Neste trabalho são apresentadas algumas extensões dos modelos potência-alfa assumindo o contexto em que as observações estão censuradas ou limitadas. Inicialmente propomos um novo modelo assimétrico que estende os modelos t-assimétrico (Azzalini e Capitanio, 2003) e t-potência (Zhao e Kim, 2016) e inclui a distribuição t de Student como caso particular. Este novo modelo é capaz de ajustar dados com alto grau de assimetria e curtose, ainda maior do que os modelos t-assimétrico e t-potência. Em seguida estendemos o modelo t-potência às situações em que os dados apresentam censura, com alto grau de assimetria e caudas pesadas. Este modelo generaliza o modelo de regressão linear t de Student para dados censurados por Arellano-Valle et al. (2012). O trabalho também introduz o modelo linear misto normal-potência para dados assimétricos. Aqui a inferência estatística é realizada desde uma perspectiva clássica usando o método de máxima verossimilhança junto com o método de integração numérica de Gauss-Hermite para aproximar as integrais envolvidas na função de verossimilhança. Mais tarde, o modelo linear com interceptos aleatórios para dados duplamente censurados é estudado. Este modelo é desenvolvido sob a suposição de que os erros e os efeitos aleatórios seguem distribuições normal-potência e normal- assimétrica. Para todos os modelos estudados foram realizados estudos de simulação a fim de estudar as suas bondades de ajuste e limitações. Finalmente, ilustram-se todos os métodos propostos com dados reais. / In this work some extensions of the alpha-power models are presented, assuming the context in which the observations are censored or limited. Initially we propose a new asymmetric model that extends the skew-t (Azzalini e Capitanio, 2003) and power-t (Zhao e Kim, 2016) models and includes the Students t-distribution as a particular case. This new model is able to adjust data with a high degree of asymmetry and cursose, even higher than the skew-t and power-t models. Then we extend the power-t model to situations in which the data present censorship, with a high degree of asymmetry and heavy tails. This model generalizes the Students t linear censored regression model t by Arellano-Valle et al. (2012) The work also introduces the power-normal linear mixed model for asymmetric data. Here statistical inference is performed from a classical perspective using the maximum likelihood method together with the Gauss-Hermite numerical integration method to approximate the integrals involved in the likelihood function. Later, the linear model with random intercepts for doubly censored data is studied. This model is developed under the assumption that errors and random effects follow power-normal and skew-normal distributions. For all the models studied, simulation studies were carried out to study their benefits and limitations. Finally, all proposed methods with real data are illustrated.

Submitted by Livia Mello (liviacmello@yahoo.com.br) on 2016-09-23T19:10:12Z No. of bitstreams: 1 TeseEBS.pdf: 936379 bytes, checksum: a7cd0812b331249755b7a9df5447e035 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-10T14:48:37Z (GMT) No. of bitstreams: 1 TeseEBS.pdf: 936379 bytes, checksum: a7cd0812b331249755b7a9df5447e035 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-10T14:48:44Z (GMT) No. of bitstreams: 1 TeseEBS.pdf: 936379 bytes, checksum: a7cd0812b331249755b7a9df5447e035 (MD5) / Made available in DSpace on 2016-10-10T14:48:50Z (GMT). No. of bitstreams: 1 TeseEBS.pdf: 936379 bytes, checksum: a7cd0812b331249755b7a9df5447e035 (MD5) Previous issue date: 2016-02-04 / Não recebi financiamento / In regression models in which a covariate is measured with error, it is common to use structures that correlate the observed covariate with the true non-observed covariate. Such structures are usually additive or multiplicative. In the literature there are several interesting works that deal with regression models having an additive measurement error, many of which are linear models with covariate and measurement error normally distributed. For models having a multiplicative measurement error, one does not find in the literature the same theoretical amount of works as one finds for models in which the measurement error is additive. The same happens in situations where the supositions of normality for the covariates and the measurement errors do not apply. The present work proposes the construction, definition, estimation methods, and diagnostic analysis for the regression models with a multiplicative measurement error in one of the covariates. For these models it is considered that the response variable may belong either to the class of modified power series regression models or to the exponential family. The list of distributions belonging to the family modified power series is rather comprehensive; for this reason this work develops, firstly and in a general way, the models estimation and validation theory, and, as an example, presents the model of negative binomial regression with measurement error. In the case where the response variable belongs to the exponential family, the model of beta regression with multiplicative measurement error is presented. All proposed models were analysed through simulation studies and applied to real data sets. / Em modelos de regressão em que uma covariável é medida com erro, é comum o uso de estruturas que relacionam a covariável observada com a verdadeira covariável não observada. Essas estruturas são usualmente aditivas ou multiplicativas. Na literatura existem diversos trabalhos interessantes que tratam de modelos de regressão com erro de medida aditivo, muitos dos quais são modelos lineares com covariáveis e erro de medida normalmente distribuídos. Para modelos em que o erro de medida é multiplicativo, não se encontra na literatura o mesmo desenvolvimento teórico encontrado para modelos em que o erro de medida é aditivo. O mesmo vale para situações em que as suposições de normalidade para as covariáveis e erro de medida não se aplicam. Este trabalho propõe a construção, definição, métodos de estimação e análise de diagnóstico para modelos de regressão com erro de medida multiplicativo em uma das covariáveis. Para esses modelos, consideramos que a variável resposta possa pertencer ou à classe de modelos de regressão série de potências modificadas ou à família exponencial. O rol de distribuições pertencentes à família série de potências modificada é bem abrangente, portanto, neste trabalho, desenvolvemos a teoria de estimação e validação do modelo primeiramente de forma geral e, para exemplificar, apresentamos o modelo de regressão binomial negativa com erro de medida. Para o caso em que a variável resposta pertença à família exponencial, apresentamos o modelo de regressão beta com erro de medida multiplicativo. Todos os modelos propostos foram analisados através de estudos de simulação e aplicados a conjuntos de dados reais.

Submitted by Luanna Matias (lua_matias@yahoo.com.br) on 2015-02-04T20:56:59Z No. of bitstreams: 2 Dissertação - Augusta Finotti Brazão - 2014.pdf: 4325407 bytes, checksum: ed015d93a79ebdcbed577af5e0f9a797 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-02-05T09:48:34Z (GMT) No. of bitstreams: 2 Dissertação - Augusta Finotti Brazão - 2014.pdf: 4325407 bytes, checksum: ed015d93a79ebdcbed577af5e0f9a797 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-02-05T09:48:34Z (GMT). No. of bitstreams: 2 Dissertação - Augusta Finotti Brazão - 2014.pdf: 4325407 bytes, checksum: ed015d93a79ebdcbed577af5e0f9a797 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-04-04 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The present study aims to investigate the influence of uncertainties in physical and geometric parameters to obtain the load parametric instability of cylindrical shell, using the Galerkin method with the stochastic polynomial Hermite-Caos. The nonlinear equations of motion of the cylindrical shell are deduced from their functional power considering the strain field proposed by Donnell´s nonlinear shallow shell theory. The uncertainties are considered as random parameters with probability density function known in the partial differential equation of motion of the cylindrical shell, which it becomes a stochastic partial differential equation due to the presence of randomness. First, the discretization of the stochastic problem is performed using the stochastic Galerkin method together with polynomial Hermite-Chaos, to transform the stochastic partial differential equation into a set of equivalent deterministic partial differential equations, which take into account the randomness of the system. Then, the discretization of the lateral field displacement is made by a perturbation procedure, indicating the nonlinear vibration modes which couple to the linear vibration mode. The set of partial differential equations is transformed into a deterministic system of equations deterministic ordinary second order in time. Uncertainty is considered in one of its parameters: the Young modulus, thickness and amplitude of initial geometric imperfection. Then we analyze the influence of randomness in two parameters simultaneously: the thickness and the Young modulus. Once obtained the system of ordinary differential equations deterministic containing the randomness of the parameters, the integration over discrete time system is made from the Runge- Kutta fourth order to obtain results as the time response, bifurcation diagrams and boundaries of instability which are compared with deterministic analysis, indicating that polynomial Hermite-Chaos is a good numerical tool for predicting the load parametric instability without the need to perform a process of sampling. / O presente trabalho tem como objetivo investigar a influência de incertezas nos parâmetros físicos e geométricos para a determinação da carga de instabilidade paramétrica da casca cilíndrica, utilizando o método de Galerkin Estocástico juntamente com o polinômio de Hermite-Caos. As equações não-lineares de movimento da casca cilíndrica são deduzidas a partir de seus funcionais de energia considerando o campo de deformações proposto pela teoria não linear de Donnell para cascas esbeltas. As incertezas são consideradas como parâmetros aleatórios com função de densidade de probabilidade conhecida na equação diferencial parcial de movimento da casca cilíndrica, que passa a ser uma equação diferencial parcial estocástica devido à presença da aleatoriedade. Primeiramente, faz-se a discretização do problema estocástico utilizando o método de Galerkin Estocástico juntamente com o polinômio de Hermite-Caos, para transformar a equação diferencial parcial estocástica em um conjunto de equações diferenciais parciais determinísticas equivalentes, que levem em consideração a aleatoriedade do sistema. Em seguida, apresenta-se a discretização do campo de deslocamentos laterais através do Método da Perturbação, indicando os modos não-lineares de vibração que se acoplam ao modo linear de vibração, para que o conjunto de equações diferenciais parciais determinísticas seja transformado em um sistema de equações ordinárias determinísticas de segunda ordem no tempo. A incerteza é considerada inicialmente em apenas um de seus parâmetros: no módulo de elasticidade, na espessura e na amplitude da imperfeição geométrica inicial. Em seguida, analisa-se a influência de aleatoriedades em dois parâmetros simultaneamente, sendo eles: a espessura e o módulo de elasticidade. Uma vez obtido o sistema de equações diferenciais ordinárias determinísticas que contêm as aleatoriedades dos parâmetros, a integração ao longo do tempo do sistema discretizado é feita a partir do método de Runge-Kutta de quarta ordem, obtendo-se resultados como resposta no tempo, diagramas de bifurcação e fronteiras de instabilidade, que são comparados com análises determinísticas, indicando que o polinômio de Hermite-Caos é uma boa ferramenta numérica para prever a carga de instabilidade paramétrica sem a necessidade de se realizar um processo de amostragens.

This thesis is divided into three parts. In the first part we study mixed norm estimates for Riesz transforms associated with various differential operators. First we prove the mixed norm estimates for the Riesz transforms associated with Dunkl harmonic oscillator by means of vector valued inequalities for sequences of operators defined in terms of Laguerre function expansions. In certain cases, the result can be deduced from the corresponding result for Hermite Riesz transforms, for which we give a simple and an independent proof. The mixed norm estimates for Riesz transforms associated with other operators, namely the sub-Laplacian on Heisenberg group, special Hermite operator on C^d and Laplace-Beltrami operator on the group SU(2) are obtained using their L^pestimates and by making use of a lemma of Herz and Riviere along with an idea of Rubio de Francia. Applying these results to functions expanded in terms of spherical harmonics, we deduce certain vector valued inequalities for sequences of operators defined in terms of radial parts of the corresponding operators. In the second part, we study the chaotic behavior of the heat semigroup generated by the Dunkl-Laplacian ∆_κ on weighted L^P-spaces. In the general case, for the chaotic behavior of the Dunkl-heat semigroup on weighted L^p-spaces, we only have partial results, but in the case of the heat semigroup generated by the standard Laplacian, a complete picture of the chaotic behavior is obtained on the spaces L^p ( R^d,〖 (φ_iρ (x ))〗^2 dx) where φ_iρ the Euclidean spherical function is. The behavior is very similar to the case of the Laplace-Beltrami operator on non-compact Riemannian symmetric spaces studied by Pramanik and Sarkar. In the last part, we study mixed norm estimates for the Cesáro means associated with Dunkl-Hermite expansions on〖 R〗^d. These expansions arise when one considers the Dunkl-Hermite operator (or Dunkl harmonic oscillator)〖 H〗_κ:=-Δ_κ+|x|^2. It is shown that the desired mixed norm estimates are equivalent to vector-valued inequalities for a sequence of Cesáro means for Laguerre expansions with shifted parameter. In order to obtain the latter, we develop an argument to extend these operators for complex values of the parameters involved and apply a version of Three Lines Lemma.

Dans cette thèse, nous étudions des algorithmes pour un problème de recherche de relations à une ou plusieurs variables. Il généralise celui de calculer une solution à un système d’équations linéaires modulaires sur un anneau de polynômes, et inclut par exemple le calcul d’approximants de Hermite-Padé ou d’interpolants bivariés. Plutôt qu’une seule solution, nous nous attacherons à calculer un ensemble de générateurs possédant de bonnes propriétés. Précisément, l’entrée de notre problème consiste en un module de dimension finie spécifié par l’action des variables sur ses éléments, et en un certain nombre d’éléments de ce module ; il s’agit de calculer une base de Gröbner du modules des relations entre ces éléments. En termes d’algèbre linéaire, l’entrée décrit une matrice avec une structure de type Krylov, et il s’agit de calculer sous forme compacte une base du noyau de cette matrice. Nous proposons plusieurs algorithmes en fonction de la forme des matrices de multiplication qui représentent l’action des variables. Dans le cas d’une matrice de Jordan,nous accélérons le calcul d’interpolants multivariés sous certaines contraintes de degré ; nos résultats pour une forme de Frobenius permettent d’accélérer le calcul de formes normales de matrices polynomiales univariées. Enfin, dans le cas de plusieurs matrices denses, nous accélérons le changement d’ordre pour des bases de Gröbner d’idéaux multivariés zéro-dimensionnels. / In this thesis, we study algorithms for a problem of finding relations in one or several variables. It generalizes that of computing a solution to a system of linear modular equations over a polynomial ring, including in particular the computation of Hermite- Padéapproximants and bivariate interpolants. Rather than a single solution, we aim at computing generators of the solution set which have good properties. Precisely, the input of our problem consists of a finite-dimensional module given by the action of the variables on its elements, and of some elements of this module; the goal is to compute a Gröbner basis of the module of syzygies between these elements. In terms of linear algebra, the input describes a matrix with a type of Krylov structure, and the goal is to compute a compact representation of a basis of the nullspace of this matrix. We propose several algorithms in accordance with the structure of the multiplication matrices which specify the action of the variables. In the case of a Jordan matrix, we accelerate the computation of multivariate interpolants under degree constraints; our result for a Frobenius matrix leads to a faster algorithm for computing normal forms of univariate polynomial matrices. In the case of several dense matrices, we accelerate the change of monomial order for Gröbner bases of multivariate zero-dimensional ideals.

Dans la première partie de la thèse, nous présentons un nouveau système permettant de produire des mouvements de caméra réalistes pour l’animation stopmotion. Le système permettra d’enrichir les logiciels d’animation 3D classiques (comme par exemple Maya et 3D Studio Max) afin de leur faire contrôler des mouvements de caméra pour la stop motion, grâce à l’utilisation d’une interface haptique. Nous décrivons le fonctionnement global du système. La première étapeconsiste à récupérer et enregistrer les données envoyées par le périphérique haptique de motion capture. Dans la seconde étape, nous réélaborons ces données par un procédé mathématique, puis les exportons vers un logiciel de 3D pour prévisualiser les mouvements de la caméra. Finalement la séquence est exécutée avec un robot de contrôle de mouvement et un appareil photo. Le système est évalué par un groupe d’étudiants du Master "Art plastiques et Création numérique" de l’Université de Valenciennes. Dans la deuxième partie, nous définissons une nouvelle classe de courbes à partir des courbes polynomiales paramétriques à hodographe pythagorien (PH) construite sur un espace algébrique-trigonométrique. Nous montrons leurs propriétés fondamentaleset leurs avantages importants par rapport à leur équivalent polynomial, grâce à l’utilisation d’un paramètre de forme. Nous introduisons une formulation complexe et nous résolvons le problème d’interpolation de Hermite. / In the first part, we present a new system that allows to create realistic cameramovements for a stop motion animation. The system improves traditional 3D software animation programs (for example Maya and 3D Studio Max) for creatingstop motion camera movements by using an haptic interface. After describing thewhole system, we explain in detail the mathematical processing to obtain differentcamera movements by using an haptic interface for motion capture. The recordedhaptic positions, once elaborated, are exported, frame by frame, to the motioncontrol software, which allows to calibrate the motion control robot, to control thecamera settings and, finally, to execute the sequences. A class of students of the"Art plastiques et Création numérique" Master of the University of Valenciennesevaluated the system. In the second part, we define a new class of Pythagorean Hodograph curves built upon a five dimensional mixed algebraic trigonometric space, and show their fundamental properties and important advantages over their well known polynomial counterpart. A complex representation for these curves is introduced and constructive approaches are provided to solve the first order Hermite interpolation problem.

壹、引言 近年來，訊號傳送的途徑，已擺脫了傳統上著重管線傳送的優勢；有愈來愈多的訊號 彌漫在廣闊的空間裡，而這種無線式的傳送所需面臨的問題是：不具有排它性，任何 有接收器材的非原始接收者都可以截聽到訊息，由於因應而生的保密技術格外受矚目 ，密碼學（CRYPTOGRAPHY）便是滿足此需要的學問。本論文所探討的排列多項式（PE RMUTATION POLYNOMIAL）是密碼學中重要的工具之一。 貳、論文主體 所謂排列多項式，即是佈於代數體上的多項式，把此多項式當成函數而作用於代數體 （FIELD ）上，如果此函數具有一對一的性質，則是排列多項式。即 ｆ（ｘ）＝ａ。+ ａ1 ｘ1 + ....ａnｘn ≡ Ｆq〔Ｘ〕且 ｆ（ａ）╪ｆ（ｂ），ａ，ｂ≡Ｆｑ，ａ╪ｂ． 在論文中，介紹先進學者對排列多項式的認識。如：LAGRANGE'S INTERPOLATION是利 用函數值來描繪多項式，著名的學者CARLITZ ，利用特殊多項式來合成出排列多項式 ，論文中有更進一步的合成法提出，而HERMITE 跟DICKSON 學者則提出Ft函數其冪次 的變化情形，來判別排列多項式之是否，是最通俗的判別理論。 此外，由吾人所蒐集的資料中發現，在祗有兩項的多項式中，被發現到其它更簡捷快 速的判別方法，故二項式的多項式的探討是本論文的第一主題，對於 k j Ｘ＋ｂｘ ≡Ｆｑ〔Ｘ〕， 給予固定類型的ｑ，ｋ，ｊ情形下，祗須檢定ｂ是否具特 殊性質就可決定是否為排列多項式，這是一種方法。另有學者並不固定ｑ，ｋ，ｊ， 反而從ｑ，ｋ，ｊ數字下手，找尋出某種關連性，其結果使得係數ｂ，只有當ｂ＝０ ，時才有機會是排列多項式，乘下單項式的判別過程，就很容易了。另外還有一種方 法也是找尋ｑ，ｋ，ｊ間的關係，不過其結果在找出：多項式為非排列多項式，是比 較特別的地方。上述三方法，本論文網羅大部份有關論文，綜合各家之長，並適當給 予一同於原作者的新觀點證明方法。 至於本論文第二主題是著名的CARLITZ'S CONJECTURE此預測敘述：對於任何具有最高 冪次是偶數的多項式，必定存在一個自然數ｋ，使得給定的代數體，其元素個數只要 超過ｋ，則此多項式必定不是排列多項式。此預測當degree n=10,12,14, and 2m 時 已被證實為真。本論文僅就n=2m，做系統地探討及重新證明。 參、結語 本論文所論的兩主題，對於佈於代數體上的多項式是否為排列多項式，在判別的過程 上應有相當的助益才是。

Title: Non-newtonian fluid flow simulation using lattice Boltzmann method Author: Bc. Pavel Kuriščák Department: Mathematical Institute, Charles University Supervisor: RNDr. Ing. Jaroslav Hron Ph.D. Supervisor's e-mail address: Jaroslav.Hron@mff.cuni.cz Abstract: The aim of this thesis is to find and estabilish a modification to the Lattice Boltzmann Method, allowing it to simulate non-newtonian behaviour of fluids. In the theoretical part of thesis, there is introduced a derivation, based on the work of [22], that is capable of arriving to macroscopical Navier-Stokes equa- tions completely a priori from the Boltzmann equation, utilizing the Hermite basis expansion. This derivation is afterwards applied to the method suggested by [11], that uses the changed equilibrium distribution to fine-tune the local fluid viscosity according to the non-newtonian model. In the last part of thesis, this method is implemented in the form of lattice kinetic scheme and tested on three sample problems. Keywords: Lattice Boltzmann Method, non-newtonian fluids, Hermite expansion, lattice kinetic scheme

Ce mémoire est dédié à la caractérisation de contrôleurs PID stabilisants pour des systèmes monovariables du premier et du second ordre avec retard sur l'entrée. Les systèmes considérés sont linéaires stationnaires, asymptotiquement stables en boucle ouverte. Un aspect de robustesse est également pris en compte ou il s'agit ici de garantir la stabilité malgré une méconnaissance des paramètres du transfert se traduisant par l'appartenance de ces paramètres à des intervalles connus. Les résultats de Vladimir L. KHARITONOV sur les quasi-polynômes intervalles sont ici utilisés à bon escient. Enfin une heuristique (algorithme génétique) est proposée pour calculer des contrôleurs optimisant des critères usuels de type intégrale de l'erreur (ISE, IAE, ITAE, ITSE).

Aeroelastic behavior prediction is often confined to analytical or highly computational methods, so I developed a low degree of freedom computational method using structural finite elements and unsteady loading to cover a gap in the literature. Finite elements are readily suitable for determination of the free vibration characteristics of eccentric, elastic structures, and the free vibration characteristics fundamentally determine the aeroelastic behavior. I used Theodorsen’s unsteady strip loading formulation to model the aerodynamic loading on linear elastic structures assuming harmonic motion. I applied Hassig’s ‘p-k’ method to predict the flutter boundary of nonsymmetric, aeroelastic systems. I investigated the application of a quintic interpolation assumed displacement shape to accurately predict higher order characteristic effects compared to linear analytical results. I show that quintic interpolation is especially accurate over cubic interpolation when multi-modal interactions are considered in low degree of freedom flutter behavior for high aspect ratio HALE aircraft wings.