Estimates for the Poisson kernel and Hardy spaces on compact manifolds

We study Hardy spaces on the boundary of a smooth open subset or R-n and prove that they can be defined either through the intrinsic maximal function or through Poisson integrals, yielding identical spaces. This extends to any smooth open subset of R-n results already known for the unit ball. As an application, a characterization of the weak boundary values of functions that belong to holomorphic Hardy spaces is given, which implies an F. and M. Riesz type theorem. (C) 2004 Elsevier B.V. All rights reserved.

PERIODIC PERTURBATION of QUADRATIC SYSTEMS WITH TWO INFINITE HETEROCLINIC CYCLES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Time-periodic perturbation of a Lienard equation with an unbounded homoclinic loop

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Periodic perturbations of quadratic planar polynomial vector fields

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estatística não-extensiva aplicada ao cálculo do calor específico eletrônico em estruturas quasiperiódicas

Systems whose spectra are fractals or multifractals have received a lot of attention in recent years. The complete understanding of the behavior of many physical properties of these systems is still far from being complete because of the complexity of such systems. Thus, new applications and new methods of study of their spectra have been proposed and consequently a light has been thrown on their properties, enabling a better understanding of these systems. We present in this work initially the basic and necessary theoretical framework regarding the calculation of energy spectrum of elementary excitations in some systems, especially in quasiperiodic ones. Later we show, by using the Schr¨odinger equation in tight-binding approximation, the results for the specific heat of electrons within the statistical mechanics of Boltzmann-Gibbs for one-dimensional quasiperiodic systems, growth by following the Fibonacci and Double Period rules. Structures of this type have already been exploited enough, however the use of non-extensive statistical mechanics proposed by Constantino Tsallis is well suited to systems that have a fractal profile, and therefore our main objective was to apply it to the calculation of thermodynamical quantities, by extending a little more the understanding of the properties of these systems. Accordingly, we calculate, analytical and numerically, the generalized specific heat of electrons in one-dimensional quasiperiodic systems (quasicrystals) generated by the Fibonacci and Double Period sequences. The electronic spectra were obtained by solving the Schr¨odinger equation in the tight-binding approach. Numerical results are presented for the two types of systems with different values of the parameter of nonextensivity q

Função de distribuição generalizada aplicada à velocidade de rotação estelar

In the present work we use a Tsallis maximum entropy distribution law to fit the observations of projected rotational velocity measurements of stars in the Pleiades open cluster. This new distribution funtion which generalizes the Ma.xwel1-Boltzmann one is derived from the non-extensivity of the Boltzmann-Gibbs entropy. We also present a oomparison between results from the generalized distribution and the Ma.xwellia.n law, and show that the generalized distribution fits more closely the observational data. In addition, we present a oomparison between the q values of the generalized distribution determined for the V sin i distribution of the main sequence stars (Pleiades) and ones found for the observed distribution of evolved stars (subgiants). We then observe a correlation between the q values and the star evolution stage for a certain range of stel1ar mass

Formação de caudas maxwellianas no Contexto da rotação estelar

In this Thesis, we analyzed the formation of maxwellian tails of the distributions of the rotational velocity in the context of the out of equilibrium Boltzmann Gibbs statistical mechanics. We start from a unified model for the angular momentum loss rate which made possible the construction of a general theory for the rotational decay in the which, finally, through the compilation between standard Maxwellian and the relation of rotational decay, we defined the (_, _) Maxwellian distributions. The results reveal that the out of equilibrium Boltzmann Gibbs statistics supplies us results as good as the one of the Tsallis and Kaniadakis generalized statistics, besides allowing fittings controlled by physical properties extracted of the own theory of stellar rotation. In addition, our results point out that these generalized statistics converge to the one of Boltzmann Gibbs when we inserted, in your respective functions of distributions, a rotational velocity defined as a distribution

Condições de energia de hawking e ellis e a equação de raychaudhuri

In the Einstein s theory of General Relativity the field equations relate the geometry of space-time with the content of matter and energy, sources of the gravitational field. This content is described by a second order tensor, known as energy-momentum tensor. On the other hand, the energy-momentum tensors that have physical meaning are not specified by this theory. In the 700s, Hawking and Ellis set a couple of conditions, considered feasible from a physical point of view, in order to limit the arbitrariness of these tensors. These conditions, which became known as Hawking-Ellis energy conditions, play important roles in the gravitation scenario. They are widely used as powerful tools for analysis; from the demonstration of important theorems concerning to the behavior of gravitational fields and geometries associated, the gravity quantum behavior, to the analysis of cosmological models. In this dissertation we present a rigorous deduction of the several energy conditions currently in vogue in the scientific literature, such as: the Null Energy Condition (NEC), Weak Energy Condition (WEC), the Strong Energy Condition (SEC), the Dominant Energy Condition (DEC) and Null Dominant Energy Condition (NDEC). Bearing in mind the most trivial applications in Cosmology and Gravitation, the deductions were initially made for an energy-momentum tensor of a generalized perfect fluid and then extended to scalar fields with minimal and non-minimal coupling to the gravitational field. We also present a study about the possible violations of some of these energy conditions. Aiming the study of the single nature of some exact solutions of Einstein s General Relativity, in 1955 the Indian physicist Raychaudhuri derived an equation that is today considered fundamental to the study of the gravitational attraction of matter, which became known as the Raychaudhuri equation. This famous equation is fundamental for to understanding of gravitational attraction in Astrophysics and Cosmology and for the comprehension of the singularity theorems, such as, the Hawking and Penrose theorem about the singularity of the gravitational collapse. In this dissertation we derive the Raychaudhuri equation, the Frobenius theorem and the Focusing theorem for congruences time-like and null congruences of a pseudo-riemannian manifold. We discuss the geometric and physical meaning of this equation, its connections with the energy conditions, and some of its several aplications.

Conceitos e técnicas da mecânica estatística e termodinâmica aplicados ao estudo dos grafos aleatórios

This dissertation briefly presents the random graphs and the main quantities calculated from them. At the same time, basic thermodynamics quantities such as energy and temperature are associated with some of their characteristics. Approaches commonly used in Statistical Mechanics are employed and rules that describe a time evolution for the graphs are proposed in order to study their ergodicity and a possible thermal equilibrium between them

Processos difusivos generalizados

We investigate several diffusion equations which extend the usual one by considering the presence of nonlinear terms or a memory effect on the diffusive term. We also considered a spatial time dependent diffusion coefficient. For these equations we have obtained a new classes of solutions and studied the connection of them with the anomalous diffusion process. We start by considering a nonlinear diffusion equation with a spatial time dependent diffusion coefficient. The solutions obtained for this case generalize the usual one and can be expressed in terms of the q-exponential and q-logarithm functions present in the generalized thermostatistics context (Tsallis formalism). After, a nonlinear external force is considered. For this case the solutions can be also expressed in terms of the q-exponential and q-logarithm functions. However, by a suitable choice of the nonlinear external force, we may have an exponential behavior, suggesting a connection with standard thermostatistics. This fact reveals that these solutions may present an anomalous relaxation process and then, reach an equilibrium state of the kind Boltzmann- Gibbs. Next, we investigate a nonmarkovian linear diffusion equation that presents a kernel leading to the anomalous diffusive process. Particularly, our first choice leads to both a the usual behavior and anomalous behavior obtained through a fractionalderivative equation. The results obtained, within this context, correspond to a change in the waiting-time distribution for jumps in the formalism of random walks. These modifications had direct influence in the solutions, that turned out to be expressed in terms of the Mittag-Leffler or H of Fox functions. In this way, the second moment associated to these distributions led to an anomalous spread of the distribution, in contrast to the usual situation where one finds a linear increase with time

Anisotropias da radiação cósmica de fundo e vínculos em modelos com decaimento do vácuo

Many astronomical observations in the last few years are strongly suggesting that the current Universe is spatially flat and dominated by an exotic form of energy. This unknown energy density accelerates the universe expansion and corresponds to around 70% of its total density being usually called Dark Energy or Quintessence. One of the candidates to dark energy is the so-called cosmological constant (Λ) which is usually interpreted as the vacuum energy density. However, in order to remove the discrepancy between the expected and observed values for the vacuum energy density some current models assume that the vacuum energy is continuously decaying due to its possible coupling with the others matter fields existing in the Cosmos. In this dissertation, starting from concepts and basis of General Relativity Theory, we study the Cosmic Microwave Background Radiation with emphasis on the anisotropies or temperature fluctuations which are one of the oldest relic of the observed Universe. The anisotropies are deduced by integrating the Boltzmann equation in order to explain qualitatively the generation and c1assification of the fluctuations. In the following we construct explicitly the angular power spectrum of anisotropies for cosmologies with cosmological constant (ΛCDM) and a decaying vacuum energy density (Λ(t)CDM). Finally, with basis on the quadrupole moment measured by the WMAP experiment, we estimate the decaying rates of the vacuum energy density in matter and in radiation for a smoothly and non-smoothly decaying vacuum

Não-extensividade em percolação por ligações de longo - alcance

A linear chain do not present phase transition at any finite temperature in a one dimensional system considering only first neighbors interaction. An example is the Ising ferromagnet in which his critical temperature lies at zero degree. Analogously, in percolation like disordered geometrical systems, the critical point is given by the critical probability equals to one. However, this situation can be drastically changed if we consider long-range bonds, replacing the probability distribution by a function like . In this kind of distribution the limit α → ∞ corresponds to the usual first neighbor bond case. In the other hand α = 0 corresponds to the well know "molecular field" situation. In this thesis we studied the behavior of Pc as a function of a to the bond percolation specially in d = 1. Our goal was to check a conjecture proposed by Tsallis in the context of his Generalized Statistics (a generalization to the Boltzmann-Gibbs statistics). By this conjecture, the scaling laws that depend with the size of the system N, vary in fact with the quantitie

On extension theorems for holomorphic generalized functions

We present two extension theorems for holomorphic generalized functions. The first one is a version of the classic Hartogs extension theorem. In this, we start from a holomorphic generalized function on an open neighbourhood of the bounded open boundary, extending it, holomorphically, to a full open. In the second theorem a generalized version of a classic result is obtained, done independently, in 1943, by Bochner and Severi. For this theorem, we start from a function that is holomorphic generalized and has a holomorphic representative on the bounded domain boundary, we extend it holomorphically the function, for the whole domain.

O papel das rotas e da obtenção de informações sobre a eficiência no forrageio de dinoponera quadriceps em ambiente natural

In this study, we investigated the role of routes and information attainment for the queenless ant species Dinoponera quadriceps foraging efficiency. Two queenless ant colonies were observed in an area of Atlantic secondary Forest at the FLONA-ICMBio of Nisia Floresta, in the state of Rio Grande do Norte, northeastern Brazil, at least once a week. In the first stage of the study, we observed the workers, from leaving until returning to the colony. In the second stage, we introduced a acrylic plate (100 x 30 x 0,8 cm) on a selected entrance of the nest early in the morning before the ants left the nest. All behavioral recordings were done through focal time and all occurence samplings. The recording windows were of 15 minutes with 1 minute interval, and 5 minute intervals between each observation window. Foraging was the main activity when the workers were outside the nest. There was a positive correlation between time outside the nest and distance travelled by the ants. These variables influenced the proportion of resource that was taken to the nest, that is, the bigger its proportion, the longer the time outside and distance travelled during the search. That proportion also influenced the time the worker remained in the nest before a new trip, the bigger the proportion of the item, the shorter was the time in the nest. During all the study, workers showed fidelity to the route and to the sectors in the home range, even when the screen was in the ant´s way, once they deviated and kept the route. The features of foraging concerning time, distance, route and flexibility to go astray by the workers indicate that decisions are made by each individual and are optimal in terms of a cost-benefit relation. The strategy chosen by queenless ants fits the central place foraging and marginal value theorem theories and demonstrate its flexibility to new informations. This indicates that the workers can learn new environmental landmarks to guide their routes

Attitude stability of artificial satellites subject to gravity gradient torque

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)