Light deflection and quadratic gravity

We study the bending of light caused by a static gravitational field generated by a localized material source in the context of quadratic gravity. Our calculation shows that for light rays passing close to the Sun the deflection Phi lies in the interval 0 < < 1.75. A tree-level approach to the same issue tells us that the vacuum concerning quadratic gravity is a dispersive medium. Nom Phi is energy dependent and ranges from 0(+) to 1.75(-) arcsec.

Short and long period optimization of drug doses in the treatment of AIDS

Técnicas de otimização numérica são úteis na solução de problemas de determinação da melhor entrada para sistemas descritos por modelos matemáticos e cujos objetivos podem ser expressos de uma maneira quantitativa. Este trabalho aborda o problema de otimizar as dosagens dos medicamentos no tratamento da AIDS em termos de um balanço entre a resposta terapêutica e os efeitos colaterais. Um modelo matemático para descrever a dinâmica do vírus HIV e células CD4 é utilizado para calcular a dosagem ótima do medicamento no tratamento a curto prazo de pacientes com AIDS por um método de otimização direta utilizando uma função custo do tipo Bolza. Os parâmetros do modelo foram ajustados com dados reais obtidos da literatura. Com o objetivo de simplificar os procedimentos numéricos, a lei de controle foi expressa em termos de uma expansão em séries que, após truncamento, permite obter controles sub-ótimos. Quando os pacientes atingem um estado clínico satisfatório, a técnica do Regulador Linear Quadrático (RLQ) é utilizada para determinar a dosagem permanente de longo período para os medicamentos. As dosagens calculadas utilizando a técnica RLQ , tendem a ser menores do que a equivalente terapia de dose constante em termos do expressivo aumento na contagem das células T+ CD4 e da redução da densidade de vírus livre durante um intervalo fixo de tempo.

Broiler litter reutilization applying different composting concepts

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

Interface entre história da matemática e ensino: uma atividade desenvolvida com base num documento do século XVI

Este artigo propõe a construção de uma interface entre história e ensino de matemática a partir de um diálogo entre historiadores e educadores da matemática. Para tanto, consideramos aspectos epistemológicos e metodológicos ligados à história da matemática, pautada em tendências historiográficas atuais, juntamente com a metodologia baseada no movimento lógico-histórico. A interface contemplou o movimento do pensamento na formação dos conceitos e o contexto no qual tais conceitos foram desenvolvidos, de modo a conduzir à reflexão sobre o processo histórico da construção do conhecimento para a elaboração de atividade didática. Esta atividade teve por base um documento do século XVI dedicado à construção e uso de instrumentos matemáticos, e sua elaboração levou em consideração uma intencionalidade e um plano de ação que viabilizaram o seu desenvolvimento. A organização do ensino articulou as conexões internas e externas trazidas pela análise do documento e a forma do pensamento do desenvolvimento do conceito.

Another connection between orthogonal polynomials and L-orthogonal polynomials

We consider a connection that exists between orthogonal polynomials associated with positive measures on the real line and orthogonal Laurent polynomials associated with strong measures of the class S-3 [0, beta, b]. Examples are given to illustrate the main contribution in this paper. (c) 2006 Elsevier B.V. All rights reserved.

Laser interferometric characterization of a vibrating speaker system

An experiment that combines opto-mechanical and electrical measurements for the characterization of a loudspeaker is presented. We describe a very simple laser vibrometer for evaluating the amplitude of the vibration (displacement) of the speaker cone. The setup is essentially a Michelson-type interferometer operated by an inexpensive semiconductor laser (diode laser). It is shown that the simultaneous measurements of three amplitudes (displacement, electrical current, and applied voltage), as functions of the frequency of vibration, allow us to characterize the speaker system. The experiment is easy to perform, and it demonstrates several useful concepts of optics, mechanics, and electricity, allowing, students to gain an intuitive physical insight into the relations between mathematical models and, an actual speaker system. (C) 2003 American Association of Physics Teachers.

Husserl's phenomenology and Weyl's predictivism

In this paper I discuss the version of predicative analysis put forward by Hermann Weyl in Das Kontinuum. I try to establish how much of the underlying motivation for Weyl's position may be due to his acceptance of a phenomenological philosophical perspective. More specifically, I analyze Weyl's philosophical ideas in connexion with the work of Husserl, in particular Logische Untersuchungen and Ideen I.I believe that this interpretation of Weyl can clarify the views on mathematical existence and mathematical intuition which are implicit in Das Kontinuum.

On the dissimilarity between the algorithms for computing the symmetric energy-momentum tensor in ordinary field theory and general relativity

The recipe used to compute the symmetric energy-momentum tensor in the framework of ordinary field theory bears little resemblance to that used in the context of general relativity, if any. We show that if one stal ts fi om the field equations instead of the Lagrangian density, one obtains a unified algorithm for computing the symmetric energy-momentum tensor in the sense that it can be used for both usual field theory and general relativity.

On bifurcation and symmetry of solutions of symmetric nonlinear equations with odd-harmonic forcings

In this work we study existence, bifurcation, and symmetries of small solutions of the nonlinear equation Lx = N(x, p, epsilon) + mu f, which is supposed to be equivariant under the action of a group OHm, and where f is supposed to be OHm-invariant. We assume that L is a linear operator and N(., p, epsilon) is a nonlinear operator, both defined in a Banach space X, with values in a Banach space Z, and p, mu, and epsilon are small real parameters. Under certain conditions we show the existence of symmetric solutions and under additional conditions we prove that these are the only feasible solutions. Some examples of nonlinear ordinary and partial differential equations are analyzed. (C) 1995 Academic Press, Inc.

Analysis of heuristic algorithms for the transportation model in static and multistage planning in network expansion systems

The usefulness of the application of heuristic algorithms in the transportation model, first proposed by Garver, is analysed in relation to planning for the expansion of transmission systems. The formulation of the mathematical model and the solution techniques proposed in the specialised literature are analysed in detail. Starting with the constructive heuristic algorithm proposed by Garver, an extension is made to the problem of multistage planning for transmission systems. The quality of the solutions found by heuristic algorithms for the transportation model is analysed, as are applications in problems of planning transmission systems.

Szego type polynomials and para-orthogonal polynomials

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

Particle Competition and Cooperation in Networks for Semi-Supervised Learning with Concept Drift

Concept drift is a problem of increasing importance in machine learning and data mining. Data sets under analysis are no longer only static databases, but also data streams in which concepts and data distributions may not be stable over time. However, most learning algorithms produced so far are based on the assumption that data comes from a fixed distribution, so they are not suitable to handle concept drifts. Moreover, some concept drifts applications requires fast response, which means an algorithm must always be (re) trained with the latest available data. But the process of labeling data is usually expensive and/or time consuming when compared to unlabeled data acquisition, thus only a small fraction of the incoming data may be effectively labeled. Semi-supervised learning methods may help in this scenario, as they use both labeled and unlabeled data in the training process. However, most of them are also based on the assumption that the data is static. Therefore, semi-supervised learning with concept drifts is still an open challenge in machine learning. Recently, a particle competition and cooperation approach was used to realize graph-based semi-supervised learning from static data. In this paper, we extend that approach to handle data streams and concept drift. The result is a passive algorithm using a single classifier, which naturally adapts to concept changes, without any explicit drift detection mechanism. Its built-in mechanisms provide a natural way of learning from new data, gradually forgetting older knowledge as older labeled data items became less influent on the classification of newer data items. Some computer simulation are presented, showing the effectiveness of the proposed method.

Nanostructured films from phthalocyanine and carbon nanotubes: Surface morphology and electrical characterization

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

As diferentes “personalidades” do número racional trabalhadas através da resolução de problemas

We address the different "personalities" of the rational number and the concept of proportionality, analyzing the possibilities for using the Mathematics Teaching and Learning through Problem-solving Method. This method is based on the principle that knowledge can be constructed through the use of problems that generate new concepts and new contents. The different meanings of rational number - rational point, quotient, fraction, ratio, and operator - are constructs that depend on mathematical theories in which they are imbedded and the situations that evoke them in problem-solving. Some data will be presented from continuing education courses for teachers, aiming to contribute to understanding regarding the different "personalities" of the rational number. In general, these "personalities" are not easily identified by teachers and students, which is the reason for the many difficulties encountered during problem-solving involving rational numbers. One of these "personalities", the ratio, provides the basis for the concept of proportionality, which is relevant because it is a unifying idea in mathematics.

Desenvolvimento da quantificacao em geografia

Considering the textbooks, papers and articles published during the last decades, this paper deals with the development of the quantitative analysis in Geography. The comments are grouped into the following thematic questions: contributions aiming to introduce concepts and techniques in the geographical issues, focusing statistical and mathematical background and specific techniques about spatial and temporal distributions; contributions evaluating the potentialities of the quantification; contributions showing the character and applicability of the quantificative techniques, and the state of the use of these techniques in Brazilian literature and teaching. -English summary