Blumenthal's theorem for Laurent orthogonal polynomials

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).

Szego polynomials and the truncated trigonometric moment problem

We show how Szego polynomials can be used in the theory of truncated trigonometric moment problem.

Companion orthogonal polynomials

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.

Chain sequences and symmetric generalized orthogonal polynomials

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.

Chebyshev-Laurent polynomials and weighted approximation

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.

Completeness of coherent states associated with self-similar potentials and Ramanujan's integral extension of the beta function

A decomposition of identity is given as a complex integral over the coherent states associated with a class of shape-invariant self-similar potentials. There is a remarkable connection between these coherent states and Ramanujan's integral extension of the beta function.

Carcass and meat quality traits of wild boar (Sus scrofa s. L.) with 2n=36 karyotype compared to those of phenotypically similar crossbreeds (2n=37 and 2n=38) raised under same farming conditions. 1. Carcass quantity and meat dressing

The aim of this study was to compare wild boar (chromosomal number 2n = 36) to phenotypically similar animals of 2n = 37 and 2n = 38 chromosomes (crossbreeds) with respect to live weight, carcass yield, meat yield, fat and weight of inner organs. All animals were born and raised on the same farm and slaughtered at 39 weeks. The final live weight of wild boar 2n = 36 was significantly lower (47.2 kg) as compared to crossbreeds (80.0 kg). Animals 2n = 36 had more carcass yields (65.5%) than 2n = 37 karyotype (64.9%) and 2n = 38 (64.4%). Wild boar had the highest yields for the cuts with bones and boneless cuts compared to crossbreeds. Therefore, variations in karyotype are accompanied by differences in some carcass quantitative traits, i.e., 2n = 36 grow and fatten slower than crossbreeds 2n = 37 and 2n = 38. (c) 2008 Elsevier Ltd. All rights reserved.

Similar anxiolytic-like effects following intra-amygdala infusions of benzodiazepine receptor agonist and antagonist: Evidence for the release of an endogenous benzodiazepine inverse agonist in mice exposed to elevated plus-maze test

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Zeros of orthogonal polynomials generated by canonical perturbations of measures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

SZEGO and PARA-ORTHOGONAL POLYNOMIALS on THE REAL LINE: ZEROS and CANONICAL SPECTRAL TRANSFORMATIONS

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On a moment problem associated with Chebyshev polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Creatine does not promote hypertrophy in skeletal muscle in supplemented compared with nonsupplemented rats subjected to a similar workload

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

Squeezed states, generalized Hermite polynomials and pseudo-diffusion equation

We show that the wavefunctions 〈pq; λ|n〈, of the harmonic oscillator in the squeezed state representation, have the generalized Hermite polynomials as their natural orthogonal polynomials. These wavefunctions lead to generalized Poisson Distribution Pn(pq;λ), which satisfy an interesting pseudo-diffusion equation: ∂Pnp,q;λ) ∂λ= 1 4 [ ∂2 ∂p2-( 1 λ2) ∂2 ∂q2]P2(p,q;λ), in which the squeeze parameter λ plays the role of time. Th entropies Sn(λ) have minima at the unsqueezed states (λ=1), which means that squeezing or stretching decreases the correlation between momentum p and position q. © 1992.

During the initiation of fermentation overexpression of hexokinase PII in yeast transiently causes a similar deregulation of glycolysis as deletion of Tps1

In the yeast Saccharomyces cerevisiae a novel control exerted by TPS1 (=GGS1=FDP1=BYP1=CIF1=GLC6=TSS1)-encoded trehalose-6-phosphate synthase, is essential for restriction of glucose influx into glycolysis apparently by inhibiting hexokinase activity in vivo. We show that up to 50-fold overexpression of hexokinase does not noticeably affect growth on glucose or fructose in wild-type cells. However, it causes higher levels of glucose-6-phosphate, fructose-6-phosphate and also faster accumulation of fructose-1,6-bisphosphate during the initiation of fermentation. The levels of ATP and Pi correlated inversely with the higher sugar phosphate levels. In the first minutes after glucose addition, the metabolite pattern observed was intermediate between those of the tps1Δ mutant and tile wild-type strain. Apparently, during the start-up of fermentation hexokinase is more rate-limiting in the first section of glycolysis than phosphofructokinase. We have developed a method to measure the free intracellular glucose level which is based on the simultaneous addition of D-glucose and an equal concentration of radiolabelled L-glucose. Since the latter is not transported, the free intracellular glucose level can be calculated as the difference between the total B-glucose measured (intracellular + periplasmic/extracellular) and the total L-glucose measured (periplasmic/extracellular). The intracellular glucose level rose in 5 min after addition of 100 mM-glucose to 0.5-2 mM in the wild-type strain, ± 10 mm in a hxk1Δ hxk2Δ glk1Δ and 2-3 mM in a tps1Δ strain. In the strains overexpressing hexokinase PII the level of free intracellular glucose was not reduced. Overexpression of hexokinase PII never produced a strong effect on the rate of ethanol production and glucose consumption. Our results show that overexpression of hexokinase does not cause the same phenotype as deletion of Tps1. However, it mimics it transiently during the initiation of fermentation. Afterwards, the Tps1-dependent control system is apparently able to restrict Properly up to 50-fold higher hexokinase activity.