We give a condition on a closed set K of real n mma trices which ensures that any W p gradient Young measure sup ported on K must be trivial the condition given is also necessary when K is bounded Introduction Assume is a smooth bounded domain in R and p is a given number Let W p R be the usual Sobolev space of maps u from to R the Jacobi or gradient matrix ru of u is L integrable and thus de n...

The goal of this paper is study closed ideals and annihilators over the class distributive dual weakly complemented lattices(DDWCL's). algebraic structure ideals, dense are shown. connection between andannihilators in obtained.

Existence of zeros for operators taking their values in the dual of a Banach space BIAGIO RICCERI Throughout the sequel, E denotes a reflexive real Banach space and E * its topological dual. We also assume that E is locally uniformly convex. This means that for each x ∈ E, with x = 1, and each ǫ > 0 there exists δ > 0 such that, for every y ∈ E satisfying y = 1 and x − y ≥ ǫ, one has x + y ≤ 2(...

a) X is strongly paracompact; b) X is paracompact; c) X is metacompact; d) X is weakly θ-refinable; e) Every open cover of X has a point-countable open refinement; f) X is subparacompact; g) If C is a closed subspace of X, then there are discrete closed sets S and T which are, respectively, well-ordered and reverse-well-ordered by the given ordering of X, have S ∪ T ⊂ C, and have the property t...

In this paper, we will define --sets, --sets and study some of their properties. Also prove that are stronger than weaker binary locally closed sets.

In this thesis, we effectively construct a predecessor function for the type definitions in the raw hierarchy for any weakly-scattered theory. Using this predecessor function, we improve a recent bounding result by Sacks for weakly-scattered theories by removing the assumption of a predecessor function from the k-splitting hypothesis. We begin by giving an introduction to the infinitary logic C...

This thesis consists of three contributions to the theory of complex approximation on Riemann surfaces. It is known that if E is a closed subset of an open Riemann surface R and f is a holomorphic function on a neighbourhood of E, then it is “usually” not possible to approximate f uniformly by functions holomorphic on all of R. In Chapter 2, we show, however, that for every open Riemann surface...

stefan problem with kinetics is reduced to a system of nonlinear volterra integral equations of second kind and newton's method is applied to linearize it. product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. an example is provided to illustrated the applicability of the method.