  For a large class of dynamical problems from mathematical physics the
skew-selfadjointness of a spatial operator of the form
$A=\left(\begin{array}{cc} 0 & -C^{*}\\ C & 0 \end{array}\right)$, where
$C:D\left(C\right)\subseteq H_{0}\to H_{1}$ is a closed densely defined linear
operator, is a typical property. Guided by the standard example, where
$C=\mathrm{grad}=\left(\begin{array}{c} \partial_{1}\\ \vdots\\ \partial_{n}
\end{array}\right)$ (and $-C^{*}=\mathrm{div}$, subject to suitable boundary
constraints), an abstract class of operators $C=\left(\begin{array}{c} C_{1}\\
\vdots\\ C_{n} \end{array}\right)$ is introduced (hence the title). As a
particular application we consider a non-standard coupling mechanism and the
incorporation of diffusive boundary conditions both modeled by setting
associated with a skew-selfadjoint spatial operator $A$.
