In the last decade, a large number of studies have been devoted to the peculiarities of correlated physics found in the quasi-two-dimensional square lattice iridium oxides. It was shown that this 5d family of transition metal oxides has strong structural and electronic similarities to the famous 3d family of copper oxides. Moreover, a delicate interplay of on-site spin-orbit coupling, Coulomb repulsion and crystalline electric field interactions is expected to drive various exotic quantum states. Many theoretical proposals were made in the last decade including the prediction of possible superconductivity in square-lattice iridates emerging as a sister system to high-Tc cuprates, which however met only limited experimental confirmation. One can, therefore, raise a general question: To what extent is the low-energy physics of the quasi-two-dimensional square-lattice iridium oxides different from other transition metal oxides including cuprates? In this thesis we investigate some of the effects which are usually neglected in studies on iridates, focusing on quasi-two-dimensional square-lattice iridates such as Sr2IrO4 or Ba2IrO4. In particular, we discuss the role of the electron-phonon coupling in the form of Jahn-Teller interaction, electron-hole asymmetry introduced by the strong correlations and some effects of coupling scheme chosen to calculate multiplet structure for materials with strong on-site spin-orbit coupling. Thus, firstly, we study the role of phonons, which is almost always neglected in Sr2IrO4, and discuss the manifestation of Jahn-Teller effect in the recent data obtained on Sr2IrO4 with the help of resonant inelastic x-ray scattering. When strong spin-orbit coupling removes orbital degeneracy, it would at the same time appear to render the Jahn-Teller mechanism ineffective. We show that, while the Jahn-Teller effect does indeed not affect the antiferromagnetically ordered ground state, it leads to distinctive signatures in the spin-orbit exciton. Second, we focus on charge excitations and determine the motion of a charge (hole or electron) added to the Mott insulating, antiferromagnetic ground-state of square-lattice iridates. We show that correlation effects, calculated within the self-consistent Born approximation, render the hole and electron case very different. An added electron forms a spin-polaron, which closely resembles the well-known cuprates, but the situation of a removed electron is far more complex. Many-body configurations form that can be either singlets and triplets, which strongly affects the hole motion. This not only has important ramifications for the interpretation of angle-resolved photoemission spectroscopy and inverse photoemission spectroscopy experiments of square lattice iridates, but also demonstrates that the correlation physics in electron- and hole-doped iridates is fundamentally different. We then discuss the application of this model to the calculation of scanning tunneling spectroscopy data. We show that using scanning tunneling spectroscopy one can directly probe the quasiparticle excitations in Sr2IrO4: ladder spectrum on the positive bias side and multiplet structure of the polaron on the negative bias side. We discuss in detail the ladder spectrum and show its relevance for Sr2IrO4 which is in general described by more complicated extended t-J -like model. Theoretical calculation reveals that on the negative bias side the internal degree of freedom of the charge excitation introduces strong dispersive hopping channels encaving ladder-like features. Finally, we discuss how the choice of the coupling scheme to calculate multiplet structure can affect the theoretical calculation of angle-resolved photoemission spectroscopy and scanning tunnelling spectroscopy spectral functions.

Made available in DSpace on 2015-03-03T15:32:44Z (GMT). No. of bitstreams: 1 AntonioMBN_DISSERT.pdf: 717546 bytes, checksum: 381030bb759313d7ef41203fde24db9f (MD5) Previous issue date: 2014-02-14 / The central objective of a study Non-Homogeneous Markov Chains is the concept of weak and strong ergodicity. A chain is weak ergodic if the dependence on the initial distribution vanishes with time, and it is strong ergodic if it is weak ergodic and converges in distribution. Most theoretical results on strong ergodicity assume some knowledge of the limit behavior of the stationary distributions. In this work, we collect some general results on weak and strong ergodicity for chains with space enumerable states, and also study the asymptotic behavior of the stationary distributions of a particular type of Markov Chains with finite state space, called Markov Chains with Rare Transitions / O objetivo central de estudo em Cadeias de Markov N?o-Homog?neas e o conceito de ergodicidade fraca e forte. Uma cadeia ? erg?dica fraca se a depend?ncia da distribui??o inicial desaparece com o tempo, e ? erg?dica forte se ? erg?dica fraca e converge em distribui??o. A maioria dos resultados te?ricos sobre a ergodicidade forte sup?e algum conhecimento do comportamento limite das distribui??es estacion?rias. Neste trabalho, reunimos alguns resultados gerais sobre ergodicidade fraca e forte para cadeias com espa?oo de estados enumer?vel, e tamb?m estudamos o comportamento assint?tico das distribui??es estacion?rias de um tipo particular de Cadeias de Markov com espa?o de estados nito, chamadas Cadeias de Markov com Transi??es Raras

Made available in DSpace on 2014-12-17T15:26:38Z (GMT). No. of bitstreams: 1 MarconioSS_DISSERT.pdf: 828358 bytes, checksum: d4bc4c24d61f5cdfad5c76519c34784e (MD5) Previous issue date: 2010-06-28 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / In this work we studied the asymptotic unbiasedness, the strong and the uniform strong consistencies of a class of kernel estimators fn as an estimator of the density function f taking values on a k-dimensional sphere / Nesse trabalho estudamos o n?o-v?cio assint?tico, a consist?ncia forte e a consist?ncia uniformemente forte de um estimador do tipo n?cleo, que como a maioria dos estimadores ? constru?do com base em n observa??es i.i.d. X1,..., Xn de X, para a densidade f(x) de um vetor aleat?rio X que assume valores em uma esfera unit?ria k-dimensional

Made available in DSpace on 2014-12-17T15:26:39Z (GMT). No. of bitstreams: 1 MarianaBS_DISSERT.pdf: 5316617 bytes, checksum: 4fb0344851aa8f373aa2dab90bb6d3c5 (MD5) Previous issue date: 2012-05-31 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / In this work, the paper of Campos and Dorea [3] was detailed. In that article a Kernel Estimator was applied to a sequence of random variables with general state space, which were independent and identicaly distributed. In chapter 2, the estimator?s properties such as asymptotic unbiasedness, consistency in quadratic mean, strong consistency and asymptotic normality were verified. In chapter 3, using R software, numerical experiments were developed in order to give a visual idea of the estimate process / Neste trabalho estudamos um dos m?todos n?o-param?trico: os Estimadores do Tipo N?cleo associado a uma sequ?ncia de vari?veis aleat?rias independentes e identicamente distribu?das com espa?o de estados geral, mais precisamente o trabalho de Campos e Dorea [3]. No Cap?tulo 2 verificamos as boas qualidades dessa classe de estimadores como n?o v?cio assint?tico, converg?ncia em m?dia quadr?tica, consist?ncia forte e normalidade assint?tica. No Cap?tulo 3 com o auxilio do software R temos uma id?ia visual do que ocorre no processo de estima??o

Dans cette thèse, nous nous intéressons aux aspects algorithmiques et applications de deux problèmes de graphes, à savoir, la coloration et les alliances. La première partie concerne deux variantes de la coloration de graphes, la coloration Grundy et la coloration forte stricte. Nous commençons par l'étude du nombre Grundy des graphes réguliers. Nous donnons une condition fixe k, nous fournissons une condition nécessaire et suffisante pour que le nombre Grundy d'un graphe régulier soit au moins égal k. Nous caractérisons la classe des graphes cubiques (3-réguliers) pour laquelle le nombre Grundy est égal à 4, et nous présentons un algorithme linéaire pour déterminer le nombre Grundy d'un graphe cubique quelconque. Par ailleurs, en se basant sur la coloration forte stricte pour décomposer les arbres en petites composantes, nous présentons un nouvel algorithme pour l'appariement d'arbres étiquetés, non-ordonnés non-enracinés. Nous montrons que la distance calculée entre deux arbres est une pseudo-métrique. Nos expérimentations sur de larges bases synthétiques et des bases de données réelles confirment nos résultats analytiques et montrent que la distance proposée est précise et son algorithme est scalable. La seconde partie de cette thèse est consacrée aux alliances dans les graphes. Nous proposons un algorithme distribué autostabilisant pour la construction d'alliance offensive globale minimale dans un graphe arbitraire. Nous démontrons que cet algorithme converge sous le démon synchrone en temps linéaire. Ensuite, nous donnons le premier algorithme distribué autostabilisant pour le problème de l'alliance forte globale minimale dans un graphe quelconque. Nous prouvons que cet algorithme est polynomial sous le démon inéquitable distribué. Nous montrons par la suite, comment cet algorithme peut être adapté pour des généralisations du problème, comme la k-alliance forte et l'alliance forte pondérée. Enfin, en se basant sur les propriétés structurelles de l'alliance offensive, nous présentons une solution pour décentraliser le protocole de signalisation SIP. Ceci rend possible son déploiement dans un réseau mobile ad hoc / This thesis investigates the algorithmic aspects and applications of two graph problems, namely, colorings and alliances. In the first part, we focus on two variants of the proper vertex coloring, the Grundy coloring and the strict strong coloring. We start by the study of Grundy number for regular graphs. We give a sufficient condition for d-regular graphs with sufficiently large girth to have Grundy number equals d + 1. Then, using graph homomorphism, we obtain a necessary and sufficient condition for d-regular graphs to have Grundy number at least k. Moreover, we characterize cubic graphs (3-regular) for which the Grundy number is d + 1, and present a linear-time algorithm to determine the Grundy number of any arbitrary cubic graph. Subsequently, based on the strict strong coloring, we present an approach for the problem of matching labeled trees. Using this coloring, we propose a new algorithm to deterministically decompose a tree into small components. This leads to an efficient algorithm to measure an accurate distance between unrooted unordered labeled trees. The second part is devoted to the alliances in graphs. We first propose a linear-time self-stabilizing algorithm for the minimal global offensive alliance set problem, under the synchronous distributed scheduler. Then, we give the first self-stabilizing algorithm for the minimal global powerful alliance set problem in arbitrary graphs. Moreover, we show how this algorithm can be adapted to find the minimal global powerful k-alliance and the minimal weighted global powerful alliance sets. We prove that all these algorithms converge in polynomial-time under the unfair distributed scheduler. Finally, based on the structural properties of the offensive alliance, we propose a solution to decentralize the signaling protocol SIP. This enables SIP applications in mobile ad hoc networks

O objetivo deste trabalho é estudar aproximação na esfera por uma soma com pesos de harmônicos esféricos. Apresentamos condições necessárias e suficientes sobre os pesos para garantir a convergência, tanto no caso contínuo quanto no caso Lp. Analisamos a ordem de convergência dos processos aproximatórios usando um módulo de suavidade esférico relacionado à derivada forte de Laplace-Beltrami. Incluímos provas para vários resultados sobre a derivada forte de Laplace-Beltrami, já que não conseguimos encontrá-las na literatura / The subject of this work is to study approximation on the sphere by weighted sums of spherical harmonics. We present necessary and sufficient conditions on the weights for convergence in both, the continuous and the Lp cases. We analyse the convergence rates of the approximation processes using a modulus of smoothness related to the strong Laplace- Beltrami derivative. We include proofs for several results related to such a derivative, since we were unable to find them in the literature

Submitted by JÚLIO HEBER SILVA (julioheber@yahoo.com.br) on 2017-03-22T20:23:25Z No. of bitstreams: 2 Tese - Gilson do Nascimento Silva - 2017.pdf: 2015008 bytes, checksum: e0148664ca46221978f71731aeabfa36 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-03-23T11:30:21Z (GMT) No. of bitstreams: 2 Tese - Gilson do Nascimento Silva - 2017.pdf: 2015008 bytes, checksum: e0148664ca46221978f71731aeabfa36 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-03-23T11:30:21Z (GMT). No. of bitstreams: 2 Tese - Gilson do Nascimento Silva - 2017.pdf: 2015008 bytes, checksum: e0148664ca46221978f71731aeabfa36 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-03-13 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / We consider Newton’s method for solving a generalized equation of the form f(x) + F(x) 3 0, where f : Ω → Y is continuously differentiable, X and Y are Banach spaces, Ω ⊆ X is open and F : X ⇒ Y has nonempty closed graph. Assuming strong regularity of the equation and that the starting point satisfies Kantorovich’s conditions, we show that the method is quadratically convergent to a solution, which is unique in a suitable neighborhood of the starting point. In addition, a local convergence analysis of this method is presented. Moreover, using convex optimization techniques introduced by S. M. Robinson (Numer. Math., Vol. 19, 1972, pp. 341-347), we prove a robust convergence theorem for inexact Newton’s method for solving nonlinear inclusion problems in Banach space, i.e., when F(x) = −C and C is a closed convex set. Our analysis, which is based on Kantorovich’s majorant technique, enables us to obtain convergence results under Lipschitz, Smale’s and Nesterov-Nemirovskii’s self-concordant conditions. / N´os consideraremos o m´etodo de Newton para resolver uma equa¸c˜ao generalizada da forma f(x) + F(x) 3 0, onde f : Ω → Y ´e continuamente diferenci´avel, X e Y s˜ao espa¸cos de Banach, Ω ⊆ X ´e aberto e F : X ⇒ Y tem gr´afico fechado n˜ao-vazio. Supondo regularidade forte da equa¸c˜ao e que o ponto inicial satisfaz as hip´oteses de Kantorovich, mostraremos que o m´etodo ´e quadraticamente convergente para uma solu¸c˜ao, a qual ´e ´unica em uma vizinhan¸ca do ponto inicial. Uma an´alise de convergˆencia local deste m´etodo tamb´em ´e apresentada. Al´em disso, usando t´ecnicas de otimiza¸c˜ao convexa introduzida por S. M. Robinson (Numer. Math., Vol. 19, 1972, pp. 341-347), provaremos um robusto teorema de convergˆencia para o m´etodo de Newton inexato para resolver problemas de inclus˜ao n˜ao–linear em espa¸cos de Banach, i.e., quando F(x) = −C e C ´e um conjunto convexo fechado. Nossa an´alise, a qual ´e baseada na t´ecnica majorante de Kantorovich, nos permite obter resultados de convergˆencia sob as condi¸c˜oes Lipschitz, Smale e Nesterov-Nemirovskii auto-concordante.

Les travaux présentés dans cette thèse portent sur l’analyse mathématique de quelques équations intervenant en dynamique des populations et en cinétique des gaz. On s’est intéressé tout d’abord à une version non linéaire d’un modèle dû à Lebowitz et Rubinow en 1974 pour décrire une population cellulaire. On a établi des résultats d’existence et d’unicité aussi bien les solutions au sens de Bénilan que les solutions fortes du problème d’évolution correspondant. Cette analyse a été étendue ensuite à une perturbation de ce modèle par un opérateur non linéaire et pour des conditions aux limites locales et non locales. Cette partie a été complétée par l’étude des résultats d’existence des solutions du problème stationnaire correspondant. Le second volet de ce travail traite de l’existence des solutions d’une version non linéaire stationnaire d’un modèle dû à Rotenberg en 1983. Le dernier chapitre de ce travail à été consacré à l’analyse spectrale d’une équation de transport neutronique faisant intervenir des opérateurs de collision élastiques et inélastiques. Le problème d’évolution correspondant ainsi que le comportement asymptotique (pour les grands temps) de la solution ont été considéré pour des conditions aux limites périodiques. / The work presented in this thesis deals with the mathematical analysis of some equations arising in the dynamics of populations and the kinetic of gas. First, we focused on a non-linear version of a model introduced by Lebowitz and Rubinow in 1974 to describe a cells population. We discussed the existence and the uniqueness of solutions of both Bénilan’s solution and strong solutions to the corresponding evolution equation. This analysis was subsequently extended to a perturbation of this model by a nonlinear operator for local and non-local boundary conditions. This part was supplemented by the study of existence of solutions to the corresponding stationary problem. In chapter 5, we discuss the existence of solutions to a stationary nonlinear version of a model describing the evolution of a cells population introduced by Rotenberg in 1983. The last chapter of this work is devoted to the spectral analysis of a neutron transport equation involving elastic and inelastic collision operators. The corresponding evolution problem as well as the asymptotic behavior (for large times) of the solution was considered for periodic boundary conditions.

Cette thèse se consacre à l'étude du modèle de dénaturation de l'ADN introduit par Poland et Scheraga dans les années soixante. Les modèles de dépiégeage en milieu aléatoire, avec lesquels la correspondance a été établie, sont également traités. Dans le cas où les interactions entre le système et l’environnement sont homogènes, le problème a été résolu : selon la valeur d'un paramètre géométrique, une transition de phase d'ordre un ou deux se produit. En revanche, lorsque les interactions sont prises aléatoires (on parle d'un système en présence de désordre), nous ne connaissons ni le point critique, ni l'ordre de la transition en régime defort désordre. Pour simplifier le problème, de nombreux auteurs font usage d'une représentation hiérarchique grâce à laquelle une renormalisation exacte de la fonction de partition peut être écrite. Mais à nouveau, la question du point critique et de l'ordre de la transition n'a pas été résolue. Nous avons introduit un nouveau système (Toymodel) plus simple que la version hiérarchique en changeant la forme de la renormalisation. Le problème, ainsi posé, permet de mettre en évidence une famille de distributions qui ne varient presque pas lors d'une renormalisation, avec lesquelles nous avons pu dériver des équations du type Berezinskii-Kosterlitz- Thouless. Aussi, en présence de désordre, la transition de phase n'admet pas de point fixe critique. Ces deux éléments, en accord avec nos résultats numériques, nous poussent à croire que nous sommes en présence d'une transition de phase d'ordre infini. La seconde partie de la thèse rapporte un travail sur le processus simple d'exclusion symétrique, qui est l'un des modèles les plus simples de physique statistique hors d'équilibre pour lequel un état stationnaire est connu. La fonction de grandes déviations a été calculée dans le passé par les approches microscopiques et macroscopiques et ici, nous en avons calculé la première correction de taille finie. Le résultat a ensuite été comparé aux corrections similaires pour des systèmes à l'équilibre. / This thesis is a study of a DNA denaturation model, introduced by Poland and Scheraga during the 1960s. The depinning models with random environment, with which the similarity has been made, are also concerned. If the interactions between the system and the environment are homogeneous, the problem has been solved: depending on the value of a geometrical parameter, a first or a second order phase transition happens. On the other hand, when the interactions are random, we know neither the critical point nor the phase transition order in the case of strong disorder. In order to simplify the problem, some authors have used a hierarchical representation through which an exact renormalization can be written. Despite this simplification, the critical point and the transition order have not been found. By changing the renormalization relation, we introduced a Toy-model which is simpler than the hierarchical version. The new problem leaded us to a family of distributions, which stay almost the same under renormalization, and allow us to derive the Berezinskii-Kosterlitz- Thouless equations. Also, with strong disorder, the phase transition does not have a critical fixed point. These two elements, according to our numerical results, predict that the order transition is infinite. The second part of this thesis reports on a work about the simple symmetric exclusion process, which is one of the simplest out of equilibrium models for which a stationary state is known. The large deviation function has been calculated in the past through microscopic and macroscopic approaches. Here, we calculated the leading finite-size correction. Then the result has been compared to similar corrections for equilibrium systems.

Cette thèse est consacrée à l’étude de la stabilisation directe et indirecte de différents systèmes d’équations d’ondes avec un contrôle frontière de type fractionnaire ou un contrôle local viscoélastique de type Kelvin-Voight. Nous considérons, d’abord, la stabilisation de l’équation d’ondes multidimensionnel avec un contrôle frontière fractionnaire au sens de Caputo. Sous des conditions géométriques optimales, nous établissons un taux de décroissance polynomial de l’énergie de système. Ensuite, nous nous intéressons à l’étude de la stabilisation d’un système de deux équations d’ondes couplées via les termes de vitesses, dont une seulement est amortie avec contrôle frontière de type fractionnaire au sens de Caputo. Nous montrons différents résultats de stabilités dans le cas 1-d et N-d. Finalement, nous étudions la stabilité d’un système de deux équations d’ondes couplées avec un seul amortissement viscoélastique localement distribué de type Kelvin-Voight. / This thesis is devoted to study the stabilization of the system of waves equations with one boundary fractional damping acting on apart of the boundary of the domain and the stabilization of a system of waves equations with locally viscoelastic damping of Kelvin-Voight type. First, we study the stability of the multidimensional wave equation with boundary fractional damping acting on a part of the boundary of the domain. Second, we study the stability of the system of coupled onedimensional wave equation with one fractional damping acting on a part of the boundary of the domain. Next, we study the stability of the system of coupled multi-dimensional wave equation with one fractional damping acting on a part of the boundary of the domain. Finally, we study the stability of the multidimensional waves equations with locally viscoelastic damping of Kelvin-Voight is applied for one equation around the boundary of the domain.