Consider the D-optimal designs for the dth-degree polynomial regression model with a bounded and positive weight function on a compact interval. As the degree of the model goes to infinity, we show that the D-optimal design converges weakly to the arcsin distribution. If the weight function is equal to 1, we derive the formulae of the values of the D-criterion for five classes of designs including (i) uniform density design; (ii) arcsin density design; (iii) J_{1/2,1/2} density design; (iv) arcsin support design and (v) uniform support design. The comparison of D-efficiencies among these designs are investigated; besides, the asymptotic expansions and limits of their D-efficiencies are also given. It shows that the D-efficiency of the arcsin support design is the highest among the first four designs.

Notre travail est motivé par le problème de l'évaluation du déterminant de Fredholm d'un opérateur intégral. Cet opérateur apparait dans l'expression de la probabilité pour qu'un intervalle [?s, s] (s > 0) ne contienne aucune valeur propre d'une matrice aléatoire hermitienne gaussienne. Cet opérateur commute avec un opérateur différentiel de second ordre dont les fonctions propres sont les fonctions d'ondes sphéroïdales de l'ellipsoïde alongé. Plus généralement nous considérons l'opérateur de Legendre perturbé. Nous montrons qu'il existe un opérateur de translation généralisée associé à cet opérateur. En?n, par une méthode d'approximation des solutions de certaines équations différentielles, dite méthode WKB, nous avons obtenu le comportement asymptotique des fonctions d'ondes sphéroïdales de l'ellipsoïde alongé Il s'exprime à l'aide des fonctions de Bessel et d'Airy. Par la même méthode nous avons obtenu le comportement asymptotique des fonctions propres de l'opérateur dfférentiel d'Airy.

A tese apresenta um método para a solução dos problemas do valor inicial (PVIs) com margens de erro comparáveis às de métodos numéricos consagrados (MN), tanto para a função quanto para suas derivadas. O método é aplicável a equações diferenciais (EDs) lineares ou não, sendo o ferramental desenvolvido até a quarta ordem, que pode ser expandido para ordens superiores. A solução é uma expressão polinomial de alto grau com coeficientes expressos pela razão entre dois inteiros. O método se mostra eficaz mesmo em alguns casos em que os MN não conseguiram dar a partida. As resoluções são obtidas considerando que o espaço de soluções é um espaço de Hilbert, equipado com a base completa dos polinômios de Legendre. Em decorrência do método aqui desenvolvido, os majorantes de erros para a função e derivadas são determinados analiticamente por um cálculo matricial também deduzido nesta tese. Paralelamente a toda fundamentação analítica, foi desenvolvido o software SAM, que automatiza todas as tarefas na busca de soluções dos PVIs. A tese propõe e verifica a validade de um novo critério de erro no qual pesam tanto os erros locais quanto os erros globais, simultaneamente. Como subprodutos dos resultados já descritos, igualmente integrados ao SAM, obtiveram-se também: (1) Um critério objetivo para analisar a qualidade de um MN, sem necessidade do conhecimento de seu algoritmo; (2) Uma ferramenta para aproximações polinomiais de alta precisão para funções de quadrado integrável em determinado intervalo limitado, com um majorante de erro; (3) Um ferramental analítico para transposição genérica (linear ou não) dos PVIs até 4ª ordem, nas mudanças de domínio; (4) As matrizes de integração e diferenciação genéricas para todas as bases polinomiais do espaço de Hilbert. / This thesis shows a new method to get polynomial solutions to the initial value problems (IVP), with an error margin comparable to the consecrate numerical methods (NM), for both the function and its derivatives. The method works with differential equations (DEs) linear or not, beeing the developed tolls available until 4th order, whose can be expanded to higher orders. The solution is a polynomial high degree expression with coefficients expressed by the ratio between two integers. The method behaves efficiently even in some cases that NM cannot get started. The resolutions are gotten considering that, the solution space is a Hilbert space, equipped with a complete set basis of Legendre Polynomials. Due the method here developed, the errors majoratives for the function and its derivatives are found analytically by a matrix calculus, also derived in this thesis. Beside all analytical foundation, a software (SAM) was developed to automate the whole process, joining all the tasks involved in the search for solutions to the IVP. This thesis proposes, verifies and validates a new error criterion, which takes in account simultaneously the local and global errors. As sub-products of the results described before, also integrated to the SAM, the following achievements should be highlighted: (1) An objective criterion to analyze the quality of any NM, despite of the knowledge of its algorithm; (2) A tool for a polynomial approximation, of high precision, for functions whose square is integrable in a given limited domain, with an errors majorative; (3) A tool-kit for a generically transpose (linear or not) of the IVPs domain and form, taking into account its derivatives, until the 4th order; (4) The generic matrices for integration and differentiation for all the polynomial basis of the Hilbert space.

Dans cette thèse, on manipule deux types d'objets fondamentaux de la topologie de contact : les sous-variétés legendriennes des espaces de 1-jets de fonctions dé finies sur une variété M, noté J1(M;R), et la notion intimement liée de fonctions génératrices. On étudie des "opérations" que l'on peut faire sur ces objets, c'est-à-dire des procédures qui construisent (génériquement) de nouvelles sous-variétés legendriennes à partir d'anciennes. On dé finit en particulier les opérations somme et convolution des sous-variétés legendriennes, qui sont conjuguées par une transformation de type transformée de Legendre. Nous montrons que ces opérations se refl ètent harmonieusement dans le monde des fonctions génératrices. Ce second point de vue nous conduit en particulier à nous interroger sur l'effet de nos opérations sur le sélecteur, notion classique de géométrie symplectique dont on adapte la construction à ce contexte. Pour fi nir, on se concentre sur l'espace à trois dimensions J1(R;R) et sur les noeuds legendriens qui admettent (globalement) une fonction génératrice. C'est une condition forte sur les sous-variétés legendriennes, que l'on choisit d'étudier en proposant plusieurs constructions explicites. On termine avec l'étude des notions de cobordisme legendrien naturellement associées, où l'opération somme évoquée plus s'avère tenir une place centrale. / This thesis concerns two types of fundamental objects of the contact topology : Legendrian submanifolds in 1-jet spaces of functions de fined on a manifold M, denoted by J1(M;R), and the closed related notion of generating functions. We study "operations" that build (generically) new Legendrian submanifolds from old ones. In particular, we de fined the operations sum and convolution of Legendrian submanifolds, which are linked by a form of the Legendre transform. We show how the operations are well re flected in terms of generating functions. It offers a second point of view and leads us to wonder the effect of our operations on the selector, which is a classical notion of symplectic geometry, and we adapt its construction to this context. Finally, we focus on the three dimensional space J1(R;R) and Legendrian knots which admit a (global) generating function. It is a strong condition for Legendrian submanifolds, and we choose to examine it by proposing several explicit constructions. We conclude by studying the notions of Legendrian cobordism which are naturally related. The operation sum mentioned before finds there a central role.

The K-distribution method is a fast approximative method used for calculating thermal infrared radiative transfer in the atmosphere, as opposed to the traditional Line-by-line method, which is precise, but very time-costly. Here we consider the atmosphere to consist of homogeneous and plane-parallel layers in local thermal equilibrium. This lets us use efficient upwards recursion for calculating the thermal infrared radiative transfer and ultimately the outgoing irradiance at the top of the atmosphere. Our specific implementation of the K-distribution method revolves around changing the integration space from the wavenumber domain to the g domain by employing Gauss-Legendre quadrature in two steps. The method is implemented in MATLAB and is shown to be several thousand times faster than the traditional Line-by-line method, with the relative error being only 3 % for the outgoing irradiance at the top of the atmosphere.

Draft tube is very important part of hydraulic turbines. Only optimum work together with turbine can bring highest performance of this machine set. Hence it is necessary to deal with character of flow in the draft tube for different operating conditions. Efficiency of the draft tube depends on many phenomena of flow. Observing these phenomena and finding their relation with energetic transformation in the draft tube is a suitable tool to judge quality of draft tube performance. Incorrect design of the draft tube can sometimes cause lower efficiency of whole machine set. The goal of this thesis is finding the main reasons causing draft tube efficiency drop for given operating conditions.

Made available in DSpace on 2016-04-28T14:16:13Z (GMT). No. of bitstreams: 1 Paulo Henrique Trentin.pdf: 779555 bytes, checksum: f4b3577b8c94884cbacb3620b3070ac2 (MD5) Previous issue date: 2011-05-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This thesis addresses the life and works of Manoel Ferreira de Araújo Guimarães (1777-1838), a major author in the History of Brazilian Mathematics. The study centers on the translation by Manoel Ferreira de Araújo Guimarães of Éleménts de Geométrie e Traité de Trigonométrie, written by Adrien Marie Legendre (1752-1833), as important contributions to the process of institutionalizing the teaching of Mathematics in Brazil at the beginning of the 19th century. The analysis of Guimarães´s translations helped shed light on the reasons that led the translator to propose changes and, based on the identification of some of his interlocutors, understand what directed Guimarães to the works of Adrien Marie Legendre. Regarding further works by the Brazilian mathematician, we have been able to identify, directly or indirectly, scholars who had access to his translated works. Therefore, this study is intended to contribute to researchers who seek to (re)study the period ranging from the beginning to the first half of the 19th century, on the teaching of Mathematics in Brazil / Este trabalho aborda a vida e a obra de Manoel Ferreira de Araújo Guimarães (1777-1838), personagem importante para o cenário da História da Matemática Brasileira. Centralizamos nosso estudo nas traduções das obras Éleménts de Geométrie e Traité de Trigonométrie de Adrien Marie Legendre (1752-1833), realizadas por Manoel Ferreira de Araújo Guimarães, como contribuições significativas para o processo de institucionalização do ensino da Matemática no Brasil, no início do século XIX. Analisando essas traduções pudemos compreender os motivos que levaram o tradutor a propor alterações e, a partir da identificação de alguns de seus interlocutores, compreender o que o levou aos trabalhos de Adrien Marie Legendre. Relativamente aos desdobramentos das produções de Manoel Ferreira de Araújo Guimarães, pudemos identificar, direta ou indiretamente, alguns nomes que tiveram acesso a suas traduções. Assim, este trabalho pretende contribuir com os pesquisadores que buscam empreender uma (re)leitura do período, que vai do início a meados do século XIX, relativo ao ensino da matemática no Brasil

No description available.

Traverses Adjustment in the surface of the ellipsoid with the objectives to guarantee the solution unicity in the transport of curvilinear geodesic coordinates (latitude and longitude) and in the azimuth transport and to get the estimates of quality. It deduces the coordinate transport and the azimuth transport by mean Legendre s series of the geodesic line. This series is based on the Taylor s series, where the argument is the length of the geodesic line. For the practical applications, it has the necessity to effect the truncation of the series and to calculate the function error for the latitude, the function error for the longitude and the function error for the azimuth. In this research, these series are truncated in the derivative third and calculates the express functions error in derivative fourth. It is described the adjustment models based on the least-squares method: combined model with weighted parameters, combined model or mixed model, parametric model or observations equations and correlates model or condition equations model. The practical application is the adjustment by mean parametric model of a traverse measured by the Instituto Brasileiro de Geografia e Estatística (IBGE), constituted of 8 vertices and the 129.661 km length. The localization of errors in the observations is calculated by the Baarda s data snooping test in the last iteration of the adjustment that showed some observations with error. The estimates of quality are in the variance-covariance matrices and calculate the semiaxes of the error ellipse or standard ellipse of each point by means of the spectral decomposition (or Jordan s decomposition) of the submatrices of the variance-covariance matrix of the adjusted parameters (the coordinates). It is important to note that the application of the Legendre s series is satisfactory for short distances until 40km length. The convergence of the series is fast for the adjusted coordinates, where the stopped criterion of the iterations is four decimals in the sexagesimal second arc, where it is obtained from interation second of the adjustment. / Ajustamento de linhas poligonais na superfície do elipsóide com os objetivos de garantir a unicidade de solução no transporte de coordenadas geodésicas curvilíneas (latitude ϕ e longitude λ ) e no transporte de azimute e de obter as estimativas de qualidade. Deduz o transporte de coordenadas e o transporte de azimute pelas séries de Legendre da linha geodésica. Essa série se fundamenta na série de Taylor, em que o argumento é o comprimento da linha geodésica. Para as aplicações práticas, há a necessidade de efetuar o truncamento da série e calcular a função erro para a latitude, função erro para a longitude e função erro para o azimute. Nesta pesquisa, trunca-se a série na derivada terceira e calculam-se as funções erro expressas em derivada quarta. Expõe os modelos de ajustamento fundamentados no método dos mínimos quadrados (MMQ): modelo combinado com ponderação aos parâmetros, modelo combinado ou implícito, modelo paramétrico ou das equações de observação e modelo dos correlatos ou das equações de condição. A aplicação prática é o ajustamento pelo modelo paramétrico de uma linha poligonal medida pelo Instituto Brasileiro de Geografia e Estatística (IBGE), constituída de 8 vértices e de comprimento igual a 129,661 km. A localização de erros nas observações é efetuada pelo teste data snooping de Baarda na última etapa do ajustamento que mostrou algumas observações com erro. As estimativas de qualidade estão nas matrizes variância-covariância (MVC) e calcula-se os semieixos da elipse dos erros (ou elipse padrão) de cada ponto mediante a decomposição espectral (ou decomposição de Jordan) das submatrizes da MVC dos parâmetros (as coordenadas) ajustados. Mostra-se que a aplicação das séries de Legendre é satisfatória para distâncias curtas até 40km. A convergência da série é rápida para as coordenadas ajustadas, onde o critério de parada das iterações seja quatro decimais do segundo de arco em que se atingiu na segunda etapa do ajustamento.

L'étude et l'introduction de nouveaux systèmes dynamiques<br /> de type gradient sont l'objet central de cette thèse. Le<br /> caractère dissipatif de telles dynamiques est au coeur de<br /> nombreux domaines en mathématiques : optimisation,<br /> mécanique, équations d'évolutions en dimension infinie.<br /><br />Dans une première partie, les champs de gradients (ou de sous-différentiels<br /> de fonction convexe) sont contrôlés à l'aide d'opérateurs-barrières. <br />La motivation essentielle est d'obtenir<br /> des méthodes intérieures de descente en vue d'optimiser<br /> une fonction sous des contraintes convexes. Le cadre<br /> d'étude proposé permet d'unifier dans un même formalisme de nombreuses<br /> méthodes continues : gradient projeté, plus grande pente riemannienne,<br /> méthode continue de Newton... Parmi les conséquences de <br />la généralisation proposée, on peut, par exemple, évoquer des <br /> résultats abstraits de viabilité et de convergence globale. Toujours <br />dans cette <br />perspective, les fonctions de Legendre jouent un rôle crucial~:<br /> elles permettent d'une part de donner lieu à des structures<br /> riemanniennes possédant de nombreuses propriétés - parmi lesquelles une<br /> propriété d'intégration caractéristique remarquable -, et d'autre part, <br /> elles fournissent en dimension infinie un cadre intéressant<br /> pour l'étude de certaines équations d'évolution de type<br /> parabolique.<br /><br />La deuxième partie est consacrée à l'étude de systèmes<br /> dynamiques du second ordre en temps avec une dissipation géométrique<br /> de type hessien. Outre leur intérêt en optimisation<br /> et leurs liens avec les méthodes de type Newton, ces systèmes<br /> sont d'une grande souplesse et permettent d'approcher certains <br />phénomènes non-lisses en mécanique unilatérale. En guise d'application,<br /> il est en effet prouvé que les systèmes considérés permettent <br />d'obtenir à la limite des dynamiques <br />satisfaisant des lois de chocs inélastiques. Les<br /> perspectives de cette étude ouvrent en particulier la voie à une approche <br />alternative de certains systèmes d'inégalités variationnelles de type <br />hyperbolique.<br /><br /><br />L'une des préoccupations majeures de cette thèse est la question<br /> de la convergence des orbites des systèmes étudiés. Dans le <br /> cadre de la minimisation convexe, quasi-convexe, ou analytique, de nombreux<br /> résultats sont proposés : convergence globale, , <br />vitesse de convergence, contrôle asymptotique, attractivité des <br /> minima sous contraintes en dimension infinie.