926 resultados para Prime-Producing Polynomials


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Hypothalamic paraventricular nucleus (PVN) has an important role in the regulation of water and sodium intake. Several researches described the presence of 5-HT1 receptors in the central nervous system. 5-HTIA was one of the prime receptors identified and it is found in the somatodendritic and post-synaptic forms. Therefore, the aim of this study was to investigate the participation of serotonergic 5-HT1A receptors in the PVN on the sodium intake induced by sodium depletion followed by 24 h of deprivation (injection of the diuretic furosemide plus 24 h of sodium-deficient diet). Rats (280-320 g) were submitted to the implant of cannulas bilaterally in the PVN. 5-HT injections (10 and 20 mu g/0.2 mu l) in the PVN reduced NaCl 1.8% intake. 8-OH-DPAT injections (2.5 and 5.0 fig/0.2 mu l) in the PVN also reduced NaCl 1.8% intake. pMPPF bilateral injections (5-HT1A antagonist) previously to 8-OH-DPAT injections have completely blocked the inhibitory effect over NaCl 1.8% intake. 5-HT1A antagonists partially reduced the inhibitory effect of 5-HT on NaCl 1.8% intake induced by sodium depletion. In contrast, the intake of palatable solution (2% sucrose) under body fluid-replete conditions was not changed after bilateral PVN 8-OH-DPTA injections. The results show that 5HT(1A) serotonergic mechanisms in the PVN modulate sodium intake induced by sodium loss. The finding that sucrose intake was not affected by PVN 5-HT1A activation suggests that the effects of the 5-HT1A treatments on the intake of NaCl are not due to mechanisms producing a nonspecific decrease of all ingestive behaviors. (c) 2006 Elsevier B.V. All rights reserved.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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Mice genetically selected for high (H) and low (L) antibody production (HIV-A and L-IV-A) were used in an experimental model of paracoccidioidomycosis. In a previous work, it was observed that male HIV-A animals were more susceptible to the infection due to adrenal gland damage. Male HIV-A and LIV-A animals were intravenously inoculated with Paracoccidioides brasiliensis (strain 18) and sacrificed 2, 4, 6, 8 and 10 weeks after inoculation. At each time interval, lungs and adrenals were removed to estimate recoverability of the fungus, as well as to determine Th1 (IFN-gamma, TNF-alpha) and Th2 (IL-4 and IL-10) cytokine profiles. While viable fungi recoverability from the lungs of HIV-A mice was higher after 4 and 8 weeks, there was less fungal recovery from the adrenals of LIV-A animals after the 2nd week, with total fungal elimination after the 8th week. With regard to Th2 cytokines, there was an inhibition in IL-4 production in the organs from infected animals, the extent of which varied according to the organ and the time period after initiation of infection. IL-10 production was found to be lower in both organs. Determination of Th1 cytokines revealed that IFN-gamma production increased in both organs, mainly in the adrenal of LIV-A after 8 and 10 weeks, when these animals showed a total fungal elimination. A significant difference was observed between HIV-A and LIV-A concerning TNF-alpha production in both organs and at all recovery times, in that LIV-A produced a higher level of this cytokine, mainly in the adrenal. These results may explain the high susceptibility of HIV-A to P. brasiliensis infection, is due, at least in part, to adrenal involvement. The higher production of Th1 cytokines by LIV-A in comparison to HIV-A mice may account for LIV-A resistance to P. brasiliensis infection. Our data reveal the importance of this experimental model in the study of the adrenal involvement in paracoccidioidomycosis, since this gland may be highly compromised in the patients, leading to the development of Addison's Disease.

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Let C-n(lambda)(x), n = 0, 1,..., lambda > -1/2, be the ultraspherical (Gegenbauer) polynomials, orthogonal. in (-1, 1) with respect to the weight function (1 - x(2))(lambda-1/2). Denote by X-nk(lambda), k = 1,....,n, the zeros of C-n(lambda)(x) enumerated in decreasing order. In this short note, we prove that, for any n is an element of N, the product (lambda + 1)(3/2)x(n1)(lambda) is a convex function of lambda if lambda greater than or equal to 0. The result is applied to obtain some inequalities for the largest zeros of C-n(lambda)(x). If X-nk(alpha), k = 1,...,n, are the zeros of Laguerre polynomial L-n(alpha)(x), also enumerated in decreasing order, we prove that x(n1)(lambda)/(alpha + 1) is a convex function of alpha for alpha > - 1. (C) 2002 Published by Elsevier B.V. B.V.

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We prove that the zeros of the polynomials P.. (a) of degree m, defined by Boros and Moll via[GRAPHICS]approach the lemmiscate {zeta epsilon C: \zeta(2) - 1\ = Hzeta < 0}, as m --> infinity. (C) 2004 Elsevier B.V. All rights reserved.

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We study the use of para-orthogonal polynomials in solving the frequency analysis problem. Through a transformation of Delsarte and Genin, we present an approach for the frequency analysis by using the zeros and Christoffel numbers of polynomials orthogonal on the real line. This leads to a simple and fast algorithm for the estimation of frequencies. We also provide a new method, faster than the Levinson algorithm, for the determination of the reflection coefficients of the corresponding real Szego polynomials from the given moments.

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We discuss an old theorem of Obrechkoff and some of its applications. Some curious historical facts around this theorem are presented. We make an attempt to look at some known results on connection coefficients, zeros and Wronskians of orthogonal polynomials from the perspective of Obrechkoff's theorem. Necessary conditions for the positivity of the connection coefficients of two families of orthogonal polynomials are provided. Inequalities between the kth zero of an orthogonal polynomial p(n)(x) and the largest (smallest) zero of another orthogonal polynomial q(n)(x) are given in terms of the signs of the connection coefficients of the families {p(n)(x)} and {q(n)(x)}, An inequality between the largest zeros of the Jacobi polynomials P-n((a,b)) (x) and P-n((alpha,beta)) (x) is also established. (C) 2001 Elsevier B.V. B.V. All rights reserved.

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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.

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In this paper, sharp upper limit for the zeros of the ultraspherical polynomials are obtained via a result of Obrechkoff and certain explicit connection coefficients for these polynomials. As a consequence, sharp bounds for the zeros of the Hermite polynomials are obtained.