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Apie trečios eilės liestinių sluoksniuočių geometriją / About the tangent bundle geometry order 3Mickutė, Laura 23 June 2005 (has links)
In this work is analysed the tangent bundle geometry order 3. Those bundles are defined like 3 - jet space. Co - ordinates transformation formulas of those bundles are received, how the object of linear connection inducted affine connections is demonstrated. In this work the theorem how the object of linear connection of tangent bundle inducted linear connection of tangent bundle order 3 is proved.
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Aplicações da geometria riemanniana em estatística matemáticaBarrêto, Felipe Fernando ângelo 27 September 2013 (has links)
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Previous issue date: 2013-09-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Cook's local infuence approach based on normal curvature is an important diagnostic tool
for assessing local infuence of minor perturbations to a statistical model. However, no rigorous
approach has been developed to address two fundamental issues: the selection of an appropriate
perturbation and the development of infuence measures for objective functions at a point with a
nonzero rst derivative. The aim of this paper is to develop a diferential-geometrical framework of
a perturbation model (called the perturbation manifold) and utilize associated metric tensor and
ane curvatures to resolve these issues. We will show that the metric tensor of the perturbation
manifold provides important information about selecting an appropriate perturbation of a model. / A Abordagem de influência local de Cook [2] com base em curvatura normal é uma importante
ferramenta de diagnóstico para avaliar a influência local de pequenas perturbações de um
modelo estatístico. No entanto, tem sido desenvolvida nenhuma abordagem rigorosa para abordar
duas questões fundamentais: a escolha de uma perturbação apropriada e o desenvolvimento de
medidas de influência para funções objetos em um ponto com a primeira derivada diferente de
zero. O objetivo deste trabalho é desenvolver uma estrutura diferencial-geométrica de um modelo
de perturbação (chamado de variedade de perturbação) e utilizar o tensor métrico associado e as
curvaturas afins para resolver esses problemas. Vamos mostrar que o tensor métrico da variedade
de perturbação fornece informações importantes sobre a seleção de uma perturbação apropriada
de um modelo.
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Controlabilidade para o sistema de Navier-StokesSilva, Felipe Wallison Chaves 15 May 2009 (has links)
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Previous issue date: 2009-05-15 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Cook's local infuence approach based on normal curvature is an important diagnostic tool
for assessing local infuence of minor perturbations to a statistical model. However, no rigorous
approach has been developed to address two fundamental issues: the selection of an appropriate
perturbation and the development of infuence measures for objective functions at a point with a
nonzero
first derivative. The aim of this paper is to develop a diferential-geometrical framework of
a perturbation model (called the perturbation manifold) and utilize associated metric tensor and
affine curvatures to resolve these issues. We will show that the metric tensor of the perturbation
manifold provides important information about selecting an appropriate perturbation of a model. / Esta dissertação é dedicada ao estudo do sistema de Navier-Stokes sob ponto
de vista da teoria do controle. Primeiramente estudamos a controlabilidade das
aproximações de Galerkin do sistema de Navier-Stokes. Utilizando argumentos de
dualidade e de ponto fixo, mostramos que, com hipóteses adequadas sobre a base
de Galerkin, estas aproximações, finito dimensionais, são exatamente controláveis.
Passando ao modelo em dimensão infinita, analisamos a controlabilidade sobre trajetórias. Isto é feito usando uma desigualdade do tipo Calerman para o sistema de
Navier-Stokes linearizado e uma versão do teorema da função inversa. Dessa forma,
temos um resultado de controlabilidade local exata para o sistema de Navier-Stokes.
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Une approche intrinsèque des foncteurs de Weil / An intrinsic approach of Weil functorsSouvay, Arnaud 23 November 2012 (has links)
Nous construisons un foncteur de la catégorie des variétés sur un corps ou un anneau topologique K, de caractéristique arbitraire, dans la catégorie des variétés sur A, où A est une algèbre de Weil, c'est-à-dire une K-algèbre de la forme A = K + N, où N est un idéal nilpotent. Le foncteur correspondant, noté T^A, et appelé foncteur de Weil, peut être interprété comme un foncteur d'extension scalaire de K à A. Il est construit à l'aide des polynômes de Taylor, dont nous donnons une définition en caractéristique quelconque. Ce résultat généralise à la fois des résultats connus pour les variétés réelles ordinaires, et les résultats obtenus dans le cas des foncteurs tangents itérés et dans le cas des anneaux de jets (A = K[X]/(X^{k+1})). Nous montrons que pour toute variété M, T^A M possède une structure de fibré polynomial sur M, et nous considérons certains aspects algébriques des foncteurs de Weil, notamment ceux liés à l'action du « groupe de Galois » Aut_K(A). Nous étudions les connexions, qui sont un outil important d'analyse des fibrés, dans deux contextes différents : d'une part sur les fibrés T^A M, et d?autre part sur des fibrés généraux sur M, en suivant l'approche d'Ehresmann. Les opérateurs de courbure d'une connexion sont induits par l'action du groupe de Galois Aut_K(A) et ils forment une obstruction à l'« intégrabilité » d'une connexion K-lisse en une connexion A-lisse / We construct a functor from the category of manifolds over a general topological base field or ring K, of arbitrary characteristic, to the category of manifolds over A, where A is a so-called Weil algebra, i.e. a K-algebra of the form A = K + N, where N is a nilpotent ideal. The corresponding functor, denoted by T^A, and called a Weil functor, can be interpreted as a functor of scalar extension from K to A. It is constructed by using Taylor polynomials, which we define in arbitrary characteristic. This result generalizes simultaneously results known for ordinary, real manifolds, and results for iterated tangent functors and for jet rings (A = K[X]/(X^{k+1})). We show that for any manifold M, T^A M is a polynomial bundle over M, and we investigate some algebraic aspects of the Weil functors, in particular those related to the action of the "Galois group" Aut_K(A). We study connections, which are an important tool for the analysis of fiber bundles, in two different contexts : connections on the Weil bundles T^A M, and connections on general bundles over M, following Ehresmann's approach. The curvature operators are induced by the action of the Galois group Aut_K(A) and they form an obstruction to the "integrability" of a K-smooth connection to an A-smooth one
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