Discrete approximations for strict convex continuous time problems and duality

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Efficient linear programming algorithm for the transmission network expansion planning problem

The transmission network planning problem is a non-linear integer mixed programming problem (NLIMP). Most of the algorithms used to solve this problem use a linear programming subroutine (LP) to solve LP problems resulting from planning algorithms. Sometimes the resolution of these LPs represents a major computational effort. The particularity of these LPs in the optimal solution is that only some inequality constraints are binding. This task transforms the LP into an equivalent problem with only one equality constraint (the power flow equation) and many inequality constraints, and uses a dual simplex algorithm and a relaxation strategy to solve the LPs. The optimisation process is started with only one equality constraint and, in each step, the most unfeasible constraint is added. The logic used is similar to a proposal for electric systems operation planning. The results show a higher performance of the algorithm when compared to primal simplex methods.

Oral health in renal transplant recipients administered cyclosporin A or tacrolimus

OBJECTIVE: the aim of this study was to determine the oral status of renal transplant recipients receiving cyclosporin A (CsA) or tacrolimus (FK-506) as immunosuppressant.SUBJECTS AND METHODS: A total of 88 renal transplant recipients receiving CsA (63 men and 25 women, mean age 51.4 years) and 67 receiving FK-506 (57 men and 10 women, mean age 33.5 years) were included in the study. Donor type, histocompatibility, cold ischemia time and prior delayed graft function were similar between the two groups. Demographics and pharmacological data were recorded for all subjects.RESULTS: the results demonstrated that CsA caused a greater number of oral diseases. A greater number of gingival overgrowth was present in patients treated with CsA. However, the combined use with calcium channel blockers increased the gingival overgrowth number. The occurrence of candida in saliva was observed in 80 renal recipients treated with CsA and 20 treated with FK-506. The presence of squamous oral carcinoma (n = 3) and herpes simplex (n = 10) was observed in patients treated with CsA. These alterations were not observed in renal recipients treated with FK-506.CONCLUSIONS: Renal recipients constitute a high-risk group for oral diseases, as they are immunocompromised. However, the FK-506 regime appears to ameliorate this effect, compared with CsA. Adequate pre- and post-transplant oral health care is recommended for these subjects, irrespective of the time interval for which the drug is administered.

ALPHA-CONTRACTIONS AND ATTRACTORS FOR DISSIPATIVE SEMILINEAR HYPERBOLIC-EQUATIONS AND SYSTEMS

In this paper we discuss the existence of compact attractor for the abstract semilinear evolution equation u = Au + f (t, u); the results are applied to damped partial differential equations of hyperbolic type. Our approach is a combination of Liapunov method with the theory of alpha-contractions.

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.

Características dos Problemas que os Alunos Constroem a partir do Enunciado de uma Questão Aberta de Matemática

The present paper shows characteristics of problems that students in the 4(th), 8(th), and 12(th) grades built in response to the enunciation of an open-ended question, taken from their written work in the common question of AVA-2002 (Parana State Large-Scale Assessment-2002). These problems are characterized, in part, by a linear resolution structure constituted based on students' interpretation of individual bits of information contained in the enunciation, one by one, without establishing relations between them; and partly by a non-linear resolution structure constituted based on relations established among the bits of information in the enunciation. Analysis of students' written work is one alternative for teachers to know students' mathematical activity, as well as their particular ways of interpretating enunciations.

O intuitivo e o lógico no conhecimento matemático: análise de uma proposta pedagógica em relação a abordagens filosóficas atuais e ao contexto educacional da matemática

In this paper, we consider Meneghetti & Bicudo's proposal (2003) regarding the constitution of mathematical knowledge and analyze it with respect to the following two focuses: in relation to conceptions of mathematical knowledge following the fundamentalist crisis in mathematics; and in the educational context of mathematics. The investigation of the first focus is done analyzing new claims in mathematical philosophy. The investigation of the second focus is done firstly via a theoretical reflection followed by an examination of the implementation of the proposal in the process of development of didactic materials for teaching and learning Mathematics. Finally, we present the main results of the application of one of those materials.

Análise de textos didáticos de Matemática: um mapeamento e uma proposta metodológica fundada numa perspectiva hermenêutica

This article discusses some methodological possibilities for analyzing textbooks in Mathematics Education. Its starting point was a review - which allowed us to build a general map - of the production developed by consolidated Research Groups that deal with this theme in Brazil. This map allowed us to propose a complementary/alternative guide to analyse textbooks according to a hermeneutical approach.

O modelo de Romberg e o percurso metodológico de uma pesquisa qualitativa em educação de uma pesquisa qualitativa em educação

The objective of this study is to present the trajectory of a research project (ALLEVATO, 2005) whose phenomenon of interest is the teaching of mathematics using problem solving with computers. The text is an attempt to portray this trajectory, from the point of view of the methodological route followed by the researcher, which was based on two main axes: the guidance of the educator Thomas A. Romberg (1992), and the guidelines provided by the foundations of qualitative research. The study was developed during a doctoral course offered by the Graduate Program in Mathematics Education at the State University of São Paulo (UNESP), Rio Claro campus.