Em direção a uma representação para equações algébricas :uma lógica equacional local

The intervalar arithmetic well-known as arithmetic of Moore, doesn't possess the same properties of the real numbers, and for this reason, it is confronted with a problem of operative nature, when we want to solve intervalar equations as extension of real equations by the usual equality and of the intervalar arithmetic, for this not to possess the inverse addictive, as well as, the property of the distributivity of the multiplication for the sum doesn t be valid for any triplet of intervals. The lack of those properties disables the use of equacional logic, so much for the resolution of an intervalar equation using the same, as for a representation of a real equation, and still, for the algebraic verification of properties of a computational system, whose data are real numbers represented by intervals. However, with the notion of order of information and of approach on intervals, introduced by Acióly[6] in 1991, the idea of an intervalar equation appears to represent a real equation satisfactorily, since the terms of the intervalar equation carry the information about the solution of the real equation. In 1999, Santiago proposed the notion of simple equality and, later on, local equality for intervals [8] and [33]. Based on that idea, this dissertation extends Santiago's local groups for local algebras, following the idea of Σ-algebras according to (Hennessy[31], 1988) and (Santiago[7], 1995). One of the contributions of this dissertation, is the theorem 5.1.3.2 that it guarantees that, when deducing a local Σ-equation E t t in the proposed system SDedLoc(E), the interpretations of t and t' will be locally the same in any local Σ-algebra that satisfies the group of fixed equations local E, whenever t and t have meaning in A. This assures to a kind of safety between the local equacional logic and the local algebras

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)

Um estudo sobre a função exponencial

Pós-graduação em Matemática em Rede Nacional - IBILCE