Notations

$x$	...	Scalar-valued quantity
${\mathbf{{x}}}$	...	Vector-valued quantity
${{\tilde{x}}}$	...	Tensor-valued quantity
$<\! \! x\! \! >$	...	Mean value of the quantity $x$
$f_1 \circ f_2$	...	Nested Function: equivalent to $f_1(f_2)$
$(\cdot)^{\mathcal{T}}$	...	Transposition of a vector or matix
${{\partial}_{t}}$	...	Time derivative operator: $\frac{\partial}{\partial{t}}$
$\nabla$	...	Nabla operator
$\nabla(\cdot)$	...	Gradient of $(\cdot)$
$\nabla\cdot(\cdot)$	...	Divergence of $(\cdot)$
$\nabla\times(\cdot)$	...	Curl (or Rotation) of $(\cdot)$
$\Delta(\cdot)$	...	LAPLACEan operator: $\nabla \cdot \nabla (\cdot)$
$\wedge$	...	Logical conjunction
$\Longrightarrow$	...	Logical implication