Search results for "Polygon"

Weighted Extrapolation Techniques for Finite Difference Methods on Complex Domains with Cartesian Meshes

2016

The design of numerical boundary conditions in high order schemes is a challenging problem that has been tackled in different ways depending on the nature of the problem and the scheme used to solve it numerically. In this paper we propose a technique to extrapolate the information from the computational domain to ghost cells for schemes with structured Cartesian Meshes on complex domains. This technique is based on the application of Lagrange interpolation with weighted filters for the detection of discontinuities that permits a data dependent extrapolation, with high order at smooth regions and essentially non oscillatory properties near discontinuities. This paper is a sequel of Baeza et…

Invariant measures for piecewise convex transformations of an interval

2002

Characterizing extreme points of polyhedra an extension of a result by Wolfgang Bühler

1982

This paper reconsiders the characterization given by Buhler admitting convex polyhedra of probability distributions on a finite or countable set which are given by systems of linear inequalities more complex than those considered before.

Some Nonlinear Methods in Fréchet Operator Rings and Ψ*-Algebras

1995

Two different inverse function theorems, one of Nash-Moser type, the other due to H. Omori, are extended to obtain special surjectivity results in locally convex and locally pseudo-convex Frechet algebras generated by group actions and derivations. In particular, the following factorization problem is discussed. Let Ψ be a locally pseudo-convex Frechet algebra with unit e and T+ : Ψ Ψ a continuous linear operator. Does there exist a neighborhood U of 0 such that the equation where T- = IΨ- T, has a solution x ∈ Ψ for every y ∈ U?

On some parameters related to weak noncompactness in L1(μ,E)

2009

Abstract A weak measure of noncompactness γU is defined in a Banach space in terms of convex compactness. We obtain relationships between the measure γU (A) of a bounded set A in the Bochner space L1 (μ,E) and two parameters Π(A) and Δ1(A). Then the criterion for relative weak compactness due to Ulger [19] and Diestel-Ruess-Schachermayer [11] is recovered.

Ordering and Convex Polyominoes

2005

We introduce a partial order on pictures (matrices), denoted by ≼ that extends to two dimensions the subword ordering on words. We investigate properties of special families of discrete sets (corresponding to {0,1}-matrices) with respect to this partial order. In particular we consider the families of polyominoes and convex polyominoes and the family, recently introduced by the authors, of L-convex polyominoes. In the first part of the paper we study the closure properties of such families with respect to the order. In particular we obtain a new characterization of L-convex polyominoes: a discrete set P is a L-convex polyomino if and only if all the elements Q≼P are polyominoes. In the seco…

Reconstruction of L-convex Polyominoes.

2003

Abstract We introduce the family of L-convex polyominoes, a subset of convex polyominoes whose elements satisfy a special convexity property. We develop an algorithm that reconstructs an L-convex polyomino from the set of its maximal L-polyominoes.

Tangency conditions for multivalued mappings

1996

We prove that interiority conditions imply tangency conditions for two multivalued mappings from a topological space into a normed vector space. As a consequence, we obtain the lower semicontinuity of the intersection of two multivalued mappings. An application to the epi-upper semicontinuity of the sum of convex vector-valued mappings is given.

Monotone Relations, Fixed Points and Recursive Definitions

2008

The paper is concerned with reflexive points of relations. The significance of reflexive points in the context of indeterminate recursion principles is shown.

Fixed point properties and proximinality in Banach spaces

2009

Abstract In this paper we prove the existence of a fixed point for several classes of mappings (mappings admitting a center, nonexpansive mappings, asymptotically nonexpansive mappings) defined on the closed convex subsets of a Banach space satisfying some proximinality conditions. In particular, we derive a sufficient condition, more general than weak star compactness, such that if C is a bounded closed convex subset of l 1 satisfying this condition, then every nonexpansive mapping T : C → C has a fixed point.