Fluorinated stationary phase in Rtx-200MS column have been characterized by determination of system constants of Abraham equation. Retention on this phase is driven by dispersive and orientation/induction forces. Significant interaction contribution of lone pair electrons or π- electrons provides unique selectivity for analytes with excess of electron density. Unusual behavior of this phase have been determined by study of separation mechanism of polar and nonpolar analytes, in comparison of their separation on polar and nonpolar phases. This behavior is due to medium polarity of the phase (system constant s), which is not so pronounced to cancel separation of nonpolar analytes due to induction forces. In some cases contribution of lone pair electrons or π-electrons can contribute to this separations. Key words fluorinated stationary phase Rtx-200MS, inverse gas chromatography, LFER method, Abraham's equation

Title: Modelling Bonus - Malus Systems Author: Marika Stroukalová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Lucie Mazurová, Ph.D., KPMS MFF UK Abstract: In this thesis we deal with bonus-malus tariff systems commonly used to adjust the a priori set premiums according to the individual claims during mo- tor third party liability insurance. The main aim of this thesis is to describe the standard model based on the Markov chain. For each bonus-malus class we also determine the relative premium ("relativity"). Another objective of this thesis is to find optimal values for the relativities taking into account the a priori set premiums. We apply the theoretical model based on the stationary distribu- tion of bonus-malus classes on real-world data and a particular real bonus-malus system used in the Czech Republic. The empirical part of this thesis compares the optimal and the real relativities and assesses the suitability of the chosen theoretical model for the particular bonus-malus system. Keywords: bonus-malus system, a priori segmentation, stationary distribution, relativity, quadratic loss function 1

This Doctoral thesis gives an introduction to the concept of kernel functionsand their signicance in the theory of special functions. Of particularinterest is the use of kernel function methods for constructing exact solutionsof Schrodinger type equations, in one spatial dimension, with interactions governedby elliptic functions. The method is applicable to a large class of exactlysolvable systems of Calogero-Moser-Sutherland type, as well as integrable generalizationsthereof. It is known that the Schrodinger operators with ellipticpotentials have special limiting cases with exact eigenfunctions given by orthogonalpolynomials. These special cases are discussed in greater detail inorder to explain the kernel function methods with particular focus on the Jacobipolynomials and Jack polynomials. / <p>QC 20161003</p>

Cette thèse comporte deux chapitres principaux. Deux problèmes indépendants de Modélisation Mathématique y sont étudiés. Au chapitre 1, on étudiera le problème de l’existence et de l’unicité des distributions quasi-stationnaires (DQS) pour un mouvement Brownien avec dérive, tué en zéro dans le cas où la frontière d’entrée est l’infini et la frontière de sortie est zéro selon la classification de Feller.Ce travail est lié à l’article pionnier dans ce sujet  par Cattiaux, Collet, Lambert, Martínez, Méléard, San Martín; où certaines conditions suffisantes ont été établies pour prouver l’existence et l’unicité de DQS dans le contexte d’une famille de Modèles de Dynamique des Populations.Dans ce chapitre, nous généralisons les théorèmes les plus importants de ce travail pionnier, la partie technique est basée dans la théorie de Sturm-Liouville sur la demi-droite positive. Au chapitre 2, on étudiera le problème d’obtenir des bornes inférieures optimales sur l’Hamiltonien du Modèle d’Ising avec interactions à longue portée, l’interaction entre deux spins situés à distance d décroissant comme d^(2-a), où a ϵ[0,1).Ce travail est lié à l’article publié en 2005 par Cassandro, Ferrari, Merola, Presutti où les bornes inférieures optimales sont obtenues dans le cas où a est dans [0,(log3/log2)-1) en termes de structures hiérarchiques appelées triangles et contours.Les principaux théorèmes obtenus dans cette thèse peuvent être résumés de la façon suivante:1. Il n’existe pas de borne inférieure optimale pour l’Hamiltonien en termes de triangles pour a dans ϵ[log2/log3,1). 2. Il existe une borne optimale pour l’Hamiltonien en termes de contours pour a dans a ϵ [0,1). / This thesis contains two main Chapters, where we study two independent problems of Mathematical Modelling : In Chapter 1, we study the existence and uniqueness of Quasi Stationary Distributions (QSD) for a drifted Browian Motion killed at zero, when $+infty$ is an entrance Boundary and zero is an exit Boundary according to Feller's classification. The work is related to the previous paper published in 2009 by { Cattiaux, P., Collet, P., Lambert, A., Martínez, S., Méléard, S., San Martín, where some sufficient conditions were provided to prove the existence and uniqueness of QSD in the context of a family of Population Dynamic Models. This work generalizes the most important theorems of this work, since no extra conditions are imposed to get the existence, uniqueness of QSD and the existence of a Yaglom limit. The technical part is based on the Sturm Liouville theory on the half line. In Chapter 2, we study the problem of getting quasi additive bounds on the Hamiltonian for the Long Range Ising Model when the interaction term decays according to d^{2-a}, a ϵ[0,1). This work is based on the previous paper written by Cassandro, Ferrari, Merola, Presutti, where quasi-additive bounds for the Hamiltonian were obtained for a in [0,(log3/log2)-1) in terms of hierarchical structures called triangles and Contours. The main theorems of this work can be summarized as follows: 1 There does not exist a quasi additive bound for the Hamiltonian in terms of triangles when a ϵ [0,(log3/log2)-1), 2. There exists a quasi additive bound for the Hamiltonian in terms of Contours for a in [0,1).

Orientador: Dionízio Paschoareli Júnior / Resumo: Resumo / Doutor

L’environnement opérationnel des pales et des structures porteuses des hydroliennes est de nature incertaine, compte tenu de la variabilité de l’écoulement (turbulence, sillage, houle, courants. . .). Ces éléments structuraux subissent donc des états de contraintes multiaxiaux complexes avec des fortes variations temporelles à caractère aléatoire. Ainsi, le dimensionnement basé sur des critères statiques déterministes apparaît insuffisant pour tenir compte de la complexité de l’histoire du chargement mécanique et de sa variabilité.Ce travail vise à établir des méthodes de dimensionnement adaptées à cette situation, pour la conception de structures hydroliennes aux risques et aux coûts maîtrisés. La démarche adoptée repose sur la description de l’écoulement et de ses grandeurs statistiques, afin de caractériser les efforts exercés sur l’hydrolienne et les contraintes mécaniques extrêmes en pied de pale. / The operating environment of tidal turbines blades and body is uncertain, due to the flow variability (turbulence,wake, tide, streams...). These structural elements then undergo strongly time-varying complex multi-axial random stress states. A design based on static and deterministic criteria thus appears insufficient to take the complexity and the variability of the mechanical loading into account. This work aims at setting sizing methods that are adapted to this situation, in order to design tidal turbines with mastered risks and costs. The proposed method lies on a statistical description of the flow, in order to characterize the load of the turbine and the extreme mechanical stresses at the blade foot.

Ce sujet de thèse s'intéresse à l'étude des effets des charges aérodynamiques sur le comportement dynamique non linéaire d'une éolienne à axe vertical de type Darrieus. Cette dernière présente, comparativement aux autres éoliennes, des profits très importants à exploiter, notamment dans les milieux urbains. Il s'agit d'une technologie fiable caractérisée surtout par son fonctionnement omnidirectionnel ainsi que son adaptation à tout type de vent. Généralement, ces éoliennes, ayant des phénomènes aérodynamiques complexes, sont affectées par des vibrations au niveau de leur système de transmission de puissance. En fait, ces vibrations commencent à se manifester à partir des pales du rotor jusqu'au génératrice. L'écoulement autour de ses pales présente également un fort caractère instationnaire. Cette caractéristique augmente d'avantage les vibrations aérodynamiques, qui sont automatiquement transmise au système d'engrenage d'éolienne. À ce niveau, nous avons développé un code de calcul numérique permettant de simuler la complexité des aspects aérodynamiques instationnaires tout en gardant un compromis entre la fiabilité des prédictions et la rapidité de calcul. Les simulations sont réalisées suivant une méthode de mécanique des fluides numérique (CFD) instationnaire bidimensionnel. Les résultats de simulation comparés avec ceux disponibles dans la littérature sont en bonne concordance, le rendement aérodynamique étant optimisé, qui présente un apport scientifique notable. Cette étude numérique a été l'objectif de l'analyse de l'impact des charges aérodynamiques vis-à-vis le comportement dynamique du système d'engrenage de l'éolienne en régime non-stationnaire. Dans ce contexte, une étude paramétrique a été développée afin d'établir le fonctionnement optimal de l'éolienne, caractérisé par un couple aérodynamique plus performant associé à des niveaux de vibrations dynamiques acceptables. En général, il est difficile d'identifier précisément la réponse dynamique des éoliennes à cause du caractère turbulent et stochastique des charges aérodynamiques. Par conséquent, il est indispensable de tenir en compte la variabilité des paramètres d'entrée pour assurer la robustesse du système étudié. Adoptons l'objectif de dimensionnement robuste. Une méthode d'évaluation basée sur des approches stochastiques, particulièrement la méthode du Chaos Polynomial, est utilisée pour simuler le comportement dynamique non-linéaire du système d'engrenage d'éolienne, en tenant compte des incertitudes. Ces dernières sont au niveau des charges aérodynamiques, inhérentes au calcul des niveaux vibratoires du système d'engrenage. Ce qui implique un apport scientifique important. Les résultats obtenus par l'approximation par Chaos Polynomial démontrent une forte dispersion des charges aérodynamiques aléatoires dans la réponse dynamique du système d'engrenage, contrairement aux études déterministes. Ce qui prouve l'insuffisance de telles études pour une analyse de robustesse. Les résultats mettent également en évidence la forte corrélation entre les phénomènes aérodynamiques complexes et les vibrations dynamiques. Le couplage établi constitue l'originalité de notre travail. / This thesis focuses on the study of the aerodynamic loads effects on the nonlinear dynamic behavior of Darrieus--type vertical axis wind turbine. The latter has received more attention due to its efficiency in urban regions compared to other wind turbines. In fact, the wind flow speed in urban regions continuously changes direction and is extremely turbulent. The inherent characteristics of its omni-directionality make it more suitable to harnessing this kind of flow. It is known that Darrieus wind turbine is characterized by an inherently unsteady aerodynamic behavior and a complex flow around rotor blades. The non-stationary behavior of the mentioned turbine increases vibration. These aerodynamic vibrations are transmitted to the gearing mechanism. We have, firstly, developed a numerical simulation, allowing to simulate the complexity of the unsteady aerodynamic phenomena keeping a compromise between the reliability of prediction and the rapidity of calculation. This numerical simulation has been carried out using a two-dimensional unsteady Computational Fluid Dynamics (CFD) method. Simulation results compared to those available in the literature are in good agreement. The Darrieus turbine efficiency is also optimized; thus introducing a significant scientific contribution. The latter is the objective of analyzing the aerodynamic load impact in the dynamic behavior of the Darrieus turbine in non-stationary regime. In this context, a parametric study has been developed in order to find optimal functioning of the studied turbine, which is characterized by the most performing aerodynamic torque associated with acceptable levels of dynamic vibration. In general, it is difficult to predict the dynamic response of the wind turbine with a good level of accuracy due to the aerodynamic loads turbulence and uncertain characteristics. It becomes necessary to take into account the uncertainty in the input parameters to ensure the robustness of the Darrieus turbine geared system. In a robustness study objective, the Polynomial Chaos method is adopted to predict the nonlinear dynamic behavior of the gearing system taking into account uncertainties which are associated to the performance coefficient of the input aerodynamic torque. This leads to an important scientific research contribution. The results have shown a large dispersion of the random parameter in the dynamic response of the gearing system compared to the deterministic study. That proves the insufficiency of that study for a robustness analyses. They have also proved that the Polynomial Chaos method is an efficient probabilistic tool for uncertainty propagation. Finally, the new proposed robust mechanical analysis indicates a good capacity to investigate the dynamic behavior of the Darrieus turbine thanks to its superior predictive capabilities in coupling complex aerodynamic phenomena with a mechanical gearing system vibration. Where the originality of such correlation in our work.

Les grandes matrices de covariance constituent certainement l’un des modèles les plus utiles pour les applications en statistiques en grande dimension, en communication numérique, en biologie mathématique, en finance, etc. Les travaux de Marcenko et Pastur (1967) ont permis de décrire le comportement asymptotique de la mesure spectrale de telles matrices formées à partir de N copies indépendantes de n observations d’une suite de variables aléatoires iid et sa convergence vers une distribution de probabilité déterministe lorsque N et n convergent vers l’infini à la même vitesse. Plus récemment, Merlevède et Peligrad (2016) ont démontré que dans le cas de grandes matrices de covariance issues de copies indépendantes d’observations d’un processus strictement stationnaire centré, de carré intégrable et satisfaisant des conditions faibles de régularité, presque sûrement, la distribution spectrale empirique convergeait étroitement vers une distribution non aléatoire ne dépendant que de la densité spectrale du processus sous-jacent. En particulier, si la densité spectrale est continue et bornée (ce qui est le cas des processus linéaires dont les coefficients sont absolument sommables), alors la distribution spectrale limite a un support compact. Par contre si le processus stationnaire exhibe de la longue mémoire (en particulier si les covariances ne sont pas absolument sommables), le support de la loi limite n'est plus compact et des études plus fines du comportement des valeurs propres sont alors nécessaires. Ainsi, cette thèse porte essentiellement sur l’étude des asymptotiques et des fluctuations des plus grandes valeurs propres de grandes matrices de covariance associées à des processus stationnaires à longue mémoire. Dans le cas où le processus stationnaire sous-jacent est Gaussien, l’étude peut être simplifiée via un modèle linéaire dont la matrice de covariance de population sous-jacente est une matrice de Toeplitz hermitienne. On montrera ainsi que dans le cas de processus stationnaires gaussiens à longue mémoire, les fluctuations des plus grandes valeurs propres de la grande matrice de covariance empirique convenablement renormalisées sont gaussiennes. Ce comportement indique une différence significative par rapport aux grandes matrices de covariance empirique issues de processus à courte mémoire, pour lesquelles les fluctuations de la plus grande valeur propre convenablement renormalisée suivent asymptotiquement la loi de Tracy-Widom. Pour démontrer notre résultat de fluctuations gaussiennes, en plus des techniques usuelles de matrices aléatoires, une étude fine du comportement des valeurs propres et vecteurs propres de la matrice de Toeplitz sous-jacente est nécessaire. On montre en particulier que dans le cas de la longue mémoire, les m plus grandes valeurs propres de la matrice de Toeplitz convergent vers l’infini et satisfont une propriété de type « trou spectral multiple ». Par ailleurs, on démontre une propriété de délocalisation de leurs vecteurs propres associés. Dans cette thèse, on s’intéresse également à l’universalité de nos résultats dans le cas du modèle simplifié ainsi qu’au cas de grandes matrices de covariance lorsque les matrices de Toeplitz sont remplacées par des matrices diagonales par blocs / Large covariance matrices play a fundamental role in the multivariate analysis and high-dimensional statistics. Since the pioneer’s works of Marcenko and Pastur (1967), the asymptotic behavior of the spectral measure of such matrices associated with N independent copies of n observations of a sequence of iid random variables is known: almost surely, it converges in distribution to a deterministic law when N and n tend to infinity at the same rate. More recently, Merlevède and Peligrad (2016) have proved that in the case of large covariance matrices associated with independent copies of observations of a strictly stationary centered process which is square integrable and satisfies some weak regularity assumptions, almost surely, the empirical spectral distribution converges weakly to a nonrandom distribution depending only on the spectral density of the underlying process. In particular, if the spectral density is continuous and bounded (which is the case for linear processes with absolutely summable coefficients), the limiting spectral distribution has a compact support. However, if the underlying stationary process exhibits long memory, the support of the limiting distribution is not compact anymore and studying the limiting behavior of the eigenvalues and eigenvectors of the associated large covariance matrices can give more information on the underlying process. This thesis is in this direction and aims at studying the asymptotics and the fluctuations of the largest eigenvalues of large covariance matrices associated with stationary processes exhibiting long memory. In the case where the underlying stationary process is Gaussian, the study can be simplified by a linear model whose underlying population covariance matrix is a Hermitian Toeplitz matrix. In the case of stationary Gaussian processes exhibiting long memory, we then show that the fluctuations of the largest eigenvalues suitably renormalized are Gaussian. This limiting behavior shows a difference compared to the one when large covariance matrices associated with short memory processes are considered. Indeed in this last case, the fluctuations of the largest eigenvalues suitably renormalized follow asymptotically the Tracy-Widom law. To prove our results on Gaussian fluctuations, additionally to usual techniques developed in random matrices analysis, a deep study of the eigenvalues and eigenvectors behavior of the underlying Toeplitz matrix is necessary. In particular, we show that in the case of long memory, the largest eigenvalues of the Toeplitz matrix converge to infinity and satisfy a property of “multiple spectral gaps”. Moreover, we prove a delocalization property of their associated eigenvectors. In this thesis, we are also interested in the universality of our results in the case of the simplified model and also in the case of large covariance matrices when the Toeplitz matrices are replaced by bloc diagonal matrices

<div>Researchers and scientists across various areas face the perennial challenge of selecting experimental conditions or inputs for computer simulations in order to achieve promising results.</div><div> The aim of conducting these experiments could be to study the production of a material that has great applicability.</div><div> One might also be interested in accurately modeling and analyzing a simulation of a physical process through a high-fidelity computer code.</div><div> The presence of noise in the experimental observations or simulator outputs, called aleatory uncertainty, is usually accompanied by limited amount of data due to budget constraints.</div><div> This gives rise to what is known as epistemic uncertainty. </div><div> This problem of designing of experiments with limited number of allowable experiments or simulations under aleatory and epistemic uncertainty needs to be treated in a Bayesian way.</div><div> The aim of this thesis is to extend the state-of-the-art in Bayesian optimal design of experiments where one can optimize and infer statistics of the expensive experimental observation(s) or simulation output(s) under uncertainty.</div>

Experimentos nos quais uma ou mais variáveis respostas são influênciadas por diversos fatores quantitativos são bastante comuns nas áreas agrícola, química, biológica, dentre outras. Nesse caso, o problema de pesquisa consiste em se estudar essa relação, sendo de grande utilidade o uso da metodologia de superfícies de resposta (MSR). Nesse contexto, a determinação dos níveis dos fatores que otimizam a resposta consiste inicialmente na obtenção das coordenadas do ponto estacionário do modelo ajustado. No entanto, como o modelo verdadeiro é desconhecido, é interessante obter uma região de confiança das coordenadas verdadeiras de modo a avaliar a precisão da estimativa obtida. Foram abordados aqui os procedimentos para construção de regiões de confiança para as coordenadas do ponto estacionário em diferentes situações considerando-se a forma das superfícies analisadas e a distribuição e magnitude da variância dos erros do modelo. Foram utilizadas a metodologia de Box e Hunter (1954) (BH), "bootstrap" e "bootstrap" Bayesiano aliados ao cálculo da distância de Mahalanobis entre as coordenadas do ponto estacionários da amostra observada e aquelas obtidas por meio das estimativas "bootstrap"(BM e BBM), e métodos "bootstrap" e "bootstrap" Bayesiano aliados a métodos não paramétricos de estimação de funções densidade de probabilidade (BNP e BBNP). A avaliaçãoda metodologia foi realizada por meio de simulação e foi aplicada a um conjunto de dados de produção de amendoim. No estudo de simulação, a metodologia BH, baseada na distribuição normal dos erros, apresentou um bom desempenho em todas as situações analisadas, havendo concordância entre as regiões de confiança nominais e reais, mesmo naquelas em que essa distribuição é bastante assimétrica. Este mesmo comportamento foi observado para os métodos BM e BBM. No entanto, os métodos BNP e BBNP não apresentaram um desempenho satisfatório, resultando em um nível de significância real menor que o nominal para os autovalores com menor valor absoluto, gerando regiões de confiança maiores. No caso de autovalores com maior valor absoluto observou-se situação inversa. No caso da análise do conjunto de dados de amendoim os métodos BH, BM e BNP apresentaram regiões de confiança mais amplas comparativamente aos métodos BBM e BBNP. No entanto, os valores das estimativas do "bootstrap" Bayesiano são mais próximas das estimativas de mínimos quadrados e apresentam menor dispersão o que explica a menor área da região de confiança. / Experiments in which one or more response variables are influenced by several quantitative factors are very common in agricultural, chemistry, biology and other areas. In this case, the research question consists in studying this relation, being of great utility the use of response surface methodology (RSM). In this context determining the level of the factors that optimize the response consists finding the coordinates of the stationary point of the model. However, as the true model is unknown, it is of interest to obtain a confidence region of the true coordinates to analyze the precision of the obtained estimate. The procedures for the construction of confidence regions for the coordinates of the stationary point were studied in diferent situations, considering the shape of the surfaces analyzed and the distribution and magnitude of the variance errors. The methodology of Box and Hunter (1954) (BH), bootstrap and Bayesian bootstrap with Mahalanobis distance among the coordinates of the stationary point of the observed sample and those obtained using bootstrap estimates(BM and BBM) and bootstrap and Bayesian bootstrap with non-parametric methods for density estimation (BNP and BBNP) were compared. The methodology evaluation was realized by means of simulation and applied to a peanut yields data set. In simulation study the BH methodology, which is based in normal distribution of errors, presented a good performance in all of the analyzed situations, having concordance among the nominal and real confidence regions, even in those which this distribution is fairly asymmetric. This behavior was also observed in BM and BBM methods. The BNP and BBNP methods did not presented a satisfactory performance, resulting in a real significance level lower than the nominal for the eigenvalue with lower absolute value, generating bigger confidence regions. The inverse was observed using eigenvalue with higher absolute value. In the analysis of the peanut yields data set the BH, BM and BNP methods presented confidence regions larger than the BBM and BBNP methods. The Bayesian bootstrap estimate values are closer of the minimum square estimates and present less dispersion what explain the confidence region lower area.