Monotonicity of zeros of Laguerre polynomials

Denote by X(nk)(alpha), k = 1, ..., n, the zeros of the Laguerre polynomial L(n)((alpha))(X). We establish monotonicity with respect to the parameter at of certain functions involving X(nk)(alpha). As a consequence we obtain sharp upper bounds for the largest zero of L(n)((alpha))(X). (C) 2009 Elsevier B.V. All rights reserved.

INEQUALITIES FOR ZEROS of JACOBI POLYNOMIALS VIA OBRECHKOFF'S THEOREM

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Distances between critical points and midpoints of zeros of hyperbolic polynomials

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The Wigner function associated with the Rogers-Szego polynomials

A Wigner function associated with the Rogers-Szego polynomials is proposed and its properties are discussed. It is shown that from such a Wigner function it is possible to obtain well-behaved probability distribution functions for both angle and action variables, defined on the compact support -pi less than or equal to theta < pi, and for m greater than or equal to 0, respectively. The width of the angle probability density is governed by the free parameter q characterizing the polynomials.

Orthogonal projections and bootstrap resampling procedures in the study of infraspecific variation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Univariate and bivariate distribution of growth traits in beef buffaloes from Brazil

The aim of this study was to analyze the weight at birth (BW) and adjusted at 205 (W205), 365 (W365) and 550 (W55O) days in beef buffaloes from Brazil, using two approaches: parametric, by normal distribution, and non-parametric, by kernel function, and thus estimating the genetic, environmental and phenotypic correlation among traits. Information of 5,169 animals at birth (BW), 3,792 at 205 days (W205), 3.883 at 365 days (W365) and 1,524 at 550 days of age (W550) were used. The birth weight distribution presented an evident discrepancy in relation to the normal distribution. However, W205, W365 and W550 presented normal distributions. The birth weight presented weak genetic, environmental, and phenotypic associations with the other weight measurements. on the other hand, the weight traits at 205, 365, 550 days of age showed a high genetic correlation.

Szego polynomials and the truncated trigonometric moment problem

We show how Szego polynomials can be used in the theory of truncated trigonometric moment problem.

Optimization of Radial Basis Function neural network employed for prediction of surface roughness in hard turning process using Taguchi's orthogonal arrays

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On a moment problem associated with Chebyshev polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A single statistic for monitoring the covariance matrix of bivariate processes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Additive genetic relationship of longevity with fertility and production traits in Nellore cattle based on bivariate models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Deformed Gaussian orthogonal ensemble and the statistical fluctuations in the spectra of the quartic oscillator

The nearest-neighbor spacing distributions proposed by four models, namely, the Berry-Robnik, Caurier-Grammaticos-Ramani, Lenz-Haake, and the deformed Gaussian orthogonal ensemble, as well as the ansatz by Brody, are applied to the transition between chaos and order that occurs in the isotropic quartic oscillator. The advantages and disadvantages of these five descriptions are discussed. In addition, the results of a simple extension of the expression for the Dyson-Mehta statistic Δ3 are compared with those of a more popular one, usually associated with the Berry-Robnik formalism. ©1999 The American Physical Society.

Inferences about the coefficient of correlation in the standard bivariate normal distribution

The study of the association between two random variables that have a joint normal distribution is of interest in applied statistics; for example, in statistical genetics. This article, targeted to applied statisticians, addresses inferences about the coefficient of correlation (ρ) in the bivariate normal and standard bivariate normal distributions using likelihood, frequentist, and Baycsian perspectives. Some results are surprising. For instance, the maximum likelihood estimator and the posterior distribution of ρ in the standard bivariate normal distribution do not follow directly from results for a general bivariate normal distribution. An example employing bootstrap and rejection sampling procedures is used to illustrate some of the peculiarities.

Nonnegative trigonometric polynomials

An extremal problem for the coefficients of sine polynomials, which are nonnegative in [0,π] , posed and discussed by Rogosinski and Szego is under consideration. An analog of the Fejér-Riesz representation of nonnegative general trigonometric and cosine polynomials is proved for nonnegative sine polynomials. Various extremal sine polynomials for the problem of Rogosinski and Szego are obtained explicitly. Associated cosine polynomials k n (θ) are constructed in such a way that { k n (θ) } are summability kernels. Thus, the L p , pointwise and almost everywhere convergence of the corresponding convolutions, is established. © 2002 Springer-Verlag New York Inc.