GENERALIZED HEAVISIDE FUNCTIONS IN THE COLOMBEAU THEORY CONTEXT

We defined generalized Heaviside functions for a variable x in R-n, and for variables (x, t) in R-n x R-m. Then study properties such as: composition, invertibility, and association relation (the weak equality). This work is developed in the Colombeau generalized functions context.

The Levi-Civita space-time

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the injectivity of C1 maps of the real plane

Let X : ℝ2 → ℝ2 be a C1 map. Denote by Spec(X) the set of (complex) eigenvalues of DXp when p varies in ℝ2. If there exists ε > 0 such that Spec(X) ∩ (-ε, ε) = ∅, then X is injective. Some applications of this result to the real Keller Jacobian conjecture are discussed.

Transmission problem for waves with frictional damping April 22, 2007

In this paper we consider the transmission problem, in one space dimension, for linear dissipative waves with frictional damping. We study the wave propagation in a medium with a component with attrition and another simply 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. ©2007 Texas State University.

Remarks on the normal bordism forgetful homomorphism

Assume that X is an oriented smooth (n+k)-manifold. Then the kernel of the forgetful map F considered in this work consists of immersions f: Mn → X nullbordant as a continuous map. Using an exact sequence of normal bordism groups previously given, we present a homological characterization of the kernel of the forgetful map F. Also, we prove that Ωi(X, εs - ηs and Hi(X,Z) are -isomorphic for i≤3 and C2-isomorphic for i≤2, where C2,3 (resp. C2 is the class of abelian groups whose elements have order 2p. 3q (resp. 2p), and ηs is an orientable stable vector bundle over X. © 2009 Pushpa Publishing House.

O conceito de saber escolar clássico em Dermeval Saviani: Implicações para a Educação Matemática

The aim of this paper is initially to consider some issues related to the relationship between humanization and alienation in the process of historical social development of human gender. These considerations are fundamental for understanding the concept of classical in Dermeval Saviani and the consequences for research about the historical development of Mathematics currently found in school curriculums. The intention is to value the appropriation of school mathematics as a humanizing element that becomes accessible through the activity of teaching.

Pesquisa em Resolução de Problemas: caminhos, avanços e novas perspectivas

We discuss the knowledge that has been constructed regarding Problem Solving in Math Education as a result of research developed by GTERP - Work and Study Group in Problem Solving, UNESP-Rio Claro/SP. The research is guided by the following general questions: How do students construct mathematical knowledge and how do teachers implement the methodology of Math Teaching-Learning-Evaluation through Problem Solving? Historical aspects of Problem Solving are very important in the configuration of the current trends for Problem Solving. One of them is the Methodology of Math Teaching-Learning- Evaluation through Problem Solving, based on clear foundations and an approach of renewal. In addition to that methodology, two aspects have been developed by the group: The conception of Math as a science of pattern and order and Discrete Mathematics. The knowledge constructed and the scientific production of GTERP prove its relevant contribution to intensifying dialogues between research and educational practice, students and teachers, and to increasing the possibilities of that practice particularly in Math work.

Discursos do professor de matemática e suas implicações na compreensão dos alunos

The primary objective of this article is to analyze situations with discursive interactions in math classrooms, which may prompt student's understanding of teacher's speech. To analyze the situations with discursive interactions, this study used elements from Bakhtin's theory of language, mainly its concept of comprehension, and introduces the new concept of intermediate comprehension . The data used in a qualitative approach were collected from class observation through video-recorded lessons. The results showed three situations with discursive interactions that contribute to understanding of the school teacher's speech: 1) speech referring to everyday situations; 2) the teacher's speech math in a less rigorous way 3) teacher comparing different mathematical objects.

A semigroups theory approach to a model of suspension bridges

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

Efeito da luminosidade e do horário do exercício de natação até a exaustão na intensidade de lactato mínimo sobre respostas bioquímicas e hematológicas de ratos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Programa pró-letramento matemática: uma abordagem de grandezas e medidas com inserção dos temas transversais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)