\def\half{\textstyle\frac{1}{2}}
\def\hhalf{\scriptstyle\frac{1}{2}}
\def\quarter{\textstyle\frac{1}{4}}
\def\qquarter{\scriptstyle\frac{1}{4}}
\def\squarter{\sfrac{1}{4}}
\def\stwelfth{\sfrac{1}{12}}
\def\sthirtysixth{\sfrac{1}{36}}
% \newcommand{\grad}{\boldsymbol{\nabla}}
% \newcommand{\gradh}{\boldsymbol{\nabla}_h}
\newcommand{\grad}{\nabla}
\newcommand{\gradh}{\nabla_h}
\def\bgamma\boldsymbol{\gamma}
\def\rdt{\Delta t}
\newcommand{\ew}[3]{{e_{3#1}}_{\,#2}^{\,#3} }
\newcommand{\vect}[1]{\ensuremath{\mathbf{#1}}} % for vectors                                % non-italic bold
\newcommand{\Div}{\grad\cdot}
% \newcommand{\curl}{\boldsymbol{\nabla} \times} % for curl
\newcommand{\curl}{\nabla \times} % for curl
\newcommand{\pd}[2][]{\frac{\partial #1}{\partial #2}}
\def\deg{\degres}                            % degrees  (NB: \r{} can % % also be used)
\newcommand{\alpbet} {\left(\alpha / \beta \right)} 	% alpha/beta  for slp computation
\newcommand{\triad}[6][]{\ensuremath{{}_{#2}^{#3}{\mathbb{#4}_{#1}}_{#5}^{\,#6}}}
\newcommand{\triadd}[5]{\ensuremath{{}_{#1}^{#2}{\mathbb{#3}}_{#4}^{\,#5}}}
\newcommand{\triadt}[5]{\ensuremath{{}_{#1}^{#2}{\tilde{\mathbb{#3}}}_{#4}^{\,#5}}}
\newcommand{\rtriad}[2][]{\ensuremath{\triad[#1]{i}{k}{#2}{i_p}{k_p}}}
\newcommand{\rtriadt}[1]{\ensuremath{\triadt{i}{k}{#1}{i_p}{k_p}}}
\newcommand{\Alts}{{A}}
\newcommand{\Alt}{{A^{lT}}}
\newcommand{\rMLt}[1][i]{\tilde{r}_{\mathrm{ML}\,#1}}
\newcommand{\rML}[1][i]{r_{\mathrm{ML}\,#1}}
\newcommand{\mygstrut}[2]{\rule[#1 em]{0pt}{#2 em}}
\newcommand{\mystrut}{\rule[-.9 em]{0pt}{1.79 em}}