In this thesis we are studying some properties of weakly sequential homeomorphisms between Banach spaces. First, we show some results that summarize how are some clas- ses of Banach spaces (specifically separable spaces, spaces with separable dual, Asplund spaces, reflexive spaces, weakly compactly generated spaces and spaces not containing isomorphic copy of ℓ1) determined by weak topology of the space. Then we show that to preserve some properties (separability, reflexivity and being weakly compactly gene- rated) it is enough for the spaces to be weakly sequentially homeomorphic. Furthermore we show that if two spaces are weakly sequentially uniformly homeomorphic then one contains isomorphic copy of ℓ1 if and only if the other spaces has this property. Finally we construct weakly sequential homeomorphisms between some class of Banach spaces.

La migration de données entre des sources aux schémas hétérogènes est un domaine en pleine croissance avec l'augmentation de la quantité de données en accès libre, et le regroupement des données à des fins d'apprentissage automatisé et de fouilles. Cependant, la description du processus de transformation des données d'une instance source vers une instance définie sur un schéma différent est un processus complexe même pour un utilisateur expert dans ce domaine. Cette thèse aborde le problème de la définition de mapping par un utilisateur non expert dans le domaine de la migration de données, ainsi que la vérification du respect par ce mapping des contraintes d'accès ayant été définies sur les données sources. Pour cela, dans un premier temps nous proposons un système dans lequel l'utilisateur fournit un ensemble de petits exemples de ses données, et est amené à répondre à des questions booléennes simples afin de générer un mapping correspondant à ses besoins. Dans un second temps, nous proposons un système permettant de réécrire le mapping produit de manière à assurer qu'il respecte un ensemble de vues de contrôle d'accès définis sur le schéma source du mapping. Plus précisément, le premier grand axe de cette thèse est la formalisation du problème de la définition interactive de mappings, ainsi que la description d'un cadre formel pour la résolution de celui-ci. Cette approche formelle pour la résolution du problème de définition interactive de mappings est accompagnée de preuves de bonnes propriétés. A la suite de cela, basés sur le cadre formel défini précédemment, nous proposons des algorithmes permettant de résoudre efficacement ce problème en pratique. Ces algorithmes visent à réduire le nombre de questions auxquelles l'utilisateur doit répondre afin d'obtenir un mapping correspondant à ces besoins. Pour cela, les mappings possibles sont ordonnés dans des structures de treillis imbriqués, afin de permettre un élagage efficace de l'espace des mappings à explorer. Nous proposons également une extension de cette approche à l'utilisation de contraintes d'intégrité afin d'améliorer l’efficacité de l'élagage. Le second axe majeur vise à proposer un processus de réécriture de mapping qui, étant donné un ensemble de vues de contrôle d'accès de référence, permet d'assurer que le mapping réécrit ne laisse l'accès à aucune information n'étant pas accessible via les vues de contrôle d'accès. Pour cela, nous définissons un protocole de contrôle d'accès permettant de visualiser les informations accessibles ou non à travers un ensemble de vues de contrôle d'accès. Ensuite, nous décrivons un ensemble d'algorithmes permettant la réécriture d'un mapping en un mapping sûr vis-à-vis d'un ensemble de vues de contrôle d'accès. Comme précédemment, cette approche est complétée de preuves de bonnes propriétés. Afin de réduire le nombre d'interactions nécessaires avec l'utilisateur lors de la réécriture d'un mapping, une approche permettant l'apprentissage des préférences de l'utilisateur est proposée, cela afin de permettre le choix entre un processus interactif ou automatique. L'ensemble des algorithmes décrit dans cette thèse ont fait l'objet d'un prototypage et les expériences réalisées sur ceux-ci sont présentées dans cette thèse / Data exchange between sources over heterogeneous schemas is an ever-growing field of study with the increased availability of data, oftentimes available in open access, and the pooling of such data for data mining or learning purposes. However, the description of the data exchange process from a source to a target instance defined over a different schema is a cumbersome task, even for users acquainted with data exchange. In this thesis, we address the problem of allowing a non-expert user to spec- ify a source-to-target mapping, and the problem of ensuring that the specified mapping does not leak information forbidden by the security policies defined over the source. To do so, we first provide an interactive process in which users provide small examples of their data, and answer simple boolean questions in order to specify their intended mapping. Then, we provide another process to rewrite this mapping in order to ensure its safety with respect to the source policy views. As such, the first main contribution of this thesis is to provide a formal definition of the problem of interactive mapping specification, as well as a formal resolution process for which desirable properties are proved. Then, based on this formal resolution process, practical algorithms are provided. The approach behind these algorithms aims at reducing the number of boolean questions users have to answers by making use of quasi-lattice structures to order the set of possible mappings to explore, allowing an efficient pruning of the space of explored mappings. In order to improve this pruning, an extension of this approach to the use of integrity constraints is also provided. The second main contribution is a repairing process allowing to ensure that a mapping is “safe” with respect to a set of policy views defined on its source schema, i.e., that it does not leak sensitive information. A privacy-preservation protocol is provided to visualize the information leaks of a mapping, as well as a process to rewrite an input mapping into a safe one with respect to a set of policy views. As in the first contribution, this process comes with proofs of desirable properties. In order to reduce the number of interactions needed with the user, the interactive part of the repairing process is also enriched with the possibility of learning which rewriting is preferred by users, in order to obtain a completely automatic process. Last but not least, we present extensive experiments over the open source prototypes built from two contributions of this thesis

Given a closed surface Sg of genus g, a mapping class f in \MCG(Sg) is said to be pseudo-Anosov if it preserves a pair of transverse measured foliations such that one is expanding and the other one is contracting by a number \lambda(f). The number \lambda(f) is called a stretch factor (or dilatation) of f. Thurston showed that a stretch factor is an algebraic integer with degree bounded above by 6g-6. However, little is known about which degrees occur. Using train tracks on surfaces, we explicitly construct pseudo-Anosov maps on Sg with orientable foliations whose stretch factor \lambda has algebraic degree 2g. Moreover, the stretch factor \lambda is a special algebraic number, called Salem number. Using this result, we show that there is a pseudo-Anosov map whose stretch factor has algebraic degree d, for each positive even integer d such that d≤g. Our examples also give a new approach to a conjecture of Penner.

The site analysis and mapping methods in the design and planning professions follow a standardized quantitative and qualitative analyis of place that favors a design process which can limit creativity and render it difficult to do anything with the normative. This work is an exploration of the development of a design approach and method that uses voice mapping as a basis for design. The voice maps contain oral histories and personal accounts of landscape experiences. Voice mapping is employed not only as a method or for site analysis but also as a generator or ideas. Voice Map Trekking is explored through a trek in the Canadian Arctic and across the Canadian Prairies. Two specific landscapes were chosen as bases for testing concepts - one near St. Gertrude SK and the other near Morinville AB. / February 2008

Orientador: Manoel Ferreira Borges Neto / Banca: Masayoshi Tsuchida / Banca: Siovani Felipussi / Resumo: Neste trabalho estudamos transformações quaseconformes no contexto dos octônios, que são hipercomplexos de oito dimensões. Por não preservar a magnitude dos ângulos, mapeamentos quaseconformes causam uma dilatação linear. A partir da definição métrica de quaseconformidade, utilizamos a forma binomial para mostrar que a distância jf(y) ¡ f(x)j pode ser escrita como um polinômio em r. Com isso, pudemos desenvolver não são um conjunto de fórmulas como também um método computacional simplificado para o cálculo analítico da dilatação. Posteriormente, utilizamos ferramentas gráficas para vizualizar as consequências da dilatação. / Abstract: In this work we study quasiconformal mappings related to octonionic algebra. Since quasicon- formal mappings do not preserve the magnitude of the angles they cause a linear dilatation. We show that it also happens to 8-dimensional hipercomplex. Based on the metric de¯nition of quasiconformal mapping we show that the distance jf(y)¡f(x)j is a polynomial of variable r. Then it¶s possible to make not only a set of formulas but also a computacional method to calculate the dilatation. We also use some graphical tools to visualize the consequences of dilatation. / Mestre

Este trabalho tem como principal objetivo estudar extensões de aplicações multilineares, de polinômios homogêneos e de funções analíticas entre espaços de Banach. Desta maneira, nos baseamos em importantes trabalhos sobre o assunto. Inicialmente apresentamos o produto de Arens para álgebras de Banach, extensões de Aron-Berner e de Davie-Gamelin para aplicações multilineares e provamos que todas estas extensões coincidem. A partir destes resultados, apresentamos a extensão de polinômios homogêneos e o Teorema de Davie-Gamelin que afirma que, assim como no caso de aplicações multilineares, as extensões de polinômios preservam a norma e, como consequência deste teorema, apresentamos uma generalização do Teorema de Goldstine. Em seguida estudamos espaços de Banach regulares e simetricamente regulares, que são propriedades relacionadas com a unicidade de extensão e são definidas a partir do ideal de operadores lineares fracamente compactos K^w(E, F) . Finalmente apresentamos a extensão de uma função de H_b(E) para H_b(E\'\') e o resultado, de Ignacio Zalduendo, que caracteriza esta extensão em termos da continuidade fraca-estrela do operador diferencial de primeira ordem. / The main purpose of this work is to study extensions of multilinear mappings, homogeneous polynomials and analytic functions between Banach Spaces. In this way, we rely on important works on the subject. Firstly we present the Arens-product for Banach algebras, the Aron-Berner and Davie-Gamelin extensions for multilinear mappings and we prove that all these extensions are the same. From these results, we present an extension for homogeneous polynomials and the Davie-Gamelin theorem which asserts that, as in the case of multilinear mappings, the polynomial extension is norm-preserving and, as a consequence of this theorem, we present a generalization of the Goldstine theorem. After that we study regular and symmetrically regular Banach spaces which are properties related to the uniqueness of the extension and are defined in the setting of weakly compact linear operators K^w(E, F) . Lastly, we present the extension of a function of H_b(E) to one in H_b(E\'\') and the result, according to Ignacio Zalduendo, which characterizes this extension in terms of weak-star continuity of the first order differential operator.

Made available in DSpace on 2014-06-11T19:22:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-05-12Bitstream added on 2014-06-13T18:48:40Z : No. of bitstreams: 1 denadai_d_me_sjrp.pdf: 370065 bytes, checksum: 6db2aacdc27e3eb4ca5f48d683ca1d56 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho provamos a existência de controle aproximado para certos sistemas não-lineares de equaçõ es diferenciais ordinárias de entrada e saída únicas e múltiplas. Utilizamos como técnica funções ou aplicações implícitas globais. / In this work we prove the existence of approximate control for certain nonlinear sys-tems of ordinary differential equations of single-input single-output and multi-input multi-output. We use global implicit functions or mappings.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE / Bibliography: leaves 155-156. / by Robert Clack Penner. / Ph.D.

Este trabalho tem como principal objetivo estudar extensões de aplicações multilineares, de polinômios homogêneos e de funções analíticas entre espaços de Banach. Desta maneira, nos baseamos em importantes trabalhos sobre o assunto. Inicialmente apresentamos o produto de Arens para álgebras de Banach, extensões de Aron-Berner e de Davie-Gamelin para aplicações multilineares e provamos que todas estas extensões coincidem. A partir destes resultados, apresentamos a extensão de polinômios homogêneos e o Teorema de Davie-Gamelin que afirma que, assim como no caso de aplicações multilineares, as extensões de polinômios preservam a norma e, como consequência deste teorema, apresentamos uma generalização do Teorema de Goldstine. Em seguida estudamos espaços de Banach regulares e simetricamente regulares, que são propriedades relacionadas com a unicidade de extensão e são definidas a partir do ideal de operadores lineares fracamente compactos K^w(E, F) . Finalmente apresentamos a extensão de uma função de H_b(E) para H_b(E\'\') e o resultado, de Ignacio Zalduendo, que caracteriza esta extensão em termos da continuidade fraca-estrela do operador diferencial de primeira ordem. / The main purpose of this work is to study extensions of multilinear mappings, homogeneous polynomials and analytic functions between Banach Spaces. In this way, we rely on important works on the subject. Firstly we present the Arens-product for Banach algebras, the Aron-Berner and Davie-Gamelin extensions for multilinear mappings and we prove that all these extensions are the same. From these results, we present an extension for homogeneous polynomials and the Davie-Gamelin theorem which asserts that, as in the case of multilinear mappings, the polynomial extension is norm-preserving and, as a consequence of this theorem, we present a generalization of the Goldstine theorem. After that we study regular and symmetrically regular Banach spaces which are properties related to the uniqueness of the extension and are defined in the setting of weakly compact linear operators K^w(E, F) . Lastly, we present the extension of a function of H_b(E) to one in H_b(E\'\') and the result, according to Ignacio Zalduendo, which characterizes this extension in terms of weak-star continuity of the first order differential operator.

In 2014, Astala, Päivärinta, Reyes, and Siltanen conducted numerical experiments reconstructing a piecewise continuous conductivity. The algorithm of the shortcut method is based on the reconstruction algorithm due to Nachman, which assumes a priori that the conductivity is Hölder continuous. In this dissertation, we prove that, in the presence of infinite-precision data, this shortcut procedure accurately recovers the scattering transform of an essentially bounded conductivity, provided it is constant in a neighborhood of the boundary. In this setting, Nachman’s integral equations have a meaning and are still uniquely solvable. To regularize the reconstruction, Astala et al. employ a high frequency cutoff of the scattering transform. We show that such scattering transforms correspond to Beltrami coefficients that are not compactly supported, but exhibit certain decay at infinity. For this class of Beltrami coefficients, we establish that the complex geometric optics solutions to the Beltrami equation exist and exhibit the same subexponential decay as described in the 2006 work of Astala and Päivärinta. This is a first step toward extending the inverse scattering map of Astala and Päivärinta to non-compactly supported conductivities.