}

\def\k{\kappa}

\predefine\Polishl{\l}
\def\l{\lambda}

\predefine\PolishL{\L}
\def\L{\Lambda}

\def\m{\mu}

\def\n{\nu}

\predefine\tieafter{\t}
\def\t{\theta}
\def\T{\Theta}

\def\r{\rho}

\def\s{\sigma}

\def\x{\xi}
\def\X{\Xi}

\def\y{\eta}

\def\z{\zeta}

\def\f{\varphi}
\def\F{\Phi}

\def\h{\chi}

\def\p{\psi}
\def\P{\Psi}

\predefine\fancyo{\o}
\def\o{\omega}

\predefine\fancyO{\O}
\def\O{\Omega}

\def\aa{{\cal A}}

\def\bb{{\cal B}}

\def\cc{{\cal C}}

\def\dd{{\cal D}}

\def\ee{{\cal E}}

\def\ff{{\cal F}}

\predefine\ggg{\gg}
\def\gg{{\cal G}}

\def\hh{{\cal H}}

\def\ii{{\cal I}}

\def\jj{{\cal J}}

\def\kk{{\cal K}}

\predefine\lll{\ll}
\def\ll{{\cal L}}

\def\mm{{\cal M}}

\def\nn{{\cal N}}

\def\oo{{\cal O}}

\def\pp{{\cal P}}

\def\qq{{\cal Q}}

\def\rr{{\cal R}}

\def\ss{{\cal S}}

\predefine\tp{\tt}
\def\tt{{\cal T}}

\def\uu{{\cal U}}

\def\vv{{\cal V}}

\def\ww{{\cal W}}

\def\xx{{\cal X}}

\def\yy{{\cal Y}}

\def\zz{{\cal Z}}

\def\ct{{\hbox{\rm const}}}

\def\pd{{\partial}}

\def\is#1{\displaystyle\int\limits_{\partial S}#1\,ds(y)}

\def\frac#1#2{{#1\over#2}}

\def\dfrac#1#2{{\displaystyle{#1\over#2}}}

\def\tfrac#1#2{{\textstyle{#1\over#2}}}

\def\pdd#1{\dfrac{\partial}{\partial#1}}

\def\lxy{\ln|x-y|}

\def\0{{C\sp{0,\alpha}(\partial S)}}

\def\1{{C\sp{1,\alpha}(\partial S)}}

\def\ds{{\partial S}}

\def\ex#1#2{\dfrac{(x_{#1}-y_{#1})(x_{#2}-y_{#2})}{|x-y|^2}}

\def\rD{{\hbox{\rm D}}}

\def\rN{{\hbox{\rm N}}}

\def\oontop#1{{\mathaccent'27#1}}
\def\H0{{\oontop H}}

\def\W0{{\oontop W}}

\def\tld{{\kern-0.1em\raise-6pt\hbox{\~{}}}} %for tilde as superscript

\def\tr{{\hbox{\sevenrm T}}}

\def\bR{{\bf R}}

\def\bC{{\bf C}}

\def\bZ{{\bf Z}}

\def\bN{{\bf N}}

\def\setR{{\bf\rm I\!R}}

\def\setZ{{\bf\rm \not \!Z}}    % NOT RIGHT

\def\setN{{\bf\rm I\!N}}

\def\setQ{{\bf\rm I\!\!\!Q}}

\def\dis{\displaystyle}

\def\tfor{.\,^{\dis\cdot}\,.}

\def\mult{{$\times$}}


\def\zb{{\bar z}}

\predefine\Real{\Re}
\def\Re{\mathop{\rm Re}\nolimits}

\predefine\Imag{\Im}
\def\Im{\mathop{\rm Im}\nolimits}

\def\grad{\mathop{\rm grad}\nolimits}

\predefine\division{\div}
\def\div{\mathop{\rm div}\nolimits}

\def\curl{\mathop{\rm curl}\nolimits}

\def\diam{\mathop{\rm diam}\nolimits}

\def\id{\mathop{\rm id}\nolimits}

\def\sgn{\mathop{\rm sgn}\nolimits}

\def\sign{\mathop{\rm sign}\nolimits}

\def\mod{\mathop{\rm mod}\nolimits}

\def\supp{\mathop{\rm supp}\nolimits}

\def\coker{\mathop{\rm coker}\nolimits}

\def\dist{\mathop{\rm dist}\nolimits}

\def\mes{\mathop{\rm mes}\nolimits}

\def\spur{\mathop{\rm sp}\nolimits}

\def\dint{\mathop{\int\!\!\!\int}}

\def\|{{\Vert}}

\def\same{{$\frac{\hskip 1.5truecm}{\hskip 1.5truecm}$}}

\def\binom#1#2{{#1\choose #2}}

\def\com#1{$\backslash${\tt#1}}

\def\loc{{\hbox{\sevenrm loc}}}