A rescaling of the phase space for Hamiltonian map: Applications on the Kepler map and mappings with diverging angles in the limit of vanishing action

A rescale of the phase space for a family of two-dimensional, nonlinear Hamiltonian mappings was made by using the location of the first invariant Kolmogorov-Arnold-Moser (KAM) curve. Average properties of the phase space are shown to be scaling invariant and with different scaling times. Specific values of the control parameters are used to recover the Kepler map and the mapping that describes a particle in a wave packet for the relativistic motion. The phase space observed shows a large chaotic sea surrounding periodic islands and limited by a set of invariant KAM curves whose position of the first of them depends on the control parameters. The transition from local to global chaos is used to estimate the position of the first invariant KAM curve, leading us to confirm that the chaotic sea is scaling invariant. The different scaling times are shown to be dependent on the initial conditions. The universality classes for the Kepler map and mappings with diverging angles in the limit of vanishing action are defined. © 2013 Published by Elsevier Inc. All rights reserved.

Perturbations on the antidiagonals of Hankel matrices

Given a strongly regular Hankel matrix, and its associated sequence of moments which defines a quasi-definite moment linear functional, we study the perturbation of a fixed moment, i.e., a perturbation of one antidiagonal of the Hankel matrix. We define a linear functional whose action results in such a perturbation and establish necessary and sufficient conditions in order to preserve the quasi-definite character. A relation between the corresponding sequences of orthogonal polynomials is obtained, as well as the asymptotic behavior of their zeros. We also study the invariance of the Laguerre-Hahn class of linear functionals under such perturbation, and determine its relation with the so-called canonical linear spectral transformations. © 2013 Elsevier Ltd. All rights reserved.

On a model for the growth of an invasive avascular tumor

This paper is devoted to study the 1D model of invasive avascular tumor growth, which takes into account cell division, death, and motility, proposed by Kolobov and collaborators in 2009. First, we examine the existence and uniqueness of the solution to this model. Second, we studied qualitatively and numerically the traveling wave solutions. Finally, we show some numerical simulations for the cell density and nutrient concentration. © 2013 NSP Natural Sciences Publishing Cor.

On computational aspects of discrete Sobolev inner products on the unit circle

In this paper, we show how to compute in O(n2) steps the Fourier coefficients associated with the Gelfand-Levitan approach for discrete Sobolev orthogonal polynomials on the unit circle when the support of the discrete component involving derivatives is located outside the closed unit disk. As a consequence, we deduce the outer relative asymptotics of these polynomials in terms of those associated with the original orthogonality measure. Moreover, we show how to recover the discrete part of our Sobolev inner product. © 2013 Elsevier Inc. All rights reserved.

O papel do vídeo nas aulas multimodais de matemática aplicada: uma análise do ponto de vista dos alunos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Perspectivas históricas da pesquisa operacional

Pós-graduação em Educação Matemática - IGCE

O processo de escolha dos temas dos projetos de modelagem matemática

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

O papel das tecnologias da informação e comunicação nos projetos de modelagem matemática

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A matemática é feminina? Um estudo histórico da presença da mulher em institutos de pesquisa em matemática do estado de São Paulo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Uma abordagem pedagógica baseada na análise de modelos para alunos de biologia: qual o papel do software?

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Classificação automática de cobertura vegetal em imagens aéreas e orbitais para uso em planejamento energético

Neste trabalho é apresentado um modelo de redes neurais que será utilizado como ferramenta para uso no planejamento energético e na construção de cenários energéticos através da identificação e agrupamento de pixels representativos de classes de água, vegetação e antropização no entorno do reservatório de Tucuruí, Estado do Pará (bacia do rio Tocantins). Para o estudo, foram utilizadas fotografias aéreas ortorretificadas e um recorte da imagem do satélite Landsat, ambos obtidos em agosto de 2001 e classificados utilizando a métrica da mínima distância no software Matlab 7.3.0 (Matrix Laboratory - software de matemática aplicada) e no Arcview 3.2a (programa de Sistemas de Informações Geográficas). Para classificação da área no Matlab, foram utilizadas redes neurais competitivas, mais especificamente as redes de Kohonen que são caracterizadas por realizar um mapeamento de um espaço de dimensão n (número de entradas) para um espaço de dimensão m (número de saídas). Os resultados obtidos no classificador utilizando rede neural e no classificador do Arcview foram semelhantes, mas houve uma divergência no que diz respeito à imagem de alta e média resolução que pode ser justificada pelo fato de que a imagem de alta resolução espacial ocasiona muita variação espectral em algumas feições, gerando dificuldades nas classificações. Esse classificador automático é uma ferramenta importante para identificar oportunidades e potenciais a serem desenvolvidos na construção de cenários energéticos programados. Os resultados deste trabalho confirmam que a imagem de média resolução ainda é a mais indicada para resolver a maioria dos problemas que envolvem identificação de cobertura do solo para utilização em planejamento energético.

Periodic solutions for nonlinear telegraph equationvia elliptic regularization

ABSTRACT: In this work we are concerned with the existence and uniqueness of T -periodic weak solutions for an initial-boundary value problem associated with nonlinear telegraph equations typein a domain. Our arguments rely on elliptic regularization technics, tools from classical functional analysis as well as basic results from theory of monotone operators.

Treatment of geophysical data as a non-stationary process

ABSTRACT: The Kalman-Bucy method is here analized and applied to the solution of a specific filtering problem to increase the signal message/noise ratio. The method is a time domain treatment of a geophysical process classified as stochastic non-stationary. The derivation of the estimator is based on the relationship between the Kalman-Bucy and Wiener approaches for linear systems. In the present work we emphasize the criterion used, the model with apriori information, the algorithm, and the quality as related to the results. The examples are for the ideal well-log response, and the results indicate that this method can be used on a variety of geophysical data treatments, and its study clearly offers a proper insight into modeling and processing of geophysical problems.

A transmission problem for the Timoshenko system

In this work we study a transmission problem for the model of beams developed by S.P. Timoshenko [10]. We consider the case of mixed material, that is, a part of the beam has friction and the other is purely elastic. We show that for this type of material, the dissipation produced by the frictional part is strong enough to produce exponential decay of the solution, no matter how small is its size. We use the method of energy to prove exponential decay for the solution.

Approximate controllability for the semilinear heat equation in RN involving gradient terms

We prove the approximate controllability of the semilinear heat equation in R^N, when the nonlinear term is globally Lipschitz and depends both on the state u and its spatial gradient Ñu. The approximate controllability is viewed as the limit of a sequence of optimal control problems. In order to avoid the difficulties related to the lack of compactness of the Sobolev embeddings, we work with the similarity variables and use weighted Sobolev spaces.