We consider the initial value problem for the equation u t = u xx +H(u), where H is the Heaviside graph, on a bounded interval with Dirichlet boundary conditions, and discuss existence, regularity and uniqueness of solutions and interfaces .

A new approach for analyzing cracked problems in 2D orthotropic materials using the well-known element free Galerkin method and orthotropic enrichment functions is proposed. The element free Galerkin method is a meshfree method which enables discontinuous problems to be modeled efficiently. In this study, element free Galerkin is extrinsically enriched by the recently developed crack-tip orthot...

We examine the e ect of constraining the number of hidden units For one hidden layer networks with fairly general type of units including perceptrons with any bounded activation function and radial basis function units we show that when also the size of parameters is bounded the best approximation property is satis ed which means that there always exists a parameterization achieving the global ...

This paper introduces a new approach to the recursive propagation of probability density functions through discrete-time stochastic nonlinear dynamic systems. An efficient recursive procedure is proposed that is based on the optimal approximation of the posterior densities after each prediction step by means of Dirac mixtures. The parameters of the individual components are selected by systemat...

By the sometimes so-called Main Theorem of Recursive Analysis, every computable real function is necessarily continuous. We wonder whether and which kinds of hypercomputation allow for the effective evaluation of also discontinuous f : R → R. More precisely the present work considers the following three super-Turing notions of real function computability: – relativized computation; specifically...

Abstract. In this paper we propose a variant of the level set formulation for identifying curves separating regions into different phases. In classical level set approaches, the sign of n level set functions are utilized to identify up to 2n phases. The novelty in our approach is to introduce a piecewise constant level set function and use each constant value to represent a unique phase. If 2n ...

An extended approach is developed by blending isogeometric analysis and the first-order local maximum entropy for standard enhanced fields, respectively. Isogeometric facilitates accurate parametrization of geometry in general, particularly exact geometric conic curves quadratic surfaces using NURBS. On other hand, leads to an improved estimate part due its infinite continuity. Moreover, paves ...