Laguerre moments and generalized functions

Here we explore the link between the moments of the Laguerre polynomials or Laguerre moments and the generalized functions (as the Dirac delta-function and its derivatives), presenting several interesting relations. A useful application is related to a procedure for calculating mean values in quantum optics that makes use of the so-called quasi-probabilities. One of them, the P-distribution, can be represented by a sum over Laguerre moments when the electromagnetic field is in a photon-number state. Consequently, the P-distribution can be expressed in terms of Dirac delta-function and derivatives. More specifically, we found a direct relation between P-distributions and the Laguerre factorial moments.

Semiclassical scaling functions of sine-Gordon model

We present an analytic study of the finite size effects in sine-Gordon model, based on the semi-classical quantization of an appropriate kink background defined on a cylindrical geometry. The quasi-periodic kink is realized as an elliptic function with its real period related to the size of the system. The stability equation for the small quantum fluctuations around this classical background is of Lame type and the corresponding energy eigenvalues are selected inside the allowed bands by imposing periodic boundary conditions. We derive analytical expressions for the ground state and excited states scaling functions, which provide an explicit description of the flow between the IR and UV regimes of the model. Finally, the semiclassical form factors and two-point functions of the basic field and of the energy operator are obtained, completing the semiclassical quantization of the sine-Gordon model on the cylinder. (C) 2004 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)

Algebraic properties of Rogers-Szego functions: I. Applications in quantum optics

By means of a well-established algebraic framework, Rogers-Szego functions associated with a circular geometry in the complex plane are introduced in the context of q-special functions, and their properties are discussed in detail. The eigenfunctions related to the coherent and phase states emerge from this formalism as infinite expansions of Rogers-Szego functions, the coefficients being determined through proper eigenvalue equations in each situation. Furthermore, a complementary study on the Robertson-Schrodinger and symmetrical uncertainty relations for the cosine, sine and nondeformed number operators is also conducted, corroborating, in this way, certain features of q-deformed coherent states.

Generalized squeezing operators, bipartite Wigner functions and entanglement via Wehrl's entropy functionals

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Quark sea structure functions of the nucleon in a statistical model

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

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

Determination of a point sufficiently close to the asymptote in nonlinear growth functions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Time-dependent effects of lead on rat reproductive functions

The effects of exposure to lead on endocrine function and the reproductive parameters were studied in pubertal rats treated with 1.0 g l(-1) lead acetate in drinking water for 20 days (subacute group) or 9 months (chronic group) in addition to i.v. injections of lead acetate (0.1 mg 100 g(-1) body wt.) every 10 (subacute group) or 15 days (chronic group). Although basal levels of testosterone were higher both in plasma and in testes of acutely intoxicated animals, the circulating levels of luteinizing hormone (LH) were not affected in either group, nor was the LH-releasing hormone content of the median eminence. The density of [I-125]LH/human chorionic gonadotrophin (hCG) binding sites in testicular homogenates was reduced by saturnism in both groups, concomitant with a significantly increased apparent affinity constant of the hormone-receptor complex. These data can be viewed as the result of a mixture of specific lead toxicity (e.g. at the enzyme level) with other more general actions (e.g. at the level of the hypothalamus-pituitary-testicular axis).

CLASSICAL DISTRIBUTION-FUNCTIONS DERIVED FROM WIGNER DISTRIBUTION-FUNCTIONS

A mapping which relates the Wigner phase-space distribution function associated with a given stationary quantum-mechanical wavefunction to a specific solution of the time-independent Liouville transport equation is obtained. Two examples are studied.

Feedforward neural networks based on PPS-wavelet activation functions

Function approximation is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. Neural networks and wavenets have been recently seen as attractive tools for developing efficient solutions for many real world problems in function approximation. In this paper, it is shown how feedforward neural networks can be built using a different type of activation function referred to as the PPS-wavelet. An algorithm is presented to generate a family of PPS-wavelets that can be used to efficiently construct feedforward networks for function approximation.

Green functions of the Dirac equation with magnetic-solenoid field

Various Green functions of the Dirac equation with a magnetic-solenoid field (the superposition of the Aharonov-Bohm field and a collinear uniform magnetic field) are constructed and studied. The problem is considered in 2+1 and 3+1 dimensions for the natural extension of the Dirac operator (the extension obtained from the solenoid regularization). Representations of the Green functions as proper time integrals are derived. The nonrelativistic limit is considered. For the sake of completeness the Green functions of the Klein-Gordon particles are constructed as well. (C) 2004 American Institute of Physics.