On the powers of quasihomogeneous Toeplitz operators

Czechoslovak Mathematical Journal - We present sufficient conditions for the existence of pth powers of a quasiho-mogeneous Toeplitz operator Teisθφ, where φ is a radial polynomial...     

Eigenfunctions of the Airyʼs integral transform: Properties,numerical computations and asymptotic behaviors

This paper is devoted to the study of the spectrum of the integral operator with Airy?s kernel. We provide the reader with some efficient methods of computing the eigenfunctions and the eigenvalues of this operator. The first method is based on the use of a differential operator which commutes with this integral operator. The second method is based on a Gaussian quadrature method applied to the finite Airy?s transform. The asymptotic behavior of the eigenfunctions is studied by the use of a WKB method. Some numerical examples are given to illustrate results of this work.     

Art networks with geometrical distances

In this paper, ART networks (Fuzzy ART and Fuzzy ARTMAP) with geometrical norms are presented. The category choice of these networks is based on the L_p norm. Geometrical properties of these architectures are presented. Comparisons between this category choice and the category choice of the ART networks are illustrated. And simulation results on the databases taken from the UCI repository are performed. It will be shown that using the L_p norm is geometrically more attractive. It will operate directly on the input patterns without the need for doing any preprocessing. It should be noted that the ART architecture requires two preprocessing steps: normalization and complement coding. Simulation results on different databases show the good generalization performance of the Fuzzy ARTMAP with L_p norm compared to the performance of a typical Fuzzy ARTMAP.     

A strong consistency of a nonparametric estimate of entropy under random censorship

The purpose of this Note is to provide the rate of strong consistency for a nonparametric estimator of entropy under random censorship. We also establish an uniform-in-bandwidth consistency for this estimator. To cite this article: S. Bouzebda, I. Elhattab, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

General equation for determining the dissociation constants of polyprotic acids and bases from additive properties. Part II. Applications

Dissociation constants of some polyprotic acids and bases are determined from spectrophotometric and reversed-phase high performance liquid chromatographic data. A general equation relating additive properties of acids and bases to the pH of the solution is used for this purpose. The method is tested by applying it to the calculation of overlapping pK_as without the prerequisite of measuring the limiting values of the property for the individual species that result from the dissociation of the solute. The possibility of applying the same method to hyperpolarizability measurements is pointed out, and a procedure, based on the general equation, for obtaining the activity coefficients of the ionic species as a function of the ionic strength is also suggested.