| 29/2007 |
On a General Class of Trigonometric Functions and Fourier Series H. Germano Pavão, Edmundo Capelas de Oliveira We discuss a general class of trigonometric functions whose corresponding Fourier series can be used to calculate several interesting numerical series. Particular cases are presented. |
| 28/2007 |
Consistent Estimator for Constrained Minimal Trajectories Ronaldo Dias, Nancy L. Garcia, Adriano Z. Zambom Consider the problem of finding a smooth function joining two points A and B with minimum length constrained to avoid fixed subsets when stochastic measurement errors are present. In this case, the estimator proposed by Dias, Garcia and Zambom (2007) is consistent, in the sense that as the number of observations increases the stochastic trajectory converges to the best deterministic one. Two applications are immediate, searching the optimal a path for an autonomous vehicle while avoiding all fixed obstacles between two points and flight planning to avoid threat or turbulence zones.  rp-2007-28.pdf |
| 27/2007 |
Robust Multivariate Measurement Error Model with Skew-Normal/Independent Distributions Víctor H. Lachos, Filidor E. Vilca-Labra, Heleno Bolfarine Skew-normal/independent distributions is a class of asymmetric thicktailed distributions that includes the skew-normal distribution as a especial case. The main virtue of the members of this class of distributions is that they are easy to simulate from and they make it possible to implement the Monte Carlo EM algorithm for maximum likelihood estimation. In this paper, we take skew-normal/independent distributions (Lachos and Vilca, 2007) for the unobserved value of the covariates (latent variable) and symmetric normal/independent (Lange and Sinsheimer, 1993) distributions for the random errors providing an appealing robust alternative to the usual symmetric process in multivariate measurement errors models. Specific distributions examined include univariate and multivariate versions of the skew-normal, the skew-t, the skew-slash and the contaminated skew-normal distribution. The results and methods are applied to a real data set. rp-2007-27.pdf |
| 26/2007 |
HJM Interest Rate Models with Fractional Brownian Motions Alberto M. F. Ohashi, Pedro J. Catuogno In this work we introduce Heath-Jarrow-Morton (HJM) interest rate models driven by fractional Brownian motions. We consider the term structure of interest rates as given by a stochastic partial differential equation driven by a cilindrical fractional white noise. We obtain a drift condition which is similar in nature to the classical HJM no-arbitrage drift restriction. By using support arguments we prove that the resulting model is arbitrage-free under proportional transaction costs. rp-2007-26.pdf |
| 25/2007 |
Invariant Manifolds for Stochastic PDE with Fractional Brownian Motion Alberto M. F. Ohashi In this work we study invariant manifolds for stochastic partial differential equations (SPDEs) driven by a fractional Brownian motion with parameter $H > 1/2$. The main ingredient in our analysis is the characterization of a controlled deterministic evolution equation where the invariant sets for the SPDE are precisely those of the controlled system. We provide a complete characterization of a given invariant finite dimensional manifold by means of Nagumo-type conditions. rp-2007-25.pdf |
| 24/2007 |
On Sums of Numerical Series and the Fourier Series H. Germano Pavão, Edmundo Capelas de Oliveira We discuss the sums associated with some Fourier series. Some new sums are obtained as particular cases of the Fourier series associated with a convenient class of functions. Two recent results involving numerical series are recovered. |
| 23/2007 |
Grupos de Heisenberg: da Geometria ao Operador de Kohn - Laplace Igor Leite Freire Neste trabalho apresentamos brevemente os Grupos de Heisenberg, algumas de suas propriedades geométricas e a equação semilinear de Kohn - Laplace.Comentamos também resultados recentes envolvendo tais equações e a geometria de $H^{n}$, bem como problemas em aberto envolvendo a estrutura geométrica de $H^{n}$ e grupos de simetrias da equação semilinear de Kohn- Laplace para $n>1$. rp-2007-23.pdf |
| 22/2007 |
Explicit Radial Bratu Solutions in Dimension n = 1, 2 Nir Cohen, Julia V. Toledo-Benavides We find the general solution \(u(x)\), \(x\in \mathbb{R}\) of the 1-D Bratu equation \(u_{xx} + \lambda e^u = 0\) and the general solution \(U(r)\), \(r>0\), of 2-D radial Bratu equation \(rU_{rr} + U_r + \lambda r e^U = 0\) . We use these results to obtain explicit solutions and bifurcation patterns for boundary value problems involving these equations, and in particular, solutions of the Bratu boundary value problem used in combustion theory. We review the history of Liouville's idea which made these results possible, and correct historical errors found in recent literature. rp-2007-22.pdf |
| 21/2007 |
A Modified Descent Direction for Newton-GMRES Method Márcia A. Gomes-Ruggiero, Véra L. R. Lopes, Julia V. Toledo-Benavides We consider general Newton-Krylov methods with a line search for solving $F(x) = 0$. In order to curb a possible increase in $||F||$, typically occurring during the first few cycles, we propose a simple modification of the Newton direction which does not require a modified Krylov procedure. rp-2007-21.pdf |
| 20/2007 |
An Optimal Path for an Autonomous Vehicle: A Nonparametric Approach Ronaldo Dias, Nancy L. Garcia, Adriano Z. Zambom The objective of this study is to find the best trajectory for an autonomous vehicle which has to move from point A to point B in the minimum distance possible while avoiding all fixed obstacles between these points. Moreover, we assume that there is a safe distance r to be kept between the vehicle and the obstacles at all times. Also, the maneuverability of the vehicle is not easy, that is it cannot make abrupt turns and the trajectory has to follow a smooth curve. Obviously, if there are no obstacles, the best route is a straight line between A and B. In this work we propose a nonparametric method of finding the best path. If there is measurement error, a consistent stochastic estimator is proposed in the sense that as the number of observations increase the stochastic trajectory converges to the deterministic one. rp-2007-20.pdf |
