The e¢ cient and accurate calculation of sensitivities of the price of …nancial derivatives with respect to perturbations of the parameters in the underlying model, the so called ‘Greeks’, remains a great practical challenge in the derivative industry. This is true regardless of whether methods for partial di¤erential equations or stochastic di¤erential equations (Monte Carlo techniques) are be...

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.

The suitability of methods from multidimensional systems theory and digital signal processing for the e cient simulation of time and space dependent problems has already been demonstrated. Properly chosen functional transformations for the time and space coordinates turn a partial di erential equation into a transfer function description of a multidimensional continuous system. It serves as the...

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...

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 ...

|This paper presents the investigations in the electric performance of di¬erential signalling transmission lines used for high speed integrated circuits (IC’s) and boards by using the parallelized ­ nite-di¬erence time-domain (FDTD) method. The FDTD method is ­ rstly parallelized with single-program multipledata (SPMD) architecture using the MPI protocol and experimentally validated. The key el...

In this work we consider the problem of control of mechanical systems subject to unilateral constraints. Impulsive forces arise whenever the constraints become active and these forces give rise to nonsmooth dynamics. The dynamics of the system is de ned by a set of di erential equations with discontinuous righthand side using Hamilton's equations of motion. A nonlinear transformation is applied...

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...

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...