We consider a family of matrix valued orthogonal polynomials obtained by Pacharoni and Tirao in connection with spherical functions for the pair (SU(N + 1), U(N)); see [I. Pacharoni and J. A. Tirao, Constr. Approx., 25 (2007), pp. 177–192]. After an appropriate conjugation, we obtain a new family of matrix valued orthogonal polynomials where the corresponding block Jacobi matrix is stochastic a...

In this paper a new method for adaptive synthesis of a smooth orthogonal wavelet, using fast neural network and genetic algorithm, is introduced. Orthogonal lattice structure is presented. A new method of supervised training of fast neural network is introduced to synthesize a wavelet with desired energy distribution between output signals from low–pass and high–pass filters on subsequent level...

In the theory of orthogonal polynomials, sum rules are remarkable relationships between a functional defined on a subset of all probability measures involving the reverse KullbackLeibler divergence with respect to a particular distribution and recursion coefficients related to the orthogonal polynomial construction. Killip and Simon (Killip and Simon (2003)) have given a revival interest to thi...

the built up layer thickness in secondary deformation zone is one of the important parameters in metal cutting process. the built up layer (bul) is formed in second deformation zone near the tool-chip interface in the back of the chip. this parameter influences the tool life and machined surface quality. this bul should not be confused with the built up edge (bue). the deformation of the bul in...

The aim of this paper is to show that for a wide class of orthogonal poly-nomials (including the classical polynomials of Hermite, Laguerre and Jacobi) there is a common universal asymptotics of root separation. We emphasize that we discuss below the asymptotic character of root separation, not the limiting distribution of roots. Let us consider a family of orthogonal polynomials fP n (u)g 1 n=...

Novel time-harmonic beam fields have been recently obtained by utilizing a non-orthogonal coordinate system which is a priori matched to the field’s planar linearly-phased Gaussian aperture distribution. These waveobjects were termed tilted Gaussian beams. The present investigation is concerned with parameterization of these time-harmonic tilted Gaussian beams and of the wave phenomena associat...

In this paper, we develop a new approximation for nonstationary multiserver queues with abandonment. Our method uses the Poisson–Charlier polynomials, which are a discrete orthogonal polynomial sequence that is orthogonal with respect to the Poisson distribution. We show that by appealing to the Poisson–Charlier polynomials that we can estimate the mean, variance, and probability of delay of ou...

We characterize the probability distributions of finite all order moments having generating functions for orthogonal polynomials of ultraspherical type. 1. Motivation: Meixner families There is a one to one correspondance between probability distributions on the real line and polynomials of a one variable satisfying a three-terms recurrence relation subject to some positive conditions ([9]). Th...