| 19/2006 |
On Global and Local Extrema Ricardo N. Cruz Find global extrema (maximuns and minimuns) is a straightforward task for a well behaved real function of a real variable. We provide two approaches for finding global extrema of real functions of many variables, explained in examples and guided exercises. In addition we provide specific examples. We fully discuss the second derivative test in all dimensions. In particular, we discuss high-dimensional saddles. |
| 18/2006 |
The Structure of Algebras Admitting Well Agreeing Near Weights Carlos Munuera, Fernando Torres We characterize algebras admitting two well agreeing near weights $\rho$ and $\sigma$. We show that such an algebra $R$ is an integral domain whose quotient field $\K$ is an algebraic function field of one variable. It contains two places $P, Q\in {\mathbb P}(\K)$ such that $\rho$ and $\sigma$ are derived from the valuations associated to $P$ and $Q$. Furthermore$\bar R=\cap_{S\in \bP(\K)\setminus\{P,Q\}} \cO_S$.  rp-2006-18.pdf |
| 17/2006 |
Riemann Problem for Random Advective Equation Maria Cristina C. Cunha, Fábio A. Dorini In this article we present an explicit expression to the solution of the random Riemann problem for the 1D random linear transport equation. We show that the random solution is a similarity solution and thestatistical moments have very simple expressions. We show that the mean, the variance, and the 3rd central moment agree quite well with Monte Carlo simulations. We guess that our approach can be useful in designing numerical methods for random transport equation, as in the deterministic case. rp-2006-17.pdf |
| 16/2006 |
Near Orders and Codes C. Carvalho, Carlos Munuera, E. Silva, Fernando Torres H\o holdt, van Lint and Pellikaan used order functions to construct codes by means of Linear Algebra and Semigroup Theory only. However, Geometric Goppa codes that can be represented by this method are mainly those based on just one point. In this paper we introduce the concept of near order function with the aim of generalize this approach in such a way that a of wider family of Geometric Goppa codes can be studied on a more elementary setting. rp-2006-16.pdf |
| 15/2006 |
Sobre a Função de Mittag-Leffler R. Figueiredo Camargo, Edmundo Capelas de Oliveira, Ary O. Chiacchio rp-2006-15.pdf |
| 14/2006 |
Quasi-Newton Acceleration for Equality-Constrained Minimization L. Ferreira-Mendonça, Véra L. R. Lopes, José Mario Martínez Optimality (or KKT) systems arise as primal-dual stationarity conditions for constrained optimization problems. Under suitable constraint qualifications, local minimizers satisfy KKT equations but, unfortunately, many other stationary points (including, perhaps, maximizers) may solve these nonlinear systems too. For this reason, nonlinear-programming solvers make strong use of the minimization structure and the naive use of nonlinear-system solvers in optimization may lead to spurious solutions. Nevertheless, in the basin of attraction of a minimizer, nonlinear-system solvers may be quite efficient. In this paper quasi-Newton methods for solving nonlinear systems are used as accelerators of nonlinear-programming (augmented Lagrangian) algorithms, with equality constraints. A periodically-restarted memoryless symmetric rank-one (SR1) correction method is introduced for that purpose. Convergence results are given and numerical experiments that confirm that the acceleration is effective are presented. rp-2006-14.pdf |
| 13/2006 |
Conformal Klein-Gordon Equations and Quasinormal Modes Roldão da Rocha Jr., Edmundo Capelas de Oliveira Using conformal coordinates associated with conformal relativity -- associated with de Sitter spacetime homeomorphic projection into Minkowski spacetime -- we obtain a conformal Klein-Gordon partial differential equation, which is intimately related to the production of quasi-normal modes (QNMs) oscillations, in the context of electromagnetic and/or gravitational perturbations around, e.g., black holes. While QNMs arise as the solution of a wave-like equation with a P\"oschl-Teller potential, here we deduce and analytically solve a conformal `radial' d'Alembert-like equation, from which we \emph{derive} QNMs formal solutions, in a proposed alternative to more completely describe QNMs. As a by-product we show that this `radial' equation can be identified with a Schr\"odinger-like equation in which the potential is exactly the second P\"oschl-Teller potential, and it can shed some new light on the investigations concerning QNMs. |
| 12/2006 |
Degenerate Resonances and Branching of Periodic Orbits, A. Jacquemard M. Firmino Silva Lima, Marco A. Teixeira In this paper we establish results on the existence of Lyapunov families of periodic orbits of reversible systems in $\mathbb{R}^6$ around an equilibrium that presents a $0:1:1-$ resonance. The main proofs are based on a combined use of normal form theory, Lyapunov-Schimdt reduction and elements of symbolic computation. rp-2006-12.pdf |
| 11/2006 |
Soliton Solution for Quasilinear Elliptic Equations Involving the $p$-Laplacian in $R ^N$ Uberlândio Batista Severo In this paper we use the variational methods, more precisely, the Mountain-Pass Theorem to obtain existence results for the following class of quasilinear elliptic problems:\[\begin{array}{lll}-\Delta_p u -\Delta_p (u^2)u +k V(x)|u|^{p-2} u= h(u), & \;\text{in}\; &\mathbb{R}^N,\\\end{array}\]where $ \Delta_p u := div(|\nabla u |^{p-2} \nabla u)$ is the $p$-Laplacian operator and $1 |
| 10/2006 |
Some Applications for Newton-Krylov Methods with a Safeguard for GMRES(m) Márcia A. Gomes-Ruggiero, Véra L. R. Lopes, Julia V. Toledo-Benavides Restarting GMRES, a linear solver frequently used in numerical schemes, is known to suffer from stagnation. In this paper, a simple strategy is proposed to detect and avoid stagnation, without modifying the standard GMRES code. Numerical tests with the modified GMRES($m$), GMRESH($m$) procedure, alone and as part of an inexact Newton procedure with several choices for the forcing term, demonstrate the efficiency of the proposed strategy. rp-2006-10.pdf |
