Dans ce mémoire, on s'intéresse à l'action du groupe des transformations affines et des homothéties sur l'axe du temps des systèmes différentiels quadratiques à foyer faible d'ordre trois, dans le plan. Ces systèmes sont importants dans le cadre du seizième problème d'Hilbert. Le diagramme de bifurcation a été produit à l'aide de la forme normale de Li dans des travaux de Andronova [2] et Artès et Llibre [4], sans utiliser le plan projectif comme espace des paramètres ni de méthodes globales. Dans [7], Llibre et Schlomiuk ont utilisé le plan projectif comme espace des paramètres et des notions à caractère géométrique global (invariants affines et topologiques). Ce diagramme contient 18 portraits de phase et certains de ces portraits sont répétés dans des parties distinctes du diagramme. Ceci nous mène à poser la question suivante : existe-t-il des systèmes distincts, correspondant à des valeurs distinctes de paramètres, se trouvant sur la même orbite par rapport à l'action du groupe? Dans ce mémoire, on prouve un résultat original : l'action du groupe n'est pas triviale sur la forme de Li (théorème 3.1), ni sur la forme normale de Bautin (théorème 4.1). En utilisant le deuxième résultat, on construit l'espace topologique quotient des systèmes quadratiques à foyer faible d'ordre trois par rapport à l'action de ce groupe. / We are interessed here in the action of the group of affine transformations and time homotheties on quadratic differential systems which have a weak focus of third order. These systems are important for Hilbert sixteenth problem. The bifurcation diagram was produced using Li's normal form in the articles of Andronova [2], and Artès and Llibre [4], without using the projective plane as parameter space, and without using global methods. In [7], Llibre and Schlomiuk used the projective plane as parameter space and global geometric methods (affine and topological invariants). This diagram contains 18 phase portraits and some of these portraits are repeated in distinct parts of the diagram. This led us to ask the following question : do there exist distinct differential systems, corresponding to distinct values of the parameter, which are on the same orbit of the group action? In this master's thesis, we prove an original result : the action of the group is not trivial on Li's normal form (theorem 3.1), neither is it trivial on Bautin's normal form (theorem 4.1). Using the second result, we construct the quotient topological space of these systems with a weak focus of third order, with respect to the group action.

In this thesis we study the Aronszajn and special Aronszajn trees, their existence and nonexistence. We introduce the most common definition of special Aronszajn tree and some of its generalizations and we examine the relations between them. Next we study the notions of the tree property and the weak tree property at a given regular cardinal κ. The tree property means that there are no Aronszajn trees at κ and the weak tree property means that there are no special Aronszajn trees at κ. We define and compare two forcings, the Mitchell forcing and the Grigorieff forcing, and we use them to obtain a model in which the (weak) tree property holds at a given cardinal. At the end, we show how to use the Mitchell forcing to construct a model in which the (weak) tree property holds at more than one cardinal. 1

Let G be a subset of the dual of a real Banach space X and F ⊂ G. Then F is a James boundary of G if each w∗ -continuous linear functional on X attains its supremum over G on an element of the set F. We ask whether a norm bounded subset of X which is countably compact for the topology generated by F is ne- cessary sequentially compact for the topology generated by G. The main content of our work is a positive solution to this problem. As a corollary we obtain James characterization of weakly compact subsets of a real Banach space. Due to the Eberlein-Šmuljan theorem a positive solution to the so called boundary problem is shown as a special case of the affirmative answer to the question raised above. The question is further discussed for a case of Banach spaces defined over the complex field. In this case we cannot use the old definition of the James boun- dary but by a "natural" way it is possible to redefine the term James boundary and then we are able to answer our question positively again. 1

Une étude théorique basée sur la théorie de la fonctionnelle de la densité (DFT) a été réalisée sur un ensemble de complexes organométalliques mono, di et trinucléaires à base de fer, de ruthénium ou de platine. Les résultats obtenus sur les complexes mononucléaires à base de fer révèlent que la longueur du chaînon π de carbone n'a qu'une influence mineure sur les propriétés électroniques mais affectent les propriétés spectroscopiques. Une étude entreprise sur des systèmes contenant un ligand aromatique polycyclique a montré que la présence de molécules de solvant coordonnant abaisse les barrières énergétiques et par conséquence, facilite le réarrangement haptotropique du greffon organoruthénium sur le ligand organique. L'étude théorique réalisée sur des nouveaux systèmes de type [2]rotaxane a révélé que la longueur du chaînon π du fil moléculaire enfilé au travers d'un macrocycle influence les énergies d'interaction non covalente dans ces systèmes. Il a été montré que ces interactions non covalentes sont principalement dues à des liaisons hydrogène formées entre le macrocycle et le fil moléculaire. / A theoretical study based on density functional theory (DFT) was performed on several series of organometallic mono, bi and trinuclear iron, ruthenium and platinum based complexes. The results on mononuclear iron based complexes indicate that the length of the π carbon bridge in these systems has only a minor influence on the electronic properties but affect somewhat the spectroscopic properties. A study was conducted on systems containing polycyclic aromatic ligand showing that the presence of a coordinating solvent molecule in the viscinity of the metal atom bound on top of the polycycle strongly lowers the energy barriers and consequently facilitates the haptotropic rearrangement of the grafted organoruthenium entity. The theoretical study of new systems of [2]rotaxane type has revealed that the length of the π bridge of the molecular wire threaded in a macrocycle influences the weak noncovalent interaction energies in these systems. It has been shown that these noncovalent interactions are mainly due to hydrogen bonds formed between the macrocycle and the threaded molecular wire.

Les fluctuations électriques des composants sont une limitation à la miniaturisation des circuits. Malgré des procédés de fabrications en continuelle évolution, les variations des caractéristiques électriques dues au désappariement entre deux dispositifs limitent les performances des circuits. Concernant les applications à faible consommation, ces fluctuations locales peuvent devenir très critiques. Dans le contexte du développement d’une technologie CMOS 90nm avec mémoire Flash embarquée pour des applications basse consommation, l’appariement de transistors MOS est étudié. Une analyse de l’impact du dopage de grille des transistors NMOS est menée. L’étude se focalise sur l’appariement en tension des paires différentielles polarisées dans la zone de fonctionnement sous le seuil. Il est démontré que cet appariement peut être dégradé à cause de l’effet « hump », c'est-à-dire la présence de transistors parasites en bord d’active. Un macro-modèle permettant aux concepteurs de modéliser cet effet est présenté. Il est étudié au niveau composant, au niveau circuit et en température. Enfin, une étude de la dégradation de l’appariement des transistors MOS sous stress porteurs chauds est réalisée, validant un modèle de dégradation. Des transistors octogonaux sont proposés pour supprimer l’effet « hump » et donnent d’excellents résultats en termes d’appariement ainsi qu’en fiabilité. / Electrical fluctuations of devices limit chip miniaturization. Despite manufacturing processes in continuous evolution, circuit performances are limited by electrical characteristics variations due to mismatch between two devices. Concerning low power applications, local fluctuations can become very critical. In the context of development of a 90nm CMOS technology with Embedded Flash memory for low power applications, MOS transistors matching is studied. A study of NMOS transistors gate doping impact is conducted. Study focuses on voltage matching of differential pairs biased under threshold. It is demonstrated that this matching can be degraded due to « hump » effect, meaning presence of parasitic devices on active edge. A macro-model allowing designers to model this effect is presented. It is studied at device level, circuit level and for different temperatures. Finally, a degradation study of MOS transistors mismatch under Hot Carriers Injection stress is performed, validating a degradation model. Octagonal devices are proposed to suppress « hump » effect and give good results in terms of matching as well as reliability.

The National Center for Complementary and Integrated Health, National Institutes of Health, U.S. Department of Health and Human Services, has highlighted a need for research to better understand the usage of complementary and alternative medicine practices. The purpose of this study was to investigate the flow of complementary and alternative medicine information among yoga practitioners. The study consisted of 51 yoga practitioners from 7 yoga studio locations. This mixed-methods study used interviews, surveys, and field notes to collect data. Content and social network analyses provided supporting evidence for Rogers' diffusion of innovations theory and Granovetter's strength of weak ties theory. Key findings included a preference for face-to-face communications, students having both strong and weak relationship ties to directors and instructors, and yoga being the top recommended practice. The study suggested that yoga practitioners related to complementary and alternative medicine information through the lens of their friends and relatives, sought information from trusted sources, and used this information to determine which practices were right for them to pursue.

Neste trabalho apresentamos alguns jogos topológicos e suas aplicações à análise. Com esse fim, se fornece condições necessárias para que funções aproximadamente contínuas se tornem contínuas, se caracteriza os conjuntos estritamente pseudo-completos nos espaços de Banach e, assim também, se constrói um espaço de diferenciabilidade Gâteaux que não é Asplund fraco. / In this work we present some topological games and their applications to analysis. For this purpose, necessary conditions are given for nearly continuous functions to become continuous, we characterize the strictly pseudo-complete sets in the Banach spaces and we also construct a Gâteaux differentiability space that is not weak Asplund.

Zufällige Bewegungen wie Diffusion sind ein allgegenwärtiges Phänomen, anzufinden nicht nur in der Physik. Das Hauptobjekt von Diffusionsmodellen ist oft die mittlere quadratische Verschiebung eines Teilchens, welche für sogenannte normal-diffusive Prozesse linear mit der Zeit anwächst. Anomale Diffusion bezeichnet Prozesse, für welche sie nicht-linear wächst; ein wichtiges Beispiel ist die Bewegung großer Moleküle in biologischen Zellen. Erscheinungen wie schwache Ergodizitätsbrechung sind ebenfalls bei anomaler Diffusion zu finden, und es gibt viele mathematische Modelle zu ihrer Beschreibung. Oft ist es schwierig für ein bestimmtes Experiment das "richtige" Modell, d.h. die physikalische Ursache der Anomalie, zu finden. Eine Methode zur Trennung oder Identifikation der physikalischen Ursachen wird also dringend benötigt. In dieser Arbeit stellten wir uns diesem Problem. Zuerst betrachteten wir ein recht allgemeines Modell zur Diffusion in ungeordneten Medien. Mithilfe der Netzwerktheorie trennten wir zwei Mechanismen, nämlich energetische und strukturelle Unordnung, welche beide zu anomaler Diffusion führen. Diese Klassen wurden dann in die Sprache der stochastischen Prozesse übertragen. Das erlaubte uns eine einfache Methode, die des fundamentalen Momentes, zu formulieren. Jene Methode ist in der Lage die energetischen und strukturellen Anteile eines Diffusionsprozesses voneinander zu trennen. Zuletzt behandelten wir Ergodizität und Ergodizitätsbrechung aus der Sicht der energetischen und strukturellen Unordnung. / Random motion, in particular diffusion, is a ubiquitous phenomenon that is encountered not only in physics. The main object of a diffusion model is usually the mean squared displacement (msd) of a particle, which for so-called normal diffusion grows linearly in time. Anomalous diffusion denotes processes, in which the msd grows non-linearly; an important example is the motion of large molecules in biological cells. Many interesting properties like weak ergodicity breaking are connected to anomalous diffusion, and there are many mathematical models exhibiting anomalous behaviour. Given an experiment, it is often difficult to decide, what is the "correct" model, i.e. the physical cause for the anomaly. Therefore, a method capable of separation and identification of different physical mechanisms is urgently required. This thesis approached the mentioned issue. First of all, we considered a quite general model for diffusion in disordered media. We used some network theory to distinguish two physical mechanisms - energetic and structural disorder. Both cause anomalous diffusion. Those classes of disorder were then translated into the language of stochastic processes. This put ourselves in position to propose a simple method, the fundamental moment, that is capable of separating the energetic and structural components of a diffusion process. At last, we discussed ergodicity and ergodicity breaking from the point of view of energetic and structural disorder.

Diese Arbeit befasst sich mit der Konstruktion verbesserter interpolierender Mesonenfelder in der Gitter-QCD. Sie hat das primäre Ziel, Korrelationsfunktionen mit einem deutlich reduzierten Beitrag des ersten angeregten Mesonenzustandes zu erhalten, um eine sicherere Bestimmung von Massen und Zerfallskonstanten der Mesonen zu ermöglichen. Eine Basis solcher interpolierender Mesonen-Randfelder wird im Schrödinger Funktional in der gequenchten Approximation benutzt. Verbesserte interpolierende Felder zur Bestimmung spektraler Eigenschaften leichter pseudoskalarer Mesonen sowie des B--Mesonensystems (letzteres wird in führender Ordnung der HQET behandelt) werden auf mehreren Wegen gewonnen. Ein Hilfsmittel, verbesserte Felder zu konstruieren, ist das Variationsprinzip. Es wird auf Matrizen von Rand-Rand-Korrelationsfunktionen angewandt. Darüber hinaus werden alternative Analysemethoden vorgestellt. Sie erlauben sowohl die Abschätzung der Grundzustandsenergie als auch der Energielücke zum ersten radial angeregten Zustand. Die Untersuchung des B-Mesonensystems ist in vielfacher Hinsicht interessant. Zum einen werden sie in sogenannten B-Fabriken, wie z. B. im BaBar- und Belle-Experiment, in grosser Zahl erzeugt, um ihre charakteristischen Eigenschaften (Masse, Zerfallsbreiten, CP-Symmetrie verletzende Zerfälle usw.) genau zu messen. Zum anderen müssen die von der Theorie vorhergesagten auftretenden Phänomene, wie z. B. die CP-Verletzung, auch verstanden werden. Die Methoden der Gittereichtheorie können unter anderem dabei helfen, bestehende Unsicherheiten in CKM-Matrixelementen durch nicht-perturbative Bestimmungen hadronischer Massen, Zerfallskonstanten usw. zu reduzieren. / The general aim of this thesis is to probe several methods to extract low-energy quantities (masses, decay constants, ...) more reliably in lattice gauge theory. We will investigate how to suppress contributions to correlation functions from the first excited meson state. We will show how to construct so-called improved meson interpolating fields, as they have only small contributions from the first excited meson state, from a basis of interpolating fields at the Schrödinger functional boundaries. The variational principle is applied to correlation matrices that are built up from boundary-to-boundary correlation functions. It will deliver information about the lowest-lying meson states in the considered channel. We also investigate the possibility to cancel the first excited state contribution by means of an alternative method. Moreover, an alternative way to extract the mass gap between the ground and the first excited state will be presented. Monte-Carlo simulations at several lattice spacings are performed in the ''quenched approximation''. Spectral properties of light-light and static-light pseudoscalar mesons are investigated. The first type is realised by two mass-degenerate quarks at about the strange quark mass, the second type by a light quark with the mass of the strange quark and an infinitely heavy b-quark. The light-light channel describes unphysically heavy pions and the static-light one is an approximation for the Bs-meson. The investigation of the latter case is particularly interesting since so-called B--factories, such as BaBar and Belle, are gathering physical information about masses, decay modes and CP--violating effects in the B--meson system.

<p>Neka je A neprazan skup&nbsp; i ℒ&nbsp;= (L, &le;) proizvoljna mreža sa nulom i jedinicom. Svako preslikavanje &micro;: A &rarr; L zovemo rasplinuti podskup od A. U ovoj tezi proučavali smo rasplinute posete i relacije rasplinutog poretka. Uveli smo neke nove pojmove: rasplinuta uređena grupa, rasplinuti pozitivan konus, rasplinuti negativan konus, rasplinuta mrežno uređena grupa. Posmatrajući strukturu svih relacija slabog rasplinutog poretka koje su podskup klasične relacije poretka &le; , do&scaron;li smo do zaključka da ova struktura predstavlja kompletnu mrežu. Takođe, važan zadatak je bio da ispitamo egzistenciju rasplinute mrežno uređene podgrupe <i>l</i>&nbsp;&ndash;uređene grupe koja nije linearno uređena. Bitan rezultat je rasplinuta mrežno uređena podgrupa date mrežno uređene grupe G, koja je konstruisana pomoću mreže svih kompleksnih <em>l</em> &ndash;podgrupa od G.</p> / <p>Let A be a nonempty set, and let <em>ℒ</em> = (L, &le;) be a lattice with 0 and 1. The mapping: &micro;: A &rarr; L is called a fuzzy subset of A. In this work we investigated fuzzy posets and fuzzy ordering relations. We introduced some new notions: fuzzy ordered groups, fuzzy positive cone, fuzzy negative cone, fuzzy lattice ordered group. Considering a structure of all weak fuzzy orderings contained in the crisp order &le;, we concluded that this structure represents a complete lattice. Also, an important task was to investigate the existence of a fuzzy lattice ordered subgroup of an <em>l</em>&ndash;ordered group which is not linearly ordered. A main result is a fuzzy lattice ordered subgroup of a given lattice ordered group G, which is constructed by the lattice of all convex <em>l</em>-subgroups of G.</p>