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

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)

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)

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.

Szego polynomials and the truncated trigonometric moment problem

We show how Szego polynomials can be used in the theory of truncated trigonometric moment problem.

Sn-polymetallic greisen-type deposits associated with late-stage rapakivi granites, Brazil: fluid inclusion and stable isotope characteristics

Tin-polymetallic greisen-type deposits in the Itu Rapakivi Province and Rondonia Tin Province, Brazil are associated with late-stage rapakivi fluorine-rich peraluminous alkali-feldspar granites. These granites contain topaz and/or muscovite or zinnwaldite and have geochemical characteristics comparable to the low-P sub-type topaz-bearing granites. Stockworks and veins are common in Oriente Novo (Rondonia Tin Province) and Correas (Itu Rapakivi Province) deposits, but in the Santa Barbara deposit (Rondonia Tin Province) a preserved cupola with associated bed-like greisen is predominant. The contrasting mineralization styles reflect different depths of formation, spatial relationship to tin granites, and different wall rock/fluid proportions. The deposits contain a similar rare-metal suite that includes Sri (+/-W, +/-Ta, +/-Nb), and base-metal suite (Zn-Cu-Pb) is present only in Correas deposit. The early fluid inclusions of the Correas and Oriente Novo deposits are (1) low to moderate-salinity (0-19 wt.% NaCl eq.) CO2-bearing aqueous fluids homogenizing at 245-450 degreesC, and (2) aqueous solutions with low CO2, low to moderate salinity (0-14 wt.% NaCl eq.), which homogenize between 100 and 340 T. In the Santa Barbara deposit, the early inclusions are represented by (1) low-salinity (5-12 wt.% NaCl eq.) aqueous fluids with variable CO2 contents, homogenizing at 340 to 390 T, and (2) low-salinity (0-3 wt.% NaCl eq.) aqueous fluid inclusions, which homogenize at 320380 degreesC. Cassiterite, wolframite, columbite-tantalite, scheelite, and sulfide assemblages accompany these fluids. The late fluid in the Oriente Novo and Correas deposit was a low-salinity (0-6 wt.% NaCl eq.) CO2-free aqueous solution, which homogenizes at (100-260 degreesC) and characterizes the sulfide fluorite-sericite association in the Correas deposit. The late fluid in the Santa Barbara deposit has lower salinity (0-3 wt.% NaCl eq.) and characterizes the late-barren-quartz, muscovite and kaolinite veins. Oxygen isotope thermometry coupled with fluid inclusion data suggest hydrothermal activity at 240-450 degreesC, and 1,0-2.6 kbar fluid pressure at Correas and Oriente Novo. The hydrogen isotope composition of breccia-greisen, stockwork, and vein fluids (delta(18)O quartz from 9.9parts per thousand to 10.9parts per thousand, deltaDH(2)O from 4.13parts per thousand to 6.95parts per thousand) is consistent with a fluid that was in equilibrium with granite at temperatures from 450 to 240 degreesC. In the Santa Barbara deposit, the inferred temperatures for quartz-pods and bed-like greisens are much higher (570 and 500 degreesC, respectively), and that for the cassiterite-quartz-veins is 415 degreesC. The oxygen and hydrogen isotope composition of greisen and quartz-pods fluids (delta(18)O(qtz-H2O)=5.5-6.1parts per thousand) indicate that the fluid equilibrated with the albite granite, consistent with a magmatic origin. The values for mica (delta(18)O(mica-H2O)=33-9.8parts per thousand) suggest mixing with meteoric water. Late muscovite veins (delta(18)O(qtz-H2O)=-6.4parts per thousand) and late quartz (delta(18)O(mica-H2O)=-3.8parts per thousand) indicate involvement of a meteoric fluid. Overall, the stable isotope and fluid inclusion data imply three fluid types: (1) an early orthomagmatic fluid, which equilibrated with granite; (2) a mixed orthomagmatic-meteoric fluid; and (3) a late hydrothermal meteoric fluid. The first two were responsible for cassiterite, wolframite, and minor coluChange in the redox conditions related to mixing-of magmatic and meteoric fluids favored important sulfide mineralization in the Correas deposit. (C) 2004 Elsevier B.V. All rights reserved.