Notation

$x$	...	scalar
$\ensuremath{\boldsymbol{\mathrm{x}}}$	...	vector
$\ensuremath{\boldsymbol{\mathrm{e}}}_x$	...	unity vector in direction $\boldsymbol{\mathrm{x}}$
$\ensuremath{\underline{X}}$	...	matrix
$\ensuremath{\widetilde{X}}$	...	tensor
$\ensuremath{\boldsymbol{\mathrm{x}}} \ensuremath{\cdot}\ensuremath{\boldsymbol{\mathrm{y}}}$	...	scalar (in) product
$\ensuremath{\boldsymbol{\mathrm{x}}} \ensuremath{\times}\ensuremath{\boldsymbol{\mathrm{y}}}$	...	vector (ex) product
$\ensuremath{\boldsymbol{\mathrm{x}}} \ensuremath{\otimes}\ensuremath{\boldsymbol{\mathrm{y}}}$	...	tensor product
$\ensuremath{\ensuremath{\boldsymbol{\mathrm{\nabla}}}}$	...	nabla operator
$\ensuremath{\ensuremath{\ensuremath{\boldsymbol{\mathrm{\nabla}}}}\ensuremath{\cdot}\ensuremath{\widetilde{X}}}$	...	divergence of $\ensuremath{\widetilde{X}}$
$\ensuremath{\ensuremath{\ensuremath{\boldsymbol{\mathrm{\nabla}}}}\ensuremath{\times}\ensuremath{\widetilde{X}}}$	...	curl of $\ensuremath{\widetilde{X}}$
$\ensuremath{\ensuremath{\ensuremath{\boldsymbol{\mathrm{\nabla}}}}\, \ensuremath{\widetilde{X}}}$	...	gradient of $\ensuremath{\widetilde{X}}$
$\ensuremath{\ensuremath{\ensuremath{\boldsymbol{\mathrm{\nabla}}}}\ensuremath{... ...ath{\ensuremath{\boldsymbol{\mathrm{\nabla}}}}\, }} = \ensuremath{\nabla^2} \,$	...	LAPLACE operator
$\ensuremath{\text{sign} \left\{ \cdot \right\} }$	...	signum function
$\ensuremath{\mathcal{B} \left( \cdot \right) }$	...	BERNOULLI function
$\ensuremath{\Gamma \left( \cdot \right) }$	...	gamma function
$\ensuremath{\partial_{t} \, (\cdot)}$	...	partial derivative with respect to $t$
$\ensuremath{\langle \cdot \rangle}$	...	statistical average
$\ensuremath{\int_{\ensuremath{\mathcal{ B }}} (\cdot) \,\, \ensuremath{\mathrm{d}}^3 k}$	...	integral over the first BRILLOUIN zone
$\ensuremath{\oint_{\partial \ensuremath{\mathcal{ B }}} (\cdot) \,\, \ensuremath{\mathrm{d}}A_k}$	...	integral over the boundary of the first BRILLOUIN zone
$\ensuremath{\int_{\ensuremath{\mathcal{ V }}_i} (\cdot) \,\, \ensuremath{\mathrm{d}}V}$	...	integral over the control volume
$\ensuremath{\oint_{\partial \ensuremath{\mathcal{ V }}_i} (\cdot) \,\, \ensuremath{\mathrm{d}}A}$	...	integral over the boundary of the control volume
$\ensuremath{\widetilde{\delta}}$	...	unity tensor
$\delta_{ij}$	...	KRONECKER symbol

$f(\ensuremath{\boldsymbol{\mathrm{r}}}, \ensuremath{\boldsymbol{\mathrm{k}}}, t)$	...	distribution function
$f_\mathrm{M}$	...	MAXWELL distribution function
$f_\mathrm{sM}$	...	shifted MAXWELL distribution function
$f_\mathrm{aM}$	...	anisotropic MAXWELL distribution function
$f_\mathrm{saM}$	...	shifted anisotropic MAXWELL distribution function
$f_\mathrm{S}$	...	symmetric function
$f_\mathrm{A}$	...	antisymmetric function
$\mathcal{Q}(f)$	...	collision operator
$\mathcal{R}(f)$	...	net recombination rate in $\boldsymbol{\mathrm{k}}$-space
$\ensuremath{\widetilde{\phi}}_j$	...	weight function of order $j$
$\ensuremath{\widetilde{M}}_j$	...	$j$-th moment of the distribution function

M. Gritsch: Numerical Modeling of Silicon-on-Insulator MOSFETs PDF