| 2/2001 |
The Cauchy problem for micropolar fluid equations Jaime Rezendiz B., Marko A. Rojas-Medar We consider the Cauchy problem for equation of a nonstationary micropolar fluid in three dimensional whole space. We show the local, global existence and the asymptotic behaviours of a strong solutions.  rp-2001-2.pdf |
| 1/2001 |
Groups with finitely generated integral homologies Dessislava H. Kochloukova Suppose $A$ is an abelian normal subgroup of a finitely generated group $G$ such that $G/A$ is abelian and $H_i(G, \BZ)$ is finitely generated for all $i$ . We show that $A$ is of finite (Pr\"ufer) rank. This generalises the main result of \cite{gr} that deals with the same problem for split extension metabelian groups. rp-2001-1.pdf |
| 44/2000 |
On the combinatorics of the Fibonacci Numbers Jose Plínio O. Santos In this paper following some ideas introduced by Andrews in \cite{an4} and results given by Santos in \cite{sa} we give new formula and combinatorial interpretation for the Fibonacci Numbers. rp-2000-44.pdf |
| 43/2000 |
On a new combinatorial interpretation for a theorem of Euler José Plínio O. Santos In this paper we describe a new set of partitions that is equinumerous with the set of partitions into odd parts. A new combinatorial interpretation for the Rogers-Ramanujan identities is given as an application. rp-2000-43.pdf |
| 42/2000 |
On the solution of mathematical programming problems with equilibrium constraints using nonlinear programming algorithms José Mario Martínez, Roberto Andreani Mathematical programming problems with equilibrium constraints (MPEC) are nonlinear programming problems where the constraints have a form that is analogous to first-order optimality conditions of constrained optimization. In these problems all the feasible points are nonregular, in the sense that the gradients of active constraints are always linearly dependent. This and other difficulties associated to the direct application of NLP algorithms to MPEC are discussed it is suggested how to overcome some of them. rp-2000-42.pdf |
| 41/2000 |
Augmented Lagrangian Algorithms based on the Spectral Projected Gradient for solving nonlinear programming problems Sandra A. Santos, José Mario Martínez, Márcia A. Gomes-Ruggiero, Maria A. Diniz-Ehrhardt The Spectral Projected Gradient method ({\tt SPG}) is an algorithm for large-scale bound-constrained optimization introduced recently by Birgin, Mart\'{\i}nez and Raydan. It is based on Raydan's unconstrained generalization of the Barzilai-Borwein method for quadratics. The {\tt SPG} algorithm turned out to be surprisingly effective for solving many large-scale minimization problems with box constraints. Therefore, it is natural to test its performance for solving the subproblems that appear in nonlinear programming methods based on augmented Lagrangians. In this work, augmented Lagrangian methods which use {\tt SPG} as underlying convex-constraint solver are introduced ({\tt ALSPG}), and the methods are tested in two sets of problems. First, a meaningful subset of large-scale nonlinearly constrained problems of the {\tt CUTE} collection is solved and compared with the performance of {\tt LANCELOT}.Second, a family of localization problems in the minimax formulation is solved against the package {\tt FFSQP}. rp-2000-41.pdf |
| 40/2000 |
The approach of St\"ohr-Voloch to the Hasse-Weil bound with applications to optimal curves and plane arcs Fernando Torres This is an expository paper concerning topics on rational points of curves defined over finite fields based on a paper by St\"ohr and Voloch. rp-2000-40.pdf |
| 39/2000 |
Experimentos com programas lineares por partes em redes Fernando A. S. Marins, Margarida P. Mello, Clóvis Perin The usual approach to solving a piecewise linear network flow problem is to transform it into an equivalent linear one. In this transformation, a piecewise network with $n$ nodes and $m$ arcs, each with $k$ intervals (corresponding to the linear pieces of the arc cost function), has an equivalent linear one with $n$ nodes and $m k$ arcs. Interior point methods have been proved successful in the solution of linear network flow problems. We show that it is advantadgeous to construct a customized interior point method to solve piecewise network problems directly, instead of applying its generic version to the equivalent linear problem. Two algorithms were implemented and tested: one using preditor-corrector and the other without the corrector step. Comparison between alternative strategies (initialization, stopping criteria) are done by means of several computacional tests. rp-2000-39.pdf |
| 38/2000 |
The Kirchhoff-Helmholtz integral for anisotropic elastic media Jörg Schleicher, Martin Tygel, Bjorn Ursin, Norman Bleistein The Kirchhoff-Helmholtz integral is a powerful tool to model the scattered wavefield from a smooth interface in acoustic or isotropic elastic media due to a given incident wavefield and observation points sufficiently far away from the interface. This integral makes use of the Kirchhoff approximation of the unknown scattered wavefield and its normal derivative at the interface in terms of the corresponding quantities of the known incident field. An attractive property of the Kirchhoff-Helmholtz integral is that its asymptotic evaluation recovers the zero-order ray theory approximation of the reflected wavefield at all observation points where that theory is valid. Here, we extend the Kirchhoff-Helmholtz modeling integral to general anisotropic elastic media. It uses the natural extension of the Kirchhoff approximation of the scattered wavefield and its normal derivative for those media. The anisotropic Kirchhoff-Helmholtz integral also asymptotically provides the zero-order ray theory approximation of the reflected response from the interface. In connection with the asymptotic evaluation of the Kirchhoff-Helmholtz integral, we also derive an extension to anisotropic media of a useful decomposition formula of the geometrical spreading of a primary reflection ray. rp-2000-38.pdf |
| 37/2000 |
Loterias Esportivas e Códigos Marcelo Firer rp-2000-37.pdf |
