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.

On computational aspects of discrete Sobolev inner products on the unit circle

In this paper, we show how to compute in O(n2) steps the Fourier coefficients associated with the Gelfand-Levitan approach for discrete Sobolev orthogonal polynomials on the unit circle when the support of the discrete component involving derivatives is located outside the closed unit disk. As a consequence, we deduce the outer relative asymptotics of these polynomials in terms of those associated with the original orthogonality measure. Moreover, we show how to recover the discrete part of our Sobolev inner product. © 2013 Elsevier Inc. All rights reserved.

Marcas de singularidade em textos escolares de alunos do 2º ano do ensino fundamental

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Aquisição/aprendizagem de LE: subjetividade e deslocamentos identitários

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A plasticidade da voz crítica: os textos de Roberto Pompeu de Toledo na revista Veja

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A prosa de Chico Buarque em Fazenda modelo

Pós-graduação em Letras - FCLAS

O percurso das ideias do círculo de Bakhtin na análise do discurso francesa

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Fazendo gênero em jornalismo: os projetos editoriais da Folha de S. Paulo em perspectiva dialógica

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Jornalismo best-seller: o livro-reportagem no Brasil contemporâneo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

As toadas do bumba-meu-boi: sobre enunciados de um gênero discursivo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

O percurso dos gêneros do discurso publicitário: considerações sobre as propagandas da Coca-cola

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)

Basic hypergeometric polynomials with zeros on the unit circle

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Jogo de papéis e linguagem: diálogos possíveis entre Vigotski e Bakhtin

In this paper we present ongoing research in which we approach the regulatory role of language in role play in children aged six and seven. In research, we seek an understanding of the relationship between language, ownership and complexity of the children's game. The hypothesis guiding the research is that the dialogical relations between children and adults and among children, while playing, contribute to children's learning game. Procedures are being used interpretive ethnographic research that focuses on the human meaning of social relations, waged by the subjects in a particular historical context and its elucidation and exposition by one researcher. This approach allows closer studies of Vygotsky and Bakhtin scholars of language that emphasize the regulatory role of language in human relationships and value the dialogic exchange between researcher and researched; active subjects of the research process. The data were produced by means of observation and interview, in a field diary records, photographs and audio recordings. They are being screened in thematic groups and analyzed using interpretative narration. The participants were two teachers and two classes of the first year of an Elementary school (EMEF) School of Municipal Elementary School Crane, State of Sao Paulo, totaling 45 subjects. Bearing in mind the above assumptions, are presented and analyzed data that allow to anticipate some results.

O conceito de ecossistema na produção acadêmica brasileira em educação ambiental: construção de significados e sentidos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)