Th.--Sci. math.--Besançon, 1984. N°: 183.

Made available in DSpace on 2015-12-10T14:23:02Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-03-07. Added 1 bitstream(s) on 2015-12-10T14:27:52Z : No. of bitstreams: 1 000852795.pdf: 576204 bytes, checksum: 28ede436e9367885bc3b672b1903caad (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / A teoria de Hamilton-Jacobi geralmente é apresentada como uma extensão da teoria de Hamilton através das transformações canônicas. No entanto, o matemático Constantin Carathéodory mostrou que essa teoria, sua existência e validade, independem do formalismo hamiltoniano. Neste trabalho, apresentaremos a abordagem de Carathéodory para a teoria de Hamilton-Jacobi. Partindo desse procedimento, construiremos uma teoria de vínculos para que se possa resolver problemas com vínculos involutivos e não-involutivos. Para isso, analisaremos a integrabilidade das equações e introduziremos a operação dos parênteses generalizados que, no lugar do parênteses de Poisson, passará a descrever a dinâmica de sistemas vinculados. Mostraremos uma aplicação dessa teoria de vínculos no modelo BF da teoria de campos. Para finalizar, trataremos da Termodinâmica Axiomática de Carathéodory e também da teoria de Hamilton-Jacobi na Termodinâmica, o que é válido para ilustrar a grande abrangência desse formalismo / The Hamilton-Jacobi theory is usually presented as an extension of the Hamilton's theory through the canonical transformations. However, the mathematician Constantin Carathéodory showed this theory, its existence and validity, is independent of the Hamiltonian formalism. In this work, we present the Caratheodory's approach to the Hamilton-Jacobi theory. From this procedure, we build a theory of constraints which can solve problems with involutive and non-involutive constraints. For this, we analyze the integrability of the equations and introduce the operation of the generalized brackets that, instead of Poisson brackets, will describe the dynamics of constrained systems. We show an application of this theory in BF model of the field theory. Finally, we will discuss the Carathéodory's Axiomatic Thermodynamics and also show the Hamilton-Jacobi theory in Thermodynamics, which is valid to illustrate the wide coverage of this formalism / CNPq: 133488/2011-0

Made available in DSpace on 2015-09-17T15:25:11Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-02-19. Added 1 bitstream(s) on 2015-09-17T15:49:10Z : No. of bitstreams: 1 000846310_20151231.pdf: 154526 bytes, checksum: 0758a595ef94b62272723a08448eaedd (MD5) Bitstreams deleted on 2016-01-04T10:26:35Z: 000846310_20151231.pdf,. Added 1 bitstream(s) on 2016-01-04T10:28:27Z : No. of bitstreams: 1 000846310.pdf: 638836 bytes, checksum: 455c057fa42c2de1060101490372b4fe (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho caracterizaremos sistemas dinâmicos na forma dos chamados domínios estratificados. Bressan e Hong[9] foram os primeiros a definir e trabalhar em domínios estratificados. Grosso modo, estes são uma coleção de domínios disjuntos, cada um tendo sua própria dinâmica; mas não se exige que seus domínios sejam proximamente suaves e nem wedged. Estes termos foram introduzidos por P. Wolenski e R. Barnard em[10]. Primeiramente, estabeleceremos condições Hamiltonianos para caracterizar invariância fraca e forte para sistemas não Lipschitz em domínios estratificados. Depois, estudamos condições Hamiltonianas para sistemas fracamente e fortemente decrescentes e apresentamos condições que garantem a estabilidade assintótica global para uma dinâmica estratificada e finalmente apresentamos o problema tipo Mayer em domínios estratificados em que mostramos que a função valor e a única solução semicontínua inferior de uma generalização adequada da clássica equação Hamilton-Jacobi-Bellman, para a dinâmica estratificada / In this work will characterize dynamical systems in the form of the so-called strati ed domain. Bressan and Hong [9] were the rst to de ne and work in strati ed domains. Roughly speaking, these are a collection of disjoint domains, each having its own dynamics; but not requiring that their domains are proximally smooth and not wedged. These terms were introduced by P. Wolenski and R. Barnard in [10]. At rst, we will establish Hamiltonian conditions to characterize weak and strong invariance for systems non-Lipschitz in strati ed domains. Secondly, we study the Hamiltonian conditions for systems weakly and strongly de- creasing and present conditions that guarantee global asymptotic stability for a strati ed dynamics and nally we present the problem Mayer type in strati ed domains where we show that the value function is the unique lower semicontinuous solution of an appropriate generalization of the classical Hamilton-Jacobi-Bellman equation for strati ed dynamics

Submitted by Gabriel Brandão de Gracia (gb9950@gmail.com) on 2018-01-31T15:49:29Z No. of bitstreams: 2 Dissertação Final.pdf: 530405 bytes, checksum: 393276cfee653f2dd2aedc610270b907 (MD5) Dissertação Final.pdf: 530405 bytes, checksum: 393276cfee653f2dd2aedc610270b907 (MD5) / Rejected by Hellen Sayuri Sato null (hellen@ift.unesp.br), reason: Favor deletar um arquivo e acrescentar o abstract on 2018-01-31T16:48:03Z (GMT) / Submitted by Gabriel Brandão de Gracia (gb9950@gmail.com) on 2018-01-31T16:56:21Z No. of bitstreams: 1 Dissertação Final.pdf: 530405 bytes, checksum: 393276cfee653f2dd2aedc610270b907 (MD5) / Approved for entry into archive by Hellen Sayuri Sato null (hellen@ift.unesp.br) on 2018-01-31T17:12:15Z (GMT) No. of bitstreams: 1 gracia_gb_me_ift.pdf.pdf: 530405 bytes, checksum: 393276cfee653f2dd2aedc610270b907 (MD5) / Made available in DSpace on 2018-01-31T17:12:15Z (GMT). No. of bitstreams: 1 gracia_gb_me_ift.pdf.pdf: 530405 bytes, checksum: 393276cfee653f2dd2aedc610270b907 (MD5) Previous issue date: 2017-02-24 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Ao longo desta dissertação desenvolvemos o formalismo de Hamilton-Jacobi para teorias de campo para o caso de sistemas singulares e não-singulares. Em seguida, aplicamos tal formalismo nos modelos BF em D=1+1, D=2+1 e D=3+1 dimensões a fim de caracterizar os seus espaços de fase. Mostramos que a partir desse formalismo é possível obter as simetrias locais desses modelos assim como os seus respectivos geradores. / Throughout this dissertation we develop the Hamilton-Jacobi formalism for field theories in the case of singular and non-singular systems. Next, apply such formalism on the BF models in D=1+1, D=2+1 e D=3+1 dimensions in order to characterize their phase spaces. We show from this formalism, that is possible to find the local symmetries of those models as well as their respective generators. / CNPq: 132619/2015-6

Orientador: Bruto Max Pimentel Escobar / Banca: Ana Lúcia Barbosa / Banca: Júlio César Fabris / Resumo: Neste trabalho estudamos a estrutura de vínculos da Relatividade Geral (RG) e do Equivalente Teleparalelo da Relatividade Geral (ETRG), utilizando o formalismo de Hamilton-Jacobi para sistemas singulares. Fazemos uma revisão destas duas teorias de gravitação e de suas formulações ADM, tendo em mente que ambas são construídas sobre variedades que são casos particulares da variedade de Riemann-Cartan. Revemos também o formalismo de Hamilton-Jacobi para o tratamento de sistemas singulares, fazendo em seguida a sua aplicação para as duas teorias supracitadas. Nesta análise constatamos que a invariância do ETRG por transformações de Lorentz no espaço tangente das tetradas faz com que a álgebra do vínculos seja diferente daquela obtida para a RG / Abstract: In this work we study the constraint structure of General Relativity (GR) and Teleparallel Equivalent of General Relativity (TEGR), using the Hamilton-Jacobi formalism for singular systems. We make a review of these two theories of gravitation and their ADM formulation, having in mind that both theories are built over manifolds that are particular cases of the Riemann-Cartan manifold. We also review the Hamilton-Jacobi formalism for singular systems, making its application to the cited theories. In this analysis we testify that the invariance of the TEGR under Lorentz transformations in the tangent space of the tetrads implies in a different constraint algebra than that obtained in GR / Mestre

Orientador: João Mauricio Rosario / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-07-22T12:11:24Z (GMT). No. of bitstreams: 1 Fenili_Andre_M.pdf: 10886441 bytes, checksum: e02c936e350afaabc08b309385e4d2ea (MD5) Previous issue date: 1997 / Resumo: Neste trabalho desenvolve-se dois modelos para estruturas flexíveis de rastreamento de membro único: um modelo para pequenas deflexões e um modelo para grandes deflexões. Tanto para um modelo quanto para o outro, utilizou-se o Princípio de Hamilton Estendido para se obter as equações dinâmicas do movimento. Estas equações são posteriormente adimensionalizadas de tal forma que um pequeno parâmetro adimensional de perturbação 'PERTENCE¿ possa ser obtido. Este parâmetro irá multiplicar todas as não linearidades de cada modelo e será o único parâmetro a se variar quando se pretende estudar casos diversos. Este pequeno parâmetro adimensional é utilizado para se verificar o grau de acoplamento entre as equações dinâmicas do movimento. Simulações são realizadas entre pequenas e grandes deflexões e comparadas enter si e com o modelo para o mesmo sistema aonde não se considera flexibilidade nenhuma. No estudo do comportamento da estrutura flexível de rastreamento realizado neste trabalho, o truncamento para a discretização das equações do movimento (método dos modos assumidos) deu-se no primeiro modo próprio do sistema viga engastada-livre / Abstract: In this work two models are developed to slewing flexible structures with just one link: a model considering small deflections and a model considering great deflections. For both models, the Extended Hamilton's PrincipIe is utilized so one can obtain the goveming euqations o fmotion. This equations are then nondimensionalized so one can obtain a smalI nondimensional perturbation parameter 'PERTENCE¿. This parameter appears multiplying alI the nonlinearities in each model and will be the only parameter one must variate when involved in the study of different cases. This smalI nondimensional parameter is utilized to verify the degrre of coupling between the dinamical equations of motion. Simulations are realized between smalI and great deflections and compared one with another and with the model to the very same system where no flexibility is considered. In the study of the behavior of the flexible structure in slewing motion realized in this work, the truncation utilized for the discretization of the equations of motion (assumed modes method) is done in the first mode of vibration of the system beam constrained-free / Mestrado / Mecanica dos Solidos / Mestre em Engenharia Mecânica

Orientador: Waldyr Alves Rodrigues Junior / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-07-26T01:36:39Z (GMT). No. of bitstreams: 1 Carvalho_AlexandreLuisTrovonde_D.pdf: 15293549 bytes, checksum: 6f77ce91b6897c18e527e4134e109ed1 (MD5) Previous issue date: 2000 / Resumo: O propósito desta tese é estudar, sob o ponto de vista algébrico, o papel desempenhado pelos operadores diferenciais nos formalismos variacionais Lagrangeano e Hamiltoneano. Apresentamos uma aplicação simples das idéias e resultados básicos da teoria dos operadores diferenciais às álgebras de Clifford, obtendo uma relação entre os operadores diferenciais e o operador de Dirac. Introduzimos um formalismo Hamiltoneano, com base nos módulos de símbolos dos operadores diferenciais, generalizando os resultados para anéis comutativos. Nesse formalismo, encontramos importantes propriedades algébricas para a Hamiltoneana, e destacamos o colchete de Poisson como uma estrutura mais básica que a forma simplética canônica. Introduzimos o conceito de adjunta de um operador diferencial e, por meio dela, caracterizamos as formas integrais em termos das formas de Berezin. Obtemos uma seqüência espectral relacionando a cohomologia das formas integrais com a cohomologia de De Rham, tanto para variedades quanto para supervariedades. Introduzimos o conceito de Lagrangeana, e analisamos sua relação com as formas de Berezin. Nesse contexto, estudamos as leis de conservação, e obtemos um equivalente algébrico para o Teorema de Noether. Finalmente, essas construções nos encaminham rumo a uma versão algébrica para o teorema do índice. / Abstract: The purpose of this thesis is to study, from the algebraic viewpoint, the rule played by the differential operators in Lagrangian and Hamiltonian variational formalisms. We present a simple application of the basic ideas and results form the theory of differential operators to the Clifford algebras, from where we obtain a relationship between differential operators and the Dirac operator. We introduce a Hamiltonian formalism based on the symbol modules, generalizing some results to commutative rings. In this formalism we find important algebraic properties for the Hamiltonian and notice that the Poisson bracket is a more fundamental structure than the canonical sympletic form. We introduce the concept of adjoint of a differential operator and by means of it we are able to charactrize the integral forms in terms of Berezin forms. We obtain a spectral sequence relating the cohomology of integral forms to the De Rham cohomology, for both manifolds and supermanifolds. In this context, we study the con- servation laws and obtain an algebraic equivalent to the Noether theorem. Finally, these constructions direct us towards an algebraic version to the index theorem. / Doutorado / Doutor em Matemática

Orientador : Aloisio Ernesto Assan / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil / Made available in DSpace on 2018-08-02T01:09:18Z (GMT). No. of bitstreams: 1 Cassiano_Jeferson_M.pdf: 1618692 bytes, checksum: 339eb54aea55535185d3828a00947e8a (MD5) Previous issue date: 2002 / Resumo: Este trabalho tem como objetivo contribuir na análise de placas de compósitos pois tais materiais tem sendo utilizados em larga escala na engenharia. A análise feita neste trabalho é a dinâmica, complementando anterior abordagem estática. O processo numérico utilizado para tal é o Método dos Elementos Finitos, processo já bastante consagrado na engenharia para resolução de equações diferenciais lineares / Abstract: This work has as objective to contribute in the analysis of boards of composites therefore such materials he is being used in wide scale in engineering. The analysis made in this work is the dynamics, complementing previous static boarding. The used numerical process for such is the Method of the Finite Elements, process already sufficient1y consecrated in engineering for resolution of linear distinguishing equations / Mestrado / Estruturas / Mestre em Engenharia Civil

Introduction: The discovery of new solutions to Einstein's field equations has long been a problem in General Relativity. However due to new techniques of Newman and Penrose [1], Carter [2] and others there has been a considerable proliferation of new solutions in recent times. Consequently a new problem has arisen. How are we to interpret the new solutions physically? The tools available, despite a spate of papers in the past fifteen years, remain inadequate although often sophisticated. Any attempts at physical interpretations of metrics are beset with difficulties. There is always the possibility that two entirely different physical pictures will emerge. For example a direct approach would be to attempt an "infilling" of the metric, that is, an extension of the metric into the region occupied by the gravitating matter. However even for the Kerr [1] metric the infilling is by no means unique, in fact a most natural "infilling" turns out to be unphysical (Israel [1]). Yet few people would doubt the physical significance of the Kerr metric. Viewed in this light our attempt to discuss, among other things, the physical interpretation of type D metrics is slightly ambitious. However the problems with regard to this type of metric are not as formidable as for most of the other metrics, since we have been able to integrate the geodesic equations. Nevertheless it is still not possible to produce complete answers to all the questions posed. After a chapter on Mathematical preliminaries the study divides naturally into four sections. We start with an outline of the Hamilton-Jacobi theory of Rund [1] and then go on to show how this theory can be applied to the Carter [2] metrics. In the process we lay a foundation in the calculus of variations for Carter's work. This leads us to the construction of Killing tensors for all but one of the Kinnersley [1] type D vacuum metrics and the Cartei [2] metrics which are not necessarily vacuum metrics. The geodesic equations, for these metrics, are integrated using the Hamilton-Jacobi procedure. The remaining chapters are devoted to the Kinnersley [1] type D vacuum metrics. We omit his class I metrics since these are the Schwarzschild metrics, and have been studied in detail before. Chapter three is devoted to a general study of his class II a metric, a generalisation of the Kerr [1] and NUT (Newman, Tamburino and Unti [1]) metrics. We integrate the geodesic equations and discuss certain general properties: the question of geodesic completeness, the asymptotic properties, and the existence of Killing horizons. Chapter four is concerned with the interpretation of the new parameter 'l', that arises in the class II a and NUT metrics. This parameter was interpreted by Demianski and Newman [1] as a magnetic monopole of mass. Our work centers on the possibility of obtaining observable effects from the presence of 'l'. We have been able to show that its presence is observable, at least in principle, from a study of the motion of particles in the field. In the first place, if l is comparable to the mass of the gravitating system, a comparatively large perihelion shift is to be expected. The possibility of anomalous behaviour in the orbits of test particles, quite unlike anything that occurs in a Newtonian or Schwarzschild field, also arises. In the fifth chapter the Kinnersley class IV metrics are considered. These metrics, which in their simplest form have been known for some time, present serious problems and no interpretations have been suggested. Our discussion is essentially exploratory and the information that does emerge takes the form of suggestions rather than conclusions. Intrinsically the metrics give the impression that interesting results should be obtainable since they are asymptotically flat in certain directions. However the case that we have dealt with does not appear to represent a radiation metric.

In this thesis, we introduce a new space of Hermitian Jacobi forms, and we determine its structure. As an application, we study heat cycles of Hermitian Jacobi forms, and we establish a criterion for the existence of U(p) congruences of Hermitian Jacobi forms. We demonstrate that criterion with some explicit examples. Finally, in the appendix we give tables of Fourier series coefficients of several Hermitian Jacobi forms.