In this paper we show how to construct the coupled (multicomponent) Harry Dym (cHD) hierarchy from classical Stäckel separable systems. Both nonlocal and purely di¤erential parts of hierarchies are obtained. We also construct various classes of solutions of cHD hierarchy from solutions of corresponding Stäckel systems.

A persistence theorem for xed points of a parameterized family of maps is specialized to give a method for detecting the existence of persistent periodic solutions of perturbed systems of di erential equa tions in particular systems of weakly coupled planar oscillators An application is make to the problem of synchronization of two detuned and weakly inductively coupled van der Pol oscillators

Comparative analysis of two ideologically distinct approaches in the theory of fuzzy di"erential equations is given. Domains of applications, advantages and shortcomings of those approaches are described. New de2nitions of solutions to fuzzy di"erential equations are proposed. c © 2002 Elsevier Science B.V. All rights reserved.

We consider the construction of geometric integrators in the class of RKMK methods. Any di erential equation in the form of an in nitesimal generator on a homogeneous space is shown to be locally equivalent to a di erential equation on the Lie algebra corresponding to the Lie group acting on the homogenous space. This way we obtain a distinction between the coordinate-free phrasing of the di er...

The method of exterior di®erential systems is applied to the problem of ̄nding propagating singular solutions to Maxwell s equations Fresnel ray and wave surfaces are computed for systems that are not restricted to the topology imposed by the symmetries of the Lorentz transformations. The methods distinguish the measurable polarization phase di®erences between global behavior in optically active...

We present a block cipher that has the best performance of all 64-bit block ciphers with the smallest proven di erential/linear probability 2 62 using the structure proposed by Matsui. One of features of his methodology is to use some power functions in GF (2 n ) with di erent n that are resistant to di erential and linear attacks. In this paper we discuss how to combine power functions x k in ...

Applying 3D di erential operators to extract point landmarks from medical images generally su ers from false detections. A considerable number of these false detections is caused by neighboring structures that are included in the region-of-interest (ROI) speci ed by the observer. The main contributions of this paper are two di erent approaches to reducing false detections resulting from neighbo...

A system of a parabolic partial di erential equation coupled with ordinary di erential inclusions that arises from a closed-loop control problem for a thermodynamic process governed by the Allen-Cahn di usion reaction model is studied. A feedback law for the closed-loop control is proposed and implemented in the case of a nite number of control devices located inside the process domain basing o...

We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population of discrete individuals characterized by one or several adaptive traits. The population is modelled as a stochastic point process whose generator captures t...

Quantitative analysis of dynamical processes requires a precise estimation of the optical ow eld from image sequences. Most articles evaluating the performance of optical ow techniques focus on the initial formulation of the minimization problem to solve the ill posed brightness change constraint equation. Performance di erences are attributed to slight di erences in the formulation of the mini...