Esta dissertação tem por objetivo a apresentação de um estudo em espaços de Banach sobre os conjuntos nos quais determinados polinômios homogêneos contínuos são fracamente sequencialmente contínuos. Algumas propriedades desses conjuntos são estudadas e ilustradas com exemplos, em maior parte no espaço $l_p$. Obtemos um fórmula para o conjunto de continuidade sequencial fraca do produto de dois polinômios e algumas consequências. Resultados mais fortes são obtidos quando restringimos nossos espaços de Banach a espaços com FDD incondicional e/ou separáveis. Os resultados estudados aqui foram obtidos por R. Aron e V. Dimant em: Aron, R. & Dimant, V., Sets of weak sequential continuity for polynomials, Indag. Mathem., N.S., 13 (3) (2002), 287-299. / This work has the purpose of presenting a study on Banach spaces about sets in which determined homogeneous continuous polynomials are weakly sequentially continuous. Some properties of these sets are studied and illustrated with examples, most in the space $l_p$. We obtain a formula for the weak sequential continuity set of the product of two polynomials, and some consequences. Stronger results are obtained when we restrict our Banach spaces to spaces with unconditional FDD and/or separable. The results studied here were obtained by R. Aron and V. Dimant in: Aron, R. & Dimant, V., {Sets of weak sequential continuity for polynomials, Indag. Mathem., N.S., 13 (3) (2002), 287-299.

Abū Zakariyaʾ Ibn Dāwūd Ḥayyūdj nasceu em Fez, Marrocos, e viveu em Córdoba, Andaluzia, entre os anos 960 e 1010 A.D. Ḥayyūdj ganhou o título de \"grande gramático\" por desvendar o mistério dos verbos fracos. Até então, palavras difíceis eram solucionadas por métodos comparativos (Seʿádia Gaʾon e Yehudá Ben Quraish); ou eram associadas à raízes, atualmente reconhecidas como compostas por três letras diferentes, à mesma raiz reduzida a duas letras ou até uma (Menaḥem, Dunash e David Alfesi). Prima facie, as teorias de Ḥayyūdj emergiram a partir de estudos gramaticais que se iniciaram como um continuum dos sábios tardios da Messorá. Porém, o presente trabalho pretende mostrar a conexão que havia entre Ḥayyūdj e a Messorá, que não foi tratada nos trabalhos acadêmicos consultados. Por isso, espera-se preencher essa lacuna existente na literatura explorando os contextos histórico, gramatical e massorético nos quais Ḥayyūdj estava inserido. Consequentemente perceber-se-á como Ḥayyūdj superou seus antecessores. No decorrer da exposição discute-se como o Texto Bíblico foi veiculado em dois canais paralelos (escrito e oral) e por tradições diferentes (judaicas babilônicas, tiberienses, israelense e Andaluz). Desmembra-se o Texto Massorético em três camadas: Texto Consonantal, sinais massoréticos e anotações massoréticas. Apresenta-se um modelo triangular no qual as anotações massoréticas (qere–ketiv) encontram-se no topo para harmonizar entre o Texto Consonantal e os sinais massoréticos. Analisa-se, diacronicamente, segundo a fonologia gerativa, a profundidade da escrita do Texto Massorético abrangendo a visão dos massoretas tiberienses (produtores) e dos andaluzes (consumidores). Discute-se a afinidade entre a Messorá, as teorias gramaticais anteriores e Ḥayyūdj. Mostra-se que Ḥayyūdj foi o primeiro gramático, fora dos círculos massoréticos, que interpretou os qere–ketiv marcados nas marginais dos códices massoréticos. Discute-se como Ḥayyūdj solucionou as contradições existentes entre as vogais massoréticas e as vogais do Texto Consonantal. Mais especificamente mostra-se como as teorias de Ḥayyūdj permearam os planos ortográfico, fonético, fonológico, melismático e morfológico da gramática. Na ortografia, as formas plenas e defectivas seriam equivalentes; no plano fonético, qamats e pataḥ, tseire e segol e por fim, ḥolam e ḥataf-qamats seriam pares de fones iguais; no plano fonológico, o qamats diferentemente do pataḥ, tseire diferentemente do segol, e ḥolam diferentemente do ḥataf-qamats seriam seguidos por uma espécie de arquifonema amorfo inspirado na Messorá e nas letras de prolongação do árabe: o sākin layyin traduzido para o português como \"repouso frágil\"; no plano melismático, as vogais massoréticas precederiam os melismas; no plano morfológico, o hebraico seria enquadrado no modelo estrutural das línguas semíticas. Em suma, mostra-se que com base no sākin layyin, Ḥayyūdj abandonou o modelo mental arraigado em seus antecessores para desenvolver teorias sólidas que solucionariam o problema dos verbos fracos e que simultaneamente traria harmonia entre o Texto Massorético e a tradição oral andaluza. / Abū Zakariyaʾ Ibn Dāwūd Ḥayyūj was born in Fez, Morocco and lived in Cordova, Andalusia between 960 and 1010 A.D. He earned the title of \"the great grammarian\" for unveiling the mystery of the weak verbs. Until Ḥayyūj, difficult words were elucidated by comparative methods (Seʿadia Gaʾon and Yehuda ben Quraish); or were associated to roots, nowadays recognized as triliteral, reduced to two or even one letter (Menaḥem, Dunash and David Alfesi). Prima facie, Ḥayyūj\'s theories emerged from grammar studies that started as a Masorah\'s continuum. However, the present work we show the link between Ḥayyūj and the Masorah, something that was not well explained in in the academic papers checked by the author. For this reason, we expect to fill the gap left in the literature analyzing Ḥayyūj theories vis-à-vis their historical, grammatical and Masoretic contexts. Therefore, we see the way Ḥayyūj revolutionized the grammar at all the levels studied at that time. The present work, discusses how the Biblical Text was transmitted by two parallel channels (written and oral) and by different traditions (Jewish-Babylonian, Tiberian, Andalusian and Israeli). We show how the Masoretic Text is composed by three layers: Consonantal Text, Masoretic signs and Masoretic annotations. We show a triangular model in which Masoretic annotations (qere-ketiv) are at the top in order to harmonize the Consonantal Text and the Masoretic signs. We diachronically analyze, according to the Orthographic Depth Hypothesis – a generative phonology\'s branch – the depth of the script of the Masoretic Text, covering the points of view of both the Tiberian (producer) and the Andalusian schools (consumer). We discuss the affinity between the Masorah, the previous grammar theories and Ḥayyūj theories. We show that Ḥayyūj was the first grammarian that clarified the Masorah, out of the Masoretic circles, who explained the qere-ketiv written in the Masoretic codice\'s margins. We discuss how Ḥayyūj solved contradictions between the Masoretic vowels, the Text Consonantal vowels and the qere-ketiv. More specifically, we discuss how Ḥayyūj\'s theories permeated into orthographic, phonetic, phonological, melismatic and morphological grammar levels. Ḥayyūj showed that in orthographic level, the full and defective forms were equivalent; in the phonetic level, qamats and pataḥ, tseire and segol, and ḥolam and ḥataf-qamats were pairs of equal phones; in the phonological level, qamats differently from pataḥ, tseire differently from segol, and ḥolam differently from ḥataf-qamats were followed by a kind of amorphous archiphoneme inspired in the Masorah and in the Arabic long letters: the sākin layyin; on the melismatic level, the Masoretic vowels had priority over the melismatic signs. In the morphological level, the Hebrew language could be considered within the structural model of Semitic languages. In other words, we show that, based on the sākin layyin, Ḥayyūj abandoned the mental model deep-rooted in his predecessors to develop consistent theories that solved the weak verbs problem and, at the same time, showed the harmony between the Masoretic Text and the Andalusian oral tradition.

In this thesis we investigate the role of odd Poisson brackets in related areas of supergeometry. In particular we study three different cases of their appearance: Courant algebroids and their homotopy analogues, weak Poisson structures and their relation to foliated manifolds, and the structure of odd Poisson manifolds and their modular class. In chapter 2 we introduce the notion of a homotopy Courant algebroid, a subclass of which is suggested to stand as the double objects to L-bialgebroids. We provide explicit formula for the higher homotopy Dorfman brackets introduced in this case, and the higher relations between these and the anchor maps. The homotopy Loday structure is investigated, and we begin a discussion of what other constructions in the theory of Courant algebroids can be carried out in this homotopy setting. Chapter 3 is devoted to lifting a weak Poisson structure corresponding to a local foliation of a submanifold to a weak Koszul bracket, and interpreting the results in terms of the cohomology of an associated differential. This bracket is shown to produce a bracket on co-exact differential forms. In chapter 5 studies classes of second order differential operators acting on semidensities on an arbitrary supermanifold. In particular, when the supermanifold is odd Poisson, we given an explicit description of the modular class of the odd Poisson manifold, and provide the first non-trivial examples of such a class. We also introduce the potential field of a general odd Laplacian, and discuss its relation to the geometry of the odd Poisson manifold and its status as a connection-like object.

In this master thesis control systems for a voltage-source converter HVDC connected to weak ac networks are investigated. HVDC stands for high voltage direct current and is a way to transfer power in the electrical power system. A HVDC uses direct current (dc) instead of alternate current (ac) to transfer power, which requires transformation between ac and dc since most power grids are ac networks. The HVDC uses converters to transform ac to dc and dc to ac and the converter requires a control system. A complete control system of a voltage source converter HVDC contains many different parts. The part investigated in this thesis is the active power control. Different structures containing PID controllers have been tested and evaluated with respect to stability and performance using control theory. The impact of weak ac networks has been evaluated in regards to the different control structures. The investigations have been conducted using mainly steady-state simulations. Based on the simulation and analyzes of the simulation results a promising control structure has been obtained and suggested for further investigation.

Introduzimos uma familia de trajetorias aleatorias coalescentes com certo tipo de comportamento radial a qual chamaremos de Teia Poissoniana radial discreta. Mostramos que o limite fraco na escala difusiva desta familia e uma familia de trajetorias aleatorias coalescentes que chamaremos de Teia Browniana radial. Por m, caraterizamos o objeto limite como um mapeamento continuo da Teia Browniana restrita num subconjunto de R2. / We introduce a family of coalescing random paths with certain kind of radial behavior. We call them the discrete radial Poisson Web. We show that under diusive scaling this family converges in distribution to a family of coalescing random paths which we call radial Brownian Web. Finally, we characterize the limiting object as a continuous mapping of the Brownian Web restricted to a subset of R2.

In this work our aim is to study several aspects related to quantum coherence as understood to correspond with the non-classical behaviour that can be observed for certain particular states of a physical system. In particular we are interested in the possible mechanisms that result in dynamically induced transitions between quantum and classical regimes. The thesis is organized as follows: The first chapter dubs as an introduction and serves to set out the basic philosophy underlying the questions addressed in this thesis. It also presents some elementary properties of states and state spaces in Quantum Theory including what we have chosen to define as classical and quantum behaviour. In chapter 2 we study some of the aspects related to observing quantum behaviour and of the properties of our main definition of classicality (and quantumness). Here we also study some of the restrictions imposed on measurements by the existence of globally conserved quantities (Wigner-Araki-Yanase theorem) and their relationship to weak measurements coupled to postselection. In the following chapter we review some of the basic tools used in the description of open quantum system dynamics that will be applied in other chapters. In chapter 4 we review the basics of decoherence and analyse the importance of the choice of initial conditions when trying to study the dynamical emergence of classical behaviour within Quantum Theory. Next we study the other direction of the transition and focus on how to obtain pure quantum states from states that originally were classically mixed. Along the same lines, in chapter 6 we cover some topics related to the production of pure quantum states from measurements. We pay special attention to a model of the non-selective continuous monitoring of a system coupled to another unmonitored system. Lastly we explore some of the possible similarities between the theory of phase transitions and the quantum-classical transition. We must emphasize that all the work done in this thesis assumes that Quantum Theory is generally valid (at least within a broad enough range of energies). Thus, when we say that a state is "classical" we will mainly be referring to one of all the possible states contained in Quantum Theory, but that is susceptible to being interpreted as corresponding to "classical" behaviour. Similarly when we speak of creating a "quantum", or "quantum coherent", state we mean that the system has evolved to this state from one of the "classical" ones, but all of these still correspond to valid states within Quantum Theory. In the opinion of the author the main original contributions that can be found in this thesis are the following: - The recognition of the relationship between the Wigner-Araki-Yanase theorem and weak measurements coupled to postselection (sections 2.2 and 2.4); - A mathematical proof of the possible ambiguities arising when two observers try to decide if a state corresponds to quantum or classical behaviour (section 2.6); - The implications of initial correlations in decoherence models. In particular how the choice of certain (correlated) initial conditions can result in residual coherence and the production of pure quantum states in a model that otherwise results in ideal decoherence when (locally equivalent) uncorrelated initial conditions are used (section 4.2); - Various results related to the production of quantum states from initially classical states (sections 5.2 to 5.4); - The analysis of the inverse of a generalized depolarizing channel (section 5.7); - The study of a model of the non-selective continuous monitoring, in the quantum Zeno limit, of a subsystem A interacting with an unmonitored subsystem B. In particular the absence of the purification of B, which has been previously predicted in the selective case, but the possibility of coherent dynamics for B (section 6.4); - The identification of the loose equivalent of a broken symmetry and order parameter in the quantum-classical transition (section 7.2).

The inflationary ΛCDM cosmology currently provides an accurate description of the Universe. It has been tested using several observational techniques over a wide redshift range, and it provides a good fit to most of them. In addition, it is a surprisingly economical model, requiring only six parameters to characterize the background cosmology and its fluctuations. In this model, the Universe is dominated by a cosmological constant Λ driving an accelerated expansion, and by cold dark matter. The strongest constraints on parameters to date come from observations of the temperature and polarization anisotropies of the cosmic microwave background measured by the Planck satellite. There are, however, indications of features in the Planck power spectra, possible differences with high redshift ground-based CMB experiments, and 'tensions' between Planck and low redshift measurements of the Hubble constant and weak gravitational lensing. In this thesis, we review possible tensions and extensions to the Planck cosmology, at both high and low redshifts. We begin with the high redshift analysis, using the Planck data to test models which introduce oscillatory features in the primordial power spectrum. We also study possible departures from slow roll inflation using the generalized slow-roll formalism, which allows for order unity deviations. Although we find models which give marginal improvements on the temperature or polarization power spectra, the combination of temperature and polarization is found to be consistent with a featureless power-law primordial spectrum. We then focus on measurements of the polarized CMB sky by the South Pole Telescope collaboration, who report tension between their measurements and the ΛCDM cosmology and with the cosmological parameters determined by Planck. We find evidence of a high χ2 in the SPTpol spectra which is unlikely to be cosmological. We report consistency between the Planck and SPTpol polarization spectra over the multipoles accessible to Planck (l ∼< 1500). We then investigate tension at low redshifts. We begin with weak gravitational lensing in which a number of surveys have suggested that the amplitude of the fluctuation spectra is lower than the Planck value. We review the small-angle approximations commonly used in galaxy weak lensing analyses and their effect on cosmological parameters. We find that these approximations are perfectly adequate for present and near future experiments. We find internal inconsistencies in the recent KiDS-450 analysis involving photometric redshifts and the KiDS covariance matrix at large scales. Finally, we investigate the difference between measurements of the present day expansion rate of the Universe. We apply a novel parameterization of the inverse distance ladder to determine the present date value of the Hubble parameter H0, which assumes General Relativity but makes no further assumptions about systematic errors or the nature of dark energy. Our analysis uses baryon acoustic oscillation data and Type Ia Supernovae to constrain the expansion history assuming a value of the sound horizon determined from the CMB. Our results are in tension with recent direct determinations of H0. We conclude that this tension, if real, cannot be solved by modifications of the ΛCDM model at late times. Instead, we would require a modification of the theory at early times which reduces the sound horizon. We conclude that at this time there is no compelling evidence that conflicts with the ΛCDM cosmology either at low or at high redshifts.

Cette thèse décrit une série d’expériences mettant en lumière l’action en retour de la mesure et la décohérence pour un système quantique ouvert élémentaire, le qubit supraconducteur. Ces observations sont rendues possibles grâce au développement récent d’amplificateurs Josephson proches de la limite quantique. L’information extraite du système peut être utilisée dans des boucles de rétroaction quantique. Pour stabiliser un état arbitraire prédéterminé du qubit, une mesure projective est réalisée périodiquement et une boucle de rétroaction permet de corriger les erreurs détectées. En se substituant à l'environnement et en réalisant une mesure hétérodyne continue de la fluorescence du qubit, nous reconstituons des trajectoires quantiques individuelles lors de sa relaxation. En conditionnant cette détection au résultat d'une mesure projective postérieure, nous déterminons les weak values du signal de fluorescence. En formant une boucle de rétroaction continue à partir de ce signal, nous stabilisons également un état arbitraire du qubit. Enfin, nous observons dans une dernière expérience la dynamique quantique Zénon d'un mode micro-onde, induite par son couplage au qubit. / This thesis presents a series of experiments highlighting measurement back action and decoherence in a basic open quantum system, the superconducting qubit. These observations are enabled by recent advances in amplification close to the quantum limit using Josephson circuits. The information extracted from the system can then be used as input in quantum feedback. A stroboscopic projective readout is performed and a feedback loop is used to correct for detected errors, thus stabilizing an arbitrary predetermined state of the qubit. When monitoring continuously the environment of the qubit by heterodyne detection of its fluorescence, we reconstruct individual quantum trajectories during relaxation. Conditioning this detection to the outcome of a following projective measurement, we access the weak values of the fluorescence signal. Included in a continuous feedback loop, this detection is also used to stabilize an arbitrary state of the qubit. Finally, a last experiment witnesses quantum Zeno dynamics of a resonant microwave mode, entailed by its coupling to the qubit.

Extensões de Ore são anéis de polinômios, denotados por R[x o &], nos quais a variável x e os elementos de R não comutam necessariamente. Algebras de Hopf fracas são algebras que tamb em são coálgebras e satisfazem um conjunto de axiomas de compatibilidade entre essas estruturas. Neste trabalho investigamos extensões de Ore cujo anel base e uma algebra de Hopf fraca. Mais especi camente, dada uma algebra de Hopf fraca R, estudamos sob quais condições R[x o &] e uma algebra de Hopf fraca com uma estrutura que estende a estrutura de R. Sob certas hipóteses, obtemos condições necessárias e su cientes para que a extensão de Ore seja uma álgebra de Hopf fraca, obtendo assim um resultado que generaliza um teorema de Panov para o contexto de algebras de Hopf fracas. / Ore extensions are polynomial rings, denoted by R[x o &], in which the variable x and the elements of R do not commute necessarily. Weak Hopf algebras are algebras which are also coalgebras and satisfy a set of axioms of compatibility betweem these structures. In this work, we investigate Ore extensions whose base ring is a weak Hopf algebra. More speci cally, if R is a weak Hopf algebra then we study under what conditions R[xo &] is a weak Hopf algebra extending the structure of R. Under certain hypotheses, we obtain necessary and su cient conditions for an Ore extension to be a weak Hopf algebra, obtaining a result that generalizes a Panov's theorem to the setting of weak Hopf algebras.

Bien que le concept philosophique original du libre arbitre d’Augustin occupe une place à part dans l’histoire de la philosophie, son argumentation philosophique relative au libre arbitre s’appuie sur les théories des philosophes antiques. Cette thèse se concentre sur quatre approches philosophiques antiques élaborées par les Stoïciens, Cicéron, Alexandre d’Aphrodise et Plotin. Augustin accepte fragmentairement le principe du mouvement de la volonté, les formes de liberté et la relation entre la providence divine et la liberté humaine, etc., proposés par les philosophes antiques. Mais aussi, le libre arbitre chez Augustin prend de plus en plus forme au cours de ses controverses avec les Manichéens et les Pélagiens. Lors des controverses contre les Manichéens, Augustin se focalise tout d’abord sur le libre arbitre humain en relation avec le problème de la cause du mal. Augustin élabore une logique philosophique pour étayer son concept et parer aux attaques manichéennes. La cause du mal n’est pas la nature mauvaise de l’âme ni ne résulte de la volonté de Dieu, mais de notre volonté libre. D’autre part, lors de ses controverses contre les Pélagiens, son concept philosophique du libre arbitre entre dans une nouvelle phase. La volonté humaine n’échappe pas à la bride du péché sans la grâce divine, il s’agit donc d’une volonté faible. Le pouvoir de la volonté humaine est affaibli par le péché originel, même si l’homme possède son propre vouloir. Toutefois, dans la pensée augustinienne, la volonté humaine n’est pas contrainte par des puissances extérieures. Ainsi, le pouvoir du choix est toujours volontaire et libre. / Although Augustine’s philosophical concept of free will occupies a special place in the history of philosophy, the philosophical arguments about free will are based on the theories of ancient philosophers. This thesis focuses on four ancient philosophical approaches, elaborated respectively by the Stoics, Cicero, Alexander of Aphrodisias, and Plotinus. Augustine accepts the principle of the fragmentary movement of the will, the forms of freedom and the relationship between divine providence and human freedom, etc., offered by the ancient philosophers, but free will in Augustine takes on more shape in his arguments with the Manichaeans and the Pelagians. In his argument with the Manichaeans, Augustine first focuses on human free will in relation to the problem of the cause of evil. He develops a philosophical logic to support his concept and defend it against the Manicheans’ attacks. The cause of evil is not the evil nature of the soul or the result of the will of God, but of our free will. In his argument with the Pelagians, his philosophical concept of free will enters a new phase. Without divine grace, human will is too weak to restrain themselves from making sin. Thus, even if a man has his own volition, the ability of human will is weakened by original sin. Nonetheless, in Augustinian thought, the human will is not constrained by outside powers. Thus, the power of choice is voluntary and free.