Generalized partition function zeros of 1D spin models and their critical behavior at edge singularities

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Cauchy-Stieltjes Integral on Time Scales in Banach Spaces and Hysteresis Operators

The play operator has a fundamental importance in the theory of hysteresis. It was studied in various settings as shown by P. Krejci and Ph. Laurencot in 2002. In that work it was considered the Young integral in the frame of Hilbert spaces. Here we study the play in the frame of the regulated functions (that is: the ones having only discontinuities of the first kind) on a general time scale T (that is: with T being a nonempty closed set of real numbers) with values in a Banach space. We will be showing that the dual space in this case will be defined as the space of operators of bounded semivariation if we consider as the bilinearity pairing the Cauchy-Stieltjes integral on time scales.

Generating Birth and Death Processes

Associated with an ordered sequence of an even number 2N of positive real numbers is a birth and death process (BDP) on {0, 1, 2,..., N} having these real numbers as its birth and death rates. We generate another birth and death process from this BDP on {0, 1, 2,..., 2N}. This can be further iterated. We illustrate with an example from tan(kz). In BDP, the decay parameter, viz., the largest non-zero eigenvalue is important in the study of convergence to stationarity. In this article, the smallest eigenvalue is found to be useful.

On a moment problem associated with Chebyshev polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

História da Matemática em contextos da Educação Matemática: contribuições do GPHM

In this article we tried to show the paths outlined during the past years by the Research Group on History of Mathematics and/or its relations with Mathematics Education (GPHM) at UNESP in Rio Claro - Brazil, as well as the contributions we believe we have made to Mathematics Education. The group's production has focused on issues that address the history of institutions and characters, linked to the history of disciplines, concepts and learning materials. Also, in broader terms of mathematics education, this article presents results from research that supports the understanding of teachers' conceptions about the use of History of Mathematics in the classroom; material on the history of mathematics accessible to the teacher; the presence of the history of mathematics in textbooks; proposed introductions of real numbers; and the subject of Analysis in teacher education and training.

Teorema de Thales: uma conexão entre os aspectos geométrico e algébrico em alguns livros didáticos de matemática

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

O papel da disciplina de análise segundo professores e coordenadores

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Contraexemplos em análise

Pós-graduação em Matemática Universitária - IGCE

Álgebra motivada pela geometria

Pós-graduação em Matemática Universitária - IGCE

A irracionalidade e transcendência do número π

Pós-graduação em Matemática em Rede Nacional - IBILCE

Um tratamento para os números reais via medição de segmentos: uma proposta, uma investigação

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Formalizando a existência dos números reais. -

Pós-graduação em Matemática em Rede Nacional - IBILCE

Sequências de números reais: uma abordagem no ensino médio

Pós-graduação em Matemática em Rede Nacional - IBILCE

Fractais de Rauzy, autômatos e frações contínuas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A dissipative Fermi-Ulam model under two different kinds of dissipation

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