Steerability is a useful and important property of “kernel” functions. It enables certain complicated operations involving orientation manipulation on images to be executed with high e±ciency. Thus, we focus our attention on the steerability of Hermite polynomials and their versions modulated by theGaussian functionwith di®erent powers, de ̄ned as the Hermite kernel. Certain special cases of suc...

In this paper, we propose Hermite collocation method for solving Thomas-Fermi equation that is nonlinear ordinary differential equation on semi-infinite interval. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with solution of other methods that shows the present solution is more accurate and faste...

Abstract. It is shown that an appropriate combination of methods, relevant to operational calculus and to special functions, can be a very useful tool to establish and treat a new class of Hermite and Konhauser polynomials. We explore the formal properties of the operational identities to derive a number of properties of the new class of Hermite and Konhauser polynomials and discuss the links w...

This contribution presents a review of results obtained from computations of approximate equations of motion for the Fermi-Pasta-Ulam lattice. These approximate equations are obtained as a finite-dimensional Birkhoff normal form. It turns out that in many cases, the Birkhoff normal form is suitable for application of the KAM theorem. In particular this proves Nishida’s 1971 conjecture stating t...

The Schubert cells eλ are the orbits of the Iwahori subgroup B̃, while the Birkhoff strata Sλ are the orbits of the opposite Iwahori subgroup B̃ . The cells and the strata are dual in the sense that Sλ ∩ eλ = {λ}, and the intersection is transverse. The closure of eλ is the affine Schubert variety Xλ. It has dimension l (λ), where l is the minimal length occuring in the coset λW̃I , and its cells ...

Let R be a real closed field. The Pierce-Birkhoff conjecture says that any piecewise polynomial function f on Rn can be obtained from the polynomial ring R[x1, . . . , xn] by iterating the operations of maximum and minimum. The purpose of this paper is threefold. First, we state a new conjecture, called the Connectedness conjecture, which asserts, for every pair of points α, β ∈ Sper R[x1, . . ...

— These notes are based on lectures held at the Lanzhou university (China) during a CIMPA summer school in july 2004 but benefit from recent devellopements. Our aim is to explain some normal form technics that allow to study the long time behaviour of the solutions of Hamiltonian perturbations of integrable systems. We are in particular interested with stability results. Our approach is centere...

Stationary interpolatory subdivision schemes for Hermite data that consist of function values and first derivatives are examined. A general class of Hermite-interpolatory subdivision schemes is proposed, and some of its basic properties are stated. The goal is to characterise and construct certain classes of nonlinear (and linear) Hermite schemes. For linear Hermite subdivision, smoothness cond...

In this paper we use the Birkhoff-von Neumann decomposition of the diffusion kernel to compute a polytopal measure of graph complexity. We decompose the diffusion kernel into a series of weighted Birkhoff combinations and compute the entropy associated with the weighting proportions (polytopal complexity). The maximum entropy Birkhoff combination can be expressed in terms of matrix permanents. ...