| 29/2006 |
Aspectos Teóricos de Simulated Annealing e um Algoritmo Duas Fases em Otimização Global Gabriel Haeser, Márcia A. Gomes-Ruggiero  rp-2006-29.pdf |
| 28/2006 |
A Comment on: "On Some Contradictory Computations in Multi-Dimensional Mathematics" Edmundo Capelas de Oliveira, Waldyr A. Rodrigues Jr. In this paper we analyze the status of some `unbelievable results' presented in the paper `On Some Contradictory Computations in Multi-Dimensional Mathematics' [1] published in Nonlinear Analysis, a journal indexed in the Science Citation Index. Among some of the unbelievable results `proved' in the paper we can find statements like that: (i) a rotation $\Tau_\theta\colon R^2\to R^2$, $\theta\ne n\pi/2$, is inconsistent with arithmetic, (ii) complex number theory is inconsistent. Besides these `results' of mathematical nature [1], offers also a `proof' that Special Relativity is inconsistent. Now, we are left with only two options (a) the results of [1] are correct and in this case we need a revolution in Mathematics (and also in Physics) or (b) the paper is a potpourri of nonsense. We show that option (b) is the correct one. All `proofs' appearing in [1] are trivially wrong, being based on a poor knowledge of advanced calculus notions. There are many examples (some of them discussed in [2, 3, 4, 5, 6]) of complete wrong papers using nonsequitur Mathematics in the Physics literature. Taking into account also that a paper like [1] appeared in a Mathematics journal we think that it is time for editors and referees of scientific journals tobecome more careful in order to avoid the dissemination of nonsense. rp-2006-28.pdf |
| 27/2006 |
Simplifying Limits for Functions of Several Variables Robson da Silva, Márcio A. F. Rosa The idea that the limit for functions of several variables cannot be done by employing only one variable has been treated in the calculus courses as a myth or taboo. A very easy-to-prove theorem shows that, for a very large class of functions, this limit can be reduced to a limit done in only one variable, the radial variable of a system of spherical coordinates centered in the limit point. This theorem is very practical to make limits for functions of several variables with the help of softwares and should be included in any calculus' book. Then the student would employ this tool, already heuristically suggested in many books, but with certainty, knowing the precise conditions for it, without any danger of improper generalizations. rp-2006-27.pdf |
| 26/2006 |
A Finite Volume Method for the Mean of the Solution of the Random Transport Equation, Maria Cristina C. Cunha, Fábio A. Dorini We present a numerical scheme, based on Godunov's method (REA algorithm), for the statistical mean of the solution of the 1D random linear transport equation, with homogeneous random velocityand random initial condition. Numerical examples are considered to validate our method. rp-2006-26.pdf |
| 25/2006 |
Otimização de Redes de Distribuição de Água com Estações de Bombeamento C. H. Dias, Francisco A. M. Gomes Neto Neste artigo, apresentamos um novo método para a otimização de redes de distribuição de água com estações de bombeamento. O método é uma adaptação do algoritmo de Hansen, Madsen e Nielsen [Math. Programming, 52 (1991), 45-58]. Nele, o problema não linear inteiro original é aproximado, a cada iteração, por um problema de programação linear com região de confiança em forma de caixa.Os valores reais assim obtidos são convertidos para soluções inteiras adjacentes, garantindo-se que as restrições sejam satisfeitas. Os resultados numéricos indicam que o algoritmo é eficiente. rp-2006-25.pdf |
| 24/2006 |
Projeto Ótimo de Treliças: Otimização Estrutural Francisco A. M. Gomes Neto, Tadao Ando Jr. Treliças são estruturas compostas por barras delgadas e ligadas entre si por meio de rótulas, geralmente sujeitas somente a cargas nos nós, apresentando, neste caso, apenas esforços axiais. Neste trabalho, determinamos a geometria ótima de uma treliça sujeita a um conjunto de forças, obtendo a estrutura mais rígida possível que obedece a restrições de material e de domínio. A abordagem escolhida engloba os problemas de dimensionamento geométrico e topológico, resultando num modelo de programação não linear. Resolvemos esse problema adaptando um algoritmo do tipo restauração inexata, para o qual propomos especializações levando em conta as particularidades do modelo e o objetivo de resolver problemas de grande porte. rp-2006-24.pdf |
| 23/2006 |
Dynamic Control of Infeasibility in Constrained Optimization Roberto H. Bielschowsky, Francisco A. M. Gomes Neto This paper describes a new algorithm for solving nonlinear programming problems with equality constraints. The method introduces the idea of using trust cylinders to keep the infeasibility under control. Each time the trust cylinder is violated, a restoration step is called and the infeasibility level is reduced. The radius of the trust cylinder has a nonincreasing update scheme, so eventually a feasible (and optimal) point is obtained. Global convergence of the algorithm is analyzed, as well as its numerical performance. The results suggest that the algorithm is promising. rp-2006-23.pdf |
| 22/2006 |
On a Theorem of A. Bassi Ricardo N. Cruz We generalize a theorem of A. Bassi about the Betti numbers of closed, connected and orientable manifolds. In addition we show the non-existence of higher dimensional analogues of Hopf's octonionic projective plane even rationally. |
| 21/2006 |
On the Concept of Genus Ricardo N. Cruz The concept of genus of a manifold was introduced by O. Cornea in \cite{co}. Applications can be found in \cite{cdr,cr}. We generalize this concept to stratified spaces. In addition, we provide an elementary computation for the genus of closed and connected surfaces and an example. |
| 20/2006 |
On the Maximum Poincaré Polynomial, Minimal Morse Functions and Whitehead´s Torsion Ricardo N. Cruz This paper is about a generalization of both, the genus of surfaces and the Heegard genus of closed orientable three manifolds, the Maximal Poincar\'e polynomial due to V. Benci and K. A. De Rezende \cite{bdr}. It is also about the related subject minimal Morse functions and the connections of minimal Morse functions to Whitehead's torsion. We establish further properties of the Maximal Poincar\'epolynomial in addition to the ones developed in \cite{bdr}. |
