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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A Characterization of L-orthogonal Polynomials from Three Term Recurrence Relations

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

Some asymptotics for Sobolev orthogonal polynomials involving Gegenbauer weights

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

GLOBAL DYNAMICS IN THE POINCARE BALL of THE CHEN SYSTEM HAVING INVARIANT ALGEBRAIC SURFACES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

PT-invariant point interactions in one dimension

By using Wu and Yu's pseudo-potential, we construct point interactions in one dimension that are complex but conform to space-time reflection (PT) invariance. The resulting point interactions are equivalent to those obtained by Albeverio, Fei and Kurasov as self-adjoint extensions of the kinetic energy operator.

The two-loop massless (lambda/4!)phi(4) model in nontranslational invariant domain

We study the (lambda/4!)phi(4) massless scalar field theory in a four-dimensional Euclidean space, where all but one of the coordinates are unbounded. We are considering Dirichlet boundary conditions in two hyperplanes, breaking the translation invariance of the system. We show how to implement the perturbative renormalization up to two-loop level of the theory. First, analyzing the full two and four-point functions at the one-loop level, we show that the bulk counterterms are sufficient to render the theory finite. Meanwhile, at the two-loop level, we must also introduce surface counterterms in the bare Lagrangian in order to make finite the full two and also four-point Schwinger functions. (c) 2006 American Institute of Physics.

Conserved currents in gravitational models with quasi-invariant Lagrangians: Application to teleparallel gravity

Conservation laws in gravitational theories with diffeomorphism and local Lorentz symmetry are studied. Main attention is paid to the construction of conserved currents and charges associated with an arbitrary vector field that generates a diffeomorphism on the spacetime. We further generalize previous results for the case of gravitational models described by quasi-invariant Lagrangians, that is, Lagrangians that change by a total derivative under the action of the local Lorentz group. The general formalism is then applied to the teleparallel models, for which the energy and the angular momentum of a Kerr black hole are calculated. The subsequent analysis of the results obtained demonstrates the importance of the choice of the frame.

Measurement of the dijet invariant mass cross section in p(p)over-bar collisions at root s=1.96 TeV

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The cohomology of superspace, pure spinors and invariant integrals

The superform construction of supersymmetric invariants, which consists of integrating the top component of a closed superform over spacetime, is reviewed. The cohomological methods necessary for the analysis of closed superforms are discussed and some further theoretical developments presented. The method is applied to higher-order corrections in heterotic string theory up to alpha'(3). Some partial results on N = 2, d = 10 and N = 1, d = 11 are also given.

A realization of the q-deformed harmonic oscillator: rogers-Szegö and Stieltjes-Wigert polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Finding invariant tori in the problem of a periodically corrugated waveguide

Some dynamic properties for a light ray suffering specular reflections inside a periodically corrugated waveguide are studied. The dynamics of the model is described in terms of a two dimensional nonlinear area preserving map. We show that the phase space is mixed in the sense that there are KAM islands surrounded by a large chaotic sea that is confined by two invariant spanning curves. We have used a connection with the Standard Mapping near a transition from local to global chaos and found the position of these two invariant spanning curves limiting the size of the chaotic sea as function of the control parameter.

Szego polynomials: some relations to L-orthogonal and orthogonal polynomials

We consider the real Szego polynomials and obtain some relations to certain self inversive orthogonal L-polynomials defined on the unit circle and corresponding symmetric orthogonal polynomials on real intervals. We also consider the polynomials obtained when the coefficients in the recurrence relations satisfied by the self inversive orthogonal L-polynomials are rotated. (C) 2002 Elsevier B.V. B.V. All rights reserved.

SYMMETRICAL ORTHOGONAL POLYNOMIALS AND THE ASSOCIATED ORTHOGONAL L-POLYNOMIALS

We show how symmetric orthogonal polynomials can be linked to polynomials associated with certain orthogonal L-polynomials. We provide some examples to illustrate the results obtained Finally as an application, we derive information regarding the orthogonal polynomials associated with the weight function (1 + kx(2))(1 - x(2))(-1/2), k > 0.

Companion orthogonal polynomials: some applications

In this paper the recurrence relations of symmetric orthogonal polynomials whose measures are related to each other in a certain way are considered. Many of the relations satisfied by the coefficients of the recurrence relations are exposed. The results are applied to obtain, for example, information regarding certain Sobolev orthogonal polynomials and regarding the measures of certain orthogonal polynomial sequences with twin periodic recurrence coefficients. (C) 2001 IMACS. Published by Elsevier B.V. B.V. All rights reserved.