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...

Prediction and ltering of continuous-time stochastic processes require a solver of a continuous-time di erential Lyapunov equation (cdle). Even though this can be recast into an ordinary di erential equation (ode), where standard solvers can be applied, the dominating approach in Kalman lter applications is to discretize the system and then apply the discrete-time di erence Lyapunov equation (d...

E↑ective di↑erential Nullstellensatz – page 1/19

The present paper gives a new view point for the di erential operators with respect to the coordinates of the quantum matrix space. A special emphasis is put on an inductive construction of these di erential operators from the q-di erence operators de ned on each columns (resp. rows). This idea for understanding our operators provides us with two important applications: (1) a construction of th...

image restoration has been an active research area. dierent formulations are eective in high qualityrecovery. partial dierential equations (pdes) have become an important tool in image processingand analysis. one of the earliest models based on pdes is perona-malik model that is a kindof anisotropic diusion (andi) lter. anisotropic diusion lter has become a valuable tool indierent elds...

of the Dissertation Axioms for Di erential Cohomology

In this paper, we are concerned with a class of nonlinear implicit fractional di?erential equation adiscrete delay. By means the contraction mapping principle, prove existence unique solution.Then, investigate continuous dependence solution upon initial delay data and Ulamstability.