A realization of the q-deformed harmonic oscillator: rogers-Szegö and Stieltjes-Wigert polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On linear combinations of L-orthogonal polynomials associated with distributions belonging to symmetric classes

This paper deals with the classes S-3(omega, beta, b) of strong distribution functions defined on the interval [beta(2)/b, b], 0 < beta < b <= infinity, where 2 omega epsilon Z. The classification is such that the distribution function psi epsilon S-3(omega, beta, b) has a (reciprocal) symmetry, depending on omega, about the point beta. We consider properties of the L-orthogonal polynomials associated with psi epsilon S-3(omega, beta, b). Through linear combination of these polynomials we relate them to the L-orthogonal polynomials associated with some omega epsilon S-3(1/2, beta, b). (c) 2004 Elsevier B.V. All rights reserved.

Random regression models using Legendre polynomials or linear splines for test-day milk yield of dairy Gyr (Bos indicus) cattle

Studies investigating the use of random regression models for genetic evaluation of milk production in Zebu cattle are scarce. In this study, 59,744 test-day milk yield records from 7,810 first lactations of purebred dairy Gyr (Bos indicus) and crossbred (dairy Gyr × Holstein) cows were used to compare random regression models in which additive genetic and permanent environmental effects were modeled using orthogonal Legendre polynomials or linear spline functions. Residual variances were modeled considering 1, 5, or 10 classes of days in milk. Five classes fitted the changes in residual variances over the lactation adequately and were used for model comparison. The model that fitted linear spline functions with 6 knots provided the lowest sum of residual variances across lactation. On the other hand, according to the deviance information criterion (DIC) and Bayesian information criterion (BIC), a model using third-order and fourth-order Legendre polynomials for additive genetic and permanent environmental effects, respectively, provided the best fit. However, the high rank correlation (0.998) between this model and that applying third-order Legendre polynomials for additive genetic and permanent environmental effects, indicates that, in practice, the same bulls would be selected by both models. The last model, which is less parameterized, is a parsimonious option for fitting dairy Gyr breed test-day milk yield records. © 2013 American Dairy Science Association.

Perturbations on the antidiagonals of Hankel matrices

Given a strongly regular Hankel matrix, and its associated sequence of moments which defines a quasi-definite moment linear functional, we study the perturbation of a fixed moment, i.e., a perturbation of one antidiagonal of the Hankel matrix. We define a linear functional whose action results in such a perturbation and establish necessary and sufficient conditions in order to preserve the quasi-definite character. A relation between the corresponding sequences of orthogonal polynomials is obtained, as well as the asymptotic behavior of their zeros. We also study the invariance of the Laguerre-Hahn class of linear functionals under such perturbation, and determine its relation with the so-called canonical linear spectral transformations. © 2013 Elsevier Ltd. All rights reserved.

Interpretação eletrostática e zeros de polinômios

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Random regression models to estimate genetic parameters for milk production of Guzerat cows using orthogonal Legendre polynomials

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

Goppa codes through polynomials of B[X;(1/2^2)Z_0] and its decoding principle

In this paper, we present a decoding principle for Goppa codes constructed by generalized polynomials, which is based on modified Berlekamp-Massey algorithm. This algorithm corrects all errors up to the Hamming weight $t\leq 2r$, i.e., whose minimum Hamming distance is $2^{2}r+1$.

Zero sets of bivariate Hermite polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Comparative study between powers of sigmoid functions, MLP-backpropagation and polynomials in function approximation problems

Function approximation is a very important task in environments where the computation has to be based on extracting information from data samples in real world processes. So, the development of new mathematical model is a very important activity to guarantee the evolution of the function approximation area. In this sense, we will present the Polynomials Powers of Sigmoid (PPS) as a linear neural network. In this paper, we will introduce one series of practical results for the Polynomials Powers of Sigmoid, where we will show some advantages of the use of the powers of sigmiod functions in relationship the traditional MLP-Backpropagation and Polynomials in functions approximation problems.

Estimation of genetic parameters for partial egg production periods by means of random regression models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Models for the analysis of growth curves for rearing tinamous (Rhynchotus rufescens) in captivity

Growth curves models provide a visual assessment of growth as a function of time, and prediction body weight at a specific age. This study aimed at estimating tinamous growth curve using different models, and at verifying their goodness of fit. A total number 11,639 weight records from 411 birds, being 6,671 from females and 3,095 from males, was analyzed. The highest estimates of a parameter were obtained using Brody (BD), von Bertalanffy (VB), Gompertz (GP,) and Logistic function (LG). Adult females were 5.7% heavier than males. The highest estimates of b parameter were obtained in the LG, GP, BID, and VB models. The estimated k parameter values in decreasing order were obtained in LG, GP, VB, and BID models. The correlation between the parameters a and k showed heavier birds are less precocious than the lighter. The estimates of intercept, linear regression coefficient, quadratic regression coefficient, and differences between quadratic coefficient of functions and estimated ties of quadratic-quadratic-quadratic segmented polynomials (QQQSP) were: 31.1732 +/- 2.41339; 3.07898 +/- 0.13287; 0.02689 +/- 0.00152; -0.05566 +/- 0.00193; 0.02349 +/- 0.00107, and 57 and 145 days, respectively. The estimated predicted mean error values (PME) of VB, GP, BID, LG, and QQQSP models were, respectively, 0.8353; 0.01715; -0.6939; -2.2453; and -0.7544%. The coefficient of determination (RI) and least square error values (MS) showed similar results. In conclusion, the VB and the QQQSP models adequately described tinamous growth. The best model to describe tinamous growth was the Gompertz model, because it presented the highest R-2 values, easiness of convergence, lower PME, and the easiness of parameter biological interpretation.

Random regressions models to describe the genetic variation of milk yield over multiple parities in Buffaloes

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

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

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

Effects of sex and age on genotype x environment interaction for beef cattle body weight studied using reaction norm models

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)