Zeros of classical orthogonal polynomials of a discrete variable

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Monotonicity, interlacing and electrostatic interpretation of zeros of exceptional Jacobi polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the zeros of a class of generalized hypergeometric polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Zeros of Jacobi functions of second kind

The number of zeros in (- 1, 1) of the Jacobi function of second kind Q(n)((alpha, beta)) (x), alpha, beta > - 1, i.e. The second solution of the differential equation(1 - x(2))y (x) + (beta - alpha - (alpha + beta + 2)x)y' (x) + n(n + alpha + beta + 1)y(x) = 0,is determined for every n is an element of N and for all values of the parameters alpha > - 1 and beta > - 1. It turns out that this number depends essentially on alpha and beta as well as on the specific normalization of the function Q(n)((alpha, beta)) (x). Interlacing properties of the zeros are also obtained. As a consequence of the main result, we determine the number of zeros of Laguerre's and Hermite's functions of second kind. (c) 2005 Elsevier B.V. All rights reserved.

Asymptotics for Jacobi-Sobolev orthogonal polynomials associated with non-coherent pairs of measures

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)

Generalized partition function zeros of 1D spin models and their critical behavior at edge singularities

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Almost strict total positivity and a class of Hurwitz polynomials

We establish sufficient conditions for a matrix to be almost totally positive, thus extending a result of Craven and Csordas who proved that the corresponding conditions guarantee that a matrix is strictly totally positive. Then we apply our main result in order to obtain a new criteria for a real algebraic polynomial to be a Hurwitz one. The properties of the corresponding extremal Hurwitz polynomials are discussed. (C) 2004 Elsevier B.V. All rights reserved.

Zeros de Polinômios Ortogonais Gerados por uma Medida Perturbada

Pós-graduação em Matematica Aplicada e Computacional - FCT

Zeros de Polinômios Perturbados

Pós-graduação em Matematica Aplicada e Computacional - FCT

Zeros de combinações lineares de polinômios

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Zeros de Polinômios Auto-Recíprocos Reais no Círculo Unitário

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Yang-Lee zeros of the two- and three-state Potts model defined on π3 Feynman diagrams

We present both analytical and numerical results on the position of partition function zeros on the complex magnetic field plane of the q=2 state (Ising) and the q=3 state Potts model defined on phi(3) Feynman diagrams (thin random graphs). Our analytic results are based on the ideas of destructive interference of coexisting phases and low temperature expansions. For the case of the Ising model, an argument based on a symmetry of the saddle point equations leads us to a nonperturbative proof that the Yang-Lee zeros are located on the unit circle, although no circle theorem is known in this case of random graphs. For the q=3 state Potts model, our perturbative results indicate that the Yang-Lee zeros lie outside the unit circle. Both analytic results are confirmed by finite lattice numerical calculations.

Polinômios de Szegö e análise de frequência

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)