Zeros of Gegenbauer-Sobolev Orthogonal Polynomials: Beyond Coherent Pairs

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

SZEGO POLYNOMIALS FROM HYPERGEOMETRIC FUNCTIONS

Szego polynomials with respect to the weight function w(theta) = e(eta theta)[sin(theta/2)](2 lambda), where eta, lambda is an element of R and lambda > -1/2 are considered. Many of the basic relations associated with these polynomials are given explicitly. Two sequences of para-orthogonal polynomials with explicit relations are also given.

BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Generating Birth and Death Processes

Associated with an ordered sequence of an even number 2N of positive real numbers is a birth and death process (BDP) on {0, 1, 2,..., N} having these real numbers as its birth and death rates. We generate another birth and death process from this BDP on {0, 1, 2,..., 2N}. This can be further iterated. We illustrate with an example from tan(kz). In BDP, the decay parameter, viz., the largest non-zero eigenvalue is important in the study of convergence to stationarity. In this article, the smallest eigenvalue is found to be useful.

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

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

Pseudechis australis Venomics: Adaptation for a Defense against Microbial Pathogens and Recruitment of Body Transferrin

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

Asymptotic soliton train solutions of Kaup-Boussinesq equations

Asymptotic soliton trains arising from a 'large and smooth' enough initial pulse are investigated by the use of the quasiclassical quantization method for the case of Kaup-Boussinesq shallow water equations. The parameter varying along the soliton train is determined by the Bohr-Sommerfeld quantization rule which generalizes the usual rule to the case of 'two potentials' h(0)(x) and u(0)(x) representing initial distributions of height and velocity, respectively. The influence of the initial velocity u(0)(x) on the asymptotic stage of the evolution is determined. Excellent agreement of numerical solutions of the Kaup-Boussinesq equations with predictions of the asymptotic theory is found. (C) 2003 Elsevier B.V. All rights reserved.

Asymptotic soliton train solutions of the defocusing nonlinear Schrodinger equation

Asymptotic behavior of initially large and smooth pulses is investigated at two typical stages of their evolution governed by the defocusing nonlinear Schrodinger equation. At first, wave breaking phenomenon is studied in the limit of small dispersion. A solution of the Whitham modulational equations is found for the case of dissipationless shock wave arising after the wave breaking point. Then, asymptotic soliton trains arising eventually from a large and smooth initial pulse are studied by means of a semiclassical method. The parameter varying along the soliton train is calculated from the generalized Bohr-Sommerfeld quantization rule, so that the distribution of eigenvalues depends on two functions-intensity rho(0)(x) of the initial pulse and its initial chirp v(0)(x). The influence of the initial chirp on the asymptotic state is investigated. Excellent agreement of the numerical solution of the defocusing NLS equation with predictions of the asymptotic theory is found.

The modulational instability in deep water under the action of wind and dissipation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Alloys and oxides on carbon-supported Pt-Sn electrocatalysts for ethanol oxidation

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

A theoretical analysis of the TiO2/Sn doped (110) surface properties

We have used the periodic quantum-mechanical method with density functional theory at the B3LYP level in order to study TiO2/Sn doped (1 1 0) surfaces and have investigated the structural, electronic and energy band properties of these oxides. Our calculated relaxation directions for TiO2 is the experimental one and is also in agreement with other theoretical results. We also observe for the doped systems relaxation of lattice positions of the atoms. Modification of Sri, O and Ti charges depend on the planes and positions of the substituted atoms. Doping can modify the Fermi levels, energy gaps as well as the localization and composition of both valence and conduction band main components. Doping can also modify the chemical, electronic and optical properties of these oxides surfaces increasing their suitability for use as gas sensors and optoelectronic devices. (c) 2005 Elsevier B.V. All rights reserved.

Another connection between orthogonal polynomials and L-orthogonal polynomials

We consider a connection that exists between orthogonal polynomials associated with positive measures on the real line and orthogonal Laurent polynomials associated with strong measures of the class S-3 [0, beta, b]. Examples are given to illustrate the main contribution in this paper. (c) 2006 Elsevier B.V. All rights reserved.

Modified Chebyshev algorithm: some applications

Two applications of the modified Chebyshev algorithm are considered. The first application deals with the generation of orthogonal polynomials associated with a weight function having singularities on or near the end points of the interval of orthogonality. The other application involves the generation of real Szego polynomials.

The influence of aluminium on the overall properties of SnO2-based varistors

The influence of aluminium on the development of the microstructure and on the electrical behaviour of the SnO2 center dot Co3O4 center dot Nb2O5 typical varistor system was studied. Two sources of Al were used, alumina (Al2O3) and boehmite (AlO(OH)). The microstructural features were characterised with scanning (SEM) and transmission (TEM) electron microscopies. The different phases present in the studied samples were also studied with XRD, EDS and electron diffraction patterns of selected areas (SAED). Particles containing Sri, Co, Al, and O were unveiled with TEM. Impedance spectroscopy measurements and current density versus electric field characteristics revealed superior electrical properties for samples with AlO(OH). The higher non-linearity (alpha = 19) was achieved with the addition of 0.1% mol of boehmite. The influence of the secondary phases on the electrical properties is also addressed in this work.

On the denominator values and barycentric weights of rational interpolants

We improve upon the method of Zhu and Zhu [A method for directly finding the denominator values of rational interpolants, J. Comput. Appl. Math. 148 (2002) 341-348] for finding the denominator values of rational interpolants, reducing considerably the number of arithmetical operations required for their computation. In a second stage, we determine the points (if existent) which can be discarded from the rational interpolation problem. Furthermore, when the interpolant has a linear denominator, we obtain a formula for the barycentric weights which is simpler than the one found by Berrut and Mittelmann [Matrices for the direct determination of the barycentric weights of rational interpolation, J. Comput. Appl. Math. 78 (1997) 355-370]. Subsequently, we give a necessary and sufficient condition for the rational interpolant to have a pole. (c) 2006 Elsevier B.V. All rights reserved.