in a recent paper, de baets et al. have characterized the fuzzytolerance and fuzzy equivalence relations that a given strict order relation iscompatible with. in this paper, we generalize this characterization by consideringan arbitrary (crisp) relation instead of a strict order relation, while payingattention to the particular cases of a reflexive or irreflexive relation. the reasoninglargely ...

— We present necessary and su‰cient conditions to guarantee that at least one solution of an infinite dimensional stochastic di¤erential equation, which starts from a regular closed subset K of an Hilbert space, remains in K for all times.

We consider global attractors Af of dissipative parabolic equations ut = uxx + f(x; u; ux) on the unit interval 0 x 1 with Neumann boundary conditions. A permutation f is de ned by the two orderings of the set of (hyperbolic) equilibrium solutions ut 0 according to their respective values at the two boundary points x = 0 and x = 1: We prove that two global attractors, Af and Ag, are globally C0...

is pocket-sized handbook off ers a concise approach to patients presenting with a variety of neurological emergencies. Each chapter is co-authored by an emergency medicine physician and a subspecialist in the area being covered (usually a neurologist). In this way, it provides a balance of both perspectives – neither neglecting the basic issues around initial stabilization and diff erential dia...

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...

This paper is devoted to the study of periodic boundary value problems for nonlinear third order di¤erential equations subjected to impulsive e¤ects. We provide su¢ cient conditions on the nonlinearity and the impulse functions that guarantee the existence of at least one solution. Our approach is based on a priori estimates, the method of upper and lower solutions combined with an iterative te...

Multigrid methods are studied for the solution of linear systems resulting from the 9-point discretization of a general linear second-order elliptic partial di erential equation in two dimensions. The rate of convergence of standard multigrid methods often deteriorates when the coe cients in the di erential equation are discontinuous, or when dominating rst-order terms are present. These di cul...

The problem of learning qualitative models of physical systems from observations of its behaviour has been addressed by several researchers in recent years. Most current techniques limit themselves to learning a single qualitative di erential equation to model the entire system. However, many systems have several qualitative differential equations underlying them. In this paper, we present an a...

We propose solving the inverse eigenvalue problem for symmetric nonnegative matrices by means of a di erential equation. If the given spectrum is feasible, then a symmetric nonnegative matrix can be constructed simply by following the solution curve of the di erential system. The choice of the vector eld is based on the idea of minimizing the distance between the cone of symmetric nonnegative m...

This paper describes the design philosophy behind the recent replacement of the NAG Ordinary Di erential Equation (ODE) sti integrators. This replacement was is intended to update the ODE chapter algorithmically but, more importantly in the context of this paper, it provides a more exible interface than has been available in the past. This interface is designed to permit a wide variety of probl...