Szego type polynomials and para-orthogonal polynomials

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

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)

Associated symmetric quadrature rules

We prove a relation between two different types of symmetric quadrature rules, where one of the types is the classical symmetric interpolatory quadrature rules. Some applications of a new quadrature rule which was obtained through this relation are also considered.

Inversely symmetric interpolatory quadrature rules

We consider interpolatory quadrature rules with nodes and weights satisfying symmetric properties in terms of the division operator. Information concerning these quadrature rules is obtained using a transformation that exists between these rules and classical symmetric interpolatory quadrature rules. In particular, we study those interpolatory quadrature rules with two fixed nodes. We obtain specific examples of such quadrature rules.

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.

Kernel polynomials from L-orthogonal polynomials

A positive measure ψ defined on [a,b] such that its moments μn=∫a btndψ(t) exist for n=0,±1,±2,⋯, is called a strong positive measure on [a,b]. If 0≤a

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.

A class of hypergeometric polynomials with zeros on the unit circle: Extremal and orthogonal properties and quadrature formulas

The class of hypergeometric polynomials F12(-m,b;b+b̄;1-z) with respect to the parameter b=λ+iη, where λ>0, are known to have all their zeros simple and exactly on the unit circle |z|=1. In this note we look at some of the associated extremal and orthogonal properties on the unit circle and on the interval (-1,1). We also give the associated Gaussian type quadrature formulas. © 2012 IMACS.

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.

Orthogonal polynomials on the unit circle and chain sequences

Szego{double acute} has shown that real orthogonal polynomials on the unit circle can be mapped to orthogonal polynomials on the interval [-1,1] by the transformation 2x=z+z-1. In the 80's and 90's Delsarte and Genin showed that real orthogonal polynomials on the unit circle can be mapped to symmetric orthogonal polynomials on the interval [-1,1] using the transformation 2x=z1/2+z-1/2. We extend the results of Delsarte and Genin to all orthogonal polynomials on the unit circle. The transformation maps to functions on [-1,1] that can be seen as extensions of symmetric orthogonal polynomials on [-1,1] satisfying a three-term recurrence formula with real coefficients {cn} and {dn}, where {dn} is also a positive chain sequence. Via the results established, we obtain a characterization for a point w(|w|=1) to be a pure point of the measure involved. We also give a characterization for orthogonal polynomials on the unit circle in terms of the two sequences {cn} and {dn}. © 2013 Elsevier Inc.

Avaliação de pacientes com sequência de Robin no pós-operatório imediato após palatoplastia primário

Pós-graduação em Enfermagem (mestrado profissional) - FMB

Petrologia e caracterização geoquímica das fontes mantélicas da região noroeste da província magmática do Paraná

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

Reações hansênicas em pacientes coinfectados com HIV/Hanseníase: Clínica e ibmunopatologia

O Brasil é um dos poucos países que permanece endêmico para a infecção pelo vírus da imunodeficiência humana (HIV) e hanseníase, e estas doenças têm grande impacto em custos sociais e em qualidade de vida. Embora seja reconhecida a relevância desta coinfecção, vários aspectos ainda não são totalmente compreendidos. Este estudo tem como objetivo descrever aspectos clínicos, histopatológicos e imunopatológicos dos estados reacionais de pacientes coinfectados HIV/hanseníase, comparando-os aos pacientes com hanseníase, sem HIV. Foram acompanhados, dois grupos: (1) com 40 pacientes coinfectados HIV/hanseníase; (2) com 107 pacientes com hanseníase. Prevaleceram indivíduos do sexo masculino em ambos os grupos. No Grupo 1, a maioria eram paucibacilar (70%), na forma borderline tuberculóide (45%) e com menor risco de ter reação hansênica em relação aos não coinfectados. Todos os coinfectados que apresentaram reação hansênica (n= 15) estavam em uso de Terapia Anti-retroviral (TARV), e a maioria no estado de aids (n=14), sendo a Síndrome da Reconstituição Imune (SRI) uma condição clínica marcadamente importante em muitos destes pacientes (n=7). No grupo dos não coinfectados, o padrão de infecção da maioria foi multibacilar (80.4%), forma borderline-borderline (40.2%), e com Risco Relativo maior de apresentar reações hansênicas (p = 0,0026). A reação reversa foi a mais frequente em ambos os grupos. No grupo de coinfectados observaram-se lesões dermatológicas com aspecto de acordo com o esperado para cada forma clínica, em geral, eritemato infiltradas, com evolução semelhante aos sem coinfecção. O edema na derme foi o achado histopatológico mais comum em ambos os grupos. No Grupo 1, foram encontradas células gigantes, em todos os histopatológicos e em maior quantidade (2+) e de tamanho grande. A morfologia do eritema nodoso hansênico não apresentou diferenças significantes entre os grupos, assim como a expressão de IL-1β e IL-6. Este estudo corrobora com as hipóteses de que o quadro clínico e imunopatológico das reações nestes pacientes é um quadro inflamatório ativo, e não de anergia, semelhante ao encontrado nos não coinfectados.

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

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