This paper analyzes a Multigrid V-cycle scheme for solving the discretized 2D Poisson equation with corner-singularities. Using weighted Sobolev spaces K a (Ω) and a space decomposition based on elliptic projections, we prove that the multigrid V -cycle with standard smoothers (Richardson, weighted Jacobi, Gauss-Seidel, etc.) and piecewise linear interpolation converges uniformly for the linear...

Typical volume meshes in three dimensions are designed to conform to an underlying two-dimensional surface mesh, with volume mesh element size growing larger away from the surface. The surface mesh may be uniformly spaced or highly graded, and may have fine resolution due to extrinsic mesh size concerns. When we desire that such a volume mesh have good aspect ratio, we require that some space-f...

Planar waveguides are useful to transport, concentrate and distribute light uniformly over large dimensions. Their capacity to collect and gather light efficiently over a large distance is interesting for many applications, like backlighting and solar concentration. For these reasons, the possibility of making them even more efficient could be of considerable interest for the community. The obs...

for all x ∈ E, where 〈·,·〉 denotes the generalized duality pairing. It is well known that if E is a uniformly smooth Banach space, then J is single valued such that J(−x) = −J(x), J(tx) = tJ(x) for all t ≥ 0, x ∈ E; and J is uniformly continuous on any bounded subset of E. In the sequel we will denote single-valued normalized duality mapping by j. In the following we give some concepts. Let T :...

We show that if Lr(X), 1 < r < ∞, has an asymptotically uniformly convex renorming of power type then X admits a uniformly convex norm of power type.

Let F(a,b;c;z) be the classical hypergeometric function and f be a normalized analytic functions defined on the unit disk . Let an operator Ia,b;c(f ) be defined by [Ia,b;c(f )](z)= zF(a,b;c;z)∗f(z). In this paper the authors identify two subfamilies of analytic functions 1 and 2 and obtain conditions on the parameters a,b,c such that f ∈ 1 implies Ia,b;c(f )∈ 2.

Managing sediments dredged from reservoirs of recharge dams is an environmental issue, however, these can be abundant and economical source fine-grained fill soil. This experimental investigation quantifies the geotechnical properties a reservoir sediment used to improve engineering poorly graded dune sand in Oman. The binary mixes were prepared with different percentages (5, 10, 20, 50, 75, 90...

in this paper, we obtained the convergence of modified noor iterative scheme for nearly lipschitzian maps in real banach spaces. our results contribute to the literature in this area of re- search.

The notion of B-convexity for operator spaces, which a priori depends on a set of parameters indexed by Σ, is defined. Some of the classical characterizations of this geometric notion for Banach spaces are studied in this new context. For instance, an operator space is BΣ-convex if and only if it has Σ-subtype. The class of uniformly non-L(Σ) operator spaces, which is also the class of BΣ-conve...