Zeros of Jacobi functions of second kind

The number of zeros in (- 1, 1) of the Jacobi function of second kind Q(n)((alpha, beta)) (x), alpha, beta > - 1, i.e. The second solution of the differential equation(1 - x(2))y (x) + (beta - alpha - (alpha + beta + 2)x)y' (x) + n(n + alpha + beta + 1)y(x) = 0,is determined for every n is an element of N and for all values of the parameters alpha > - 1 and beta > - 1. It turns out that this number depends essentially on alpha and beta as well as on the specific normalization of the function Q(n)((alpha, beta)) (x). Interlacing properties of the zeros are also obtained. As a consequence of the main result, we determine the number of zeros of Laguerre's and Hermite's functions of second kind. (c) 2005 Elsevier B.V. All rights reserved.

Monotonicity of zeros of Jacobi polynomials

Denote by x(nk)(alpha, beta), k = 1...., n, the zeros of the Jacobi polynornial P-n((alpha,beta)) (x). It is well known that x(nk)(alpha, beta) are increasing functions of beta and decreasing functions of alpha. In this paper we investigate the question of how fast the functions 1 - x(nk)(alpha, beta) decrease as beta increases. We prove that the products t(nk)(alpha, beta) := f(n)(alpha, beta) (1 - x(nk)(alpha, beta), where f(n)(alpha, beta) = 2n(2) + 2n(alpha + beta + 1) + (alpha + 1)(beta + 1) are already increasing functions of beta and that, for any fixed alpha > - 1, f(n)(alpha, beta) is the asymptotically extremal, with respect to n, function of beta that forces the products t(nk)(alpha, beta) to increase. (c) 2007 Elsevier B.V. All rights reserved.

On the behaviour of zeros of Jacobi polynomials

Denote by x(n,k)(alpha, beta) and x(n,k) (lambda) = x(n,k) (lambda - 1/2, lambda - 1/2) the zeros, in decreasing order, of the Jacobi polynomial P-n((alpha, beta))(x) and of the ultraspherical (Gegenbauer) polynomial C-n(lambda)(x), respectively. The monotonicity of x(n,k)(alpha, beta) as functions of a and beta, alpha, beta > - 1, is investigated. Necessary conditions such that the zeros of P-n((a, b)) (x) are smaller (greater) than the zeros of P-n((alpha, beta))(x) are provided. A. Markov proved that x(n,k) (a, b) < x(n,k)(α, β) (x(n,k)(a, b) > x(n,k)(alpha, beta)) for every n is an element of N and each k, 1 less than or equal to k less than or equal to n if a > alpha and b < β (a < alpha and b > beta). We prove the converse statement of Markov's theorem. The question of how large the function could be such that the products f(n)(lambda) x(n,k)(lambda), k = 1,..., [n/2] are increasing functions of lambda, for lambda > - 1/2, is also discussed. Elbert and Siafarikas proved that f(n)(lambda) = (lambda + (2n(2) + 1)/ (4n + 2))(1/2) obeys this property. We establish the sharpness of their result. (C) 2002 Elsevier B.V. (USA).

Monotonicity of zeros of Jacobi-Sobolev type orthogonal polynomials

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INEQUALITIES FOR ZEROS of JACOBI POLYNOMIALS VIA OBRECHKOFF'S THEOREM

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Asymptotics for Jacobi-Sobolev orthogonal polynomials associated with non-coherent pairs of measures

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Rational approximations of the Arrhenius integral using Jacobi fractions and gaussian quadrature

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

Ensaios em parcelas subdivididas delineados em blocos incompletos balanceados. I - Equações normais

Com o objetivo de ampliar o uso dos ensaios com parcelas subdivididas na pesquisa agropecuária, realizou-se um estudo de tais ensaios delineados em blocos incompletos balanceados. Adotou-se, para tanto, o modelo tradicionalmente usado no delineamento completo. Optou-se pela existência de correlação constante entre subparcelas distintas. A obtenção das estimativas para efeitos de blocos ocorreu como nos ensaios em blocos incompletos balanceados, enquanto que as estimativas para efeitos de tratamentos secundários e para a interação tratamentos principais x tratamentos secundários portaram-se como nos ensaios com parcelas subdivididas em blocos (completos), casualizados.

Práticas de gestão da cadeia de suprimentos e seus eventuais relacionamentos com as prioridades competitivas da produção: evidências empíricas do setor eletroeletrônico à luz de modelagem de equações estruturais

Este artigo tem como objetivo identificar as práticas de gestão da cadeia de suprimentos que estão sendo adotadas no setor eletroeletrônico brasileiro e verificar se as prioridades competitivas da produção das empresas desse setor se relacionam com a adoção de tais práticas. Desenvolveu-se uma pesquisa empírica, de cunho quantitativo, a partir da realização de uma pesquisa survey por e-mail com gerentes de empresas do setor eletroeletrônico da Associação Brasileira da Indústria Elétrica e Eletrônica. Técnicas estatísticas descritivas e multivariadas de segunda geração (modelagem de equações estruturais) foram empregadas para analisar os dados obtidos. Como principais resultados deste artigo destacam-se: a) as práticas de gestão da cadeia de suprimentos que estão sendo mais implantadas são voltadas à integração e apoio das atividades de desenvolvimento de produtos com os clientes; e b) não foram verificadas relações significativas entre as prioridades competitivas das empresas estudadas e a adoção de práticas de gestão da cadeia de suprimentos.

Jacobi script v sign-functions and discrete Fourier transforms

Properties of the Jacobi script v sign3-function and its derivatives under discrete Fourier transforms are investigated, and several interesting results are obtained. The role of modulo N equivalence classes in the theory of script v sign-functions is stressed. An important conjecture is studied. © 2006 American Institute of Physics.

Comparações entre equações de predição de consumo de capim-elefante cortado para vacas lactantes

This work aimed to compare intake prediction equations with values obtained by direct methods using chopped elephant-grass offered to crossbreed lactating cows with rumen canulas. The experimental design was a 3 x 3 Latin square (three animals and three cutting ages: 30, 45 and 60 days). The equations used for intake prediction (y) were: (1) y= -1.19 + 0.035(a+b) + 28.5c; (2) y= [%NDF on DM]*[NDF intake]/[(1- a - b)/KP+b/(c+kp)]/24; (3) y= -0.822 + 0.0748(a+b) + 40.7c and (4) equation 2 with values of intake measured directly. The predictions of NDF intake by equations were not different among treatments, instead of the difference among values measured directly: the 30 day-old had lower intake (5.29 kg/day) in relation to 45 (6.57 kg/day) and 60 (7.31 kg/day) day-old grasses. In general, equations overestimated the DM intake in relation to direct measuring (9.0 kg/cow/day), with exception of equation 3 which underestimated the intake (7.7 kg/day). The means of DM intake found by equations 1 and 2 (13.7 and 13.4 kg/cow/day, respectively) were similar between themselves and superior in relation to those found by equation 4 (9.7 kg/cow/day). The intakes measured directly were similar to those found in equation 4 and higher than those found by equation 3. The mean of rumen fill of 7.5 kg was superior to those of 5.2 kg estimated by equation. The prediction equations based on in situ degradability parameters do not supply estimates of DM intake, NDF intake and rumen fill in agreement with values obtained by direct methods.

Proposição e validações de equações para estimativa da erosividade de dois municípios do estado de São Paulo

The equations and extrapolation use to localities whose characteristics of soil and climate, even if partial, distinguish the town to which they were generated, still permeate in studies to estimate the rainfall erosivity (EI 30). This work has objective to propose and validate mathematical equations to estimate the rainfall erosivity of two cities of Sao Paulo State's. The adjusted to estimate obtaining and validate data of equations of erosivity (EI 30) according to values of coefficient of rain (Rc) were obtained from pluviographic and pluviometric rainfall data, respectively, using of distinct historical rainfall series. Mutiple comparisions test and confidence intervals were performed to compare absolute average of EI 30, pluviometric data (Pp), and Rc. The correlation between EI 30 and Rc was verified by of Pearson correlation coefficient. Test of the hypothesis of equality between population variance was used to compare the equations. Pluviometrics data of historical series rainfall data different than those that the models were generated were used to validate and to assess the performance of the equations, proposed of this study and compare them with another equation already consolidated in literature. The results show that for the conditions under which the study was conducted, the simple linear equations, shown to be the most appropriate to estimate the rainfall erosivity these two cities. According to the test of the hypothesis of equality variances between populations, the equations adjusted for each city differ statistically so that the rainfall erosivity of each city must be estimated by their respective equation.

Zeros of Jacobi-Sobolev orthogonal polynomials following non-coherent pair of measures

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Tópicos de equações diferenciais parciais elípticas

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