926 resultados para Prime-Producing Polynomials
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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.
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Relation between two sequences of orthogonal polynomials, where the associated measures are related to each other by a first degree polynomial multiplication (or division), is well known. We use this relation to study the monotonicity properties of the zeros of generalized orthogonal polynomials. As examples, the Jacobi, Laguerre and Charlier polynomials are considered. (c) 2005 Elsevier B.V. All rights reserved.
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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.
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We consider a connection that exists between orthogonal polynomials associated with positive measures on the real line and orthogonal Laurent polynomials associated with strong measures of the class S-3 [0, beta, b]. Examples are given to illustrate the main contribution in this paper. (c) 2006 Elsevier B.V. All rights reserved.
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We investigate polynomials satisfying a three-term recurrence relation of the form B-n(x) = (x - beta(n))beta(n-1)(x) - alpha(n)xB(n-2)(x), with positive recurrence coefficients alpha(n+1),beta(n) (n = 1, 2,...). We show that the zeros are eigenvalues of a structured Hessenberg matrix and give the left and right eigenvectors of this matrix, from which we deduce Laurent orthogonality and the Gaussian quadrature formula. We analyse in more detail the case where alpha(n) --> alpha and beta(n) --> beta and show that the zeros of beta(n) are dense on an interval and that the support of the Laurent orthogonality measure is equal to this interval and a set which is at most denumerable with accumulation points (if any) at the endpoints of the interval. This result is the Laurent version of Blumenthal's theorem for orthogonal polynomials. (C) 2002 Elsevier B.V. (USA).
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We show how Szego polynomials can be used in the theory of truncated trigonometric moment problem.
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We give some properties relating the recurrence relations of orthogonal polynomials associated with any two symmetric distributions d phi(1)(x) and d phi(2)(x) such that d phi(2)(x) = (I + kx(2))d phi(1)(x). AS applications of these properties, recurrence relations for many interesting systems of orthogonal polynomials are obtained.
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in this paper, we derive an explicit expression for the parameter sequences of a chain sequence in terms of the corresponding orthogonal polynomials and their associated polynomials. We use this to study the orthogonal polynomials K-n((lambda.,M,k)) associated with the probability measure dphi(lambda,M,k;x), which is the Gegenbauer measure of parameter lambda + 1 with two additional mass points at +/-k. When k = 1 we obtain information on the polynomials K-n((lambda.,M)) which are the symmetric Koornwinder polynomials. Monotonicity properties of the zeros of K-n((lambda,M,k)) in relation to M and k are also given. (C) 2002 Elsevier B.V. B.V. All rights reserved.
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Let (a, b) subset of (0, infinity) and for any positive integer n, let S-n be the Chebyshev space in [a, b] defined by S-n:= span{x(-n/2+k),k= 0,...,n}. The unique (up to a constant factor) function tau(n) is an element of S-n, which satisfies the orthogonality relation S(a)(b)tau(n)(x)q(x) (x(b - x)(x - a))(-1/2) dx = 0 for any q is an element of Sn-1, is said to be the orthogonal Chebyshev S-n-polynomials. This paper is an attempt to exibit some interesting properties of the orthogonal Chebyshev S-n-polynomials and to demonstrate their importance to the problem of approximation by S-n-polynomials. A simple proof of a Jackson-type theorem is given and the Lagrange interpolation problem by functions from S-n is discussed. It is shown also that tau(n) obeys an extremal property in L-q, 1 less than or equal to q less than or equal to infinity. Natural analogues of some inequalities for algebraic polynomials, which we expect to hold for the S-n-pelynomials, are conjectured.
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The culture supernatant of Escherichia coli, isolated from ostriches with diarrhea in Brazil, caused elongation in Vero cell, rounding in Chinese hamster ovary (CHO) cells and a cytoplasmic vacuolation in ostrich embryo fibroblasts (OEF), but it was not cytotoxic for chicken embryo fibroblasts (CEF). These effects were not neutralized by antiserum to cholera toxin. Polymerase chain reaction assays showed that the ostrich E.coli contained the gene encoding (eltII-A), but not those for type 1 heat-labile enterotoxin (eltA), heat-stable enterotoxins (estA, estB), verocytotoxins (stx-I, stx-II), or cytotoxic necrotizing factors (cnf 1, cnf 2). All isolates belonged to serotype O15:H8. The enteropathogenic relevance of LT-II in ostrich diarrhea remains undetermined. (C) 2004 Elsevier B.V. All rights reserved.
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Rheological studies were carried out in the fermentation broth of a polysaccharide-producing microorganism free of soil. This microorganism was designated 4B. The bacteria 4B was inoculated in the fermentation broth, which consisted of a carbon source and mineral salts, and it was incubated in a rotating agitator at 30 degreesC for 72 h at 210 rpm. A rheometer of concentric cylinders equipped with a thermostatic bath was used and the readings were taken at 25 degreesC. A study was made of the influence of the fermentation time and the readings were made after 24, 48 and 72 h of incubation, using, separately, sucrose and glucose as carbon sources. The influence of the salt concentrations was determined in each carbon source; the salts used were NaCl, KCl and CaCl2 in the concentrations of 0.4%, 1.0%, 2.0% and 3.0%. It was observed that the fermentation broth behaves as a non-Newtonian fluid and it presents pseudoplastic behaviour. Calculations were made of the flow behaviour index (n) and the consistency index (k) of the samples after 24, 48 and 72 h of fermentation, and it was observed that the 72 h sample presented higher k and consequently higher apparent viscosity. of the carbon sources used, the sucrose presented higher viscous broths after 24 and 48 h, and the glucose after 72 h of fermentation. With relation to the effect of the addition of salts, the CaCl2 presented a higher influence on the viscosity of the fermentation broths. (C) 2001 Elsevier B.V. Ltd. All rights reserved.
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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
SZEGO and PARA-ORTHOGONAL POLYNOMIALS on THE REAL LINE: ZEROS and CANONICAL SPECTRAL TRANSFORMATIONS
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)