L-orthogonal polynomials associated with related measures

A positive measure psi defined on [a, b] such that its moments mu(n) = integral(b)(a)t(n) d psi(t) exist for n = 0, +/-1, +/-2. can be called a strong positive measure on [a, b] When 0 <= a < b <= infinity the sequence of polynomials {Q(n)} defined by integral(b)(a) t(-n+s) Q(n)(t) d psi(t) = 0, s = 0, ., n - 1, exist and they are referred here as L-orthogonal polynomials We look at the connection between two sequences of L-orthogonal polynomials {Q(n)((1))} and {Q(n)((0))} associated with two closely related strong positive measures and th defined on [a, b]. To be precise, the measures are related to each other by (t - kappa) d psi(1)(t) = gamma d psi(0)(t). where (t - kappa)/gamma is positive when t is an element of (n, 6). As applications of our study. numerical generation of new L-orthogonal polynomials and monotonicity properties of the zeros of a certain class of L-orthogonal polynomials are looked at. (C) 2010 IMACS Published by Elsevier B V All rights reserved

Distances between critical points and midpoints of zeros of hyperbolic polynomials

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

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

Inner products of the type < f, g >(S) = < f, g >psi(0) + < f', g'>psi(1), where one of the measures psi(0) or psi(1) is the measure associated with the Gegenbauer polynomials, are usually referred to as Gegenbauer-Sobolev inner products. This paper deals with some asymptotic relations for the orthogonal polynomials with respect to a class of Gegenbauer-Sobolev inner products. The inner products are such that the associated pairs of symmetric measures (psi(0), psi(1)) are not within the concept of symmetrically coherent pairs of measures.

Zeros of Gegenbauer-Sobolev Orthogonal Polynomials: Beyond Coherent Pairs

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Some asymptotics for Sobolev orthogonal polynomials involving Gegenbauer weights

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The Wigner function associated with the Rogers-Szego polynomials

A Wigner function associated with the Rogers-Szego polynomials is proposed and its properties are discussed. It is shown that from such a Wigner function it is possible to obtain well-behaved probability distribution functions for both angle and action variables, defined on the compact support -pi less than or equal to theta < pi, and for m greater than or equal to 0, respectively. The width of the angle probability density is governed by the free parameter q characterizing the polynomials.

Multitrace operators and the generalized AdS/CFT prescription

We show that multitrace interactions can be consistently incorporated into an extended AdS conformal field theory (CFT) prescription involving the inclusion of generalized boundary conditions and a modified Legendre transform prescription. We find new and consistent results by considering a self-contained formulation which relates the quantization of the bulk theory to the AdS/CFT correspondence and the perturbation at the boundary by double-trace interactions. We show that there exist particular double-trace perturbations for which irregular modes are allowed to propagate as well as the regular ones. We perform a detailed analysis of many different possible situations, for both minimally and nonminimally coupled cases. In all situations, we make use of a new constraint which is found by requiring consistency. In the particular nonminimally coupled case, the natural extension of the Gibbons-Hawking surface term is generated.

New thought experiment to test the generalized second law of thermodynamics

We propose an extension of the original thought experiment proposed by Geroch, which sparked much of the actual debate and interest on black hole thermodynamics, and show that the generalized second law of thermodynamics is in compliance with it.

Mathematical models of generalized diffusion

We discuss in this paper equations describing processes involving non-linear and higher-order diffusion. We focus on a particular case (u(t) = 2 lambda (2)(uu(x))(x) + lambda (2)u(xxxx)), which is put into analogy with the KdV equation. A balance of nonlinearity and higher-order diffusion enables the existence of self-similar solutions, describing diffusive shocks. These shocks are continuous solutions with a discontinuous higher-order derivative at the shock front. We argue that they play a role analogous to the soliton solutions in the dispersive case. We also discuss several physical instances where such equations are relevant.

Generalized non-abelian Toda models of dyonic type

The construction of a class of non-abelian Toda models admiting dyonic type soliton solutions is reviewed.

Generalized sine-Gordon/massive Thirring models and soliton/particle correspondences

We consider a real Lagrangian off-critical submodel describing the soliton sector of the so-called conformal affine sl(3)((1)) Toda model coupled to matter fields. The theory is treated as a constrained system in the context of Faddeev-Jackiw and the symplectic schemes. We exhibit the parent Lagrangian nature of the model from which generalizations of the sine-Gordon (GSG) or the massive Thirring (GMT) models are derivable. The dual description of the model is further emphasized by providing the relationships between bilinears of GMT spinors and relevant expressions of the GSG fields. In this way we exhibit the strong/weak coupling phases and the (generalized) soliton/particle correspondences of the model. The sl(n)((1)) case is also outlined. (C) 2002 American Institute of Physics.

Generalized squeezing operators, bipartite Wigner functions and entanglement via Wehrl's entropy functionals

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Extended 2D generalized dilaton gravity theories

We show that an anomaly-free description of matter in (1+1) dimensions requires a deformation of the 2D relativity principle, which introduces a non-trivial centre in the 2D Poincare algebra. Then we work out the reduced phase space of the anomaly-free 2D relativistic particle, in order to show that it lives in a noncommutative 2D Minkowski space. Moreover, we build a Gaussian wave packet to show that a Planck length is well defined in two dimensions. In order to provide a gravitational interpretation for this noncommutativity, we propose to extend the usual 2D generalized dilaton gravity models by a specific Maxwell component, which guages the extra symmetry associated with the centre of the 2D Poincare algebra. In addition, we show that this extension is a high energy correction to the unextended dilaton theories that can affect the topology of spacetime. Further, we couple a test particle to the general extended dilaton models with the purpose of showing that they predict a noncommutativity in curved spacetime, which is locally described by a Moyal star product in the low energy limit. We also conjecture a probable generalization of this result, which provides strong evidence that the noncommutativity is described by a certain star product which is not of the Moyal type at high energies. Finally, we prove that the extended dilaton theories can be formulated as Poisson-Sigma models based on a nonlinear deformation of the extended Poincare algebra.

Path integral quantization of generalized quantum electrodynamics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)