Wave functions for the methane molecule

If the potential field due to the nuclei in the methane molecule is expanded in terms of a set of spherical harmonics about the carbon nucleus, only the terms involving s, f, and higher harmonic functions differ from zero in the equilibrium configuration. Wave functions have been calculated for the equilibrium configuration, first including only the spherically symmetric s term in the potential, and secondly including both the s and the f terms. In the first calculation the complete Hartree-Fock S.C.F. wave functions were determined; in the second calculation a variation method was used to determine the best form of the wave function involving f harmonics. The resulting wave functions and electron density functions are presented and discussed

Skew-symmetric identities of octonions

Quadratic alternative superalgebras are introduced and their super-identities and central functions on one odd generator are described. As a corollary, all multilinear skew-symmetric identities and central polynomials of octonions are classified. (C) 2008 Elsevier B.V. All rights reserved.

An eigenvalue problem for the biharmonic operator on Z(2)-symmetric regions

In this work we show that the eigenvalues of the Dirichlet problem for the biharmonic operator are generically simple in the set Of Z(2)-symmetric regions of R-n, n >= 2, with a suitable topology. To accomplish this, we combine Baire`s lemma, a generalised version of the transversality theorem, due to Henry [Perturbation of the boundary in boundary value problems of PDEs, London Mathematical Society Lecture Note Series 318 (Cambridge University Press, 2005)], and the method of rapidly oscillating functions developed in [A. L. Pereira and M. C. Pereira, Mat. Contemp. 27 (2004) 225-241].

Wannier functions of a one-dimensional photonic crystal with inversion symmetry

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Effect of bound nucleon internal structure change on nuclear structure functions

Effect of bound nucleon internal structure change on nuclear structure functions is investigated based on local quark-hadron duality. The bound nucleon structure functions calculated for charged-lepton and (anti)neutrino scattering are all enhanced in symmetric nuclear matter at large Bjorken-x (x greater than or similar to 0.85) relative to those in a free nucleon. This implies that a part of the enhancement observed in the nuclear structure function F-2 (in the resonance region) at large Bjorken-x (the EMC effect) is due to the effect of the bound nucleon internal structure change. However, the x dependence for the charged-lepton and (anti)neutrino scattering is different. The former (latter) is enhanced (quenched) in the region 0.8 less than or similar to x less than or similar to 0.9 (0.7 less than or similar to x less than or similar to 0.85) due to the difference of the contribution from axial vector forrn factor. Because of these differences charge symmetry breaking in parton distributions will be enhanced in nuclei. (c) 2005 Elsevier B.V. All rights reserved.

On the calculation of inner products of Schur functions

Two methods for calculating inner products of Schur functions in terms of outer products and plethysms are given and they are easy to implement on a machine. One of these is derived from a recent analysis of the SO(8) proton-neutron pairing model of atomic nuclei. The two methods allow for generation of inner products for the Schur functions of degree up to 20 and even beyond.

A discrete finite-dimensional phase space approach for the description of Fe8 magnetic clusters: Wigner and Husimi functions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Quasiprobability distribution functions for finite-dimensional discrete phase spaces: Spin-tunneling effects in a toy model

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Evaluating and classifying contaminated areas based on loss functions using annealing simulations

This paper presents a methodology based on geostatistical theory for quantifying the risks associated with heavy-metal contamination in the harbor area of Santana, Amapa State, Northern Brazil. In this area there were activities related to the commercialization of manganese ore from Serra do Navio. Manganese and arsenic concentrations at unsampled sites were estimated by postprocessing results from stochastic annealing simulations; the simulations were used to test different criteria for optimization, including average, median, and quantiles. For classifying areas as contaminated or uncontaminated, estimated quantiles based on functions of asymmetric loss showed better results than did estimates based on symmetric loss, such as the average or the median. The use of specific loss functions in the decision-making process can reduce the costs of remediation and health maintenance. The highest global health costs were observed for manganese. (c) 2008 Elsevier B.V. All rights reserved

On linear combinations of L-orthogonal polynomials associated with distributions belonging to symmetric classes

This paper deals with the classes S-3(omega, beta, b) of strong distribution functions defined on the interval [beta(2)/b, b], 0 < beta < b <= infinity, where 2 omega epsilon Z. The classification is such that the distribution function psi epsilon S-3(omega, beta, b) has a (reciprocal) symmetry, depending on omega, about the point beta. We consider properties of the L-orthogonal polynomials associated with psi epsilon S-3(omega, beta, b). Through linear combination of these polynomials we relate them to the L-orthogonal polynomials associated with some omega epsilon S-3(1/2, beta, b). (c) 2004 Elsevier B.V. All rights reserved.

Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Associated symmetric quadrature rules

We prove a relation between two different types of symmetric quadrature rules, where one of the types is the classical symmetric interpolatory quadrature rules. Some applications of a new quadrature rule which was obtained through this relation are also considered.

Local power properties of some asymptotic tests in symmetric linear regression models

In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of symmetric linear regression models. This is a wide class of models which encompasses the t model and several other symmetric distributions with longer-than normal tails. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, Monte Carlo simulations are presented. An empirical application to a real data set is considered for illustrative purposes. (C) 2011 Elsevier B.V. All rights reserved.

Investigating interocclusal perception in tactile teeth sensibility using symmetric and asymmetric analysis

The purpose of this clinical trial was to determine the active tactile sensibility of natural teeth and to obtain a statistical analysis method fitting a psychometric function through the observed data points. On 68 complete dentulous test persons (34 males, 34 females, mean age 45.9 ± 16.1 years), one pair of healthy natural teeth each was tested: n = 24 anterior teeth and n = 44 posterior teeth. The computer-assisted, randomized measurement was done by having the subjects bite on thin copper foils of different thickness (5-200 µm) inserted between the teeth. The threshold of active tactile sensibility was defined by the 50% value of correct answers. Additionally, the gradient of the sensibility curve and the support area (90-10% value) as a description of the shape of the sensibility curve were calculated. For modeling the sensibility curve, symmetric and asymmetric functions were used. The mean sensibility threshold was 14.2 ± 12.1 µm. The older the subject, the higher the tactile threshold (r = 0.42, p = 0.0006). The support area was 41.8 ± 43.3 µm. The higher the 50% threshold, the smaller the gradient of the curve and the larger the support area. The curves showing the active tactile sensibility of natural teeth demonstrate a tendency towards asymmetry, so that the active tactile sensibility of natural teeth can mathematically best be described by using the asymmetric Weibull function.