Some experiments with high order compact methods using a computer algebra software - Part II (non-uniform grid)

We generalize a procedure proposed by Mancera and Hunt [P.F.A. Mancera, R. Hunt, Some experiments with high order compact methods using a computer algebra software-Part 1, Appl. Math. Comput., in press, doi: 10.1016/j.amc.2005.05.015] for obtaining a compact fourth-order method to the steady 2D Navier-Stokes equations in the streamfunction formulation-vorticity using the computer algebra system Maple, which includes conformal mappings and non-uniform grids. To analyse the procedure we have solved a constricted stepped channel problem, where a fine grid is placed near the re-entrant corner by transformation of the independent variables. (c) 2006 Elsevier B.V. All rights reserved.

Boundary of the rauzy fractal sets in R x C generated by P(x)=x(4)-x(3)-x(2)-x-1

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Free actions of abelian p-groups on the n-torus

In this work we make some contributions to the theory of actions of abelian p-groups on the n-Torus T-n. Set congruent to Z(pk1)(h1) x Z(pk2)(h2) x...x Z(pkr)(hr), r >= 1, k(1) >= k(2) >=...>= k(r) >= 1, p prime. Suppose that the group H acts freely on T-n and the induced representation on pi(1)(T-n) congruent to Z(n) is faithful and has first Betti number b. We show that the numbers n, p, b, k(i) and h(i) (i = 1,..,r) satisfy some relation. In particular, when H congruent to Z(p)(h), the minimum value of n is phi(p) + b when b >= 1. Also when H congruent to Z(pk1) x Z(p) the minimum value of n is phi(p(k1)) + p - 1 + b for b >= 1. Here phi denotes the Euler function.

On codimensions k immersions of m-manifolds for k=1 and k=m-2

Let us consider M a closed smooth connected m-manifold, N a smooth ( 2m-2)-manifold and f: M -> N a continuous map, with m equivalent to 1( 4). We prove that if f*: H(1)(M; Z(2)) -> H(1)(f(M); Z(2)) is injective, then f is homotopic to an immersion. Also we give conditions to a map between manifolds of codimension one to be homotopic to an immersion. This work complements some results of Biasi et al. (Manu. Math. 104, 97-110, 2001; Koschorke in The singularity method and immersions of m-manifolds into manifolds of dimensions 2m-2, 2m-3 and 2m-4. Lecture Notes in Mathematics, vol. 1350. Springer, Heidelberg, 1988; Li and Li in Math. Proc. Camb. Phil. Soc. 112, 281-285, 1992).

On the denominator values and barycentric weights of rational interpolants

We improve upon the method of Zhu and Zhu [A method for directly finding the denominator values of rational interpolants, J. Comput. Appl. Math. 148 (2002) 341-348] for finding the denominator values of rational interpolants, reducing considerably the number of arithmetical operations required for their computation. In a second stage, we determine the points (if existent) which can be discarded from the rational interpolation problem. Furthermore, when the interpolant has a linear denominator, we obtain a formula for the barycentric weights which is simpler than the one found by Berrut and Mittelmann [Matrices for the direct determination of the barycentric weights of rational interpolation, J. Comput. Appl. Math. 78 (1997) 355-370]. Subsequently, we give a necessary and sufficient condition for the rational interpolant to have a pole. (c) 2006 Elsevier B.V. All rights reserved.

DIFFERENT MEDIA, DIFFERENT TYPES OF COLLECTIVE WORK IN ONLINE CONTINUING TEACHER EDUCATION: WOULD YOU PASS THE PEN, PLEASE?

This paper presents some findings regarding the interaction between different computer interfaces and different types of collective work. We want to claim that design in online learning environments has a paramount role in the type of collaboration that happens among participants. In this paper, we report on data that illustrate how teachers can collaborate online in order to learn how to use geometry software in teaching activities. A virtual environment which allows that construction to be carried out collectively, even if the participants are not sharing a classroom, is the setting for the research presented in this paper.

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.

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.

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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A dialética do conhecimento científico, a prática e a experimentação: uma análise do ideário de licenciandos e sua relação com a epistemologia da ciência moderna

Pós-graduação em Educação para a Ciência - FC

Educação Matemática e Nova Alta Paulista: orientação para tecer paisagens

Pós-graduação em Educação Matemática - IGCE