ÐBoth experimental and simulation results have indicated the deviation from Arrhenius law of the di€usion coecient of hydrogen in metallic glasses. This deviation was traditionally explained by the existence of various kinds of jumps or in terms of continuous distributions of activation energies due to di€erent kinds of disorder. A new model is suggested, which relates this deviation to the te...

in this paper, we consider an inverse problem of linear heat equation with nonlinear boundary condition. we identify the temperature and the unknown radiation tern from an overspecified condition on the boundary

Market illiquidity, feedback e ects, presence of transaction costs, risk from unprotected portfolio Note 1: In the title, insert “a” or “the” before “Analytical”? and other nonlinear e ects in PDE-based option pricing models can be described by solutions to the generalized Black–Scholes parabolic equation with a di usion term nonlinearly depending on the option price itself. In this paper, di e...

In this note we reconsider the continuous time limit of the GARCH(1, 1) process. Let > k and p2 k denote, respectively, the cumulative returns and the volatility processes. We consider the continuous time approximation of the couple (> k , p2 k ). We show that, by choosing di!erent parameterizations, as a function of the discrete interval h, we can obtain either a degenerate or a non-degenerate...

We design a general mathematical framework to analyze the properties of nearest neighbor balancing algorithms of the di€usion type. Within this framework we develop a new Optimal Polynomial Scheme (OPS) which we show to terminate within a ®nite number m of steps, where m only depends on the graph and not on the initial load distribution. We show that all existing di€usion load balancing algorit...

Algorithms for resolution enhancement are needed in various applications of image processing and communication such as compression, and HDTV. We develop a geometrical algorithm, based on diffusion processes which are used both for smoothing of colored images and enhancement of the colored images. The latter is accomplished by \solving" an inverse diffusion problem which is ill posed. In order t...

In this paper, we present a parallel Newton–Krylov–Schwarz (NKS)-based non-linearly implicit algorithm for the numerical solution of the unsteady non-linear multimaterial radiation di usion problem in two-dimensional space. A robust solver technology is required for handling the high non-linearity and large jumps in material coe cients typically associated with simulations of radiation di usion...

We study the weak approximation of a multidimensional di usion (Xt)06t6T killed as it leaves an open set D, when the di usion is approximated by its continuous Euler scheme (X̃t)06t6T or by its discrete one (X̃ti )06i6N , with discretization step T=N . If we set := inf{t ¿ 0: Xt 6∈ D} and ̃c := inf{t ¿ 0: X̃t 6∈ D}, we prove that the discretization error Ex[5T¡̃c f(X̃T )]−Ex[5T¡ f(XT )] can be expan...