Generalizing this convention, a finite-net multi-CCS process may be represented as ({(mathbf{nu } L }t), where L is a set of actions (if L is empty, the restriction operator is not present) and t is a restriction-free process.
({(mathbf{nu } a }p) is process p where the name a is made private by applying the restriction operator over a.
As we have chosen a CCS-like naming convention, the scoping operator, which can occur syntactically only at the top level, is the CCS restriction operator.
Considering the situation in which H=L2(Rn) and τ is the trace (restriction) operator along some null subset, we give various applications to singular perturbations of non necessarily elliptic pseudo-differential operators, thus unifying and extending previously known results.
In finite-net multi-CCS, parallel composition may occur inside the body of a recursively defined constant C; on the contrary, the restriction operator ({(mathbf{nu } a)}) is not allowed in the body of C. So, a finite-net process may be represented as ({(mathbf{nu } L }t), where L is a set of actions (if L is empty, the restriction operator is not present) and t a restriction-free process.
The realization for the operator in which is the restriction of to.
These conditions are related to the accuracy of the restriction operators, the choice of the boundary conditions, the distortion of the grids and the magnitude of the iteration error.
Furthermore, let P h H : V h → V H be the orthogonal projection operator (called restriction operator) with respect to a, i.e. (38) a P h H v h, w H = a (v h, w H ), ∀ w H ∈ V H. Another projection operator P H h : V H → V h, called prolongation operator, is analogously defined.
