On some classes of exactly-solvable Klein-Gordon equations

In this work we discuss some exactly solvable Klein-Gordon equations. We basically discuss the existence of classes of potentials with different nonrelativistic limits, but which shares the intermediate effective Schroedinger differential equation. We comment about the possible use of relativistic exact solutions as approximations for nonrelativistic inexact potentials. (c) 2005 Elsevier B.V. All rights reserved.

Fundamental fermion masses from deformed SUq(2) triplets

A spectrum-generating q-algebra, within the framework of SUq(2), as firstly suggested by Iachello, is studied in order to describe the mass spectrum of three generations of quarks and leptons. The SUq(2) quantum group is a q-deformed extension of SU(2), where q = e(alpha) (with alpha real) is the deformation parameter. In this work, the essential use of inequivalent representations of SUq(2) is introduced. The inequivalent representations are labelled by (j, nu(0)), where j = 0, 1/2, 1, ... and nu(0) is a positive real number. A formula for the fermion masses M-m(j, nu(0)), with -j less than or equal to m less than or equal to j is derived. As an example, a possible scheme which corresponds to two triplets (j = 1) associated to up and down quarks is presented here in some detail. They are associated to different values of the deformation parameter, indicating a dependence of the charge Q on the parameter alpha. The masses of the charged leptons are treated in a similar way. The current results show that some mass relations for quarks and leptons found in the literature can be considered as approximations of the equations obtained in the j = 1 representations. The breaking of SUq(2) necessary to describe the Cabibbo-Kobayashi-Maskawa (CKM) flavor mixing is briefly discussed.

A BEM formulation based on Reissner's theory to perform simple bending analysis of plates reinforced by rectangular beams

In this work, the plate bending formulation of the boundary element method (BEM), based on the Reissner's hypothesis, is extended to the analysis of plates reinforced by rectangular beams. This composed structure is modelled by a zoned plate, being the beams represented by narrow sub-regions with larger thickness. The integral equations are derived by applying the weighted residual method to each sub-region, and summing them to get the equation for the whole plate. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. In order to decrease the number of degrees of freedom, some approximations are considered for both displacements and tractions along the beam width. The accuracy of the proposed model is illustrated by simple examples whose exact solution are known as well as by more complex examples whose numerical results are compared with a well-known finite element code.

An objective reconstruction of the chain of contagion

North's clustering method, which is based on a much used ecological model, the nearest neighbor distance, was applied to the objective reconstruction of the chain of household-to-household transmission of variola minor (the mild form of smallpox). The discrete within-household outbreaks were considered as points which were ordered in a time sequence using a 10-40 day interval between introduction of the disease into a source household and a receptor household. The closer points in the plane were assumed to have a larger probability of being links of a chain of household-to-household spread of the disease. The five defining distances (Manhattan or city-block distance between presumptive source and receptor dwellings) were 100, 200, 300, 400 and 500 m. The subchain sets obtained with the five defining distances were compared with the subchains empirically reconstructed during the field study of the epidemic through direct investigation of personal contacts of the introductory cases with either introductory or subsequent cases from previously affected households. The criteria of fit of theoretical to empirical clusters were: (a) the number of clustered dwellings and subchains, (b) number of dwellings in a subchain and (c) position of dwellings in a subchain. The defining distance closet to the empirical findings was 200 m, which fully agrees with the travelling habits of the study population. Less close but acceptable approximations were obtained with 100, 300, 400 and 500 m. The latter two distances gave identical results, as if a clustering ceiling had been reached. It seems that North's clustering model may be used for an objective reconstruction of the chain of contagious whose links are discrete within-household outbreaks. © 1984.

The theory of vibronic transitions in rare earth compounds

The theory of vibronic transitions in rare earth compounds is re-examined in the light of a more reliable representation for the ligand field Hamiltonian than the crude electrostatic model. General expressions that take into account the relevant contributions from the forced electric dipole and dynamic coupling mechanisms are derived for the vibronic intensity parameters. These include additional terms, from charge and polarizability gradients, which have not been considered in previous work. Emphasis is given to the relative signs of these various contributions. Under certain approximations these expressions may be conveniently written in terms of accessible ligand field parameters. A comparison with experimental values for the compounds Cs2NaEuCl6 and LiEuF4 is made and satisfactory agreement between theory and experiment is found. A discussion is given on the sensitivity of the calculated intensities to the values of radial integrals, interconfigurational energy differences and ligand field parameters that may be used. Finally, the problem in which a vibronic and an electronic level are in resonance, or near resonance, is analyzed. Suitable expressions to describe the effects of the even-rank components of the vibronic Hamiltonian are obtained. It is found that, depending on the strength of the vibronic interaction and the resonance conditions, the admixture between these two levels may lead to intensities of nearly equal values. © 1995.

Competition between spin, charge, and bond waves in a Peierls-Hubbard model

We study a one-dimensional extended Peierls-Hubbard model coupled to intracell and intercell phonons for a half-filled band. The calculations are made using the Hartree-Fock and adiabatic approximations for arbitrary temperature. In addition to static spin, charge, and bond density waves, we predict intermediate phases that lack inversion symmetry, and phase transitions that reduce symmetry on increasing temperature.

Infrared finite solutions for the gluon propagator and the QCD vacuum energy

Nonperturbative infrared finite solutions for the gluon polarization tensor have been found, and the possibility that gluons may have a dynamically generated mass is supported by recent Monte Carlo simulation on the lattice. These solutions differ among themselves, due to different approximations performed when solving the Schwinger-Dyson equations for the gluon polarization tensor. Only approximations that minimize energy are meaningful, and, according to this, we compute an effective potential for composite operators as a function of these solutions in order to distinguish which one is selected by the vacuum. © 1997 Elsevier Science B.V.

PCM thermal insulation in buildings

This paper presents the results of a numerical and experimental study of phase change material (PCM) filled walls and roofs under real operational conditions to achieve passive thermal comfort. The numerical part of the study was based on a one-dimensional model for the phase change problem controlled by pure conduction. Real radiation data was used to determine the external face temperature. The numerical treatment was based upon using finite difference approximations and the ADI scheme. The results obtained were compared with field measurements. The experimental set-up consisted of a small room with movable roof and side wall. The roof was constructed in the traditional way but with the phase change material enclosed. Thermocouples were distributed across the cross section of the roof. Another roof, identical but without the PCM, was also used during comparative tests. The movable wall was also constructed as is done traditionally but with the PCM enclosed. Again, thermocouples were distributed across the wall thickness to enable measurement of the local temperatures. Another wall, identical but without the PCM, was also used during comparative tests. The PCM used in the numerical and experimental tests was composed of a mixture of two commercial grades of glycol in order to obtain the required fusion temperature range. Comparison between the simulation results and the experiments indicated good agreement. Field tests also indicated that the PCM used was adequate and that the concept was effective in maintaining the indoor temperature very close to the established comfort limits. Further economical analysis indicated that the concept could effectively help in reducing the electric energy consumption and improving the energy demand pattern. © 1997 by John Wiley & Sons, Ltd.

Activation function study for wavelet network

The main purpose of this paper is to investigate theoretically and experimentally the use of family of Polynomial Powers of the Sigmoid (PPS) Function Networks applied in speech signal representation and function approximation. This paper carries out practical investigations in terms of approximation fitness (LSE), time consuming (CPU Time), computational complexity (FLOP) and representation power (Number of Activation Function) for different PPS activation functions. We expected that different activation functions can provide performance variations and further investigations will guide us towards a class of mappings associating the best activation function to solve a class of problems under certain criteria.

Quantum section method for the soft stadium

The soft stadium is defined by a monomial potential with exponent α as a parameter, such that α → ∞ corresponds to the billiard. The practical use of the quantum section method depends only on the partial separability of the system on both sides of the section, which holds for all α's. In particular, for α = 1.0, the system becomes globally separable, allowing for a general test of the method. For various values of the parameter, we also tested the use of the asymptotic WKB-type approximation in the construction of Green's functions and asymptotic overlap integrals to obtain higher energy eigenvalues. We show these approximations to be reliable. © 2000 Elsevier Science B.V. All rights reserved.

Phenomenological tests for the freezing of the QCD running coupling constant

We discuss phenomenological tests for the frozen infrared behavior of the running coupling constant and gluon propagators found in some solutions of Schwinger-Dyson equations of the gluonic sector of QCD. We verify that several observables can be used in order to select the different expressions of αs found in the literature. We test the effect of the nonperturbative coupling in the τ-lepton decay rate into nonstrange hadrons, in the ρ vector meson helicity density matrix that are produced in the χc2 → ρρ decay, in the photon to pion transition form factor, and compute the cross-sections for elastic proton-proton scattering and exclusive ρ production in deep inelastic scattering. These quantities depend on the infrared behavior of the coupling constant at different levels, we discuss the reasons for this dependence and argue that the existent and future data can be used to test the approximations performed to solve the Schwinger-Dyson equations and they already seem to select one specific infrared behavior of the coupling.

Using cubic splines to mitigate systematic errors in GPS relative positioning

Systematic errors can have a significant effect on GPS observable. In medium and long baselines the major systematic error source are the ionosphere and troposphere refraction and the GPS satellites orbit errors. But, in short baselines, the multipath is more relevant. These errors degrade the accuracy of the positioning accomplished by GPS. So, this is a critical problem for high precision GPS positioning applications. Recently, a method has been suggested to mitigate these errors: the semiparametric model and the penalised least squares technique. It uses a natural cubic spline to model the errors as a function which varies smoothly in time. The systematic errors functions, ambiguities and station coordinates, are estimated simultaneously. As a result, the ambiguities and the station coordinates are estimated with better reliability and accuracy than the conventional least square method.

Precision of yule-walker methods for the arma spectral model

In this work a new method is proposed of separated estimation for the ARMA spectral model based on the modified Yule-Walker equations and on the least squares method. The proposal of the new method consists of performing an AR filtering in the random process generated obtaining a new random estimate, which will reestimate the ARMA model parameters, given a better spectrum estimate. Some numerical examples will be presented in order to ilustrate the performance of the method proposed, which is evaluated by the relative error and the average variation coefficient.

Schwinger-dyson equations and dynamical gluon mass generation

We discuss the solutions obtained for the gluon propagador in Landau gauge within two distinct approximations for the Schwinger-Dyson equations (SDE). The first, named Mandelstam's approximation, consist in neglecting all contributions that come from fermions and ghosts fields while in the second, the ghosts fields are taken into account leading to a coupled system of integral equations. In both cases we show that a dynamical mass for the gluon propagator can arise as a solution. © 2005 American Institute of Physics.

Mitigating systematic errors for single frequency GPS receivers employing a penalized least squares methodology

Among the positioning systems that compose GNSS (Global Navigation Satellite System), GPS has the capability of providing low, medium and high precision positioning data. However, GPS observables may be subject to many different types of errors. These systematic errors can degrade the accuracy of the positioning provided by GPS. These errors are mainly related to GPS satellite orbits, multipath, and atmospheric effects. In order to mitigate these errors, a semiparametric model and the penalized least squares technique were employed in this study. This is similar to changing the stochastical model, in which error functions are incorporated and the results are similar to those in which the functional model is changed instead. Using this method, it was shown that ambiguities and the estimation of station coordinates were more reliable and accurate than when employing a conventional least squares methodology.