Characterization of generalized Bessel polynomials in terms of polynomial inequalities

Generalized Bessel polynomials (GBPs) are characterized as the extremal polynomials in certain inequalities in L-2 norm of Markov type. (C) 1998 Academic Press.

Schur-SzegA composition of entire functions

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

Efficient robust optimization based on polynomial chaos and tabu search algorithm

The study of robust design methodologies and techniques has become a new topical area in design optimizations in nearly all engineering and applied science disciplines in the last 10 years due to inevitable and unavoidable imprecision or uncertainty which is existed in real word design problems. To develop a fast optimizer for robust designs, a methodology based on polynomial chaos and tabu search algorithm is proposed. In the methodology, the polynomial chaos is employed as a stochastic response surface model of the objective function to efficiently evaluate the robust performance parameter while a mechanism to assign expected fitness only to promising solutions is introduced in tabu search algorithm to minimize the requirement for determining robust metrics of intermediate solutions. The proposed methodology is applied to the robust design of a practical inverse problem with satisfactory results.

Multiscale Fractal Descriptors and Polynomial Classifier for Partial Pixels Identification in Regions of Interest of Mammographic Images

Computer systems are used to support breast cancer diagnosis, with decisions taken from measurements carried out in regions of interest (ROIs). We show that support decisions obtained from square or rectangular ROIs can to include background regions with different behavior of healthy or diseased tissues. In this study, the background regions were identified as Partial Pixels (PP), obtained with a multilevel method of segmentation based on maximum entropy. The behaviors of healthy, diseased and partial tissues were quantified by fractal dimension and multiscale lacunarity, calculated through signatures of textures. The separability of groups was achieved using a polynomial classifier. The polynomials have powerful approximation properties as classifiers to treat characteristics linearly separable or not. This proposed method allowed quantifying the ROIs investigated and demonstrated that different behaviors are obtained, with distinctions of 90% for images obtained in the Cranio-caudal (CC) and Mediolateral Oblique (MLO) views.

A class of reversible quadratic polynomial vector fields on S-2

We study a class of quadratic reversible polynomial vector fields on S-2. We classify all the centers of this class of vector fields and we characterize its global phase portrait. (C) 2010 Elsevier B.V. All rights reserved.

On the reversible quadratic polynomial vector fields on S-2

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

STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

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

Relaxation algorithm to hyperbolic states in Gross-Pitaevskii equation

A new version of the relaxation algorithm is proposed in order to obtain the stationary ground-state solutions of nonlinear Schrodinger-type equations, including the hyperbolic solutions. In a first example, the method is applied to the three-dimensional Gross-Pitaevskii equation, describing a condensed atomic system with attractive two-body interaction in a non-symmetrical trap, to obtain results for the unstable branch. Next, the approach is also shown to be very reliable and easy to be implemented in a non-symmetrical case that we have bifurcation, with nonlinear cubic and quintic terms. (c) 2006 Elsevier B.V. All rights reserved.

Isomery of SU3 states in the strictly restricted dynamics model

Employing the general principles of classification of SU3 states, we have found 285 quantum number isomers (QNI), i.e. nuclei for which there are two possible SU3 quantum number sets, characterized by the maximal eigenvalue of the SU3 group Casimir operator, at the minimal value N-0(min) for the quantum number N-0 of the group U3(A-1) symmetric representation, allowed by the Pauli principle. 41 of these QNI can be attributed to the nun-excited, ground SU3 configurations of realistic nuclei. Two examples of QNI: Si-28 and Zn-60, have been studied in detail in the framework of the strictly restricted dynamics model (SRDM).

Flavor changing interaction models and strictly massless neutrinos

It is well known that experimental data, coming from solar and atmospheric neutrino detectors and also from experiments which look for neutrino oscillations. strongly suggest that neutrinos must have a mass different from zero. However at least the solar and/or the atmospheric neutrino data can be related to new flavor changing interactions beyond the standard model instead to the finite mass of neutrinos. This new physics may induce i) extra effects in neutrino-matter interactions, ii) CP violation in pion and lepton decays and, iii) muonium to antimuonium transition. We give two examples of models in which all those effects arise even with strictly massless neutrinos: the 331 model and multi-Higgs doublet extension of the standard model (mHDM) with flavor changing neutral currents in the charged lepton sector. It means that in this kind of models if neutrino masses were eventually needed, they will be independent of the parameters of the new interactions.

Casimir energy in a small volume multiply connected static hyperbolic preinflationary universe

A few years ago, Cornish, Spergel and Starkman (CSS) suggested that a multiply connected small universe could allow for classical chaotic mixing as a preinflationary homogenization process. The smaller the volume, the more important the process. Also, a smaller universe has a greater probability of being spontaneously created. Previously DeWitt, Hart and Isham (DHI) calculated the Casimir energy for static multiply connected fat space-times. Because of the interest in small volume hyperbolic universes (e.g., CSS), we generalize the DHI calculation by making a numerical investigation of the Casimir energy for a conformally coupled, massive scalar field in a static universe, whose spatial sections are the Weeks manifold, the smallest universe of negative curvature known. In spite of being a numerical calculation, our result is in fact exact. It is shown that there is spontaneous vacuum excitation of low multipolar components.

Casimir energy density in closed hyperbolic universes

The original Casimir effect results from the difference in the vacuum energies of the electromagnetic field, between that in a region of space with boundary conditions and that in the same region without boundary conditions. In this paper we develop the theory of a similar situation, involving a scalar field in spacetimes with closed spatial sections of negative curvature.

On the birth of a closed hyperbolic universe

We clarify and develop the results of a previous paper on the birth of a closed universe of negative spatial curvature and multiply connected topology. In particular we discuss the initial instanton and the second topology change in more detail, This is followed by a short discussion of the results.

Casimir energy in multiply connected static hyperbolic universes

We generalize a previously obtained result for the case of a few other static hyperbolic universes with manifolds of nontrivial topology as spatial sections.

A note about the appearance of non-hyperbolic solutions in a mechanical pendulum system

The investigation of the behavior of a nonlinear system consists in the analysis of different stages of its motion, where the complexity varies with the proximity of a resonance region. Near this region the stability domain of the system undergoes sudden changes due basically to competition and interaction between periodic and saddle solutions inside the phase portrait, leading to the occurrence of the most different phenomena. Depending of the domain of the chosen control parameter, these events can reveal interesting geometric features of the system so that the phase portrait is not capable to express all them, since the projection of these solutions on the two-dimensional surface can hide some aspects of these events. In this work we will investigate the numerical solutions of a particular pendulum system close to a secondary resonance region, where we vary the control parameter in a restrict domain in order to draw a preliminary identification about what happens with this system. This domain includes the appearance of non-hyperbolic solutions where the basin of attraction in the center of the phase portrait diminishes considerably, almost disappearing, and afterwards its size increases with the direction of motion inverted. This phenomenon delimits a boundary between low and high frequency of the external excitation.