Orientador: Djairo Guedes de Figueiredo / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Científica / Made available in DSpace on 2018-08-04T21:17:17Z (GMT). No. of bitstreams: 1 Diniz_HugoAlexCarneiro_D.pdf: 770650 bytes, checksum: 55f077fc4cf6042e72a4b852d549e423 (MD5) Previous issue date: 2005 / Resumo: Neste trabalho estudamos a unicidade e a não-degenerescência de soluções positi-vas radiais para problemas não-autônomos envolvendo o p-Iaplaciano em anéis e bolas, com condição de Neumann na parte interna do anel, e condição de Dirichlet na parte externa. Quando o domínio é uma bola, temos apenas a condição de Dirichlet. Consideraremos três perfis diferentes para o problema: sublinear, superlinear e positivo, superlinear com parte negativa. Utilizando a técnica de Coffman, a qual consiste em estudar os zeros da solu-ção do problema linearizado, através de argumentos de comparação de Sturm, provamos primeiramente a não-degenerescência. Pelo método de "shooting", obtemos a unicidade. Como aplicação, demonstramos um resultado de unicidade para o laplaciano em domínios não-simétricos (até mesmo não-convexos) "próximos" a uma bola / Abstract: In this work, we study uniqueness and non-degeneracy of positive radial solutions for non-autonomous problems involving p-Iaplacian in annuli and balls, with Neumann condition in the inner part of annulus, and Dirichlet condition in the outer part. We consider three different problems: sublinear, superlinear and positive, superlinear with a negative part. Using the Coffman's technique, which consists in studying the zeros of the solution of the linearized problem, through Sturm comparison arguments we prove non-degeneracy. By the "shooting" method, we prove uniqueness. As an application, we demonstrate a uniqueness result for laplacian in non-symmetric (even non-convex) domains ''near'' a baIl / Doutorado / Doutor em Matemática

Submitted by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2017-02-20T14:12:48Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese - Marcos A. Alcantara.pdf: 8400753 bytes, checksum: 2ef1ddefa929adecd87c6c952124ec8b (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2017-02-20T14:13:03Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese - Marcos A. Alcantara.pdf: 8400753 bytes, checksum: 2ef1ddefa929adecd87c6c952124ec8b (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2017-02-20T14:13:19Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese - Marcos A. Alcantara.pdf: 8400753 bytes, checksum: 2ef1ddefa929adecd87c6c952124ec8b (MD5) / Made available in DSpace on 2017-02-20T14:13:19Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese - Marcos A. Alcantara.pdf: 8400753 bytes, checksum: 2ef1ddefa929adecd87c6c952124ec8b (MD5) Previous issue date: 2015-12-15 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Let M be a compact orientable Riemannian manifold with boundary. We first study in this thesis the transversality of a family of metrics via a family of Bilaplacian opera-tors parametrised by the metrics themselves. We next consider a family of Bilaplacian operators with variation of their dominion in flat Riemannian manifolds and establish a condition of transversality in this case. In the case of arbitrary Riemannian manifold, we obtain that the spectrum of 2g. is simple and the set of parameters is residual. We complete this thesis by studying the generic propeties of the eigenvalues of the Laplacian of a family of hyper-surfaces of revolution in the vector space Rn+1 / Nesta tese primeiramente tratamos de transversalidade de famílias de métricas, em que foi tomada uma família de operadores Bilaplacianos parametrizada pelas métricas de uma variedade Riemanniana orientável M compacta com bordo. Em seguida foi considerada uma família de operadores Bilaplacianos em que o parâmetro é o domínio de definição do operador, no caso da variação do domínio em variedades Riemannianas flat foi mostrada a condição de transversalidade para a família de operadores Bilaplacianos parametrizados por tais domínios. Porém no caso de variedades Riemannianas quaisquer, obtemos a simplicidade genérica dos autovalores associados ao 2g. Por último, estudamos a situação genérica dos autovalores do Laplaciano numa família de hipersuperficies de rotação no espaço vetorial Rn+1.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / This work shows results existence and uniqueness of graphs with prescribed mean curvature. We demonstrate that a natural fixation Dirichlet problem for graphs of average curvature is required to consider those graphs like leaves on a Riemannian submersion Killing transversal cylinder, the cylinder given by flow lines of a Killing vector field. Using this approach, we are able to solve the problem in a way more comprehensive, giving a unified proof and existence results. / O objetivo deste trabalho à exibir resultados de existÃncia e unicidade de grÃficos com curvatura mÃdia prescrita. Demonstraremos que uma fixacÃo natural do problema de Dirichlet para grÃficos de curvatura mÃdia prescrita à considerar esses grÃficos como folhas em uma submersÃo Riemanniana transversal ao cilindro de Killing, isto Ã, ao cilindro dado pelas linhasde fluxo de um campo de vetores de Killing. Usando essa aproximaÃÃo, somos capazes de resolver o problema em um modo mais compreensivo, dando uma prova unificada e resultados de existÃncia para uma ampla gama do ambiente de variedades Riemannianas.

Orientador: Djairo Guedes de Figueiredo / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Científica / Made available in DSpace on 2018-08-04T17:25:30Z (GMT). No. of bitstreams: 1 Pereira_FabioRodrigues_D.pdf: 1468332 bytes, checksum: 3e4d6ad380a672eddddbebbfbe9c85f4 (MD5) Previous issue date: 2005 / Doutorado / Doutor em Matemática

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In dieser Arbeit werden die zu einem m-sektoriellen Operator assoziierten Halbgruppen betrachtet, die die Lösungen des Anfangswertproblems der zugehörigen Evolutionsgleichung beschreiben. Es wird eine 1987 von Davies veröffentlichte Methode zur Abschätzung dieser Halbgruppen verallgemeinert. Einen Schwerpunkt bilden die zu Dirichlet-Formen assoziierten Markov-Halbgruppen. Für diese werden die Resultate spezialisiert und der Zusammenhang zur intrinsischen Metrik dargelegt. Die Arbeit schließt mit verschiedenen Beispielen, die zeigen, wie mit diesen Verallgemeinerungen von Davies Methode neue Anwendungsgebiete erschlossen werden können. / This thesis is about m-sectorial operators and their associated semigroups describing the solutions of the initial value problem of the corresponding evolution equation. We generalize a method published by Davies 1987 to estimate these semigroups. A focus is set on Markov semigroups associated with Dirchlet forms. The results are applied to them and the connection to the intrinsic metric is presented. The thesis ends with different examples showing how this generalization of Davies method can be applied into new fields of application.

En recherche d’information, les documents sont le plus souvent considérés comme des "sacs-de-mots". Ce modèle ne tient pas compte de la structure temporelle du document et est sensible aux bruits qui peuvent altérer la forme lexicale. Ces bruits peuvent être produits par différentes sources : forme peu contrôlée des messages des sites de micro-blogging, messages vocaux dont la transcription automatique contient des erreurs, variabilités lexicales et grammaticales dans les forums du Web. . . Le travail présenté dans cette thèse s’intéresse au problème de la représentation de documents issus de sources bruitées.La thèse comporte trois parties dans lesquelles différentes représentations des contenus sont proposées. La première partie compare une représentation classique utilisant la fréquence des mots à une représentation de haut-niveau s’appuyant sur un espace de thèmes. Cette abstraction du contenu permet de limiter l’altération de la forme de surface du document bruité en le représentant par un ensemble de caractéristiques de haut-niveau. Nos expériences confirment que cette projection dans un espace de thèmes permet d’améliorer les résultats obtenus sur diverses tâches de recherche d’information en comparaison d’une représentation plus classique utilisant la fréquence des mots.Le problème majeur d’une telle représentation est qu’elle est fondée sur un espace de thèmes dont les paramètres sont choisis empiriquement.La deuxième partie décrit une nouvelle représentation s’appuyant sur des espaces multiples et permettant de résoudre trois problèmes majeurs : la proximité des sujets traités dans le document, le choix difficile des paramètres du modèle de thèmes ainsi que la robustesse de la représentation. Partant de l’idée qu’une seule représentation des contenus ne peut pas capturer l’ensemble des informations utiles, nous proposons d’augmenter le nombre de vues sur un même document. Cette multiplication des vues permet de générer des observations "artificielles" qui contiennent des fragments de l’information utile. Une première expérience a validé cette approche multi-vues de la représentation de textes bruités. Elle a cependant l’inconvénient d’être très volumineuse,redondante, et de contenir une variabilité additionnelle liée à la diversité des vues. Dans un deuxième temps, nous proposons une méthode s’appuyant sur l’analyse factorielle pour fusionner les vues multiples et obtenir une nouvelle représentation robuste,de dimension réduite, ne contenant que la partie "utile" du document tout en réduisant les variabilités "parasites". Lors d’une tâche de catégorisation de conversations,ce processus de compression a confirmé qu’il permettait d’augmenter la robustesse de la représentation du document bruité.Cependant, lors de l’élaboration des espaces de thèmes, le document reste considéré comme un "sac-de-mots" alors que plusieurs études montrent que la position d’un terme au sein du document est importante. Une représentation tenant compte de cette structure temporelle du document est proposée dans la troisième partie. Cette représentation s’appuie sur les nombres hyper-complexes de dimension appelés quaternions. Nos expériences menées sur une tâche de catégorisation ont montré l’efficacité de cette méthode comparativement aux représentations classiques en "sacs-de-mots". / In the Information Retrieval field, documents are usually considered as a "bagof-words". This model does not take into account the temporal structure of thedocument and is sensitive to noises which can alter its lexical form. These noisescan be produced by different sources : uncontrolled form of documents in microbloggingplatforms, automatic transcription of speech documents which are errorprone,lexical and grammatical variabilities in Web forums. . . The work presented inthis thesis addresses issues related to document representations from noisy sources.The thesis consists of three parts in which different representations of content areavailable. The first one compares a classical representation based on a term-frequencyrepresentation to a higher level representation based on a topic space. The abstractionof the document content allows us to limit the alteration of the noisy document byrepresenting its content with a set of high-level features. Our experiments confirm thatmapping a noisy document into a topic space allows us to improve the results obtainedduring different information retrieval tasks compared to a classical approach based onterm frequency. The major problem with such a high-level representation is that it isbased on a space theme whose parameters are chosen empirically.The second part presents a novel representation based on multiple topic spaces thatallow us to solve three main problems : the closeness of the subjects discussed in thedocument, the tricky choice of the "right" values of the topic space parameters and therobustness of the topic-based representation. Based on the idea that a single representationof the contents cannot capture all the relevant information, we propose to increasethe number of views on a single document. This multiplication of views generates "artificial"observations that contain fragments of useful information. The first experimentvalidated the multi-view approach to represent noisy texts. However, it has the disadvantageof being very large and redundant and of containing additional variability associatedwith the diversity of views. In the second step, we propose a method based onfactor analysis to compact the different views and to obtain a new robust representationof low dimension which contains only the informative part of the document whilethe noisy variabilities are compensated. During a dialogue classification task, the compressionprocess confirmed that this compact representation allows us to improve therobustness of noisy document representation.Nonetheless, during the learning process of topic spaces, the document is consideredas a "bag-of-words" while many studies have showed that the word position in a7document is useful. A representation which takes into account the temporal structureof the document based on hyper-complex numbers is proposed in the third part. Thisrepresentation is based on the hyper-complex numbers of dimension four named quaternions.Our experiments on a classification task have showed the effectiveness of theproposed approach compared to a conventional "bag-of-words" representation.

We characterize the structure of the domain of a pure jump-type Dirichlet form which is given by a Beurling–Deny formula. In particular, we obtain su cient conditions in terms of the jumping kernel guaranteeing that the test functions are a core for the Dirichlet form and that the form is a Silverstein extension. As an application we show that for recurrent Dirichlet forms the extended Dirichlet space can be interpreted in a natural way as a homogeneous Dirichlet space. For reflected Dirichlet spaces this leads to a simple purely analytic proof that the active reflected Dirichlet space (in the sense of Chen, Fukushima and Kuwae) coincides with the extended active reflected Dirichlet space. / Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.