We give a precise mathematical formulation of a variational model for the irreversible quasi-static evolution of brittle fractures proposed by G.A. Francfort and J.-J. Marigo, and based on Griffith’s theory of crack growth. In the two-dimensional case we prove an existence result for the quasi-static evolution and show that the total energy is an absolutely continuous function of time, although...

We discuss a general class of boundary conditions for bosons living in an extra spatial dimension compactified on S/Z2. Discontinuities for both fields and their first derivatives are allowed at the orbifold fixed points. We analyze examples with free scalar fields and interacting gauge vector bosons, deriving the mass spectrum, that depends on a combination of the twist and the jumps. We discu...

A variety of image artifacts are routinely observed on MRI images. We concentrate on the Gibbs Ringing that manifests itself as bright or dark rings seen at the borders of abrupt intensity change on the images. Gegenbauer High Resolution Reconstruction method has been previously shown to eliminate the undesirable ringing at the jump discontinuities in MRI. Prior work concentrated on applying th...

One of the most significant problems arising out of range data analysis is image segmentation. This correspondence describes a hybrid approach to the problem, where hybrid refers to a comhination of both regionand edge-based considerations. The range image of 3-D objects is divided into surface primitives which are homogeneous in their intrinsic differential geometric properties and do not cont...

This paper is concerned with a 1D Schrödinger scattering problem involving both oscillatory and evanescent regimes, separated by jump discontinuities in the potential function, to avoid "turning points". We derive a non-overlapping domain decomposition method to split the original problem into sub-problems on these regions, both for the continuous and afterwards for the discrete problem. Furthe...

Professor Jirousek has been a very important driving force in the modern development of Trefftz method, contributing to its application in many different fields such as elasticity, shells and plates theory, Poisson equation and transient heat analysis. This article is dedicated to him. The focus of the paper is to incorporate Jirousek method into a very general framework of Trefftz method which...

In this work we design hybrid continuous-discontinuous finite element spaces that permit discontinuities on non-matching element interfaces of non-conforming meshes. Then, we develop an equal-order stabilized finite element formulation for incompressible flows over these hybrid spaces, which combines the element interior stabilization of SUPGtype continuous Galerkin formulations and the jump st...

The paper is devoted to the study of Toeplitz operators with piecewise continuous symbols. We clarify the geometric regularities of the behaviour of the essential spectrum of Toeplitz operators in dependence on their crucial data: the angles between jump curves of symbols at a boundary point of discontinuity and on the limit values reached by a symbol at that boundary point. We show then that t...

Abstract. Let ∑∞ n=0 en[f ]Pn(x) be the Legendre expansion of a function f(x) on (−1, 1). In an earlier work [A. Sidi, Asymptot. Anal., 65 (2009), pp. 175–190], we derived asymptotic expansions as n → ∞ for en[f ], assuming that f ∈ C∞(−1, 1), but may have arbitrary algebraic-logarithmic singularities at one or both endpoints x = ±1. In the present work, we extend this study to functions f(x) t...

is piecewise smooth, having jump discontinuities along a finite number of smooth shock curves. (We assume that f is C” and strictly convex.) In this paper we extend the result of [5] to show that generically the topological and differentiable structure of the shock set is unaffected by small perturbations of the initial data. As in [5] we consider initial data in the Schwartz space, although an...