STOCHASTIC HEAT EQUATION WITH FRACTIONAL LAPLACIAN AND FRACTIONAL NOISE:EXISTENCE OF THE SOLUTION AND ANALYSIS OF ITS DENSITY

In this paper we study a fractional stochastic heat equation on Rd （d 〉 1） with additive noise /t u（t, x） = Dα/δ u（t, x）＋ b（u（t, x） ） ＋ WH （t, x） where D α/δ is a nonlocal fractional differential operator and W H is a Gaussian-colored noise. We show the existence and the uniqueness of the mild solution for this equation. In addition, in the case of space dimension d = 1, we prove the existence of the density for this solution and we establish lower and upper Gaussian bounds for the density by Malliavin calculus.

Kinetic Modeling of Isothermal or Non-isothermal Adsorption in a Pellet：Application to Adsorption Heat Pumps

Understanding the interaction between a fluid and a solid phase is of fundamental importance to the design of an adsorption process.Because the heat effects associated with adsorption are comparatively large,the as-sumption of isothermal behavior is a valid approximation only when uptake rates are relatively slow.In this article,we propose to determine when it is needed to choose the isothermal or non-isothermal assumption according to two physical parametersα（ratio convection/capacity） andβ（quantity of energy/capacity） .The proposed problem is solved by a mathematical method in the Laplace domain.Whenα→∞（infinitely high heat transfer coefficient） or β→0（infinitely large heat capacity） ,the limiting case is isothermal.When the diffusion is rapid（α10） the kinetics of sorption is controlled entirely by heat transfer.If the adsorption process is to be used as a heat pump,it shall be represented by an isotherm model withαandβas high as possible.

FRACTIONAL 2D-STOCHASTIC CURRENTS

Using multiple stochastic integrals and the stochastic calculus for the frac-tional Brownian sheet, we define and we analyze the 2D-fractional stochastic currents.

An Approximation Method for a Maximum Likelihood Equation System and Application to the Analysis of Accidents Data

There exist many iterative methods for computing the maximum likelihood estimator but most of them suffer from one or several drawbacks such as the need to inverse a Hessian matrix and the need to find good initial approximations of the parameters that are unknown in practice. In this paper, we present an estimation method without matrix inversion based on a linear approximation of the likelihood equations in a neighborhood of the constrained maximum likelihood estimator. We obtain closed-form approximations of solutions and standard errors. Then, we propose an iterative algorithm which cycles through the components of the vector parameter and updates one component at a time. The initial solution, which is necessary to start the iterative procedure, is automated. The proposed algorithm is compared to some of the best iterative optimization algorithms available on R and MATLAB software through a simulation study and applied to the statistical analysis of a road safety measure.

OLD AND RECENT RESULTS IN THE ANALYTIC THEORY OF DIRICHLET SERIES:A SURVEY

This survey is dedicated to the memory of Professor Jiarong Yu,who recently passed away.It is concerned by a topic of which he was fond,an interest shared by myself:the analytic theory of Dirichlet series.

A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schrodinger Equations

In this review article we discuss different techniques to solve numerically the time-dependent Schrodinger equation on unbounded domains.We present in detail the most recent approaches and describe briefly alternative ideas pointing out the relations between these works.We conclude with several numerical examples from different application areas to compare the presented techniques.We mainly focus on the one-dimensional problem but also touch upon the situation in two space dimensions and the cubic nonlinear case.

Computation of Shock Profiles in Radiative Hydrodynamics

This article is devoted to the construction of a numerical scheme to solve the equations of radiative hydrodynamics.We use this numerical procedure to compute shock profiles and illustrate some earlier theoretical results about their smoothness and monotonicity properties.We first consider a scalar toy model,then we extend our analysis to a more realistic system for the radiative hydrodynamics that couples the Euler equations and an elliptic equation.

Derivation of a Non-Local Model for Diffusion Asymptotics--Application to Radiative Transfer Problems

In this paper,we introduce a moment closure which is intended to provide a macroscopic approximation of the evolution of a particle distribution function,solution of a kinetic equation.This closure is of non local type in the sense that it involves convolution or pseudo-differential operators.We show it is consistent with the diffusion limit and we propose numerical approximations to treat the non local terms.We illustrate how this approach can be incorporated in complex models involving a coupling with hydrodynamic equations,by treating examples arising in radiative transfer.We pay a specific attention to the conservation of the total energy by the numerical scheme.

Absorbing Boundary Conditions for Solving N-Dimensional Stationary Schr¨odinger Equations with Unbounded Potentials and Nonlinearities

We propose a hierarchy of novel absorbing boundary conditions for the onedimensional stationary Schr¨odinger equation with general(linear and nonlinear)potential.The accuracy of the new absorbing boundary conditions is investigated numerically for the computation of energies and ground-states for linear and nonlinear Schr¨odinger equations.It turns out that these absorbing boundary conditions and their variants lead to a higher accuracy than the usual Dirichlet boundary condition.Finally,we give the extension of these ABCs to N-dimensional stationary Schr¨odinger equations.