| 20/2005 |
On Periodicity of Solutions for the Nonstationary Convection Problem Elder J. Villamizar-Roa We study the existence and the uniqueness of strong periodic solutions for the Boussinesq equations in unbounded domains for the prescribed external forces.  rp-2005-20.pdf |
| 19/2005 |
Projetos para o ensino de Cálculo Variacional Gabriel Lima, Vera L. X. Figueiredo, Sandra A. Santos Este trabalho propõe o uso de projetos como uma ferramenta auxiliar para o ensino do Cálculo Variacional. Após uma breve introdução à filosofia do trabalho com projetos, e exercícios preliminares envolvendo problemas de otimização para funções de várias variáveis e multiplicadores de Lagrange, são encaminhadas duas propostas de projetos visando resgatar o problema da geodésica e o problemada braquistócrona com os olhares histórico, físico, geométrico, analítico e computacional. Este resgate procura engajar o estudante em um trabalho autônomo, na busca da compreensão e apropriação da matemática envolvida. São abordados desde conceitos introdutórios do Cálculo Variacional até aspectos mais elaborados presentes nesse ramo damatemática. rp-2005-19.pdf |
| 18/2005 |
E a quadratura foi para o espaço ... Vera L. X. Figueiredo, Sandra A. Santos Arquimedes demonstrou que a área de um segmento parabólico é 4/3 da área do trinâgulo inscrito de mesma base e de vértice no ponto em que a tangente é paralela à base. Este trabalho estende a quadratura de Arquimedes para R^n, permitindo interpretar a razão entre áreas no caso plano em termos da dimensão. O problema em R^n é estabelecido, com a construção dos objetos correspondentes no cálculo deseus volumes n-dimensionais. Assim como ocorre com a n-esfera unitária em R^n, os volumes dos objetos envolvidos vão para zero quando n tende a infinito. A relação entre estes volumes, no entanto, apresenta um curioso comportamento assintótico. Com base nos cálculos efetuados, uma outra relação estabelecida por Arquimedes, entre os volumes da semi-esfera, do cilindro circunscrito e do cone inscrito, é estendida e ampliada. rp-2005-18.pdf |
| 17/2005 |
Entropy and Widths of Multiplier Operators on Compact Globally Symmetric Spaces of Rank 1 Alexander Kushpel, Sérgio A. Tozoni The main aim of the present article is to give a unified treatment for a wide range of multiplier operators $\Lambda$ on symmetric manifolds. Namely, we investigate entropy numbers and $n$-widths of decaying multipliers sequences of real numbers $\Lambda = \{\lambda_{n}\}_{k=1}^{\infty}$, $|\lambda_{1}| \geq |\lambda_{2}| \geq \ldots$, $\Lambda:L_{p}(M^{d}) \rightarrow L_{q}(M^{d})$ on $M^{d}$, on the compact globally symmetric spaces of rank 1 or on two-point homogeneous spaces $M^{d}$: $S^{d}$, $P^{d}(\RR)$, $P^{d}(\CC)$, $P^{d}(\HH)$, $P^{16}({\rm Cay})$. In particular, wegive sharp orders of entropy and $n$-widths of standard Sobolev's classes $W^{\gamma}_{p}(M^{d})$ in $L_{q}(M^{d})$ for all $1 < p, q < \infty$. rp-2005-17.pdf |
| 16/2005 |
Recurrent Neural Net Regression Models with Space-Varying Coefficients for Pedotransfer Function Estimation and Prediction of Soil Properties Daniel Takata Gomes, Emanuel P. Barbosa, Luis Carlos Timm The paper aim is to propose a new regression model for relating soil variables of difficult or complex measurement with other variables easier to measure, in order to predict the first one based on data about the last ones. The measurements are taken along soil lines called transects. The study of these relations (pedotransfer functions) presents the complexity of simultaneous presence of 3 elements: data spatial dependence, soil non-homogeneity and non-linearity of the relationship.The main models usually considered in the literature for such relations (namely, linear state-space and feedforward neural nets) have the limitation of expressing only two of these 3 characteristics of the problem. In order to overcome such limitations, it is proposed here a regression model for pedotransfer mapping based on recurrent neural nets (the feedback helps to better express the spatial dependence), but with weights varying smoothly along the space in order to incorporate the soil non-homogeneity. The algorithm developed for model estimation and prediction is based on a second order non-linear extension of theKalman filter in Bayesian form. The comparative advantages of the proposed model in relation to the other ones are shown, considering different prediction performance measures for the transect extremes. rp-2005-16.pdf |
| 15/2005 |
On Conformal d´Alembert-Like Equations Edmundo Capelas de Oliveira, Roldão da Rocha Jr. Using conformal coordinates associated with projective conformal relativity we obtain a conformal Klein-Gordon partial differential equation. As a particular case we present and discuss a conformal 'radial'd'Alembert-like equation. As a by-product we show that this 'radial' equation can be identified with a one-dimensional Schrödinger-like equation in which the potential is exactly the second Pöschl-Teller potential. rp-2005-15.pdf |
| 14/2005 |
An Ambiguous Statement Called 'Tetrad Postulate' and the Correct Field Equations Satisfied by the Tetrad Fields Waldyr A. Rodrigues Jr., Quintino A. G. de Souza rp-2005-14.pdf |
| 13/2005 |
Hidden Consequence of Active Local Lorentz Invariance Waldyr A. Rodrigues Jr., Roldão da Rocha Jr., Jayme Vaz Jr. |
| 12/2005 |
Riemann and Ricci Fields in Geometric Structures Antonio M. Moya, Virginia V. Fernández, Waldyr A. Rodrigues Jr. rp-2005-12.pdf |
| 11/2005 |
Derivative Operators in Metric and Geometric Structures Antonio M. Moya, Virginia V. Fernández, Waldyr A. Rodrigues Jr. rp-2005-11.pdf |
