| 74/2002 |
On the differentiability of fuzzy-valued mappings and the stability of a fuzzy differential inclusion M. D. Jiménez-Gamero, Yurilev Chalco-Cano, Marko A. Rojas-Medar, Adilson J. Vieira-Brandão We introduce a new concept of differentiability for fuzzy-valued mapping and we study some of its properties. Using this concept, we give a result on stability of the Lyapunov type for fuzzy differential inclusions and a simple application in Biology.  rp-2002-74.pdf |
| 73/2002 |
Parametric Modelling of Genomic Sequences Distance Aluísio Pinheiro, Pranab Kumar Sen, Hildete P. Pinheiro The paper considers the problem of homogeneity among groups by comparison of genomic sequences. Among the problems in that kind of analysis two points are specially addressed here. Genetic data perceives information as categorical variables and as a consequence the overall view of it generates strong dependence between genetic sites. The second problem is that usually models are built on the cleaned data (functional genetic such as genes) and the rest of the data that also carries information is dismissed as useless. We proceed here with emphasis on the available heuristic evidences of great diversity in statistical distributions for the categorical data available. A fully operational parametric statistical model is proposed. The model is built with flexibility to withstand use in several different organisms and adapt itself to that usually dismissed material and the dependence between sites. Consistency of the estimators and of derived test procedures are shown. rp-2002-73.pdf |
| 72/2002 |
Comparison of genomic sequences using the Hamming Distance Hildete P. Pinheiro, Aluísio Pinheiro, Pranab Kumar Sen The paper considers the problem of homogeneity among groups by comparison of genomic sequences. Some alternative procedures that attach less emphasis on the likelihood approach, and more on alternative measures that deal with similar homogeneity problems are considered here. On this approach, a one-sided hypothesis test is considered and the classical ANOVA decomposition can be directly adapted to sample measures based on the Hamming distance, without necessarily going through their second moments. Some results of U-statistics theory will be useful for the decomposition of the test statistic and to find its asymptotic distribution. An application of this test with real data is shown and the p-value of the test statistic is found via bootstrap resampling. rp-2002-72.pdf |
| 71/2002 |
Theoretical evaluation of elliptic integrals based on computer graphics Valério Ramos Batista We use numerical simulations to build theoretical estimates for some elliptic integrals. The procedures explained herein can be generalized to a larger class of integrals and transcendental functions. rp-2002-71.pdf |
| 70/2002 |
Critical and Subcritical Elliptic Systems in dimension two Djairo G. Figueiredo, João Marcos Bezerra do Ó, Bernhard Ruf In this paper we study the existence of nontrivial solutions for the following system of two coulped semilinear Poisson equations:\[\left{\begin{array}{rclccl}-\Delta u&=&g(v),&v>0&in &\Omega,\\-\Delta v&=&f(u),&u>0&in&\Omega,\\u &=&0, &v=0&on&\partial\Omega,\\\end{array}\right.\]where $\Omega$ is a bounded domain in $\mathbb{R}^2$ with smooth boundary $\partial\Omega$, and the functions $f$ and $g$ have the maximal growth which allow us to treat problem (S) variationally in the Sobolev space $H_0^1(\Omega)$. We consider the case with nonlinearities in the critical growth range suggested by the so-called Trudinger-Moser inequality. |
| 69/2002 |
Positive quadratic differential forms: topological equivalence through Newton Polyhedra Carlos Gutierrez, R. D. S. Oliveira, Marco A. Teixeira A germe of a positive quadratic differential form in the plane can be written as$$\omega = a(x,y)dy^2+b(x,y)dxdy+c(x,y)dx^2,$$where $a$, $b$, $c \in C^{\infty}$. This kind of differential form appears in the study of the curvature lines and asymptotic curves in surfaces and in partial differential equations (in gas dynamics). Here, we show that this germ is topologically equivalent to its principal part, defined by the Newton Polyhedra, under suitable conditions. rp-2002-69.pdf |
| 68/2002 |
On quadratic differential forms in the plane with polynomial coefficients R. D. S. Oliveira, Marco A. Teixeira In this article we deal with a special class of planar quadratic differential forms with polynomial coefficients. The main results concern global and local structural stability as well as the finite determinacy in this class. rp-2002-68.pdf |
| 67/2002 |
A strong law of large numbers and a central limit theorem for fuzzy random variables M. D. Jiménez-Gamero, Yurilev Chalco-Cano, Marko A. Rojas-Medar, Filidor E. Vilca-Labra In this paper we give a strong law of large numbers and a central limit theorem for fuzzy random variables. To do this, we use the embedding of the space of compact fuzzy sets with continuous levels applications into a Banach space, via support functions. rp-2002-67.pdf |
| 66/2002 |
Semi-Galerkin Approximation and Strong Solutions to the Equations of the Nonhomogeneous Asymmetric Fluids José Luiz Boldrini, Marko A. Rojas-Medar, Enrique Fernández-Cara Dans ce papier, on analyse un problème de valeurs initiales et valeurs aux limites pour un systeème d'èquations aux dèrivées partielles qui modélise le flux instationnaire d'un fluide asymmétrique incompressible non homogène. Sous des conditions similaires aux conditions usuellement imposées aux équations tridimensionelles de Navier-Stokes non homogènes, à l'aide d'une méthode de type semi-Galerkin, nous démontrons l'éxistence d'une solution forte locale en temps. On établit aussi l'unicité de solution forte et quelques résultats d'éxistence globale. Tous ces résultats reposent sur des estimations appropriées pour les solutions et leurs approximations qui permettent d'ailleurs déduire des estimations de l'erreur. rp-2002-66.pdf |
| 65/2002 |
Fully summing multilinear and holomorphic mappings into Hilbert spaces Daniel M. Pellegrino, Marcela L. V. Souza It is known that whenever $E_{1}$, \dots, $E_{n}$ are infinite dimensional $\mathcal{L}_{\infty}$-spaces and $F$ is any infinite dimensional Banach space, there exists a bounded $n$-linear mapping that fails to be absolutely $(1;2)$-summing. In this paper we obtain a sufficient condition in order to assure that a given $n$-linear mapping $T$ from infinite dimensional $\mathcal{L}_{\infty}$-spaces into an infinite dimensional Hilbert space is absolutely $(1;2)$-summing. Besides, we also give a sufficient condition in order to obtain a fully $(1;1)$-summing multilinear mapping from $l_{1}\times \ldots \times l_{1}\times l_{2}$ into an infinite dimensional Hilbert space. In the last section we introduce the concept of fully summing holomorphic mappings and give the first examples of this kind of maps. rp-2002-65.pdf |
