Under appropriate assumptions, it is shown that there is a di eomorphism that transforms solutions of the implicit di erential equation

The goal of this paper is to prove a convergence rate for WongZakai approximations of semilinear stochastic partial di erential equations driven by a nite dimensional Brownian motion.

We present an AXIOM environment called JET for geometric computations with partial dierential equations within the framework of the jet bundle formalism. This comprises especially the completion of a given dierential equation to an involutive one according to the Cartan-Kuranishi Theorem and the setting up of the determining system for the generators of classical and non-classical Lie symmetrie...

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Steady vortex ows past a circular cylinder are obtained numerically as solutions of the partial di erential equation = f( ). We illustrate several classes of solutions.

The problem of nding adapted solutions to systems of coupled linear forward-backward stochastic dierential equations (FBSDEs, for short) is investigated. A necessary condition of solvability leads to a reduction of general linear FBSDEs to a special one. By some ideas from controllability in control theory, using some functional analysis, we obtain a necessary and sucient condition for the solv...

This paper surveys recent work on the problems of calculating Galois groups of diierentialequations and of constructingdiierentialequations with given groups as their Galois groups.

A large class of engineering systems are modeled by coupled Diierential and Algebraic Equations (DAEs). Due to the singular nature of the algebraic equations, DAE systems do not satisfy the standard state-space description and require special techniques. So far, the literature has concentrated mostly on the numerical analysis and control aspects of DAE systems. This paper investigates the probl...

This paper studies the application of interval analysis and consistency techniques to ordinary di erential equations. It presents a unifying framework to extend traditional numerical techniques to intervals. In particular, it shows how to extend explicit methods to intervals. The paper also took a fresh look at the traditional problems encountered by interval techniques and studied how consiste...

Stomach cancer has an important place in medicine. Unfortunately, diagnosis of gastric is being established majority cases at the IV stage. So, yt necessary to detect tumors earliest stages carcinogenesis and evaluate treat precancerous diseases, such as atrophy intestinal metaplasia. Aims : To estimate value Narrow-band imaging Dual focus (NBI Focus) endoscopy capabilities differential metapla...