In this paper we discuss the problem of calculating the reach able states of a dynamical system de ned by ordinary di erential equa tions or inclusions We present a prototype system for approximating this set and demonstrate some experimental results

A detailed description is given of the parallel algorithms used in AUTO94P, an experimental parallel version of the software AUTO for the numerical bifurcation analysis of systems of ordinary di erential equations. Timing results and user instructions for the Intel Delta are included. The sequential version of the software, AUTO94, is fully described in [8]. For a related tutorial paper see [5,...

Observers are usually formulated as explicit systems of di erential equations and implemented using standard ODE solvers. In this paper, we show that there can be advantages in formulating the observer as a DAE (Di erential-Algebraic Equation). We review the general idea of DAE observer design of [10]. We give two special normal forms for which DAE observer design yields an observer with linear...

Herein, an averaging theory for the solutions to Cauchy initial value problems of arbitrary order, "-dependent parabolic partial di erential equations is developed. Indeed, by directly developing bounds between the derivatives of the fundamental solution to such an equation and derivatives of the fundamental solution of an \averaged" parabolic equation, we bring forth a novel approach to compar...

Stochastic di erential games are considered in a non-Markovian setting. Typically, in stochastic di erential games the modulating process of the di usion equation describing the state ow is taken to be Markovian. Then Nash equilibria or other types of solution such as Pareto equilibria are constructed using Hamilton-Jacobi-Bellman (HJB) equations. But in a non-Markovian setting the HJB method i...

This paper concerns a new type of approximant for series analysis. By incorporating linear recurrence techniques, such as are involved with second order di erential approximants, algebraic approximants can be extended to nonlinear di erential approximants. The discussion of nonlinearities is constrained by discussing approximants just one step removed from second order algebraic approximants. T...

| This work proposes a pair of models for subcutaneous (sc) insulin kinetics. Three sc injections are considered over a 24 hour time period. Each injection delivers both fast and slow insulin, so that a third order system is built, whose components are the fast and slow sc masses of insulin and the plasma insulin concentration. The insulin injections are modeled as impulsive inputs. ODE (Ordina...

this paper describes an approximating solution, based on lagrange interpolation and spline functions, to treat functional integral equations of fredholm type and volterra type. this method can be extended to functional dierential and integro-dierential equations. for showing eciency of the method we give some numerical examples.

This work deals with the design of the low{level stages of any di erential{ based optical ow algorithm. The problem is the accurate estimaton of the spatio{temporal derivatives of the moving image, to be used in the solution of the gradient constraint equation. We claim that the \traditional" techniques for the partial derivatives estimation can be improved by i) exploiting all the information ...

This article shows how a (linear) scale-space representation can be de ned for discrete signals of arbitrary dimension. The treatment is based upon the assumptions that (i) the scale-space representation should be de ned by convolving the original signal with a one-parameter family of symmetric smoothing kernels possessing a semi-group property, and (ii) local extrema must not be enhanced when ...