Resumo em Inglês:

The present article discusses the relation between boundary conditions and the Sommerfeld radiation condition underlying the dynamics of unbounded domains. It is shown that the classical Dirichlet, Neumann and mixed boundary conditions do not fulfill the radiation condition. In the sequence, three strategies to incorporate the radiation condition in numerical methods are outlined. The inclusion of Infinite Elements in the realm of the Finite Element Method (FEM), the Dirichlet-to-Neumann (DtN) mapping and the Boundary Element Method (BEM) are described. Examples of solved dynamic problems in unbounded domains are given for the Helmholtz and the Navier operators. The advantages and limitations of the methodologies are discussed and pertinent literature is provided.

Resumo em Inglês:

In order to have accurate operation, synchronous telecommunication networks need a reliable time basis signal extracted from the line data stream in each node. When the nodes are synchronized, routing and detection can be performed, guaranteeing the correct sequence of information distribution among the several users of a transmission trunk. Consequently, an auxiliary network is created inside the main network, a sub-network, dedicated to the distribution of the clock signals. There are different solutions for the architecture of the time distribution sub-network and choosing one of them depends on cost, precision, reliability and operational security. In this work we analyze the possible time distribution networks and formulate problems related to precision and stability of the timing signals by using the qualitative theory of differential equations. Correspondences between constitutive parameters of the networks and the dynamics of the spatial phase and frequency errors are established.

Resumo em Inglês:

Stability analysis and a systematic robust fuzzy control design for uncertain nonlinear systems with polytopic uncertainties are presented. The approach given uses the T-S fuzzy systems which are represented by a family of local uncertain linear systems with aggregation. The resulting fuzzy controller is a blending of state feedback gains obtained from a guaranteed cost control (GCC) problem. A sufficient condition for the robust stability of the feedback T-S fuzzy system with uncertainties using a quadratic Lyapunov function is given. A feature of the proposed approach is that an upper bound on the guaranteed cost is minimized by solving an optimization problem with linear matrix inequalities (LMIs).

Resumo em Inglês:

One of the main goals of the pest control is to maintain the density of the pest population in the equilibrium level below economic damages. For reaching this goal, the optimal pest control problem was divided in two parts. In the first part, the two optimal control functions were considered. These functions move the ecosystem pest-natural enemy at an equilibrium state below the economic injury level. In the second part, the one optimal control function stabilizes the ecosystem in this level, minimizing the functional that characterizes quadratic deviations of this level. The first problem was resolved through the application of the Maximum Principle of Pontryagin. The Dynamic Programming was used for the resolution of the second optimal pest control problem.

Resumo em Inglês:

Fractal codification of images is based on self-similar and self-affine sets. The codification process consists of construction of an operator which will represent the image to be encoded. If a complicated picture can be represented by an operator then it will be transmitted or stored very efficiently. Clearly, this has many applications on data compression. The great disadvantage of the automatic form of fractal compression is its encoding time. Most of the time spent in construction of such operator is due on finding the best match between parts of the image to be encoded. However, since the conception of automatic fractal image compression, researches on improvement of the compression time are widespread. This work aims to provide a new idea for decrease the encoding time: a classification of image parts based on their local fractal dimension. The idea is implemented on two steps. First, a preprocessing analysis of the image identify the complexity of each image block computing its dimension. Then, only parts within the same range of complexity are used for testing the better self-affine pairs, reducing the compression time. The performance of this proposition, is compared with others fractal image compression methods. The points considered are image fidelity, encoding time and amount of compression on the image file.

Resumo em Inglês:

Considering hypothetical co-orbital asteroids with the Earth, Tatum (1997) presented a study about the necessary radial distance in order to produce collision. He adopted an analysis considering a composition of circular two-body systems, Sun-Earth and Sun-Asteroid. He found that asteroids with radial positions between 0.9943 and 1.0057 AU would necessarily collide with the Earth. In the present work, we show that this problem cannot be treated in this way. Adopting the circular restricted three-body problem, we verified that asteroids in the supposed region of collision with the Earth have stable horseshoe trajectories. Therefore, in the co-orbital region the dynamical system has to be studied as a restricted three-body problem since the composition of two-body problems gives a misleading result.

Resumo em Inglês:

In this paper, numerical simulations are made, using the restricted three-body problem as the mathematical model, to calculate the effects of a swing-by with the planet Jupiter in the orbit of a comet. In particular, the orbital elements of the comets are calculated after the passage by Jupiter, the distribution obtained is shown and the probability of capture is calculated as a function of the Jacobian constant of the comet. The results show that the probability of capture goes from 0.2% to 3.6%, depending on the value of the Jacobian constant of the comet. The details of this mechanism and some trajectories are shown. It is also concluded that more than 95% of the captured comets have pericenter distance less than 5 AU (what makes them visible) and that about 70% of them are short-period comets.

Resumo em Inglês:

This work deals with noise removal by the use of an edge preserving method whose parameters are automatically estimated, for any application, by simply providing information about the standard deviation noise level we wish to eliminate. The desired noiseless image u(x), in a Partial Differential Equation based model, can be viewed as the solution of an evolutionary differential equation u t(x) = F(u xx, u x, u, x, t) which means that the true solution will be reached when t ® ¥. In practical applications we should stop the time ''t'' at some moment during this evolutionary process. This work presents a sufficient condition, related to time t and to the standard deviation s of the noise we desire to remove, which gives a constant T such that u(x, T) is a good approximation of u(x). The approach here focused on edge preservation during the noise elimination process as its main characteristic. The balance between edge points and interior points is carried out by a function g which depends on the initial noisy image u(x, t0), the standard deviation of the noise we want to eliminate and a constant k. The k parameter estimation is also presented in this work therefore making, the proposed model automatic. The model's feasibility and the choice of the optimal time scale is evident through out the various experimental results.