Szegö polynomials: quadrature rules on the unit circle and on [-1, 1]

We consider some of the relations that exist between real Szegö polynomials and certain para-orthogonal polynomials defined on the unit circle, which are again related to certain orthogonal polynomials on [-1, 1] through the transformation x = (z1/2+z1/2)/2. Using these relations we study the interpolatory quadrature rule based on the zeros of polynomials which are linear combinations of the orthogonal polynomials on [-1, 1]. In the case of any symmetric quadrature rule on [-1, 1], its associated quadrature rule on the unit circle is also given.

Breeding value accuracy estimates for growth traits using random regression and multi-trait models in Nelore cattle

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

Effects of a probiotic soy product and physical exercise on formation of pre-neoplastic lesions in rat colons in a short-term model of carcinogenic

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

Polynomials generated by a three term recurrence relation: bounds for complex zeros

This paper deals with the zeros of polynomials generated by a certain three term recurrence relation. The main objective is to find bounds, in terms of the coefficients of the recurrence relation, for the regions where the zeros are located. In most part, the zeros are explored through an Eigenvalue representation associated with a corresponding Hessenberg rnatrix. Applications to Szego polynomials, para-orthogonal polynomials and polynomials with non-zero complex coefficients are considered. (C) 2004 Elsevier B.V. All rights reserved.

L-orthogonal polynomials associated with related measures

A positive measure psi defined on [a, b] such that its moments mu(n) = integral(b)(a)t(n) d psi(t) exist for n = 0, +/-1, +/-2. can be called a strong positive measure on [a, b] When 0 <= a < b <= infinity the sequence of polynomials {Q(n)} defined by integral(b)(a) t(-n+s) Q(n)(t) d psi(t) = 0, s = 0, ., n - 1, exist and they are referred here as L-orthogonal polynomials We look at the connection between two sequences of L-orthogonal polynomials {Q(n)((1))} and {Q(n)((0))} associated with two closely related strong positive measures and th defined on [a, b]. To be precise, the measures are related to each other by (t - kappa) d psi(1)(t) = gamma d psi(0)(t). where (t - kappa)/gamma is positive when t is an element of (n, 6). As applications of our study. numerical generation of new L-orthogonal polynomials and monotonicity properties of the zeros of a certain class of L-orthogonal polynomials are looked at. (C) 2010 IMACS Published by Elsevier B V All rights reserved

Dynamics of follicle populations and gonadotropin concentrations in fillies age two to ten months

Follicle populations and concentrations of circulating gonadotropins were studied during age 2-10 months in 10 spring-born pony fillies. Blood sampling and ultrasound scanning were done every 4 days and daily for four 30 day periods. During 5-12 weeks, FSH concentrations were lower in 6 fillies with follicles greater than or equal to 6 mm (mean +/- s.e. 1.4 +/- 0.1 ng/ml) than in 4 fillies with follicles <6 mm (2.8 + 0.3 ng/ml). The diameters and numbers of follicles and gonadotropin concentrations increased progressively during age 2-4 months. A plateau in follicle activity and reduced levels of gonadotropins occurred during 5-7 months. During 8-10 months, follicles grew to >10 mm and gonadotropin concentrations increased. Waves of follicular growth were identified during the 30 day periods by significant increases in the diameter of the 10 largest follicles. The waves did not partition into dominant and subordinate follicles. Results indicated an initial postnatal period of negative ovarian feedback, temporally related changes in gonadotropins and follicles for months 3-10, and development of follicles in waves.

Companion orthogonal polynomials: some applications

In this paper the recurrence relations of symmetric orthogonal polynomials whose measures are related to each other in a certain way are considered. Many of the relations satisfied by the coefficients of the recurrence relations are exposed. The results are applied to obtain, for example, information regarding certain Sobolev orthogonal polynomials and regarding the measures of certain orthogonal polynomial sequences with twin periodic recurrence coefficients. (C) 2001 IMACS. Published by Elsevier B.V. B.V. All rights reserved.

Characterization and quantification of blood cells from the umbilical cord of dogs

Background: Models for the study of hematopoietic stem cells in dogs provide important information for bone marrow transplantation in humans. Recent studies have reported the importance of human umbilical cord blood (UCB) as an alternative to allogenic bone marrow for hematopoietic reconstitution. However, there are no studies on the UCB cells of dogs. Objective: the aim of this experiment was to characterize and quantify the blood cells of the umbilical cord of dogs. Methods: the blood of the umbilical cord of 20 neonatal dogs, delivered at term, with a median gestation time of 58 days, was collected with a 5-mL syringe containing EDTA. Total RBC, WBC, and platelet counts, HCT, hemoglobin (Hgb) concentration, and RBC indices were determined using an automatic cell counter. The differential leukocyte count was determined manually in blood smears stained with May-Grunwald-Giemsa. Reticulocyte percentages were determined on blood smears stained with brilliant cresyl blue and counterstained with May-Grunwald Giemsa. Results: the MCHC and numbers of RBCs, WBCs, neutrophils, and eosinophils in UCB were lower as compared with reference values for the peripheral blood of healthy neonatal and adult dogs; whereas, the MCV and reticulocyte percentages were higher. Conclusion: Erythrocyte macrocytosis and hypochromasia in UCB were consistent with marked reticulocytosis and indicative of high erythropoietic activity. The results of this study are an important first step in the characterization of UCB from neonatal dogs.

Dynamic modeling and simulation of a flexible robotic manipulator

This work focuses on the dynamic modeling of a flexible robotic manipulator with two flexible links and two revolute joints, which rotates in the horizontal plane. The dynamic equations are derived using the Newton-Euler formulation and the finite element method, based on elementary beam theory. Computer simulation results are presented to illustrate this study. The dynamic model becomes necessary for use in future design and control applications.

Multivariate sobolev-type orthogonal polynomials

Multivariate orthogonal polynomials associated with a Sobolev-type inner product, that is, an inner product defined by adding to a measure the evaluation of the gradients in a fixed point, are studied. Orthogonal polynomials and kernel functions associated with this new inner product can be explicitly expressed in terms of those corresponding with the original measure. We apply our results to the particular case of the classical orthogonal polynomials on the unit ball, and we obtain the asymptotics of the kernel functions. © 2011 Universidad de Jaén.

Quasi-exactly-solvable confining solutions for spin-1 and spin-0 bosons in (1+1)-dimensions with a scalar linear potential

We point out a misleading treatment in the recent literature regarding confining solutions for a scalar potential in the context of the Duffin-Kemmer-Petiau theory. We further present the proper bound-state solutions in terms of the generalized Laguerre polynomials and show that the eigenvalues and eigenfunctions depend on the solutions of algebraic equations involving the potential parameter and the quantum number. (C) 2014 Elsevier Inc. All rights reserved.

Para-orthogonal polynomials from constant Verblunsky coefficients

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Growth and mortality parameters of Paranchurus brasiliensis (Scianidae) captured as bycatch in southeastern of Brazil

The present work provides preliminary informations on the growth and mortality of Paralonchurus brasiliensis captured as a bycatch in the inner shelf of São Paulo Southeastern Brazil. The samplings were carried out using a shrimp fishery trawl. After trawling, the specimens were separated from the other organisms and the fish size and numbers of individuals captured were recorded. A total of 5,943 specimens ranging from 3.6 to 19.9 cm in standard length were sampled.

Estimação de parâmetros genéticos para peso do nascimento aos 550 dias de idade para animais da raça Tabapuã utilizando-se modelos de regressão aleatória

Foram utilizados 21.762 registros de peso do nascimento aos 550 dias de idade de 4.221 animais para estimativa das funções de covariância empregando modelos de regressão aleatória. Os modelos incluíram, como aleatórios, os efeitos genéticos aditivo direto e materno, de ambiente permanente de animal e de ambiente permanente materno e, como fixos, os efeitos de grupo contemporâneo, a idade da vaca ao parto (linear e quadrático) e o polinômio ortogonal de Legendre da idade do animal (regressão cúbica), como covariáveis. As variâncias residuais foram modeladas por uma função de variâncias com ordens de 2 a 6. Análises com polinômios ortogonais de diversas ordens foram realizadas para os efeitos genético aditivo direto, genético aditivo materno, de ambiente permanente de animal e de ambiente permanente materno. Os modelos foram comparados pelos critérios de informação Bayesiano de Schwarz (BIC) e Akaike (AIC). O melhor modelo indicado por todos os critérios foi o que considerou o efeito genético aditivo direto ajustado por um polinômio cúbico, o efeito genético materno ajustado por um polinômio quadrático, o efeito de ambiente permanente de animal ajustado por polinômio quártico e o efeito de ambiente permanente materno ajustado por polinômio linear. As estimativas de herdabilidade para o efeito direto foram maiores no início e no final do período estudado, com valores de 0,28 ao nascimento, 0,21 aos 240 dias e 0,24 aos 550 dias de idade. As estimativas de herdabilidade materna foram maiores aos 160 dias de idade (0,10) que nas demais fases do crescimento. As correlações genéticas variaram de moderadas a altas, diminuindo conforme o aumento da distância entre as idades. Maior eficiência na seleção para peso pode ser obtida considerando os pesos pós-desmama, período em que as estimativas de variância genética e herdabilidade foram superiores.

Random regression analyses using B-splines functions to model growth from birth to adult age in Canchim cattle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)