196 resultados para Zeros of orthogonal polynomials


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Pós-graduação em Agronomia (Energia na Agricultura) - FCA

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Pós-graduação em Matemática em Rede Nacional - IBILCE

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Pós-graduação em Engenharia Elétrica - FEIS

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Employing the method of least squares and quadratic B-spline polynomials, different statistical models were tested to identify the most appropriate to model the mean trajectories of live weight and carcass yield of Nile tilapia (Oreochromis niloticus). Data of live weight (8,758) and carcass yield (2,042) of tilapias with ages between 106 and 245 days were obtained from 72 families derived from 36 males and 72 females. The sex and tank variables were considered as classificatory and the coefficients of quadratic polynomials B-spline of two to five intervals of the same size were used as covariables. According to most fit criteria used, the models with quadratic B-spline polynomial with five intervals of the same size presented the best adjustments. The increase in number of intervals of B-spline polynomial improved the fit of the polynomials to the data. The inclusion of classificatory effects from sex, tank, the interaction of these effects and the quadratic polynomial B-spline nested in this interaction indicated that, over time, each sex, grown in different tank, presented different mean trajectory, necessitating the inclusion of nesting time in the interaction sex x tank in order to avoid the under or overestimation of breeding values of the selection candidates in breeding programs of this species.

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The objective of the study was to analyze the features of the relief through the variables: maximum altitude (HM); mean altitude (Hmd); minimum altitude (Hm); altitude range (H); average slope length (CVm); minimum length of run-off (Cd) and average steepness of circular samples (I) of the Capivara River Watershed – Botucatu (SP). A total of 4 circular samples were obtained per unit of soil (Quartzipsamment alfisol oxisol - RQ, Udox - LVA and Udorthent - RL). Multivariable analysis and aerial color photographs of 2000, Brazilian Chart and Soil Chart of Botucatu city-SP were used for data analyses. Soil differentiation was performed using the Student-t Test for analyzes of orthogonal contrasts among means of the three soils and analysis of groupings and major components. The grouping analysis of the variables of relief differentiated 75% of LVA and 100% of RL and RQ soil circular samples. The most efficient parameters of relief for differentiation of soils according to their order of importance were as follows: HM, Hm, Hmd and H.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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We prove that the only Jensen polynomials associated with an entire function in the Laguerre-Polya class that are orthogonal are the Laguerre polynomials. (C) 2009 Elsevier B.V. All rights reserved.

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

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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.

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

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)