| 45/2004 |
A Note on the Number of Nodal Solutions of an Elliptic Equation with Symmetry Marcelo F. Furtado We consider the semilinear problem $-\Delta u + \lambda u =|u|^{p-2}u$ in $\Omega$, $u=0$ on $\partial \Omega$ where $\Omega \subset \mathbb{R}^N$ is a bounded smooth domain and $2  rp-2004-45.pdf |
| 44/2004 |
Evolution Equations Driven by a Fractional White Noise in Spaces of Abstract Stochastic Distributions Alberto M. F. Ohashi In this paper we study stochastic evolution equations driven by a fractional white noise with arbitrary Hurst parameter in infinite dimension. We establish the existenceand uniqueness of a mild solution for a nonlinear equation with multiplicative noise under Lipschitz condition by using a fixed point argument in an appropriate inductive limit space. In the linear case with additive noise a strong solution is obtained. Those results are applied to stochastic parabolic partial differentialequations perturbed by a fractional white noise. rp-2004-44.pdf |
| 43/2004 |
Variações do Método de Máxima Descida em Otimização Irrestrita Momoe Sakamori, Márcia A. Gomes-Ruggiero rp-2004-43.pdf |
| 42/2004 |
On Iterative Methods for Incompressible Fluids with Mass Diffusion Francisco Guillén González, P. Damázio, Marko A. Rojas Medar In this paper, we study the strong solutions of incompressible fluids with mass diffusion. We use an iterative method in order to approach the strong solutions and some convergence rates for this scheme are obtained, depending on weak, strong and more regular norms (latter only for strictly positive times). rp-2004-42.pdf |
| 41/2004 |
Optimal Control and Partial Differential Equations I. Gayte Delgado, Francisco Guillén González, F. P. Marques Lopes, Marko A. Rojas Medar In this work, some type of optimal control problems with equality constraints given by Partial Differential Equations (PDE) and convex inequality constraints are considered, obtaining their corresponding first order necessary optimality conditions by means of Dubovitskii-Milyutin (DM) method. Firstly, we consider problems with one objective functional (or scalar problems) but non-well posed equality constraints, where existence and uniqueness of state in function on control is not true (either one has existence but not uniqueness of state, or one has not existence of state for any control). In both cases, the classical Lions argument (re-writing the problem as an optimal control problem for the control without equality constraints, see for instance [14]) can not be applied.Afterwards, we consider multiobjective problems (or vectorial problems), considering three different concepts of solution: Pareto, Nash and Stackelberg. In all cases, an adequate abstract DM method is developed followed by an example. rp-2004-41.pdf |
| 40/2004 |
Chain Codes and Spherical Tits Buildings Luciano Panek, Marcelo Firer To a $n$-dimensional vector space $V$ over a finite field $\mathbb{F}_q$ it is possible to associate a structure of spherical Tits building. The chambers of such building are maximal flags: maximal sequences of nested subspaces. In the case $q=2$, there is a unique $( n-1) $-dimensional 1-MDS code $C\subset V$. We show the existence of chambers associated to such a code that are chain type (in the sense of codes theory) and given a complete characterization of the connected components of the chain type chambers. rp-2004-40.pdf |
| 39/2004 |
Some Properties of a Class of Abstract Stationary Equations Elder J. Villamizar-Roa, Marko A. Rodríguez-Bellido, Marko A. Rojas-Medar We study a class of abstract nonlinear equations in a separable Hilbert space for which we prove properties of the set of solutions. The results apply, in particular, in several models of hydrodynamics, such as magneto-micropolar equations, micropolar fluid equations, Boussinesq and Navier-Stokes equations. rp-2004-39.pdf |
| 38/2004 |
A Semilinear Heat Equation with Singular Nonlinearity M. Loayza We are interested in the parabolic equation $u_t-\Delta u=f(x,u)$ in a bounded domain of $\R^N$ with Dirichlet boundary condition and $f:\Omega \por [0,\infty) \to [0,\infty)$ a Carath\'eodory function. We study the existence of solution, life span and analyze the behavior of the global(when the time $t\to \infty$) solution with respect to the solution of the ellipticcorresponding problem $-\Delta u=f(x,u)$ with the Dirichlet boundary condition. A typical example where the results areapplied is when $f(x,s)=a(x)s^q+b(x)s^p$ with $0 rp-2004-38.pdf |
| 37/2004 |
Alocação de Clientes em Grupos Usando Classificação via Boosting: Uma Comparação com os Métodos Tradicionais de Classificação Alexandre Rübesam, Ronaldo Dias The traditional statistical methods used in classification are, basically, logistic regression and discriminant analysis.Recently, other methods have been used in applications, e.g., classification trees and neural networks. The traditional methodsare computationally cheap, but lack flexibility, while methods such as neural networks are flexible, but computationallyexpensive and complicated. The method presented in this work, boosting, combines simple base classifiers, increasing at eachstep the weights of the observations that were previously misclassified.This work presents the method of boosting, as well as two applications. One is on simulated data, and the other on real data. The real-data application consists of classifying clients of a retail store into previously defined groups, which define the clients' profiles. The results obtained with boosting in both applications are compared to the results of the traditional methods. rp-2004-37.pdf |
| 36/2004 |
Augmented Lagrangian Methods Under the Constant Positive Linear Dependence Constraint Qualification Roberto Andreani, E. G. Birgin, José Mario Martínez, M. L. Schuverdt Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented. rp-2004-36.pdf |
