Szego type polynomials and para-orthogonal polynomials

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

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)

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.

Multi-dimensional effects on Cladoceran (Crustacea, Anomopoda) assemblages in two cascade reservoirs in Southeast Brazil

The Cladocera assemblages in two cascade reservoirs located in the Paranapanema River in Brazil were studied during two consecutive years. Upstream Chavantes Reservoir is an accumulation system, with a long water retention time, high depth and oligo-mesotrophic status. The downstream Salto Grande Reservoir is a small, run-of-river reservoir, with a short water retention time, shallow depth and meso-eutrophic status. The goal of this study was to determine the inter- and intra-reservoir limnological differences with emphasis on the Cladocerans assemblages. The following questions were posed: (i) what are the seasonal dynamics of the reservoir spatial structures; (ii) how dynamics, seasonally, is the reservoirs spatial structure; and (iii) are the reservoir independent systems? A total of 43 Cladoceran species were identified in this study. Ceriodaphnia silvestrii was the most abundant and frequent species found in Chavantes Reservoir, while C. cornuta was most abundant and frequent in Salto Grande Reservoir. The Cladoceran species richness differed significantly among sampling sites for both reservoirs. In terms of abundance, there was a significant variation among sampling sites and periods for both reservoirs. A cluster analysis indicated a higher similarity among the deeper compartments, and the intermediate river-reservoir zones was grouped with the riverine sampling sites. For the smaller Salto Grande Reservoir, the entrance of a middle size tributary causes major changes in the system. A distinct environment was observed in the river mouth zone of another small tributary, representing a shallow environment with aquatic macrophyte stands. A canonical correlation analysis between environmental variables and Cladoceran abundance explained 75% of the data variability, and a complementary factorial analysis explained 65% of the variability. The spatial compartmentalization of the reservoirs, as well as the particular characteristics of the two study reservoirs, directly influenced the structure of the Cladoceran assemblages. The conditions of the lacustrine (dam) zone of the larger Chavantes Reservoir were reflected in the upstream zone of the smaller downstream Salto Grande Reservoir, highlighting the importance of plankton exportation in reservoir cascade systems. The comparative spatial-temporal analysis indicated conspicuous differences between the two reservoirs, reinforcing the necessity of considering tropical/subtropical reservoirs as complex, multi-compartmental water systems. © 2010 The Authors. Journal compilation © 2010 Blackwell Publishing Asia Pty Ltd.

Monotonicity and asymptotics of zeros of Laguerre-Sobolev-type orthogonal polynomials of higher order derivatives

In this paper we analyze the location of the zeros of polynomials orthogonal with respect to the inner product where α >-1, N ≥ 0, and j ∈ N. In particular, we focus our attention on their interlacing properties with respect to the zeros of Laguerre polynomials as well as on the monotonicity of each individual zero in terms of the mass N. Finally, we give necessary and sufficient conditions in terms of N in order for the least zero of any Laguerre-Sobolev-type orthogonal polynomial to be negative. © 2011 American Mathematical Society.

Szego{double acute} and para-orthogonal polynomials on the real line: Zeros and canonical spectral transformations

We study polynomials which satisfy the same recurrence relation as the Szego{double acute} polynomials, however, with the restriction that the (reflection) coefficients in the recurrence are larger than one in modulus. Para-orthogonal polynomials that follow from these Szego{double acute} polynomials are also considered. With positive values for the reflection coefficients, zeros of the Szego{double acute} polynomials, para-orthogonal polynomials and associated quadrature rules are also studied. Finally, again with positive values for the reflection coefficients, interlacing properties of the Szego{double acute} polynomials and polynomials arising from canonical spectral transformations are obtained. © 2012 American Mathematical Society.

Response surface methodology applied to the evaluation of the SO 2 sorption process in two Brazilian limestones

This paper proposes a response surface methodology to evaluate the influence of the particle size and temperature as variables and their interaction on the sulfation process using two Brazilian limestones, a calcite (ICB) and a dolomite (DP). Experiments were performed according to an experimental design [central composite rotatable design (CCRD)] carried out on a thermogravimetric balance and a nitrogen adsorption porosimeter. In the SO 2 sorption process, DP was shown to be more efficient than ICB. The best results for both limestones in relation to conversion and Brunauer-Emmett-Teller (BET) surface area were obtained under central point conditions (545 μm and 850 C for DP and 274 μm and 815 C for ICB). The optimal values for conversion were 52% for DP and 37% for ICB. For BET surface area, the optimal values were 35 m2 g-1 for DP and 45 m2 g-1 for ICB. A relationship between conversion and pore size distribution has been established. The experiments that showed higher conversions also exhibited more pores in the region between 20 and 150 Å and larger BET surface area, indicating that the amount of smaller pores may be an important factor in the reactivity of limestones. © 2013 American Chemical Society.

Zeros of a family of hypergeometric para-orthogonal polynomials on the unit circle

Para-orthogonal polynomials derived from orthogonal polynomials on the unit circle are known to have all their zeros on the unit circle. In this note we study the zeros of a family of hypergeometric para-orthogonal polynomials. As tools to study these polynomials, we obtain new results which can be considered as extensions of certain classical results associated with three term recurrence relations and differential equations satisfied by orthogonal polynomials on the real line. One of these results which might be considered as an extension of the classical Sturm comparison theorem, enables us to obtain monotonicity with respect to the parameters for the zeros of these para-orthogonal polynomials. Finally, a monotonicity of the zeros of Meixner-Pollaczek polynomials is proved. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Interlacing of zeros of orthogonal polynomials under modification of the measure

We investigate the mutual location of the zeros of two families of orthogonal polynomials. One of the families is orthogonal with respect to the measure dμ (x), supported on the interval (a, b) and the other with respect to the measure |x -c|τ|x -d|γdμ (x), where c and d are outside (a, b) We prove that the zeros of these polynomials, if they are of equal or consecutive degrees, interlace when either 0 < τ, γ ≤ 1 or γ = 0 and 0 < τ ≤ 2. This result is inspired by an open question of Richard Askey and it generalizes recent results on some families of orthogonal polynomials. Moreover, we obtain further statements on interlacing of zeros of specific orthogonal polynomials, such as the Askey-Wilson ones. © 2013 Elsevier Inc.

Risk factors for perinatal death in two different levels of care: a case-control study

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Zeros of classical orthogonal polynomials of a discrete variable

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A Favard type theorem for orthogonal polynomials on the unit circle from a three term recurrence formula

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Stieltjes functions and discrete classical orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Para-orthogonal polynomials from constant Verblunsky coefficients

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)