In this work we study two random procedures in cubic graphs with large girth. The first procedure finds a probability distribution on edge-cuts such that each edge is in a randomly chosen cut with probability at least 0.88672. As corollaries, we derive lower bounds for the size of maximum cut in cubic graphs with large girth and in random cubic graphs, and also an upper bound for the fractional cut covering number in cubic graphs with large girth. The second procedure finds a probability distribution on independent sets such that each vertex is in an independent set with probability at least 0.4352. This implies lower bounds for the size of maximum independent set in cubic graphs with large girth and in random cubic graphs, as well as an upper bound for the fractional chromatic number in cubic graphs with large girth.

Wooden objects have been widely used in the history of humanity and play an important role in our cultural heritage. The preservation of such objects is of great importance and can be a challenging task. This thesis investigates the static and time-dependent mechanical behaviour of archaeological oak wood from the Vasa warship. Characterisation of mechanical properties is necessary for the formulation of a numerical model to design an improved support structure. The ship was impregnated with polyethylene glycol (PEG) for dimensional stabilisation. All elastic engineering constants of the Vasa oak have been identified and compared with those of recent oak by means of the static and dynamic testing. The experiments were done on samples with cubic geometry, which allowed obtaining all elastic constants from a single sample. The usage of cubic samples with orthotropic mechanical properties during compressive experiments was validated with finite-element simulations. The Young's moduli of the Vasa oak in all orthotropic directions were smaller than those for the recent oak. The shear moduli of Vasa oak was determined and verified with the resonant ultrasound spectroscopy. The time-dependent mechanical behaviour of the Vasa oak has been studied. Creep studies were performed in uniaxial compression on the cubic samples in all orthotropic directions. The samples loaded in the longitudinal direction were subjected to different stress levels. A stress level below 15% of the yield stress in the longitudinal direction did not result in non-linear creep with increasing creep rates within the time frame of the tests. The results of the studies in radial and tangential directions showed that creep was dominated by the effect of annual fluctuations in relative humidity and temperature. The weight changes based on annual fluctuations of relative humidity were measured for Vasa oak and recent oak. The Vasa oak showed higher variations due to an increased hygroscopicity which is the result of the impregnation with PEG. In conceiving a full-scale finite-element model of Vasa ship, not only the stress-strain relations of the material but also those of the structural joints are needed. Since the in-situ measurement of joints is not an option, a replica of a section of the ship hull was built and tested mechanically. The load-induced displacements were measured using 3D laser scanning which proved to have advantages to conventional point displacement measurements. The mechanical characteristics of the Vasa oak and joint information presented in this work can be used as input for a finite-element model of the Vasa ship for simulation of static and time-dependent behaviour on a larger scale. / Stötta Vasa

Nous avons réalisé des calculs de structure électronique ab initio, basés sur la théorie de lafonctionnelle de la densité (DFT), pour étudier les propriétés des dislocations vis h111i dansles métaux de transition cubiques centrés (V, Nb, Ta, Mo, W et Fe). Dans tous ces éléments,le coeur facile non-dégénéré est la configuration d’énergie minimale et la configuration de coeurdissociée a une énergie très élevée, comparable ou plus élevée que celle du coeur difficile, encontradiction avec les prédictions des potentiels interatomiques. Nous avons mis en évidence destendances de groupe marquées sur l’énergie de coeur de la dislocation facile, reliées à la positiondu niveau de Fermi par rapport au minimum du pseudo-gap de la densité d’états électroniques.Notre travail fait aussi apparaitre un comportement atypique du fer, avec une énergie relativedu coeur difficile basse, proche de celle du point col entre deux coeurs faciles, conduisant à unpotentiel de Peierls plat autour de la configuration difficile, contrairement aux autres éléments.A partir de ces calculs DFT, nous avons construit le paysage énergétique à deux dimensionsdans le plan {111} (potentiel de Peierls) et nous avons étudié plusieurs propriétés relativesau glissement des dislocations, et en particulier l’énergie de formation de la paire de décrochementset la dépendance de la contrainte de Peierls en fonction de l’orientation cristalline.Nous proposons une modification simple de la loi de Schmid, qui prend en compte la trajectoirenon rectiligne de la dislocation et qui permet d’expliquer qualitativement pourquoi l’asymétriemaclage/antimaclage est moins marquée dans Fe que dans les autres métaux cubiques centrés. / We performed electronic structure ab initio calculations based on density functional theory(DFT) to study the h111i screw dislocation properties in body-centered cubic transition metals(V, Nb, Ta, Mo, W and Fe). In all investigated elements, the nondegenerate easy coreis the minimum energy configuration and the split core configuration has a high energy nearor above that of the hard core, contrary to interatomic potential predictions. A strong groupdependence of the core energy of the easy dislocation is also evidenced, related to the positionof the Fermi level with respect to the minimum of the pseudogap of the electronic density ofstates. Our work also reveals an atypical behavior in Fe, with a low relative energy at the hardcore position, close to that of the saddle configuration between easy cores, resulting in a flatPeierls potential around the hard core configuration, at variance with other elements. Fromthese DFT calculations, the two-dimensional energetic landscape in the {111} plane (Peierlspotential) is constructed and we investigated several properties of dislocation glide and in particular,the kink-pair formation enthalpy, as well as the dependence of the Peierls stress oncrystal orientation. We proposed a simple modification to the Schmid law that takes accountof the non-straight trajectory of the dislocation and that qualitatively explains why the twinning/antitwinning asymmetry is less pronounced in Fe than in other body-centered cubic metals.

Nesta dissertação apresentamos métodos de diagnóstico em modelos semiparamétricos sob erros normais, em especial os modelos semiparamétricos com uma variável explicativa não paramétrica, conhecidos como modelos lineares parciais. São utilizados splines cúbicos para o ajuste da variável resposta e são aplicadas funções de verossimilhança penalizadas para a obtenção dos estimadores de máxima verossimilhança com os respectivos erros padrão aproximados. São derivadas também as propriedades da matriz hat para esse tipo de modelo, com o objetivo de utilizá-la como ferramenta na análise de diagnóstico. Gráficos normais de probabilidade com envelope gerado também foram adaptados para avaliar a adequabilidade do modelo. Finalmente, são apresentados dois exemplos ilustrativos em que os ajustes são comparados com modelos lineares normais usuais, tanto no contexto do modelo aditivo normal simples como no contexto do modelo linear parcial. / In this master dissertation we present diagnostic methods in semiparametric models under normal errors, specially in semiparametric models with one nonparametric explanatory variable, also known as partial linear model. We use cubic splines for the nonparametric fitting, and penalized likelihood functions are applied for obtaining maximum likelihood estimators with their respective approximate standard errors. The properties of the hat matrix are also derived for this kind of model, aiming to use it as a tool for diagnostic analysis. Normal probability plots with simulated envelope graphs were also adapted to evaluate the model suitability. Finally, two illustrative examples are presented, in which the fits are compared with usual normal linear models, such as simple normal additive and partially linear models.

In this thesis we study Schrödinger-Poisson systems and we look for positive solutions. Our work consists in three chapters. Chapter 1 includes some basic facts on critical point theory. In Chapter 2 we consider a fractional Schrödinger-Poisson system in the whole space R^N in presence of a positive potential and depending on a small positive parameter . We show that, for suitably small (i.e. in the \"semiclassical limit\") the number of positive solutions is estimated below by the Ljusternick-Schnirelmann category of the set of minima of the potential. Finally, in Chapter 3, we analyze a Schrödinger-Poisson system in R^3 under an asymptotically cubic nonlinearity. We prove the existence of positive, radial solutions inside a ball and in an exterior domain. / Nesta tese nós estudamos sistemas de Schrödinger-Poisson e procuramos soluções positivas. Nosso trabalho consiste em três capítulos. O Capítulo 1 contém alguns fatos básicos sobre a teoria de pontos críticos. No Capítulo 2 nós consideramos um sistema fracionário de Schrödinger-Poisson em todo o espaço R^N em presença de um potencial positivo e que depende de um pequeno parâmetro positivo . Nós mostramos que, para suficentemente pequeno (i.e. no limite semiclássico) o número de soluções positivas é estimado por abaixo pela categoria de Ljusternick-Schnirelmann dos conjuntos onde o potencial é mínimo. Finalmente, no Capítulo 3 nós analisamos um sistema Schrödinger-Poisson em R^3 sob a não linearidade assintoticamente cúbica. Mostramos a existência de soluções radiais positivas dentro de uma bola e em um domínio exterior.

O objetivo principal deste trabalho é discutir estimação e diagnóstico em modelos semiparamétricos com resposta binomial negativa, mais especificamente, modelos de regressão com resposta binomial negativa em que uma das variáveis explicativas contínuas é modelada de forma não paramétrica. Iniciamos o trabalho com um exemplo ilustrativo e fazemos uma breve revisão dos modelos paramétricos com resposta binomial negativa. Em seguida, introduzimos os modelos semiparamétricos com resposta binomial negativa e discutimos alguns aspectos de estimação, inferência e seleção de modelos. Dedicamos um capítulo a procedimentos de diagnóstico, tais como desenvolvimento de medidas de alavanca e de influência sob os aspectos de deleção de pontos e influência local, além de abordar a análise de resíduos. Reanalizamos o exemplo ilustrativo sob o enfoque semiparamétrico e apresentamos algumas conclusões. / The aim of this work is to discuss some aspects on estimation and diagnostics in negative binomial regression models which an explanatory continuous variable is modeled nonparametrically. First, an illustrative example is presented and analyzed under parametric negative binomial regression models. The proposed models are then introduced and some aspects on estimations, inference and model selection are presented. Particular emphasis is given on the development of diagnostic procedures, such as leverage measures, Cook distances, local influence approach and residuals. The motivated example is reanalyzed under the semiparametric viewpoint and some conclusions are given.

Neste trabalho foi estudado o efeito da adição de íons haletos (Cl-, Br- e I-) sobre a morfologia das nanopartículas de Pt na produção de catalisadores de Pt/C e PtSnO2/C. Foi desenvolvida uma metodologia de síntese simples capaz de produzir nanopartículas de Pt predominantemente cúbicas com orientação preferencial Pt(100), diretamente suportadas em carbono sem o uso de agentes estabilizantes. Brometo de potássio foi utilizado como agente direcionador de superfície para obtenção do material preferencialmente orientado. O controle de adição do precursor de Pt e de KBr foi crucial para obter nanocubos de Pt de 8 nm bem dispersos sobre o suporte. Na preparação dos catalisadores de PtSnO2/C, o processo de adição do SnCl2 também foi decisivo na obtenção das nanopartículas de Pt com tamanho e morfologia de interesse. Nanocubos de Pt coexistindo com SnO2 disperso foram exclusivamente obtidos ao adicionar o SnCl2 na etapa final da síntese, quando as nanopartículas cúbicas de Pt já estavam formadas. Enriquecidos de domínios Pt(100), os materiais em forma cúbica de Pt/C e PtSnO2/C se mostraram menos afetados pelo acúmulo dos intermediários indesejados provenientes da reação de eletro-oxidação de etanol e foram mais tolerantes ao envenenamento por monóxido de carbono. Resultados similares foram observados para a oxidação de CO e metanol, utilizados como apoio para compreensão da eletro-oxidação de etanol. O efeito morfológico destes materiais no desempenho elétrico em célula a combustível de etanol direto foi avaliado. Pt/C e PtSnO2/C contendo nanopartículas de Pt com orientação preferencial Pt(100) forneceram maiores valores de densidade de potência e de seletividade para CO2 comparados aos catalisadores de Pt/C e PtSnO2/C com nanopartículas de Pt sem orientação preferencial. / The effect of the addition of halide ions (Cl-, Br- and I-) on the shape of Pt nanoparticles of Pt/C and PtSnO2/C catalysts was studied in this work. It was developed a simple methodology synthesis capable of producing Pt nanoparticles predominantly cubic with Pt(100) preferential orientation, directly supported on carbon without the use of stabilizing agents. Potassium bromide was used as a surface directing agent to obtain the preferentially oriented material. The control in addition of the Pt precursor and KBr was crucial to obtain well dispersed 8 nm Pt nanocubes on the support. For the preparation of PtSnO2/C catalysts, the addition process of SnCl2 was also decisive to obtain the Pt nanoparticles with desirable size and morphology. Pt nanocubes coexisting with disperse SnO2 were exclusively obtained by adding SnCl2 in the final step of the synthesis, when the cubic Pt nanoparticles were already formed. Enriched with Pt (100) domains, the Pt/C and PtSnO2/C cubic materials were less affected by the undesirable intermediates accumulation from the ethanol electro-oxidation reaction and were more tolerant to the poisoning of monoxide carbon. Similar results were observed for methanol and CO electro-oxidation reactions, which were employed to understand ethanol electro-oxidation. The morphological effect of these materials on electrical performance in direct ethanol fuel cell was evaluated. Pt/C and PtSnO2/C containing Pt(100) nanoparticles provided higher power density and CO2 selectivity values compared to Pt/C and PtSnO2/C catalysts with Pt nanoparticles without ant preferential orientation.

Dans cette thèse, nous étudions un problème de contrôle et un problème inverse pour les équationsde la chaleur. Notre premier travail concerne la contrôlabilité à zéro pour une équation de la chaleur semi-linéaire. Il est à noter que sans contrôle, la solution est instable et il y aura en général explosion de la solution en un temps fini. Ici, nous proposons un résultat positif de contrôlabilité à zéro sous une hypothèse quantifiée de petitesse sur la donnée initiale. La nouveauté réside en la construction de ce contrôle pour amener la solution à l’état d’équilibre.Notre second travail aborde l’équation de la chaleur rétrograde dans un domaine borné et sous la condition de Dirichlet. Nous nous intéressons à la question suivante: peut-on reconstruire la donnée initiale à partir d’une observation de la solution restreinte à un sous-domaine et à un temps donné? Ce problème est connu pour être mal-posé. Ici, les deux principales méthodes proposées sont: une approche de filtrage des hautes fréquences et une minimisation à la Tikhonov. A chaque fois, nous reconstruisons de manière approchée la solution et quantifions l’erreur d’approximation / My thesis focuses on two main problems in studying the heat equation: Control problem and Inverseproblem.Our first concern is the null controllability of a semilinear heat equation which, if not controlled, can blow up infinite time. Roughly speaking, it consists in analyzing whether the solution of a semilinear heat equation, underthe Dirichlet boundary condition, can be driven to zero by means of a control applied on a subdomain in whichthe equation evolves. Under an assumption on the smallness of the initial data, such control function is builtup. The novelty of our method is computing the control function in a constructive way. Furthermore, anotherachievement of our method is providing a quantitative estimate for the smallness of the size of the initial datawith respect to the control time that ensures the null controllability property.Our second issue is the local backward problem for a linear heat equation. We study here the followingquestion: Can we recover the source of a linear heat equation, under the Dirichlet boundary condition, from theobservation on a subdomain at some time later? This inverse problem is well-known to be an ill-posed problem,i.e their solution (if exists) is unstable with respect to data perturbations. Here, we tackle this problem bytwo different regularization methods: The filtering method and The Tikhonov method. In both methods, thereconstruction formula of the approximate solution is explicitly given. Moreover, we also provide the errorestimate between the exact solution and the regularized one.

Nesta dissertação apresentamos métodos de diagnóstico em modelos semiparamétricos sob erros normais, em especial os modelos semiparamétricos com uma variável explicativa não paramétrica, conhecidos como modelos lineares parciais. São utilizados splines cúbicos para o ajuste da variável resposta e são aplicadas funções de verossimilhança penalizadas para a obtenção dos estimadores de máxima verossimilhança com os respectivos erros padrão aproximados. São derivadas também as propriedades da matriz hat para esse tipo de modelo, com o objetivo de utilizá-la como ferramenta na análise de diagnóstico. Gráficos normais de probabilidade com envelope gerado também foram adaptados para avaliar a adequabilidade do modelo. Finalmente, são apresentados dois exemplos ilustrativos em que os ajustes são comparados com modelos lineares normais usuais, tanto no contexto do modelo aditivo normal simples como no contexto do modelo linear parcial. / In this master dissertation we present diagnostic methods in semiparametric models under normal errors, specially in semiparametric models with one nonparametric explanatory variable, also known as partial linear model. We use cubic splines for the nonparametric fitting, and penalized likelihood functions are applied for obtaining maximum likelihood estimators with their respective approximate standard errors. The properties of the hat matrix are also derived for this kind of model, aiming to use it as a tool for diagnostic analysis. Normal probability plots with simulated envelope graphs were also adapted to evaluate the model suitability. Finally, two illustrative examples are presented, in which the fits are compared with usual normal linear models, such as simple normal additive and partially linear models.

O objetivo principal deste trabalho é discutir estimação e diagnóstico em modelos semiparamétricos com resposta binomial negativa, mais especificamente, modelos de regressão com resposta binomial negativa em que uma das variáveis explicativas contínuas é modelada de forma não paramétrica. Iniciamos o trabalho com um exemplo ilustrativo e fazemos uma breve revisão dos modelos paramétricos com resposta binomial negativa. Em seguida, introduzimos os modelos semiparamétricos com resposta binomial negativa e discutimos alguns aspectos de estimação, inferência e seleção de modelos. Dedicamos um capítulo a procedimentos de diagnóstico, tais como desenvolvimento de medidas de alavanca e de influência sob os aspectos de deleção de pontos e influência local, além de abordar a análise de resíduos. Reanalizamos o exemplo ilustrativo sob o enfoque semiparamétrico e apresentamos algumas conclusões. / The aim of this work is to discuss some aspects on estimation and diagnostics in negative binomial regression models which an explanatory continuous variable is modeled nonparametrically. First, an illustrative example is presented and analyzed under parametric negative binomial regression models. The proposed models are then introduced and some aspects on estimations, inference and model selection are presented. Particular emphasis is given on the development of diagnostic procedures, such as leverage measures, Cook distances, local influence approach and residuals. The motivated example is reanalyzed under the semiparametric viewpoint and some conclusions are given.