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We extend the theory of singular integral operators and multiplier theorems to the setting of anisotropic Hardy spaces. We first develop the theory of singular integral operators of convolution type in the anisotropic setting and provide a molecular decomposition on Hardy spaces that will help facilitate the study of these operators. We extend two multiplier theorems, the first by Taibleson and Weiss and the second by Baernstein and Sawyer, to the anisotropic setting. Lastly, we characterize the Fourier transforms of Hardy spaces and show that all multipliers are necessarily continuous.

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abstract: Skyline queries are a well-established technique used in multi criteria decision applications. There is a recent interest among the research community to efficiently compute skylines but the problem of presenting the skyline that takes into account the preferences of the user is still open. Each user has varying interests towards each attribute and hence "one size fits all" methodology might not satisfy all the users. True user satisfaction can be obtained only when the skyline is tailored specifically for each user based on his preferences. This research investigates the problem of preference aware skyline processing which consists of inferring the preferences of users and computing a skyline specific to that user, taking into account his preferences. This research proposes a model that transforms the data from a given space to a user preferential space where each attribute represents the preference of the user. This study proposes two techniques "Preferential Skyline Processing" and "Latent Skyline Processing" to efficiently compute preference aware skylines in the user preferential space. Finally, through extensive experiments and performance analysis the correctness of the recommendations and the algorithm's ability to outperform the naïve ones is confirmed. / Dissertation/Thesis / Masters Thesis Computer Science 2014

Orientador: Helio Vasconcelos Fagundes / Banca: José Geraldo Pereira / Banca: Maria Emília Xavier Guimarães / Resumo: No final do século XIX, L. Bianchi [1] fez a classificação das geometrias riemanianas em espaços tridimensionais, segundo seus possíveis grupos de isometrias. Parte de seus resultados foi adaptada, em uma linguagem mais moderna, por C. G. Behr [17] e outros, para o estudo de modelos cosmológicos espacialmente homogêneos mas não necessariamente isotrópicos. Esta dissertação expõe as idéias e resultados de Bianchi, e também os formalismos mais recentes no estudo desse problema. Por completeza, o espaço tridimensional do modelo de Kantowski-Sachs também é aqui incluído / Abstract: At the end of the 19th century, L. Bianchi [1] found a classification of the Riemannian geometries oni three-dimensional spaces, according to their possible isometry groups. A part of his results has been adapted, in a more modern language, by C. G. Behr [17] and others, for the study of cosmological models with homogeneous but not necessarily isotropic spatial sections. This dissertation presents Bianchi's ideas and results, and also more recent formalisms in the study of this problem. For completeness, the three-space of Kantowski-Sachs cosmological model is also here included / Mestre

In this dissertation we are interested in studying two extremal problems in the Bergman space. The topics are divided into three chapters. In Chapter 2, we study Putnam’s inequality in the Bergman space setting. In [32], the authors showed that Putnam’s inequality for the norm of self-commutators can be improved by a factor of 1 for Toeplitz operators with analytic symbol φ acting on the Bergman space A2(Ω). This improved upper bound is sharp when φ(Ω) is a disk. We show that disks are the only domains for which the upper bound is attained. In Chapter 3, we consider the problem of finding the best approximation to z ̄ in the Bergman space A2(Ω). We show that this best approximation is the derivative of the solution to the Dirichlet problem on ∂Ω with data |z|2 and give examples of domains where the best approximation is a polynomial, or a rational function. Finally, in Chapter 4 we study Bergman analytic content, which measures the L2(Ω)-distance between z ̄ and the Bergman space A2(Ω). We compute the Bergman analytic content of simply connected quadrature domains with quadrature formula supported at one point, and we also determine the function f ∈ A2(Ω) that best approximates z ̄. We show that, for simply connected domains, the square of Bergman analytic content is equal to torsional rigidity from classical elasticity theory, while for multiply connected domains these two domain constants are not equivalent in general.

A new class of functions, called somewhat e-continuous functions, has been defined and studied by making use of e-open sets. Characterizations and properties of somewhat e-continuous functions are presented.

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Cette recherche se situant au carrefour de plusieurs champs de la sociologie interroge la façon dont des figures du monde rural renaissant, à la fois différentes et proches, dans leur rapport au travail, comme dans leur rapport négatif à la ville, parviennent dans une société en crise à s'imaginer une nouvelle existence, en se séparant partiellement ou durablement de l'activité salariée qui n'est plus considérée comme l'unique moyen de réussir leur vie. Le rapport au travail comme le rapport au territoire se trouve rediscuté, et mis en tension, rééclairant cette dualité renaissante entre communauté et société, alors que l'on croyait que la modernité symbolisée par l'urbain et la ville avait définitivement tout emporté en modifiant de façon quasi irréversible la nature des liens sociaux. Nos figures, Hérauts involontaires, entendent nous dire à leur façon que l'esprit communautaire plane encore sur les territoires ruraux où ils se sont installés et qu'il favorise une réactivation des supports sociaux quelque soit notre niveau de vulnérabilité. Ils font fonction de bouclier de protection contre les risques de désaffiliation sociale en redéfinissant les conditions d'un vivreensemble possible largement débarrassées des contraintes d'une vie communautaire de la pré-modernité, sans nécessairement transformer la vie des individus. Les membres de la communauté se comportent comme des tiers invisibles désinstitutionnalisés qui relient, rapprochent et soutiennent les plus en risque dans cet espace vécu, facilitant le réenchâssement d'individus dans des réseaux possibles, redéfinissant ainsi les frontières mouvantes entre la précarité des villes et la précarité des champs. / This research which is at a crossroads of several socio\ogy areas questions the way the figures from the re-awakening of rural areas, which are at the same time different and close, in their relationship to the work, as weil as to the negative relationship to the city, succeed in a society in crisis in imaginating a new existence, by getting partially or permanently rid of the gainful employment which is no longer considered as the only way to have a successful life. Ther elationship to the work as well as the relationship to the territory is re-discussed, and kept in tension, futther illustrating this re-emerging duality between community and society, while it was believed thal modernity symbolized by urban spaces and the city had definitively taken everything away by changing in a near-irreversible way the nature of social connections. Our figures, unwitting heralds want to tell us in their own way, that the community spirit still exists in rural territories where they have settled and thal it favors a reactivation of the social supports regardless of our level of vulnerability. They act as a protective shield against the risks of social disaffiliation in redefining the conditions of a possible "living together" largely freed from the constraints of a community life of pre-modernity, without necessarily transforming the lives of individuals. The community members are behaving like deinstitutionalized, invisible third parties, who connect, bring closer and support those who are the most at risk in this experienced space, easing the re-entrechment of individuals in possible networks, thus reshaping the moving boundaries between the precariousness in the cities and the precariousness in the countrysides.

Ma recherche se situe à la croisée d'un ensemble de questions complexes que sont la genèse et les pratiques de la mémoire collective, les lieux en tant que chargés de significations sociales et les espaces en tant que cadres sociaux de la mémoire (M Halbwachs). Il s'agit des motivations individuelles partagées, à travers lesquelles la mémoire collective se maintient et trouve des traductions diverses, épousant chaque fois des situations nouvelles, là où les membres du collectif se trouvent réunis. Une dynamique dans laquelle l'espace, la religion et même la langue ne seront que des outils, mobilisés pour construire et puis maintenir cette mémoire. Ce faisant, je me rattache à une littérature en expansion qui cherche à montrer l'extrême importance, pour la compréhension de cette mémoire collective, de facteurs comme le lieu, le lien social et l'expérience narrative (Blokland, 2001 ). C'est avec des immigrés originaires de la même ville algérienne, située à 400 km au sud d'Alger, qui se sont regroupés en partie dans la banlieue sud de Lyon et d'autres dans la ville d'Alger que j'entreprendrai mon analyse. Depuis le début du XX ème siècle, plusieurs générations d' immigrés se sont succédé à Lyon comme à Alger, marquant le paysage urbain, social et même politique des lieux de leurs implantations. Sans apparente organisation, ni protocole laissé par des ancêtres dictant leurs conduites, les uns comme les autres ont montré une ubiquité socio-spatiale qui raisonne fortement avec la ville d'origine. Tout au long de la recherche, j'étais confronté à une trame de pratiques de mémoire qui consistait à faire la navette entre le présent et le passé, l' individuel et le collectif. / My research is at the cross of a set of complex issues that are the genesis and the practices of the collective memory, the places charged of social signification, and the spaces being social frames of the memory (M Halbwachs). It is a question of shared individual motivations, through which the collective memory is maintained and finds different translations,married up every time to a new situation, where the members of the collective are gathered. A dynamic where the space,the religion and even the language will be only tools, mobilized to build and keep the memory alive. Thus, I use an expanding literature seeking to show the extreme importance of understanding this collective memory, of factors such as the location, the social link and the narrative experience (Blokland, 2001; Mistral, 2003).The researchis based upon immigrants from the same algerian hometown, located about 400 km from the capital Algiers (south of Algiers), who gathered mainly in the suburbs south of Lyon and others in Algiers. Since the beginning of the20th century, several generations of immigrants have corne successively to Lyon and Algiers, leaving its mark on the urban, social and even political landscape of their location. Without any apparent organization, or any protocol bequeathed by their ancestors, all of them have shown a socio-spatial ubiquity that goes strongly with the original hometown. Through the research, I have been confronted to a number of memory practices that consisted in commuting between the present and the past, the individual and the collective.