In this note we address the variational property of singular values of matrix and point out that a theorem in [Matrix Computations, John Hopkins University Press, Baltimore, MD, 1989,1993,1996] is incomplete. 2002 Elsevier Science Inc. All rights reserved.

In this paper, we study mixed variational nite element methods for the unilateral problems arising in contact mechanics.The presented discrete spaces can handle the case of non matching meshes in the contact area. We rst state the static problem and then extend it to the frictional contact case, and end with the dynamic frictional problem.

We reformulate the dynamics of homogeneous cosmologies with a scalar field matter source with an arbitrary selfinteraction potential in the language of jet bundles and extensions of vector fields. In this framework, the Bianchi— scalar field equations become subsets of the second Bianchi jet bundle, J , and every Bianchi cosmology is naturally extended to live on a variety of J . We are interes...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..*................... 1 GENERAL INTRODUCTION ~.~O................................*............ 3 Part I: Confinement in Periodic Quantum Electrodynamics for Low Couplings

We establish the existence of three distinct solutions for a perturbed p-Laplacian boundary value problem with impulsive effects. Our approach is based on variational methods.

1. The object of the research [ l ] with which this address is concerned is twofold : first, to demonstrate, by direct methods, the existence of solutions, perhaps in some generalized sense, for a wide class of variational problems for multiple integrals, and second, to investigate further differentiability properties of the generalized solutions thus obtained. We consider only problems in nonp...

We introduce FactorVAE, a method that disentangles by encouraging the distribution of codes, the variational posterior averaged over the training set, to be factorial and hence independent in the dimensions. Furthermore, we propose a new measure of disentanglement that addresses some weaknesses of commonly used metrics.

This paper is devoted to the study, with variational technique, of the following quasilinear elliptic problem: