Sentence examples for by a simple layer from inspiring English sources
We note that, if any constant vector c can be represented by a simple layer potential, then any sufficiently smooth solution of the system Eu = 0 can be represented by a simple layer potential as well (see Section 5 below).
there exists a constant vector which cannot be represented in Ω by a simple layer potential (i.e., there exists c ∈ ℝ2 such that c ∉ S p ); III.
If there exists some constant vector which cannot be represented in the simply connected domain Ω by a simple layer potential, we say that the boundary of Ω is exceptional.
The advantages are: an ionic liquid is formed and the products can be easily recovered by a simple layer separation; the enhancing of polymer yield; reducing of the corrosion problem.
Here we show that also in some (m + 1 -connected domains one cannot represent any constant vectors by a simple layer potential and that this happens if, and only if, the exterior boundary Σ0 (considered as the boundary of the simply connected domain Ω0) is exceptional.
The vector-valued function u belongs to S p if, and only if, there exists φ ∈ [L p ] n such that u can be represented by a simple layer potential u ( x ) = ∫ Σ Γ ( x, y ) φ ( y ) d σ y, x ∈ Ω. (3).
In contrast to the interpenetrating bulk heterojunction structure synthesized by blending the p- and n-type materials, template-assisted method of porous alumina could produce a versatile and unique heterostructured nanostructure such as composite nanorods and nanotubes by a simple layer-by-layer approach [4,13].
The purpose of this section is to represent the solution of the Dirichlet problem in an (m + 1 -connected domain by means of a simple layer potential.
In Section 5 we find the solution of the Dirichlet problem in a multiply connected domain by means of a simple layer potential.
This implies that in Ω R, for such a value of R, we cannot represent any smooth solution of the system E u = 0 by means of a simple layer potential.
This is known as a simple layer integral.
