Campos de Killing, curvatura média e translações

D. Hoffman, R. Osserman e R. Schoen mostraram que se a aplicação de Gauss de uma superfície orientada completa de curvatura média constante M imersa em R³ está contida em um hemisfério fechado de S² (equivalentemente, a função não muda de sinal em M, onde n é um vetor unitário normal de M e v algum vetor não nulo de R³), então M é invariante por um subgrupo a um parâmetro de translações de R³ (aquele determinado por v). Neste trabalho obtemos uma extensão deste resultado para o caso em que o espaço ambiente é uma variedade riemanniana e M uma hipersuperfície em N requerendo que a função não mude de sinal em M, onde V é um campo de Killing em N. Na parte final deste trabalho consideramos uma variedade riemanniana Killing paralelizável N para definir uma translação Y: M -> Rn de uma hipersuperfície M de N que é uma extensão natural da aplicação de Gauss de uma hipersuperfície de Rn. Considerando as mesmas hipóteses para a imagem de y obtemos uma extensão do resultado original de Hoffman-Osserman-Schoen.

Fundamentos epistemológicos da museologia: uma proposta ao problema curricular

O objetivo deste trabalho é responder as perguntas: o que é museologia, o que a diferencia dos outros saberes, isto é, quais são os seus estatutos epistemológicos, porque a Museologia assume no Brasil aspecto predominantemente técnico o que afasta, quase sempre seus profissionais dos postos de comando e/ou decisão na área que lhe é afeta. O tema educacional está imbricado na problemática epistemológica. O tema é abordado através de diferentes aspectos e sucessivas visões: - como o Curso de Museus se inseriu no contexto histórico que lhe deu origem, a longa proposta ideológica do então único Curso de Museus do país, o desempenho deste mesmo curso de sua fundação até os dias de hoje, duas divisões de seus currículos uma quanto a sua coerência ou não com cada momento educacional e outra quanto aos conteúdos. O museu sua gênese e desempenho mundial até hoje. Estas primeiras aproximações nos levaram a constatar faltar à Museologia a evidenciação de seus estatutos epistemológicos, princípios e categorias, que a mostrasse como um saber diferenciado. Aquelas múltiplas visões nos permitiram chegar aos conceitos adequados, na área, para nosso trabalho. Passamos a ordenar o assunto por campos e destes extraímos princípios museológicos e reconhecemos estes como relacionados com a Antropologia Filosófica. Levantamos as Categorias de Antropologia Filosófica contidas nas obras de Jolif e conectamos aqueles "Princípios Museológicos" com estas categorias. Passamos, assim, a ter uma correlação Museologia/ Antropologia Filosófica que ~ permite a Museologia desenvolver-se estruturadamente passando a ter "background" para sustentar uma proposta de ensino universitário e de formação superior para o profissional de museologia e para consequentemente sustentar a pesquisa, a reflexão e a decisão nas lides e no desenvolvi menta contínuo do saber diferenciado: Museologia.

A organização social e o acesso à cultura: o caso das bibliotecas parque do Estado do Rio de Janeiro

Esta dissertação procura analisar qual a contribuição das Organizações Sociais para o acesso a direitos culturais, a partir da experiência das Bibliotecas Parque do Estado do Rio de Janeiro, em especial a de Manguinhos e a da Rocinha. Ciente de que as formas de cooperação para a efetivação de direitos culturais são múltiplas e que precisam ser pensadas a partir da inter-relação de vários atores e aspectos, todas invariavelmente necessitam desaguar em molduras de gestão viabilizadoras do acesso à cultura. A pesquisa adota o método do estudo de caso, valendo-se de pesquisas bibliográfica, documental e de campo. Apresenta o cenário de construção dos direitos culturais, em larga expansão no Brasil, e destaca que, para materializá-los, torna-se necessário estudar, avaliar e adotar modelos organizacionais alternativos aos tradicionais que caracterizam a administração pública direta e indireta. Aborda o campo da gestão e dos direitos culturais no contexto das três principais reformas do aparelho do Estado Republicano, ocorridas nas décadas de 30, 60 e 90, com ênfase na última, que incorpora a teoria da Nova Gestão Pública, base desta dissertação. Focaliza a Organização Social como modelo opcional à gestão de instituições ou programas culturais, a partir da realidade existente, das motivações, das vantagens e das perspectivas e aduz uma narrativa acerca do processo de concepção da legislação do estado do Rio de Janeiro. Verifica como surgiram esses equipamentos culturais e como se deu a formação da rede de Bibliotecas Parque. Descreve o processo de implantação das Organizações Sociais de Cultura no estado e apresenta o gestor das bibliotecas e sua relação com a secretaria de Cultura. Conclui que há necessidade de aperfeiçoamento de mecanismos de gestão, a fim de que o modelo possa, de fato, oferecer contribuição para o acesso a direitos culturais.

Studies in non-Gaussian analysis

This thesis presents general methods in non-Gaussian analysis in infinite dimensional spaces. As main applications we study Poisson and compound Poisson spaces. Given a probability measure μ on a co-nuclear space, we develop an abstract theory based on the generalized Appell systems which are bi-orthogonal. We study its properties as well as the generated Gelfand triples. As an example we consider the important case of Poisson measures. The product and Wick calculus are developed on this context. We provide formulas for the change of the generalized Appell system under a transformation of the measure. The L² structure for the Poisson measure, compound Poisson and Gamma measures are elaborated. We exhibit the chaos decomposition using the Fock isomorphism. We obtain the representation of the creation, annihilation operators. We construct two types of differential geometry on the configuration space over a differentiable manifold. These two geometries are related through the Dirichlet forms for Poisson measures as well as for its perturbations. Finally, we construct the internal geometry on the compound configurations space. In particular, the intrinsic gradient, the divergence and the Laplace-Beltrami operator. As a result, we may define the Dirichlet forms which are associated to a diffusion process. Consequently, we obtain the representation of the Lie algebra of vector fields with compact support. All these results extends directly for the marked Poisson spaces.

Nonautonomous difference equations with applications

This work is divided in two parts. In the first part we develop the theory of discrete nonautonomous dynamical systems. In particular, we investigate skew-product dynamical system, periodicity, stability, center manifold, and bifurcation. In the second part we present some concrete models that are used in ecology/biology and economics. In addition to developing the mathematical theory of these models, we use simulations to construct graphs that illustrate and describe the dynamics of the models. One of the main contributions of this dissertation is the study of the stability of some concrete nonlinear maps using the center manifold theory. Moreover, the second contribution is the study of bifurcation, and in particular the construction of bifurcation diagrams in the parameter space of the autonomous Ricker competition model. Since the dynamics of the Ricker competition model is similar to the logistic competition model, we believe that there exists a certain class of two-dimensional maps with which we can generalize our results. Finally, using the Brouwer’s fixed point theorem and the construction of a compact invariant and convex subset of the space, we present a proof of the existence of a positive periodic solution of the nonautonomous Ricker competition model.

Estudo de manejo de águas pluviais urbanas na cidade Natal-Rio Grande do Norte

Urban stormwater can be considered as potential water resources as well as problems for the proper functioning of the manifold activities of the city, resulting from inappropriate use and occupation of the soil, usually due to poor planning of the occupation of the development areas, with little care for the environmental aspects of the drainage of surface runoff. As a basic premise, we must seek mechanisms to preserve the natural flow in all stages of development of an urban area, preserving the soil infiltration capacity in the scale of the urban area, comprising the mechanisms of natural drainage, and noting preserving natural areas of dynamic water courses, both in the main channel and in the secondary. They are challenges for a sustainable urban development in a harmonious coexistence of modern developmental, which are consistent with the authoritative economic environmental and social quality. Integrated studies involving the quantity and quality of rainwater are absolutely necessary to achieve understanding and obtaining appropriate technologies, involving both aspects of the drainage problems and aspects of use of water when subjected to an adequate management of surface runoff , for example, the accumulation of these reservoirs in detention with the possibility of use for other purposes. The purpose of this study aims to develop a computer model, adjusted to prevailing conditions of an experimental urban watershed in order to enable the implementation of management practices for water resources, hydrological simulations of quantity and, in a preliminary way, the quality of stormwater that flow to a pond located at the downstream end of the basin. To this end, we used in parallel with the distributed model SWMM data raised the basin with the highest possible resolution to allow the simulation of diffuse loads, heterogeneous characteristics of the basin both in terms of hydrological and hydraulic parameters on the use and occupation soil. The parallel work should improve the degree of understanding of the phenomena simulated in the basin as well as the activity of the calibration models, and this is supported by monitoring data acquired during the duration of the project MAPLU (Urban Stormwater Management) belonging to the network PROSAB (Research Program in Basic Sanitation) in the years 2006 to 2008

Reversibility properties of semigroup actions on homogeneous spaces

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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.

Self-energies for interacting fields with a compactified spatial dimension

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Synchronization and Non-Smooth Dynamical Systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Galilean covariant Lagrangian models

We construct non-relativistic Lagrangian field models by enforcing Galilean covariance with a (4, 1) Minkowski manifold followed by a projection onto the (3, 1) Newtonian spacetime. We discuss scalar, Fermi and gauge fields, as well as interactions between these fields, preparing the stage for their quantization. We show that the Galilean covariant formalism provides an elegant construction of the Lagrangians which describe the electric and magnetic limits of Galilean electromagnetism. Similarly we obtain non-relativistic limits for the Proca field. Then we study Dirac Lagrangians and retrieve the Levy-Leblond wave equations when the Fermi field interacts with an Abelian gauge field.

Casimir energy in a small volume multiply connected static hyperbolic preinflationary universe

A few years ago, Cornish, Spergel and Starkman (CSS) suggested that a multiply connected small universe could allow for classical chaotic mixing as a preinflationary homogenization process. The smaller the volume, the more important the process. Also, a smaller universe has a greater probability of being spontaneously created. Previously DeWitt, Hart and Isham (DHI) calculated the Casimir energy for static multiply connected fat space-times. Because of the interest in small volume hyperbolic universes (e.g., CSS), we generalize the DHI calculation by making a numerical investigation of the Casimir energy for a conformally coupled, massive scalar field in a static universe, whose spatial sections are the Weeks manifold, the smallest universe of negative curvature known. In spite of being a numerical calculation, our result is in fact exact. It is shown that there is spontaneous vacuum excitation of low multipolar components.

On the algebraic K theory of the massive D8 and M9-branes

In this paper we review some basic relations of algebraic K theory and we formulate them in the language of D-branes. Then we study the relation between the D8-branes wrapped on an orientable, compact manifold W in a massive Type IIA, supergravity background and the M9-branes wrapped on a compact manifold Z in a massive d = 11 supergravity background from the K-theoretic point of view. By interpreting the D8-brane charges as elements of K-0(C(W)) and the (inequivalent classes of) spaces of gauge fields on the M9-branes as the elements of K-0(C(Z) x ((k) over bar*) G) where G is a one-dimensional compact group, a connection between charges and gauge fields is argued to exists. This connection could be realized as a composition map between the corresponding algebraic K theory groups.

Quantum state density and critical temperature in M-theory

We discuss the asymptotic properties of quantum states density for fundamental p-branes which can yield a microscopic interpretation of the thermodynamic quantities in M-theory. The matching of the BPS part of spectrum for superstring and supermembrane gives the possibility of getting membrane's results via string calculations. In the weak coupling limit of M-theory, the critical behavior coincides with the first-order phase transition in the standard string theory at temperature less than the Hagedorn's temperature T-H. The critical temperature at large coupling constant is computed by considering M-theory on manifold with topology R-9 circle times T-2. Alternatively we argue that any finite temperature can be introduced in the framework of membrane thermodynamics.

Regge calculus in teleparallel gravity

In the context of the teleparallel equivalent of general relativity, the Weitzenbock manifold is considered as the limit of a suitable sequence of discrete lattices composed of an increasing number of smaller and smaller simplices, where the interior of each simplex (Delaunay lattice) is assumed to be flat. The link lengths l between any pair of vertices serve as independent variables, so that torsion turns out to be localized in the two-dimensional hypersurfaces (dislocation triangle, or hinge) of the lattice. Assuming that a vector undergoes a dislocation in relation to its initial position as it is parallel transported along the perimeter of the dual lattice (Voronoi polygon), we obtain the discrete analogue of the teleparallel action, as well as the corresponding simplicial vacuum field equations.