Fabio Antonio Dorini

The probability density function to the random linear transport equation

We present a formula to calculate the probability density function of the solution of the random linear transport equation in terms of the density functions of the velocity and the initial condition. We also present an expression for the joint probability density function of the solution in two different points. Our results have shown good agreement with Monte Carlo simulations.

Statistical moments of the random linear transport equation

This paper deals with a numerical scheme to approximate the mth moment of the solution of the one-dimensional random linear transport equation. The initial condition is assumed to be a random function and the transport velocity is a random variable. The scheme is based on local Riemann problem solutions and Godunovs method. We show that the scheme is stable and consistent with an advective-diffusive equation. Numerical examples are added to illustrate our approach.

Original articles: On the linear advection equation subject to random velocity fields

This paper deals with the random linear advection equation for which the time-dependent velocity and the initial condition are independent random functions. Expressions for the density and joint density functions of the solution are given. We also verify that in the Gaussian time-dependent velocity case the probability density function of the solution satisfies a convection-diffusion equation with a time-dependent diffusion coefficient. Some exact examples are presented.

On fuzzy uncertainties on the logistic equation

Abstract It is recognized that handling uncertainty is essential to obtain more reliable results in modeling and computer simulation. This paper aims to discuss the logistic equation subject to fuzzy uncertainties in the initial conditions and parameters. Here we consider the population density at a specific time as a fuzzy variable in which the possibility distribution function depends on the possibility distribution functions of the environmental carrying capacity, the initial population density and the intrinsic growth rate. We provide closed-form expressions for the expected value of the fuzzy variables population density and for the time of maximum growth. We also perform some numerical simulations to illustrate our main results.

A Samambaia de Barnsley.

Este trabalho objetiva apresentar as ideias matematicas principais da Samambaia de Barnsley, um fractal que recria uma imagem que assemelha-se a uma folha de samambaia da variedade Black Spleenwort e tem como base quatro transformacoes afins elementares.

Uma análise qualitativa de um método gradiente baseado em tensores para imagens coloridas

Este trabalho apresenta uma analise qualitativa de um metodo gradiente baseado em tensores para imagens coloridas. Este metodo consiste na representacao de cores por tensores e na utilizacao de medidas de similaridade entre tensores para mensurar a similaridade entre cores. O gradiente morfologico tensorial em cada pixel da imagem e definido como a maxima dissimilaridade calculada em sua vizinhanca. Sao analisados neste trabalho a forma como cores sao representadas por tensores, algumas medidas de similaridade entre tensores e o gradiente morfologico tensorial.

A mathematical analysis of the Tensorial Morphological Gradient approach

A qualitative analysis of the Tensorial Morphological Gradient approach is presented.Frobenius norm leads the Tensorial Morphological Gradient approach to the best results.Some (dis)similarity measures used in Tensorial Morphological Gradient are not well defined. This paper presents a mathematical analysis of the Tensorial Morphological Gradient, an approach to estimate color image gradients based on a color representation scheme that establishes a correspondence between different color models and tensors. We detail and provide the necessary theoretical explanations for six (dis)similarity measures used to compute the gradient considering the HSV color model and conclude that only one is pertinent to the Tensorial Morphological Gradient approach. The other measures present different types of limitations, including the computation of unbounded values, that disturb the results. The experimental results are consistent with the theoretical conclusions.