Polinômios de Szegö e análise de frequência

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Polinômios para-ortogonais e análise de freqüência

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On Connection, Linearization and Duplication Coefficients of Classical Orthogonal Polynomials

In this work, we have mainly achieved the following: 1. we provide a review of the main methods used for the computation of the connection and linearization coefficients between orthogonal polynomials of a continuous variable, moreover using a new approach, the duplication problem of these polynomial families is solved; 2. we review the main methods used for the computation of the connection and linearization coefficients of orthogonal polynomials of a discrete variable, we solve the duplication and linearization problem of all orthogonal polynomials of a discrete variable; 3. we propose a method to generate the connection, linearization and duplication coefficients for q-orthogonal polynomials; 4. we propose a unified method to obtain these coefficients in a generic way for orthogonal polynomials on quadratic and q-quadratic lattices. Our algorithmic approach to compute linearization, connection and duplication coefficients is based on the one used by Koepf and Schmersau and on the NaViMa algorithm. Our main technique is to use explicit formulas for structural identities of classical orthogonal polynomial systems. We find our results by an application of computer algebra. The major algorithmic tools for our development are Zeilberger’s algorithm, q-Zeilberger’s algorithm, the Petkovšek-van-Hoeij algorithm, the q-Petkovšek-van-Hoeij algorithm, and Algorithm 2.2, p. 20 of Koepf's book "Hypergeometric Summation" and it q-analogue.

BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Szego polynomials: some relations to L-orthogonal and orthogonal polynomials

We consider the real Szego polynomials and obtain some relations to certain self inversive orthogonal L-polynomials defined on the unit circle and corresponding symmetric orthogonal polynomials on real intervals. We also consider the polynomials obtained when the coefficients in the recurrence relations satisfied by the self inversive orthogonal L-polynomials are rotated. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Orthogonal polynomials associated with related measures and Sobolev orthogonal polynomials

Connection between two sequences of orthogonal polynomials, where the associated measures are related to each other by a first degree polynomial multiplication (or division), are looked at. The results are applied to obtain information regarding Sobolev orthogonal polynomials associated with certain pairs of measures.

Effect of loading type on the fatigue strength of symmetric and asymmetric welded joints made of ultra high strength steel

In this study, finite element analyses and experimental tests are carried out in order to investigate the effect of loading type and symmetry on the fatigue strength of three different non-load carrying welded joints. The current codes and recommendations do not give explicit instructions how to consider degree of bending in loading and the effect of symmetry in the fatigue assessment of welded joints. The fatigue assessment is done by using effective notch stress method and linear elastic fracture mechanics. Transverse attachment and cover plate joints are analyzed by using 2D plane strain element models in FEMAP/NxNastran and Franc2D software and longitudinal gusset case is analyzed by using solid element models in Abaqus and Abaqus/XFEM software. By means of the evaluated effective notch stress range and stress intensity factor range, the nominal fatigue strength is assessed. Experimental tests consist of the fatigue tests of transverse attachment joints with total amount of 12 specimens. In the tests, the effect of both loading type and symmetry on the fatigue strength is studied. Finite element analyses showed that the fatigue strength of asymmetric joint is higher in tensile loading and the fatigue strength of symmetric joint is higher in bending loading in terms of nominal and hot spot stress methods. Linear elastic fracture mechanics indicated that bending reduces stress intensity factors when the crack size is relatively large since the normal stress decreases at the crack tip due to the stress gradient. Under tensile loading, experimental tests corresponded with finite element analyzes. Still, the fatigue tested joints subjected to bending showed the bending increased the fatigue strength of non-load carrying welded joints and the fatigue test results did not fully agree with the fatigue assessment. According to the results, it can be concluded that in tensile loading, the symmetry of joint distinctly affects on the fatigue strength. The fatigue life assessment of bending loaded joints is challenging since it depends on whether the crack initiation or propagation is predominant.

Influence of the type of dental trauma on the pulp vitality and the time elapsed until treatment: a study in patients aged 0-3 years

The purpose of the present study was to determine the influence of the type of trauma on the pulp vitality and the time elapsed until seeking dental care in children aged 0-3 years seen at the Baby Clinic of the Aracatuba Dental School, UNESP. A total of 1813 records were analyzed. Two hundred and three patients, corresponding to 302 traumatized teeth, were assessed clinically and radiographically. Hard-tissue injuries were the most frequent (52%), with a predominance of enamel crown fractures (41.4%), followed by concussions (12.6%) and intrusions (11.6%). Clinical and radiographic examination revealed that 72% of the traumatized teeth maintained pulp vitality. In the case of supporting-tissue lesions, 51.1% of the patients sought care within 1-15 days after injury, while in the case of hard-tissue injuries, 52.7% sought care only after 16 days. The results showed that supporting-tissue injuries had a significant influence on the faster seeking of dental care.

Connection coefficients and zeros of orthogonal polynomials

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.

A realization of the q-deformed harmonic oscillator: rogers-Szegö and Stieltjes-Wigert polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Monotonicity of the zeros of orthogonal polynomials through related measures

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.

Another connection between orthogonal polynomials and L-orthogonal polynomials

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.

On the Asymptotic Behavior of the Ratio between the Numbers of Binary Primitive and Irreducible Polynomials

This work was presented in part at the 8th International Conference on Finite Fields and Applications Fq^8 , Melbourne, Australia, 9-13 July, 2007.

Pharmacological antagonism of Anchietia salutaris extracts on the contraction induced by prostaglandin D2 and U46619 in guinea-pig lung parenchymal strips

Anchietia salutaris tea is traditionally used in Brazil to treat allergies, suggesting it contains compounds with antagonistic activity on the allergic mediators. We have evaluated extracts and semi-purified fractions of Anchietia salutaris as a source of compounds having this type of antagonism on the contraction induced in guinea-pig lung parenchymal strips and on platelet aggregation and shape change. After 10 min pre-incubation dichloromethane extracts containing 30 or 100 μg mL-1 inhibited the contraction induced by prostaglandin D2 (PGD2) in guinea-pig lung parenchymal strips with dose ratios (DR) of 0.76 ± 0.14 and 0.93 ± 0.19, respectively; the amount of inhibition depended both on the concentration and on the time of preincubation (DR after 30 min pre-incubation was 1.21 ± 0.51). The dichloromethane extract and its semi-purified fractions also inhibited the contractions induced by U46619, a more potent, stable, synthetic agonist of thromboxane A2 (TxA2) prostanoid (TP) receptors, the receptors acted upon by PGD2 to produce lung contractions. The dichloromethane extract did not inhibit the lung parenchymal contractions induced by histamine, leukotriene D4 (LTD4) or platelet-activating factor (PAF). Platelet aggregation induced by U46619, adenosine 5'-diphosphate (ADP) or PAF was not inhibited by the dichloromethane extract. Indeed, the extract potentiated platelet aggregation induced by low concentrations of these agonists and also potentiated the shape change induced by U46619. These results imply that the dichloromethane extract of Anchietia salutaris and its semipurified fractions contain an active principle that competitively inhibits TxA2 TP receptors, the stimulation of which causes lung parenchymal contraction. The inhibition seems to be selective for this receptor subtype, because the extract fails to inhibit platelet aggregation or shape change. This provides additional support of earlier reports suggesting the occurrence of TP receptor subtypes.

Polinômios ortogonais e análise de freqüência

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)