This dissertation is focused on an algebraic approach of some many-valued generalizations of modal logics. The starting point is the definition of the [0,1]-valued and the Ł_n-valued Kripke models, where [0,1] denotes the well known MV-algebra and Ł_n its finite subalgebra {0, 1/n, ... , (n-1)/n,1} for any positive integer n. Two types of structures are used to define validity of formulas: the class of L-frames and the class of Ł_n-valued L-frames. The latter structures are L-frames in which we specify in each world u the set Ł_m (where m is a divisor of n) of the possible truth values of the formulas in u. These two classes of structures define two distinct notions of validity. We use these notions to study the problem of definability of classes of structures with modal formulas. We obtain for these two classes an equivalent of the Goldblatt-Thomason theorem. We are able to consider completeness problems with respect to these relational semantics thanks to the connections between relational and algebraic semantics. Our strongest results are about Ł_n-valued logics. We are indeed able to apply and develop algebraic tools (namely, canonical and strong canonical extensions) that allow to generate complete Ł_n-valued logics. / Nous consacrons cette dissertation à une étude algébrique de certaines généralisations multivaluées des logiques modales. Notre point de départ est la définition des modèle de Kripke [0,1]-valués et Ł_n-valués, où [0,1] désigne la MV-algèbre bien connue et Ł_n sa sous-algèbre {0, 1/n, ... , (n-1)/n,1} pour tout naturel non nul n. Nous utilisons deux types de structures pour définir une relation de validité: la classe des L-structures et celles des L-structures Ł_n-valuées. Ces dernières sont des L-structures dans lesquelles nous précisons pour chaque monde u l'ensemble Ł_m (où m est un diviseur de n) des valeurs de vérité que les formules sont autorisées à prendre en u. Ces deux classes de structures définissent deux notions distinctes de validité. Nous les utilisons pour étudier le problème de la définissabilité des classes de structures à l'aide du langage modal. Nous obtenons dans les deux cas l'équivalent du théorème de Goldblatt-Thomason. Nous considérons aussi les problèmes de complétude vis-à-vis de ces sémantiques relationnelles à l'aide des liens qui les lient à la sémantique algébrique. Les résultats les plus forts que nous obtenons concernent les logiques modales Ł_n-valuées. En effet, dans ce cas, nous pouvons appliquer et développer des outils algébriques (à savoir, les extensions canoniques et les extensions canoniques fortes) qui permettent de générer des logiques complètes.

Soit p un nombre premier, soit K/k une extension galoisienne finie de corps de nombres de degré premier à p et soit S un ensemble fini de premiers de k. Le groupe de Galois G(K,S) de la pro-p extension maximale de K non ramifiée en dehors de S est l'objet central de ce mémoire.On se place dans un premier temps dans le cas modéré : on suppose que S ne contient pas les places divisant p. Les travaux combinés de Labute, Minac et Schmidt sur les pro-p groupes mild ont permis d'exhiber les premiers exemples de groupes G(K,S) de dimension cohomologique 2. En implémentant un corollaire de leur critère dans le logiciel PARI/GP, on observe un phénomène de propagation : si k=Q et si le groupe G(Q,S) est mild, un fort pourcentage des groupes G(K,S) l'est également, pour K quadratique imaginaire. En associant au groupe G(K,S) deux graphes orientés dont les arcs sont définis par la ramification dans des extensions p-élémentaires, on démontre un critère théorique pour que ce phénomène de propagation ait lieu.On considère ensuite le cas sauvage : toutes les places au-dessus de p sont contenues dans S. Le groupe de Galois Δ:=Gal(K/k) agit sur G(K,S) ; on note G le plus grand quotient de G(K,S) sur lequel Δ agit trivialement et H le sous-groupe fermé de G(K,S) correspondant. Maire a étudié la liberté du Zp[[G]]-module H^{ab}. Nous poussons plus loin ses résultats en considérant les φ-composantes de H^{ab} sous l'action de Δ. Sous de bonnes hypothèses et sous la conjecture de Leopoldt, on démontre une condition nécessaire et suffisante pour que les φ-composantes soient libres ou non. La théorie du corps de classes permet de ramener cette condition à l'étude du régulateur normalisé, et donc à la p-rationalité du corps K. Les expérimentations faites sur PARI/GP dans des familles d'extensions cubiques cycliques, diédrales et cycliques de degré 4 du corps des rationnels corroborent une conjecture de Gras selon laquelle tout corps de nombres est p-rationnel pour p suffisant grand. / Let p be a prime number, let K/k be a Galois extension of number fields and let S be a finite set of primes of K. We suppose that the degree of K/k is finite and coprime to p. We denote by G(K,S) the Galois group of the pro-p maximal extension of K unramified outside S. We focus on this thesis on two differents aspects of this pro-p group.We are first interested in the tame case : we suppose that S does not contain any place above p. The works of Labute, Minac and Schmidt about mild pro-p groups brought the first examples of groups G(K,S) of cohomological dimension two. Using a corollary of their criterium, we compute some examples with PARI/GP and we observe a propagation phenomenum : if we take K=Q and if we suppose that G(Q,S) is mild, a large part of the pro-p groups G(K,S) with K imaginary quadratic are mild too. We then associate two oriented graphs to G(K,S) and we show a theoretical criterium proving mildness of some imaginary quadratic fields.We then consider the wild case where all the places dividing p belong to S. The Galois group Δ:=Gal(K/k) acts on G(K,S). The action of Δ is trivial on some quotients of G(K,S) ; we denote by G the maximal one and by H the corresponding closed subgroup of G(K,S). Maire has studied the Zp[[G]]-freeness of the module H^{ab}. We extend his results considering the φ-component of H^{ab} under the action of Δ. In a favourable context and under Leopoldt's conjecture, we show a necessary and sufficient condition for the freeness of the φ-components. This condition is connected to p-rational fields by class field theory. We present experiments with PARI/GP in some families of cubic cyclic, dihedral and quartic cyclic extensions of Q which support the following conjecture from Gras : every number field is p-rational for sufficiently large p.

L'objet de cette thèse est l'étude mathématique de familles d'espaces-temps satisfaisant aux équations d'Einstein de la Relativité Générale. Deux approches sont considérées pour cette étude. La première partie, composée des trois premiers chapitres, examine les propriétés géométriques des espaces-temps d'Emparan-Reall et dePomeransky-Senkov, de dimension 5. Nous montrons qu'ils contiennent un trou noir, dont l'horizon des événements est à sections compactes non-homéomorphes à la sphère. Nous en construisons une extension analytique et prouvons que cette extension est maximale et unique dans une certaine classe d'extensions pour les espaces-temps d'Emparan-Reall. Nous établissons ensuite le diagramme de Carter-Penrose de ces extensions, puis analysons la structure de l'ergosurface des espaces-temps de Pomeransky-Senkov. La deuxième partie est consacrée à l'étude de données initiales, solutions des équations des contraintes, induites par les équations d'Einstein. Nous effectuons un recollement d'une classe de données initiales avec des données initiales d'espaces-temps de Kerr-Kottler-deSitter, en utilisant la méthode de Corvino. Nous construisons, d'autre part, des métriques asymptotiquement hyperboliques en dimension 3, satisfaisant les hypothèses du théorème de masse positive à l'exception de la complétude, et ayant un vecteur moment-énergie de genre causal arbitraire. / The aim of this thesis is the mathematical study of families of spacetimes satisfying the Einstein's equations of General Relativity. Two methodsare used in this context.The first part, consisting of the first three chapters of this work,investigates the geometric properties of the Emparan-Reall andPomeransky-Senkov families of 5-dimensional spacetimes. We show that they contain a black-hole region, whose event horizon has non-spherical compact cross sections. We construct an analytic extension, and show its maximality and its uniqueness within a natural class in the Emparan-Reallcase. We further establish the Carter-Penrose diagram for these extensions, and analyse the structure of the ergosurface of the Pomeransky-Senkovspacetimes.The second part focuses on the study of initial data, solutions of theconstraint equations induced by the Einstein's equations. We perform agluing construction between a given family of inital data sets andinitial data of Kerr-Kottler-de Sitter spacetimes, using Corvino'smethod.On the other hand, we construct 3-dimensional asymptotically hyperbolicmetrics which satisfy all the assumptions of the positive mass theorem but the completeness, and which display an energy-momentum vector of arbitry causal type.

Cette thèse est consacrée aux quelques problèmes mathématiques concernant les extensions minimales de Lipschitz. Elle est organisée de manière suivante. Le chapitre 1 est dédié à l’introduction des extensions minimales de Lipschitz. Dans le chapitre 2, nous étudions la relation entre la constante de Lipschitz d’ 1-field et la constante de Lipschitz du gradient associée à ce 1-field. Nous proposons deux formules explicites Sup-Inf, qui sont des extensions extrêmes minimales de Lipschitz d’1-field. Nous expliquons comment les utiliser pour construire les extensions minimales de Lipschitz pour les applications Rmà Rn . Par ailleurs, nous montrons que les extensions de Wells d’1- fields sont les extensions absolument minimales de Lipschitz (AMLE) lorsque le domaine d’expansion d’1-field est infini. Un contreexemple est présenté afin de montrer que ce résultat n’est pas vrai en général. Dans le chapitre 3, nous étudions la version discrète de l’existence et l’unicité de l’AMLE. Nous montrons que la fonction tight introduite par Sheffield and Smart est l’extension de Kirszbraun. Dans le cas réel, nous pouvons montrer que cette extension est unique. De plus, nous proposons un algorithme qui permet de calculer efficacement la valeur de l’extension de Kirszbraun en complexité polynomiale. Pour conclure, nous décrivons quelques pistes pour la future recherche, qui sont liées au sujet présenté dans ce manuscrit. / The thesis is concerned to some mathematical problems on minimal Lipschitz extensions. Chapter 1: We introduce some basic background about minimal Lipschitz extension (MLE) problems. Chapter 2: We study the relationship between the Lipschitz constant of 1-field and the Lipschitz constant of the gradient associated with this 1-field. We produce two Sup-Inf explicit formulas which are two extremal minimal Lipschitz extensions for 1-fields. We explain how to use the Sup-Inf explicit minimal Lipschitz extensions for 1-fields to construct minimal Lipschitz extension of mappings from Rm to Rn. Moreover, we show that Wells’s extensions of 1-fields are absolutely minimal Lipschitz extensions (AMLE) when the domain of 1-field to expand is finite. We provide a counter-example showing that this result is false in general. Chapter 3: We study the discrete version of the existence and uniqueness of AMLE. We prove that the tight function introduced by Sheffield and Smart is a Kirszbraun extension. In the realvalued case, we prove that the Kirszbraun extension is unique. Moreover, we produce a simple algorithm which calculates efficiently the value of the Kirszbraun extension in polynomial time. Chapter 4: We describe some problems for future research, which are related to the subject represented in the thesis.

<p>In today’s world, cloud machines store an ever-increasing amount of sensitive user data, but it remains challenging to guarantee the security of our data. This is because a cloud machine’s system software—critical components like the operating system and hypervisor that can access and thus leak user data—is subject to attacks by numerous other tenants and cloud administrators. Trusted execution environments (TEEs) like Intel SGX promise to alter this landscape by leveraging a trusted CPU to create execution contexts (or enclaves) where data cannot be directly accessed by system software. Unfortunately, the protection provided by TEEs cannot guarantee complete data security. In particular, our data remains unprotected if a third-party service (e.g., Yelp) running inside an enclave is adversarial. Moreover, data can be indirectly leaked from the enclave using traditional memory side-channels.</p> <p><br></p> <p>This dissertation takes a significant stride towards strong user data protection in cloud machines using TEEs by defeating the critical threats of adversarial cloud services and memory side-channels. To defeat these threats, we systematically explore both software and hardware designs. In general, we designed software solutions to avoid costly hardware changes and present faster hardware alternatives.</p> <p><br></p> <p>We designed 4 solutions for this dissertation. Our Chancel system prevents data leaks from adversarial services by restricting data access capabilities through robust and efficient compiler-enforced software sandboxing. Moreover, our Obliviate and Obfuscuro systems leverage strong cryptographic randomization and prevent information leakage through memory side-channels. We also propose minimal CPU extensions to Intel SGX called Reparo that directly close the threat of memory side-channels efficiently. Importantly, each designed solution provides principled protection by addressing the underlying root-cause of a problem, instead of enabling partial mitigation.</p> <p><br></p> <p>Finally, in addition to the stride made by our work, future research thrust is required to make TEEs ubiquitous for cloud usage. We propose several such research directions to pursue the essential goal of strong user data protection in cloud machines.</p>

The dissertation is divided into two parts. The first part mainly treats a conjecture of Emil Artin from the 1930s. Namely, if f = a_1x_1^d + a_2x_2^d +...+ a_{d^2+1}x^d where the coefficients a_i lie in a finite unramified extension of a rational p-adic field, where p is an odd prime, then f is isotropic. We also deal with systems of quadratic forms over finite fields and study the isotropicity of the system relative to the number of variables. We also study a variant of the classical Davenport constant of finite abelian groups and relate it to the isotropicity of diagonal forms. The second part deals with the theory of finite groups. We treat computations of Chermak-Delgado lattices of p-groups. We compute the Chermak-Delgado lattices for all p-groups of order p^3 and p^4 and give results on p-groups of order p^5.

Research report presented for the degree of Master of Arts (Anthropology) at the University of the Witwatersrand, 2016 / According to the 2014 Euromonitor report on black South African haircare trends, the country exhibited a decrease in sales of damaging hair care products. This trend coincided with the exponential influx of imported Indian hair into the country for the purposes of artificial hair integrations i.e. weaves and extensions. To understand the meaning of these patterns, this project seeks to understand the significance Indian hair held for black women. By analysing anthropological literature on commodities, this work reveals how the purchase of Indian hair not only exposed the state of black hair in contemporary South Africa, but how black women engaged with that environment through its usage. Further, hair’s purchase situated women within a transnational exchange network that was buttressed by racial and gendered hierarchies. As such, hair’s consumption placed women within an “economy of otherness”. However women also utilized this economy by converting the racially charged commodity into social and symbolic capital which they leveraged for their own gain. As such, the purchase of Indian hair not only integrated women within an economy of otherness, but also provided them with the capital to participate within it. / GR2017

Webben kan användas i många syften och kan skapa ett mervärde både i arbetslivet och det privata livet för människor. Idag förekommer användande av datorer, webben och IT generellt i ett flertal branscher. IT har också blivit en del av det svenska utbildningssystemet där det händer att skolan förser eleverna med en dator och tillhörande program att utföra studier med. De flesta av svenskarna får idag någon form av datorvana genom antingen jobb eller studier, något som vissa seniorer har gått miste om. Personer över 75 år är med marginal den åldersgrupp (räknat från tolv år och äldre) som i Sverige använder internet mest sällan. När frågan ställs om varför är svaret ”det är för krångligt” vanligt förekommande. Denna studie syftar att ta reda på hur användande av webben kan underlättas för seniorer (definierat till personer 75 år och äldre i denna studie). Till en början gick studien ut på att ta reda på vad seniorer kan få ut av att använda internet och webben. Det gjordes genom en litteratursökning och genom ett antal intervjuer. Det framkom att seniorer som faktiskt använder webben på ett eller annat sätt nyttjar exempelvis internetbank, mail och nyheter genom såväl dator som smartphone och surfplatta. Dessa tre områden (mail, internetbank och nyheter) användes i studien som centra för testen som skulle undersöka hur seniorers interaktion med webben kan underlättas. Ett webbläsartillägg utformades anpassat till ovan tre beskrivna områden. Kort beskrivet är ett webbläsartillägg ett lokalt program/tillägg som går att installera i sin webbläsare för att personligen ha tillgång till extern funktionalitet, exempelvis att blockera reklam. Webbläsartillägget som skapades i denna studie gav användarens webbläsare grafiska element som var tänkta att hjälpa användaren att lösa ett antal fördefinierade uppgifter. Tre olika koncept testades under studien. Med koncept syftas här hur den grafiska hjälpen utformas. Användartester utfördes med och utan webbläsartillägg som hjälp för att kunna se om det var någon skillnad på resultaten. När tester utfördes med webbläsartillägget roterades koncepten beskrivna ovan så att alla tre koncept testades under likvärdiga förutsättningar. Testpersonerna som utförde tester med webbläsartillägget fick även möjlighet att ge anonym respons på koncepten genom att fylla i enkäter. Enligt resultaten av denna studie lyckas seniorer bättre (större andel lyckade försök) och snabbare att utföra vardagliga uppgifter när det fanns tillgång till en lista med hur uppgiften ska utföras eller genom att viktiga rubriker och knappar för uppgiften är markerade. / The web can be used in multiple purposes and can create a value both at work and in the personal life of people. Today computers, internet and IT in general are commonly used in multiple professions. IT has also become a part of the Swedish educational system where it happens that the schools provides the students with a computer with including programs to conduct their studies. Most swedes today gets some kind of computer habit from either work or education, something that certain seniors have missed out on. People above the age of 75 is by margin the age-group (taking in to account twelve years and older) that most seldom uses internet in Sweden. When asked why a common answer is “it is too hard”. This study aims to find out in what ways the use of the web can be made easier for seniors (in this study defined as 75 years of age and older). For starters the study focused on finding out what seniors can get out of using internet and the web. That was done by literature searching and a number of interviews. It showed that seniors who actually uses the web one way or the other uses for example internet banking, mail and news by computer, smartphone and/or tablet. These three areas (internet banking, mail and news) was used as a Centre in the user tests who was conducted in order to find out how seniors can be assisted in their interaction with the web. A browser extension was formed suited to the three areas mentioned above. Browser extensions is a sort of a local program/extension to install in your browser to personally have access to external functionality, such as blocking advertisement. The browser extension formed in this study gave the users browser graphic elements with the purpose to help the user solve a number of predetermined tasks. Three concepts was tested in the study. In the context of this study a concept is the way that the graphic assist is formed. User tests was conducted with and without the browser extension as an assist in order to see if there was a difference in the results. When tests was conducted with the browser extension the concepts was rotated so that all three concepts was tested on equal basis. The test persons who conducted the tests with the browser extension also got the opportunity to give anonymous feedback on the concepts through an inquiry that was filled out after conducted test. The result of the user tests and the inquiry indicates that seniors would appreciate a step by step guide for tasks on the web. According to the results of this study seniors conducts everyday tasks both quicker and with more success when there is a step by step list or highlighted headlines and buttons describing said task.

Este trabalho aborda diversos aspectos da extensão de marcas. A construção de marcas fortes tem sido uma alternativa para criar diferenciação e vantagem competitiva. O sucesso em um determinado mercado costuma ser decorrente de fatores que vão além do próprio produto; a percepção do consumidor sobre uma marca é formada por um complexo conjunto de associações onde coexistem aspectos racionais, funcionais e objetivos, bem como elementos emocionais, subjetivos e abstratos. A marca representa um código, um resumo de todas estas associações e percepções, e o posicionamento psicológico da marca influencia a decisão de compra dentro de uma categoria. Muitas empresas adotam as extensões de marca como uma estratégia de crescimento, o que resulta em uma proliferação de marcas estendidas para categorias adicionais de produto, categorias muitas vezes sem similaridade com a categoria original da marca. O objetivo principal e razão de ser da extensão é a transferência de valores da marca original para o novo produto, encurtando os caminhos que ele deve percorrer para sua consolidação e aumentando suas chances de sucesso. Entretanto, há diversos casos de extensão onde a marca não passa de um nome que caracteriza a origem do novo produto ou, pior ainda, sua aplicação naquela categoria resulta na erosão de seu significado. Sendo assim, este trabalho busca trazer referências que indiquem se faz sentido estender uma marca para outras categorias. A metodologia adotada consiste em duas etapas: uma de revisão bibliográfica, que aborda os principais aspectos da extensão de marca-suas motivantes, vantagens e riscos, resultados de pesquisas anteriores, o processo de avaliação pelos consumidores, a reciprocidade da marca estendida na marca original; e uma etapa de verificação de uma realidade específica usando a visão de uma empresa-alvo de estudo de caso. Os resultados apontam para uma relação entre o posicionamento psicológico da marca e sua extensão para categorias próximas e distantes daquela onde a marca se originou, indicando a possibilidade de que quanto mais filosófico o posicionamento da marca, isto é, menos vinculado ao produto em si e seus aspectos funcionais, maior sua capacidade em ser aplicada em categorias de produto diferentes da categoria original. À medida que a dissimilaridade entre o produto original e o estendido aumenta, é cada vez menos freqüente e intensa a transferência de valores de marca. Os valores transferidos para categorias mais dissimilares, ou seja, os valores de maior alcance de extensão, têm natureza predominantemente subjetiva ao invés de racional ou vinculada a atributos de produto. Os resultados também sugerem que os atributos e benefícios considerados relevantes dentro de cada categoria funcionam como um filtro para a transferência de associações, ressaltando a influência do contexto da categoria da extensão no processo. / This study analyzes many aspects of brand extension. Building strong brands is seen as an opportunity to create differentiation and competitive advantage. Success in certain markets is a result of factors beyond the product itself; brand consumer perception is formed by a complex set of associations of rational, functional and objective aspects as well as emotional, subjective and abstract elements. A brand represents a code, a summary of all these associations and perceptions. The psychological positioning of a brand influences the purchase decision inside a category. Many companies implement brand extensions as a growth strategy. This results in a huge list of extended brands to additional product categories, many times without any similarity to the original brand category. The main reason and objective of an extension is transferring brand equity from the original product to the new one, reducing the path towards product consolidation and improving its chances for success. Nevertheless, there are many cases when brand extension is nothing more than just a name that reminds the product\'s origin or, even worse, its application in a certain category will result in loosing brand value and meaning. Based on this assumption, this study aims at bringing new references that indicate if it makes sense to extend a brand to other categories. The adopted methodology consists of two phases: one is a reviewed bibliography about the main aspects of extension - its motivations, advantages and risks, earlier researches results, consumer evaluation process and reciprocal effect of the extended brand over the original one; and second, the verification of an specific case study with a target company. Results point out a relation between brand\'s psychological positioning and its extension to closer and farther categories in relation to the original brand. It indicates that the more philosophical the brand positioning, meaning little association to the product itself and its functional aspects, the bigger its capacity of being applied to product categories different than the original one. As soon as dissimilarities grow in between the original product and the extended one, the least frequent and intense is the brand equity transfer. Values transferred to less similar categories, or, values of bigger extension capacity have a subjective nature instead of rational one linked to product attributes. Results also suggest that relevant attributes and benefits in each category works as an associations transferring filter, reinforcing the category content influence over the extension process.

Nessa tese, mostramos que a Hamiltoniana H e o operador helicidade de uma partícula de Dirac que se movimenta em duas dimensões na presença de um tubo de fluxo magnético infinitamente fino na origem admitem, cada um, uma família de quatro parâmetros de extensões auto-adjuntas. Para cada extensão correspondem condições de contorno a serem satisfeitas pelas auto-fuções na origem. Apesar dos operadores H e formalmente comutarem antes da especificação das condições de contorno, para garantirmos a conservação da helicidade, não é suficiente obtermos as mesmas condições de contorno para ambos os operadores, ou seja, não é suficiente a determinação de um domínio comum a ambos. Mostramos que, para certas relações entre os parâmetros das extensões satisfeitas, é possível a determinação dos domínios mais gerais onde ambos os operadores H e são auto-adjuntos e onde a helicidade é conservada, simultaneamente com a preservação da simetria de Aharonov-Bohm ( + 1), onde é o fluxo magnético em unidades naturais. Nossos resultados implicam que, nem a conservação da helicidade nem a simetria de Aharonov-Bohn, resolvem o problema da escolha da condição de contorno fisicamente correta. / We show that both the Hamiltonian H and the helicity operator of a Dirac particle moving in two dimension in the presence of an infinitely thin magnetic flux tube admit each a four- parameter family of self-adjoint extensions. Each extension is in one-to-one correspondence with the boundary conditions (BC\'s) to be satisfied by the eigenfunctions at the origin. Althou- gh the actions af these two operators commute before specification of boundary conditions, to ensure helicity conservation it is not sufficient to take the same BC\'s for both operators. We show that, given certain relations between the parameters of the extensions it is possible to write down the most general domain where both operators H and are self-adjoint with heli- city conservation and also Aharonov-Bohm symmetry ( + 1) preserved, where is the magnetic flux in natural units. The continuity of the dynamics is also obtained. Our results im- ply that neither helicity conservation nor Aharonov-Bohm symmetry by themselves solves the problem of choosing the \"physical \"boundary conditions for this system.