| 19/2007 |
Non-Parametric Estimation for Aggregated Functional Data for Electric Load Monitoring Ronaldo Dias, Nancy L. Garcia, Angelo Martarelli In this work we address the problem of estimating mean and covariance curves when the available sample consists on aggregated functional data. Consider a population divided into sub-populations for which one wants to estimate the mean (typology) and covariance curves for each sub-population. However, it is not possible (or too expensive) to obtain sample curves for single individuals. The available data are collective curves, sum of curves of different subsets of individuals belonging to the sub-populations. We propose an estimation method based on B-splines expansion. This method is consistent and simulation studies suggest that the proposed mean estimator is suitable even with very few replications. This problem was motivated by a real problem concerning the efficient distribution of electric energy in Southeast Brazil.  rp-2007-19.pdf |
| 18/2007 |
Approximation by $sk$-spline interpolants in $L_q$ Alexander Kushpel Rates of convergence of $sk$-spline interpolants are established on a wide range of sets of smooth functions $\RR \oplus K \ast U_{p}$ in $L_q$ (including sets of differentiable, infinitely differentiable, analytic and entire functions) for any $1 < p, q < \infty$. We show that on such function classes $sk$-spline interpolants with equidistant knots and points of interpolation give the same order of convergence as the subspace of trigonometric polynomials of the same dimension. |
| 17/2007 |
Noether Symmetries and Conservation Laws For Non-Critical Kohn -Laplace Equations on Three-Dimensional Heisenberg Group Igor Leite Freire We show which Lie point symmetries of non-critical semilinear Kohn-Laplace equations on the Heisenberg group $H^1$ are Noether symmetries and we establish their respectives conservations laws. rp-2007-17.pdf |
| 16/2007 |
Circulant Graphs Viewed as Graphs on Flat Tori Sueli I. R. Costa, J. E. Strapasson, M. Muniz, T. B. Carlos Circulant graphs can be viewed as vertices connected by a knot on a $k$-dimensional flat torus tessellated by hypercubes or hyperparallelotopes. This approach allows to see some results on circulant graph minimum diameter, to derive bounds for the genus of certain circulant graphs and also to establish connections with spherical codes and perfect graph codes in Lee spaces. rp-2007-16.pdf |
| 15/2007 |
Statistical Moments of the Random Linear Transport Equation Fábio A. Dorini, Maria Cristina C. Cunha This paper deals with a numerical scheme to approximate the $m$th moment of the solution of the one-dimensional random linear transport equation. The initial condition is assumed to be a random functionand the transport velocity is a random variable. The scheme is based on local Riemann problem solutions and Godunov's method. We show that the scheme is stable and consistent with an advective-diffusive equation. Numerical examples are added to illustrate our approach. rp-2007-15.pdf |
| 14/2007 |
A Skewed Version of the Non-Central Sinh-Normal Distribution and its Properties and Application Víctor Leiva, Filidor E. Vilca-Labra, N. Balakrishnan In this article, we introduce a skewed version of the non-central sinh-normal distribution and discuss some of its properties. In addition, the associated Birnbaum-Saunders distribution is characterized from a probabilistic viewpoint along with a reliability analysis. Finally, the proposed model is fitted to a lifetime data in order to illustrate its usefulness. rp-2007-14.pdf |
| 13/2007 |
A Outra Face da Moeda Honesta Laura L. R. Rifo |
| 12/2007 |
The Die Race Paradox Jordana A. de Oliveira, Renata L. Spagnol, Laura L. R. Rifo This work presents a playable version of the so-called Waiting Time Paradox, suggesting how to construct a physical mechanism for visualizing it. A simple and intuitive proof of this result for the discrete uniform case is presented. rp-2007-12.pdf |
| 11/2007 |
Statistical Moments of the Solution of the Random Burgers-Riemann Problem Maria Cristina C. Cunha, Fábio A. Dorini We solve Burgers' equation with random Riemann initial conditions. The closed solution allows simple expressions for its statistical moments. Using these ideas we design an efficient algorithm to calculate the statistical moments of the solution. Our methodology is an alternative to the Monte Carlo method. The present approach does not demand a random numbers generator as does the Monte Carlo method.Computational tests are added to validate our approach. rp-2007-11.pdf |
| 10/2007 |
The Replacement of Lotka-Volterra Model by a Formulation Involving Fractional Derivatives R. Figueiredo Carmargo, Edmundo Capelas de Oliveira, Francisco A. M. Gomes Neto This paper proposes a generalization to the Lotka-Volterra system utilizing fractional derivates. The aim of this generalization is to improve the description of the phenomenon in an analogous way to the one that was made in recent works concerning viscoelastic systems, such as human blood. The classical predator-prey model, i.e., the Lotka-Volterra system with derivatives of integer order is discussed and, using a linearization technique, a solution is obtained in terms of the constant parameters. In addition, a solution of the so-called Lotka-Volterra fractional differential system, which is a system of two non linear fractional differential equations where each fractional derivative has order lower than one, is obtained in terms of the Mittag-Leffler function, using the Laplace transform methodology associated with the linearization technique. |
