in this paper, a new and ecient approach is applied for numerical approximationof the linear dierential equations with variable coecients based on operational matriceswith respect to hermite polynomials. explicit formulae which express the hermite expansioncoecients for the moments of derivatives of any dierentiable function in terms of theoriginal expansion coecients of the function itse...

This paper surveys recent results on the classi cation of di erential invari ants of transformation groups and their applications to invariant di erential equations and variational problems Consider a group of transformations acting on a jet space coordinatized by the inde pendent variables the dependent variables and their derivatives Scalar functions which are not a ected by the group transfo...

Degenerate parabolic equations of Kolmogorov type occur in many areas of analysis and applied mathematics. In their simplest form these equations were introduced by Kolmogorov in 1934 to describe the probability density of the positions and velocities of particles but the equations are also used as prototypes for evolution equations arising in the kinetic theory of gases. More recently equation...

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This paper considers the ®xed-structure, discrete-time mixed H2=H1 controller synthesis problem in the delta operator (di€ erence operator) framework. The di€ erential operator and shift operator versions of the problem are reviewed for comparison, and necessary conditions are derived for all three formulations. A quasi-Newton/continuation algorithm is then used to obtain approximate solutions ...

In this contribution, we are concerned with the detection and re ned localization of 3D point landmarks. We propose multi-step di erential procedures which are generalizations of an existing two-step procedure for subpixel localization of 2D point landmarks. This two-step procedure combines landmark detection by applying a di erential operator with re ned localization through a di erential edge...

The estimation of camera egomotion is an old problem in computer vision. Since the 1980s, many approaches based on both the discrete and the di#erential epipolar constraint have been proposed. The discrete case is used mainly in self-calibrated stereoscopic systems, whereas the di#erential case deals with a single moving camera. This article surveys several methods for 3D motion estimation unif...

In this study we analyze a non-overlapping domain decomposition method for the solution of elliptic Partial Di erential Equation (PDE) problems. This domain decomposition method involves the solution of Dirichlet and Neumann PDE problems on each subdomain, coupled with smoothing operations on the interfaces of the subdomains. The convergence analysis of the method at the di erential equation le...

The existence, uniqueness, and global exponential stability of traveling wave solutions of a class of nonlinear and nonlocal evolution equations are established. It is assumed that there are two stable equilibria so that a tr aveling wave is a solution that connects them. A basic assumption is the comparison principle: a smaller initial value produces a smaller solution. When applied to di eren...

We study some classes of generalized a¢ ne functions, using a generalized di¤erential. We study some properties and characterizations of these classes and we devise some characterizations of solution sets of optimization problems involving such functions or functions of related classes. Key words: colinvex, colin…ne, generalized di¤erential, optimization problem, protoconvex function, pseudocon...