Szegö polynomials: quadrature rules on the unit circle and on [-1, 1]

We consider some of the relations that exist between real Szegö polynomials and certain para-orthogonal polynomials defined on the unit circle, which are again related to certain orthogonal polynomials on [-1, 1] through the transformation x = (z1/2+z1/2)/2. Using these relations we study the interpolatory quadrature rule based on the zeros of polynomials which are linear combinations of the orthogonal polynomials on [-1, 1]. In the case of any symmetric quadrature rule on [-1, 1], its associated quadrature rule on the unit circle is also given.

SYMMETRICAL ORTHOGONAL POLYNOMIALS AND THE ASSOCIATED ORTHOGONAL L-POLYNOMIALS

We show how symmetric orthogonal polynomials can be linked to polynomials associated with certain orthogonal L-polynomials. We provide some examples to illustrate the results obtained Finally as an application, we derive information regarding the orthogonal polynomials associated with the weight function (1 + kx(2))(1 - x(2))(-1/2), k > 0.

Effect of bur type and conditioning on the surface and interface of dentine

The purpose of this in vitro study was to evaluate the surface and resin-dentine interface characteristics of permanent tooth dentine cut with diamond or carbide burs and treated with phosphoric acid (PA) or an acidic conditioner. Labial surfaces of permanent incisors were prepared into dentine with high-speed carbide or diamond burs and divided into two halves. Phosphoric acid 36% was applied on one half and non-rinse conditioner (NRC) was applied on the other half. Ten randomly selected scanning electron microscopy (SEM) fields from each specimen (n = 15) were evaluated. Occlusal surfaces of third molars were divided in two halves for evaluation of the resin-dentine interface. The halves were randomly assigned to one of each conditioner and restored with Prime & Bond NT/Spectrum. Ten specimens were analysed by SEM to evaluate hybrid layer formation and interfacial seal. We observed that surfaces prepared with carbide bur presented less residual smear plugs (P < 0.05) than surfaces prepared with diamond burs. Surfaces conditioned with NRC, which is a smear layer modifier, presented more residual smear plugs than surfaces conditioned with PA (P < 0.05). Treatment with PA resulted in more sealed interfaces than specimens treated with NRC. Within the limitations of this study the results showed that carbide burs leave a surface that is more conducive to bonding than diamond burs.

On perturbed Szego recurrences

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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)

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.

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.

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.