Finite group actions on products of spheres

In this work we make some contributions to the theory of actions of finite groups on products of spheres. Suppose that the group Z(q)(tau) acts freely on the product of k copies of spheres. Question: Is r less than or equal to k? We solve this question for several values of r and k.

A finite element free convection model for the side wall heated cavity

This paper presents a finite element numerical solution of free convection in a cavity with side walls maintained at constant but different temperatures. The predictions from the model and the method of solution were validated by comparison with the 'bench mark' solution and Vahl Davis' results and good agreement was found. The present model was used to obtain additional results over a wide range of Rayleigh number (10(3)-10(6)) and L/H ratios varying from 0.1 to 1.0. The predicted stream function patterns, temperature and velocity profiles as well as the mean Nusselt number were presented and discussed. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

UNIFORMLY ACCELERATED FINITE-TIME DETECTORS

The behavior of uniformly accelerated detectors in the Minkowski and Rindler vacua is analyzed when the detector is coupled to a scalar field during a finite amount of time T. We point out that the logarithmic ultraviolet divergences reported in the literature are due to the instantaneous switching of the detector. We explicitly show this by considering a detector switched on and off continuously. The usual Planckian spectrum for the excitation probability is recovered in the limit T --> infinity.

Uniform estimates of attracting sets of extended Lurie systems using LMIs

This research presents a systematic procedure to obtain estimates, via extended Lyapunov functions, of attracting sets of a class of nonlinear systems, as well as an estimate of their stability regions. The considered class of nonlinear systems, called in this note the extended Lurie system, consists of nonlinear systems like those of the Lurie problem where one of the nonlinear functions can violate the sector conditions of the Lurie problem around the origin. In case of nonautonomous systems the concept of absolute stability is extended and uniform estimates of the attracting set are obtained. Two classical nonlinear systems, the forced duffing equation and the Van der Pol system, are analyzed with the proposed procedure.

The generator coordinate Hartree-Fock method as strategy for building Gaussian basis sets to ab initio study of the process of adsorption of sulfur on platinum (200) surface

The scheme named generator coordinate Hartree-Fock method (GCHF) is used to build (22s14p) and (33s22p16d9f) gaussian basis sets to S ((3)P) and Pt ((3)D) atoms, respectively. Theses basis sets are contracted to [13s10p] and [19s13p9d5f] through of Dunning's segmented contraction scheme and are enriched with d and g polarization functions, [13s10p1d] and [19s13p9d5flg]. Finally, the [19s13p9d5f1g] basis Set to Pt ((3)D) was supplemented with s and d diffuse functions, [20s13p10d5flg], and used in combination with [13s10p1d] to study the effects of adsorption of S ((3)D) atom on a pt ((3)D) atom belonged to infinite Pt (200) surface. Atom-atom overlap population, bond order, and infrared spectrum of [pt(_)S](2 -) were calculated properties and were carried out at Hartree-Fock-Roothaan level. The results indicate that the process of adsorption of S ((3)P) on pt ((3)D) in the infinite Pt (200) surface is mainly caused by a strong contribution of sigma between the 3p(z) orbital of S ((3)P) and the 6s orbital of pt ((3)D). (c) 2004 Elsevier B.V. All rights reserved.

Vortices in superconductors with a columnar defect: Finite size effects

In the present work we investigate the behavior of a vortex in a long superconducting cylinder near to a columnar defect at the center. The derivations of the local magnetic field distribution and the Gibbs free energy will be carried out for a cylinder and a cavity of arbitrary sizes. From the general expressions, it is considered two particular limits: one in which the radius of the cavity is very small but the radius of the superconducting cylinder is kept finite; and one in which the radius of the superconducting cylinder is taken very large (infinite) but the radius of the cavity is kept finite. In both cases the maximum number of vortices which are allowed in the cavity is determined. In addition, the surface barrier field for flux entrance into the cavity is calculated. (c) 2005 Elsevier B.V. All rights reserved.

Design of Gaussian basis sets to the theoretical interpretation of IR-spectrum of hexaaquachromium (III) ion, tetraoxochromium (IV) ion, and tetraoxochromium (VI) ion

The Generator Coordinate Hartree-Fock (GCHF) method is employed to design 16s, 16s10p, 24s17p13d, 25s17p13d, and 26s17p Gaussian basis sets for the H ((2)S), O ((3)P), O(2-) ((1)S), Cr(3+) ((4)F), Cr(4+) ((3)F), and Cr(6+) ((1)S) atomic species. These basis sets are then contracted to (4s) for H ((2)S), (6s4p) for O ((3)P), and O(2-) ((1)S), (986p3d) for Cr(3+) ((4)F), (10s8p3d) for Cr(4+) ((3)F), and (13s7p) for Cr(6+) (1S) by a standard procedure. For evaluation of the quality of those basis sets in molecular calculations, we have accomplished studies of total and orbital (HOMO and HOMO-1) energies at the HF-Roothaan level for the molecular species of our interest. The results obtained with the contracted basis sets are compared to the values obtained with our extended basis sets and to the standard 6-311G basis set from literature. Finally, the contracted basis sets are enriched with polarization function and then utilized in the theoretical interpretation of IR-spectrum of hexaaquachromium (III) ion, [Cr(H(2)O)(6)](3+), tetraoxochromium (IV) ion, [CrO(4)](4-), and tetraoxochromium (VI) ion, [CrO(4)](2-). The respective theoretical harmonic frequencies and IR-intensities were computed at the density functional theory (DFT) level. In the DFT calculations we employed the Becke's 1988 functional using the LYP correlation functional. The comparison between the results obtained and the corresponding experimental values indicates a very good description of the IR-spectra of the molecular ions studied, and that the GCHF method is still a legitimate alternative for selection of Gaussian basis sets. (C) 2003 Elsevier B.V. All rights reserved.

Basis sets applied to the theoretical study of the vibrational structure of hexaaquaaluminum(III) ion

Gaussian basis sets were developed with the Generator Coordinate Hartree-Fock (GCHF) method for the atoms from H (14s), O (23s16p), and Al (29sl9p) in the ground state. These basis sets were then contracted to 3s (12,1,1), 5s3p (18,2,1,1,1/14,1,1), and 7s5p (20,3,2,1,1,1,1/14,2,1,1,1) for H, O and Al atoms, respectively, by a standard procedure. The quality of contracted basis sets in molecular calculations was evaluated through studies of the total and orbital (epsilon(HOMO) and epsilon(HOMO-1)) energies at the HF level for the hexaaquaaluminum(III) ion, [AI(H(2)O)(6)](3+). For the O atom, the 5s3p was supplemented with d polarization function and it was used in combination with 3s, and 7s5p for H and Al atoms was used to the theoretical interpretation of the Infrared (IR) spectrum of hexaaquaaluminum(III) ion. The calculations of the IR-spectrum were also performed at the HF level and it showed that the basis sets obtained with the aid of GCHF method lead to the selection of useful contracted Gaussian basis sets for the theoretical study of vibrational property of ionic specie of our interest. (C) 2004 Elsevier B.V. All rights reserved.

Discrete coherent states and probability distributions in finite-dimensional spaces

Operator bases are discussed in connection with the construction of phase space representatives of operators in finite-dimensional spaces, and their properties are presented. It is also shown how these operator bases allow for the construction of a finite harmonic oscillator-like coherent state. Creation and annihilation operators for the Fock finite-dimensional space are discussed and their expressions in terms of the operator bases are explicitly written. The relevant finite-dimensional probability distributions are obtained and their limiting behavior for an infinite-dimensional space are calculated which agree with the well known results. (C) 1996 Academic Press, Inc.

HEAT-KERNEL EXPANSION AT FINITE TEMPERATURE

We show how the zero-temperature result for the heat-kernel asymptotic expansion can be generalized to the finite-temperature one. We observe that this general result depends on the interesting ratio square-root tau/beta, where tau is the regularization parameter and beta = 1/T, so that the zero-temperature limit beta --> infinity corresponds to the cutoff limit tau --> 0. As an example, we discuss some aspects of the axial model at finite temperature.

Designing Gaussian basis sets to the theoretical study of the piezoelectric effect of perovskite (BaTiO3)

Gaussian basis sets (24s14p, 30s19p14d, and 33s21p14d for O (P-3), Ti (S-5), and Ba (S-1) atoms, respectively), are designed with the strategy of the Generator Coordinate Hartree-Fock method. The basis sets are then contracted to [6s4p], [10s5p4d], and [16s9p5d] to O, Ti, and Ba atoms, respectively, and used in calculations of total and orbital energies of (TiO+2)-Ti-1 and (BaO)-Ba-1 fragments for quality evaluation in molecular studies. For O atom, the [6s4p] basis set is enriched with d polarization function and used along with the [10s5p4d] and [16s9p5d] basis sets for the theoretical study of the piezoelectric effect of perovskite (BaTiO3). The results of this work evidence that the piezoelectric properties in BaTiO3 can be caused by electrostatic interactions. (C) 2003 Elsevier B.V. All rights reserved.

ANOMALIES IN CURVED SPACETIME AT FINITE TEMPERATURE

We discuss the problem of the breakdown of conformal and gauge symmetries at finite temperature in curved-spacetime background, when the changes in the background are gradual, in order to have a well-defined quantum field theory at finite temperature. We obtain the expressions for Seeley's coefficients and the heat-kernel expansion in this regime. As applications, we consider the self-interacting lambdaphi4 and chiral Schwinger models in curved backgrounds at finite temperature.