<p>The research work carried out in this thesis is aimed&nbsp;&nbsp; at fuzzifying algebraic and relational structures in the framework of Ω-sets, where Ω is a complete lattice.<br />Therefore we attempt to synthesis universal algebra and fuzzy set theory. Our&nbsp; investigations of Ω-algebraic structures are based on Ω-valued equality, satisability of identities and cut techniques. We introduce Ω-algebras, Ω-valued congruences,&nbsp; corresponding quotient&nbsp; Ω-valued-algebras and&nbsp; Ω-valued homomorphisms and we investigate connections among these notions. We prove that there is an Ω-valued homomorphism from an Ω-algebra to the corresponding quotient Ω-algebra. The kernel<br />of an Ω-valued homomorphism is an Ω-valued congruence. When dealing with cut structures, we prove that an Ω-valued homomorphism determines classical homomorphisms among the corresponding quotient structures over cut&nbsp; subalgebras. In addition, an&nbsp; Ω-valued congruence determines a closure system of classical congruences on cut subalgebras. In addition, identities are preserved under Ω-valued homomorphisms. Therefore in the framework of Ω-sets we were able to introduce Ω-attice both as an ordered and algebraic structures. By this Ω-poset is defined as an Ω-set equipped with&nbsp; Ω-valued order which is&nbsp; antisymmetric with respect to the corresponding Ω-valued equality. Thus defining the notion of pseudo-infimum and pseudo-supremum we obtained the definition of Ω-lattice as an ordered structure. It is also defined that the an Ω-lattice as an algebra is a bi-groupoid equipped with an Ω-valued equality fulfilling some particular lattice Ω-theoretical formulas. Thus using axiom of choice we proved that the two approaches are equivalent. Then we also introduced the notion of complete Ω-lattice based on Ω-lattice. It was defined as a generalization of the classical complete lattice.<br />We proved results that characterizes Ω-structures and many other interesting results.<br />Also the connection between Ω-algebra and the notion of weak congruences is presented.<br />We conclude with what we feel are most interesting areas for future work.</p> / <p>Tema ovog rada je fazifikovanje algebarskih i relacijskih struktura u okviru omega- skupova, gdeje Ω kompletna mreza. U radu se bavimo sintezom oblasti univerzalne algebre i teorije rasplinutih (fazi) skupova. Na&scaron;a istraživanja omega-algebarskih struktura bazirana su na omega-vrednosnoj jednakosti,zadovoljivosti identiteta i tehnici rada sa nivoima. U radu uvodimo omega-algebre,omega-vrednosne kongruencije, odgovarajuće omega-strukture, i omega-vrednosne homomorfizme i istražujemo veze izmedju ovih pojmova. Dokazujemo da postoji Ω -vrednosni homomorfizam iz Ω -algebre na odgovarajuću količničku Ω -algebru. Jezgro Ω -vrednosnog homomorfizma je Ω- vrednosna kongruencija. U vezi sa nivoima struktura, dokazujemo da Ω -vrednosni homomorfizam odredjuje klasične homomorfizme na odgovarajućim količničkim strukturama preko nivoa podalgebri. Osim toga, Ω-vrednosna kongruencija odredjuje sistem zatvaranja klasične kongruencije na nivo podalgebrama. Dalje, identiteti su očuvani u Ω- vrednosnim homomorfnim slikama.U nastavku smo u okviru Ω-skupova uveli Ω-mreže kao uredjene skupove i kao algebre i dokazali ekvivalenciju ovih pojmova. Ω-poset je definisan kao Ω -relacija koja je antisimetrična i tranzitivna u odnosu na odgovarajuću Ω-vrednosnu jednakost. Definisani su pojmovi pseudo-infimuma i pseudo-supremuma i tako smo dobili definiciju Ω-mreže kao uredjene strukture. Takodje je definisana Ω-mreža kao algebra, u ovim kontekstu nosač te strukture je bi-grupoid koji je saglasan sa Ω-vrednosnom jednako&scaron;ću i ispunjava neke mrežno-teorijske formule. Koristeći aksiom izbora dokazali smo da su dva pristupa ekvivalentna. Dalje smo uveli i pojam potpune Ω-mreže kao uop&scaron;tenje klasične potpune mreže. Dokazali smo jo&scaron; neke rezultate koji karakteri&scaron;u Ω-strukture.Data je i veza izmedju Ω-algebre i pojma slabih kongruencija.Na kraju je dat prikaz pravaca daljih istrazivanja.</p>

<p>In this work a comparative analysis of several approaches to fuzzy algebraic structures and comparison of previous approaches to the recent one developed at University of&nbsp; Novi Sad has been done. Special attention is paid to reducts and expansions of algebraic structures in fuzzy settings. Besides mentioning all the relevant algebras and properties developed in this setting, particular new algebras and properties are developed and investigated. Some new structures, in particular Omega Boolean algebras, Omega Boolean lattices and Omega Boolean rings are developed in the framework of omega structures. Equivalences among these structures are elaborated in details. Transfers from Omega groupoids to Omega groups and back are demonstrated. Moreover, normal subgroups are introduced in a particular way. Their connections to congruences are elaborated in this settings. Subgroups, congruences and normal subgroups are investigated for Ω-groups. These are latticevalued algebraic structures, defined on crisp algebras which are not necessarily groups, and in which the classical equality is replaced by a lattice-valued one. A normal Ω-subgroup is defined as a particular class in an Ω-congruence. Our main result is that the quotient groups over cuts of a normal Ω- subgroup of an Ω-group G, are classical normal subgroups of the corresponding quotient groups over G. We also describe the minimal normal Ω-subgroup of an Ω-group, and some other constructions related to Ω-valued congruences.Further results that are obtained are theorems that connect various approaches of fuzzy algebraic structures. A special notion of a generalized lattice valued Boolean algebra is introduced. The universe of this structure is an algebra with two binary, an unary and two nullary operations (as usual), but which is not a crisp Boolean algebra in general. A main element in our approach is a fuzzy&nbsp; quivalence relation such that the Boolean algebras identities are approximately satisfied related to the considered fuzzy equivalence. Main properties of the new introduced notions are proved, and a connection with the notion of a structure of a generalized fuzzy lattice is provided.</p> / <p>Ovaj rad bavi se komparativnom analizom različitih pristupa rasplinutim (fazi) algebarskim strukturama i odnosom tih struktura sa odgovarajućim klasičnim&nbsp;&nbsp; algebrama. Posebna pažnja posvećena je poredenju postojećih pristupa ovom&nbsp;&nbsp; problemu sa novim tehnikama i pojmovima nedavno razvijenim na Univerzitetu u Novom Sadu. U okviru ove analize, proučavana su i pro&scaron;irenja kao i redukti algebarskih struktura u kontekstu rasplinutih algebri. Brojne važne konkretne algebarske strukture istraživane su u ovom kontekstu, a neke nove uvedene su i ispitane. Bavili smo se detaljnim istrazivanjima Ω-grupa, sa stanovista kongruencija, normalnih podgrupa i veze sa klasicnim grupama. Nove strukture koje su u radu uvedene u posebnom delu, istrazene su sa aspekta svojstava i medusobne ekvivalentnosti. To su Ω-Bulove algebre, kao i odgo-varajuce mreže i Bulovi prsteni. Uspostavljena je uzajamna ekvivalentnost tih struktura analogno odnosima u klasičnoj algebri. U osnovi na&scaron;e konstrukcije su mrežno vrednosne algebarske strukture denisane na klasičnim algebrama koje ne zadovoljavaju nužno identitete ispunjene na odgovarajucim klasičnim strukturama (Bulove algebre, prsteni, grupe itd.), već su to samo algebre istog tipa. Klasična jednakost zamenjena je posebnom kompatibilnom rasplinutom (mrežno-vrednosnom) relacijom ekvivalencije. Na navedeni nacin i u cilju koji je u osnovi teze (poredenja sa postojecim pristupima u ovoj naucnoj oblasti) proucavane su (vec denisane)&nbsp; Ω-grupe. U nasim istraživanju uvedene su odgovarajuće normalne podgrupe. Uspostavljena je i istražena njihova veza sa Ω-kongruencijama. Normalna podgrupa&nbsp; Ω-grupe definisana je kao posebna&nbsp; klasa Ω-kongruencije. Jedan od rezultata u ovom delu je da su količničke grupe definisane pomocu nivoa Ω-jednakosti klasične normalne podgrupe odgovarajućih količničkih podgrupa polazne&nbsp; -grupe. I u ovom slučaju osnovna&nbsp; struktura na kojoj je denisana Ω-grupa je grupoid, ne nužno grupa. Opisane su osobine najmanje normalne podgrupe u terminima Ω-kongruencija, a date su i neke konstrukcije&nbsp; Ω-kongruencija.</p><p>Rezultati koji su izloženi u nastavku povezuju različite pristupe nekim mrežno- vrednosnim strukturama. Ω-Bulova algebra je uvedena na strukturi sa dve binarne, unarnom i dve nularne operacije, ali za koju se ne zahteva ispunjenost klasičnih aksioma. Identiteti za Bulove algebre važe kao mrežno-teoretske formule u odnosu na mrežno-vrednosnu jednakost. Klasicne Bulove algebre ih zadovoljavaju, ali obratno ne vazi: iz tih formula ne slede standardne aksiome za Bulove algebre. Na analogan nacin uveden je i&nbsp; Ω-Bulov prsten. Glavna svojstva ovih struktura su opisana. Osnovna osobina je da se klasične Bulove algebre odnosno Bulovi prsteni javljaju kao količničke strukture na nivoima Ω -jednakosti. Veza ove strukture sa Ω-Bulovom mrežom je pokazana.</p><p>Kao ilustracija ovih istraživanja, u radu je navedeno vi&scaron;e primera.</p>

Dans cette thèse nous regardons plusieurs modèles de populations structurés s’écrivant à l’aide d’équations de transport. Le caractère bien posé ainsi que la positivité des solutions sont montrés de manière systématique au sens des sémiologues dans un cadre L1. Un premier travail est consacré à un système de type proie prédateur structuré en âge. Une étude de stabilité des équilibres nous permet de formuler explicitement un seuil un seuil d’extinction ainsi qu’in seuil pouvant amener à l’explosion des populations. On obtient numériquement la possibilité d’un cycle limite ainsi que la convergence vers un équilibre de coexistence des populations. Dans un cas particulier, ce modèle se réécrit comme un système différentiel à retard. A l’aide de fonctionnelle de Lyapunov, on montre la stabilité globale de cet équilibre sous certaines conditions. On étudie également 2 modèles structuré en taille, issus de la dynamique cellulaire. L’un est composé de deux équations de transport où la cellule peut être soit prolifèrent soit quiescente ; et le deuxième est une équation de type transport/ diffusion avec des conditions aux bords FELLER. On vérifie à chaque fois l’irréductibilité du semi groupe puis des arguments de faibles capacité L1 nous donne l’existence d’un « gap spectral » sous certaines conditions. On démontre ainsi dans certains cas la croissance exponentielle asynchrone du semi groupe / This thesis is dedicated to some structured populations models described with transport or transport-diffusion equations. The well-posedness, in the semigroupes setting in L1 and the positivity of the solutions are systematically shown. A first work is dedicated to an age-structured predator/prey system. A stability study of the equilibria allow us to give explicit formulations of an extinction threshold and an threshold which can lead to explosion of solutions. We numerically obtain the possibility to get a limit cycle and the convergence to a coexistence equilibrium of the populations. In a specific case, this model rewrites as a delay differential system. Using Lyapunov functional, we show the global stability of this equilibrium under some assumptions. We also study two size-structured models that come from cellular dynamics. The first one consists on two transport equations, where the cell can either proliferate or be quiescent, and the second one is a transport-diffusion equation with Feller boundary conditions. The irreducibility of the semigroup governing this latter model is always satisfied using the Hopf maximum principle. However, the irreducibility for the first model is true only under a necessary and sufficient condition that we give. We also show for these two models, using some weak compactness arguments in L1, the existence of a `spectral gap' (essential type strictly less than the type) ensuring the asynchronous exponential growth of the semigroup.

Le « marché intérieur » est générateur de contrats internationaux intra et extra-européens. La multiplication de ces contrats nécessite un marché intérieur « espace de liberté, de sécurité et de justice ». Le règlement « Rome I », instrument de droit international privé communautaire, assure la liberté contractuelle et la sécurité juridique par l’élaboration de règles générales de conflit de lois. La volonté d’assurer la justice contractuelle a donné lieu pour sa part à l’élaboration de règles spéciales de conflit de lois, qui visent à protéger les contractants en situation de faiblesse sociale ou économique face à leur cocontractant partie forte. Le règlement « Rome I » a ainsi consacré des règles spéciales de conflit de lois protectrices des intérêts des travailleurs, des consommateurs, des passagers voyageant au départ ou à destination de leur pays de résidence, des preneurs d’assurance de risques de masse communautaires, ainsi que des distributeurs et des franchisés. Toutefois, le succès du marché intérieur impose de parvenir à établir un équilibre entre la justice contractuelle, la liberté contractuelle et la sécurité juridique, même dans le cadre des règles spéciales protectrices de conflit de lois. Cet équilibre ne peut être atteint que par des correctifs de proximité. Le correctif de proximité inséré dans le cadre des règles spéciales protectrices de conflit de lois participe non seulement à la fonction principale de la règle de conflit de droit, à savoir la désignation de la compétence du système juridique le plus étroitement lié au contrat, mais également à la création et au fonctionnement de ce marché intérieur espace de liberté, de sécurité et de justice / The “internal market" generates international contracts within and outside Europe. The proliferation of these contracts in fact requires an internal market established as an "area of freedom, security and justice". Regulation "Rome I", instrument of private international and European law, displays the purpose of ensuring the contractual freedom and legal security per elaborating general rules of conflict of laws. The will of the European legislator to ensure contractual justice within the internal market give rise thus, to special rules of conflict of laws that protect the contracting parties in a weak position face their co-contractor in dominant position. Regulation "Rome I" consecrates conflict of laws rules protecting the interests of certain contracting parties, that it considers that they are "weak parties"; they are the workers, the consumers, the passengers traveling to or from their country of residence, the policyholders of mass risks located on European territory, as well as distributors and franchisees. However, the success of the internal market requires achieving a balance between contractual justice, contractual freedom and legal security, even under protective special rules of conflict of laws. This balance can be achieved by correctives of proximity. The corrective of proximity inserted as part of the protective special rules of conflict of laws not only participates in the main function of the rule of law conflict, namely the designation of the competence of the legal system most closely related to the contract, but also to the establishment and operation of an internal market, area of freedom, security and justice

Les nucléolipides sont des molécules amphiphiles dont la structure bio-inspirée dérive de celle des acides nucléiques. Leur auto-assemblage en milieu aqueux aboutit à la formation d’objets supramoléculaires de morphologies et structures très diverses. La morphologie a été caractérisée par des techniques complémentaires de microscopie optique et de diffusion de la lumière, tandis que leur structure a été déterminée par la diffusion des rayons X. Il a ainsi été mis en évidence l’existence et le rôle fondamental des interactions faibles entre têtes polaires, au sein des auto-assemblages. La nature de ces interactions faibles a été déterminée par des techniques de spectroscopies IR et UV. Un premier objectif a été de mettre en évidence l’importance de ces interactions, ainsi que leur corrélation avec d’autres facteurs qui régissent le mécanisme d’auto-assemblage, tels que la nature chimique des amphiphiles, ou la morphologie et la structure des objets supramoléculaires en présence.Par ailleurs, la tête polaire nucléotide permet également d’imaginer la formation d’interactions faibles entre les auto-assemblages et un monobrin d’acide nucléique, à l’image des interactions spécifiques entre bases azotées présentes dans l’ADN. Lors de ce travail, nous nous sommes intéressés à une méthode de vectorisation d’acides nucléiques par des objets eux aussi chargés négativement. Contrairement aux approches classiques, l’interaction électrostatique est ici défavorable et l’association repose alors uniquement sur des interactions faibles spécifiques, estimées en spectroscopie. De façon surprenante, la formation des complexes a pu être mise en évidence par des expériences de diffraction des rayons X et un modèle approprié a permis de proposer des mécanismes de formation des complexes. Les propriétés thermodynamiques des différents complexes formés ont été évaluées par la technique de Calorimétrie à Titration Isotherme (ITC). Un point remarquable a été la mise en évidence systématique de trois types de comportements sur l’ensemble des complexes étudiés en fonction de la nature et de la spécificité des interactions mises en jeu. Ceci nous a ainsi permis de proposer différents mécanismes de formation pour chaque type de complexe observé. / Nucleolipids are amphiphilic molecules which bio-inspired structure derives from nucleic acid structure. Their self-assembling behaviour in aqueous medium leads to the formation of supramolecular objects of very different morphologies and structures. The morphology has been characterized with optical microscopy and light scattering complementary techniques, whereas their structure has been determined with X-ray scattering. Thus the existence and the fondamental role of weak interactions between polar heads inside the self-assemblies have been highlighted. The nature of these weak interactions has been determined with IR and UV spectroscopies techniques. A first objectif has been to highlight the importance of these interactions, as well as the their correlation with other factors which drive the mechanism of self-assembly, such as the chemical nature of amphiphiles or the morphology and structure of the supramolecular objects.Moreover the nucleotide polar hear also allows to imagine the formation of weak interactions between the self-assemblies and a single-stranded nucleic acid, such as those highlighted in DNA. In this work, we found interest in a nucleic acid vectorisation method with negatively charged objects as well. On the contrary of classic approaches, electrostatic interaction was here defavorable and assembling relies only on specific weak interactions, estimated with spectroscopy methods. Surprisingly, complexes formation could be highlighted with X-ray scattering experiments, and an appropriate model has allowed the proposal of mechanisms for the formation of complexes. Thermodynamic properties of the different complexes formed have been evaluated with Isothermal Titration Calorimetry (ITC) technique. A remarkable point was the systematic highlighting of three types of behaviour on the whole set of complexes studied, depending of the nature and the specificity of the weak interactions implied. This led us to different proposals for the mechanism of formation of each type of complex studied.

Le but de cette thèse est de définir puis d'étudier différentes notions d'irrégularité uniforme ou ponctuelle permettant de traduire le fait qu'une fonction peut avoir des 'grands accroissements' à toutes les échelles. Pour cela on 'inverse' les notions de régularité Höldérienne usuelles. L'objectif principal du travail est ensuite de relier ces différentes notions à la théorie des ondelettes. Les critères ondelettes établis vont ainsi permettre de définir des fonctions ou des champs aléatoires dont le comportement est différent suivant la gamme d'échelles considérée. Par ailleurs, si on se place du point de vue ponctuel, une question naturelle est celle de la définition d'une analyse multifractale -dite faible- liée à la notion d'irrégularité ponctuelle. Les ondelettes vont alors permettre de définir des séries d'ondelettes multifractales pour l'irrégularité ponctuelle. Enfin, nous étudions des exemples de champs aléatoires où des propriétés de régularité directionelle apparaissent. Nous nous sommes ainsi centré sur l'étude d'un modèle de champ aléatoire gaussien particulier vérifiant une relation d'autosimilarité matricielle. Nous avons ensuite généralisé ce modèle et introduit des champs gaussiens autosimilaires par rapport à un groupe / The main purpose of this thesis is the definition and the study of different concepts of uniform or pointwise irregularity which enable one to account for the fact that a function may have 'large increments' at any scales. To this end, we 'invert' the usual notions of Hölderian regularity. The main goal is then to relate these different concepts to wavelet theory. The wavelet criteria supplied enable to define functions or random fields the behavior of which differ with respect the family of scales chosen. Moreover, if we consider the pointwise point of view, a natural question is that of the definition of a weak multifractal analysis related to pointwise irregularity. Finally, we study examples of random fields with some properties of directional regularity. Thus we focus on the study of a special model of operator scaling Gaussian field. We then extend this model and introduced group self-similar Gaussian fields

This thesis consists of three independent papers. They are put in reverse chronological order according to when they were initiated. The first paper, which is a joint work with Özgür Evren, extends the standard rational choice framework with the option to postpone the act of selecting an alternative. In that paper, we propose an axiomatic model of choice over risky prospects that restricts the classical rationality axioms solely to those instances in which the decision maker does not defer. The cardinal approach we follow allows us to identify the preference relation of the decision maker over lotteries, even if the choice data is very scarce due to deferral. Moreover, we also derive the value of deferring choice from a given set of options, which turns out to be an affine utility function over choice sets. At each choice situation, the decision maker compares the utility of each available alternative with that of deferral so as to decide on opting for an alternative immediately. The second paper is a model of status quo bias with choice avoidance. It describes the choice behavior of an otherwise standard decision maker whose choices are affected by the presence of a status quo alternative. The status quo emerges as a temporary choice, which may be reversed upon arrival of new (introspective or objective) information, or upon finding new alternatives. The third paper considers the network formation problem from a matching perspective. In that paper, agents want to link with each other and each has preferences over the subsets of others. We consider various solution concepts regarding the stability of a matching between the agents, establish relations between these concepts under several preference restrictions, and provide sufficient conditions for these solutions to be nonempty. / Diss. Stockholm : Handelshögskolan i Stockholm, 2011

The Standard Model of Elementary Particle Physics (SM) is the present theoryfor the elementary particles and their interactions and is a well-established theorywithin the physics community. The SM is a combination of Quantum Chromodynamics(QCD) and the Glashow{Weinberg{Salam (GWS) electroweak model. QCDis a theory for the strong force, whereas the GWS electroweak model is a theoryfor the weak and electromagnetic forces. This means that the SM describes allfundamental forces in Nature, except for the gravitational force. However, the SMis not a nal theory and some of its problems will be discussed in this thesis.In the rst part of this thesis, several properties of baryons are studied suchas spin structure, spin polarizations, magnetic moments, weak form factors, andnucleon quark sea isospin asymmetries, using the chiral quark model (QM). TheQM is an eective chiral eld theory developed to describe low energy phenomena of baryons, since perturbative QCD is not applicable at low energies. The resultsof the QM are in good agreement with experimental data.The second part of the thesis is devoted to the concept of quantum mechanicalneutrino oscillations. Neutrino oscillations can, however, not occur within the GWSelectroweak model. Thus, this model has to be extended in some way. All studiesincluding neutrino oscillation are done within three avor neutrino oscillationmodels. Both vacuum and matter neutrino oscillations are considered. Especially,global ts to all data of candidates for neutrino oscillations are presented and alsoan analytical formalism for matter enhanced three avor neutrino oscillations usingtime evolution operators is derived. Furthermore, investigations of matter eectswhen neutrinos traverse the Earth are included.The thesis begins with an introductory review of the QM and neutrino oscillationsand ends with the research results, which are given in the nine accompanyingscientic articles. / QC 20100616

The Bayesian nonparametric inference requires the construction of priors on infinite dimensional spaces such as the space of cumulative distribution functions and the space of cumulative hazard functions. Well-known priors on the space of cumulative distribution functions are the Dirichlet process, the two-parameter Poisson-Dirichlet process and the beta-Stacy process. On the other hand, the beta process is a popular prior on the space of cumulative hazard functions. This thesis is divided into three parts. In the first part, we tackle the problem of sampling from the above mentioned processes. Sampling from these processes plays a crucial role in many applications in Bayesian nonparametric inference. However, having exact samples from these processes is impossible. The existing algorithms are either slow or very complex and may be difficult to apply for many users. We derive new approximation techniques for simulating the above processes. These new approximations provide simple, yet efficient, procedures for simulating these important processes. We compare the efficiency of the new approximations to several other well-known approximations and demonstrate a significant improvement. In the second part, we develop explicit expressions for calculating the Kolmogorov, Levy and Cramer-von Mises distances between the Dirichlet process and its base measure. The derived expressions of each distance are used to select the concentration parameter of a Dirichlet process. We also propose a Bayesain goodness of fit test for simple and composite hypotheses for non-censored and censored observations. Illustrative examples and simulation results are included. Finally, we describe the relationship between the frequentist and Bayesian nonparametric statistics. We show that, when the concentration parameter is large, the two-parameter Poisson-Dirichlet process and its corresponding quantile process share many asymptotic pr operties with the frequentist empirical process and the frequentist quantile process. Some of these properties are the functional central limit theorem, the strong law of large numbers and the Glivenko-Cantelli theorem.

Generating functions express a sequence as coefficients arising from a power series in variables. They have many applications in combinatorics and probability. In this paper, we will investigate the important properties of four kinds of generating functions in one variables: ordinary generating unction, exponential generating function, probability generating function and moment generating function. Many examples with applications in combinatorics and probability, will be discussed. Finally, some well-known contest problems related to generating functions will be addressed.