Made available in DSpace on 2015-03-03T15:32:44Z (GMT). No. of bitstreams: 1 AnnaRSM_DISSERT.pdf: 991497 bytes, checksum: 8cd89e56b698033013c824b49f639a4e (MD5) Previous issue date: 2014-01-30 / We present a dependent risk model to describe the surplus of an insurance portfolio, based on the article "A ruin model with dependence between claim sizes and claim intervals"(Albrecher and Boxma [1]). An exact expression for the Laplace transform of the survival function of the surplus is derived. The results obtained are illustrated by several numerical examples and the case when we ignore the dependence structure present in the model is investigated. For the phase type claim sizes, we study by the survival probability, considering this is a class of distributions computationally tractable and more general / Neste trabalho apresentamos um modelo de risco dependente para descrever o excedente de uma carteira de seguros, com base no artigo "A ruin model with dependence between claim sizes and claim intervals"(Albrecher e Boxma [1]). Obtemos uma express?o exata para a probabilidade de sobreviv?ncia atrav es da Transformada de Laplace da fun??o de sobreviv?ncia do superavit. Ilustramos os resultados obtidos atrav?s de exemplos num?ricos e investigamos o que acontece ao se ignorar a estrutura de depend?ncia presente no modelo. Estudamos tamb?m a probabilidade de sobreviv?ncia para indeniza??es que possuem distribui??o do Tipo Fase, considerando que esta ? uma classe de distribui??es, computacionalmente trataveis, bem mais geral

A aplicação de uma sequência de pulsos com tempo de repetição muito menor que os tempos de relaxação Tp << T2; T1, faz com que a magnetização atinja um estado estacionário descrito por H.Y. Carr como Estado Estacionário em Precessão Livre, Steady State Free Precession (SSFP). Nessa condição, o sinal é composto pela complexa sobreposição das componentes FID e eco. Sequências tipo SSFP são utilizadas na aquisição rápida de sinais, resultando em uma boa razão sinal ruído (s/r) em curto intervalo de tempo, porém introduzem fortes anomalias de fase e amplitude devido a complexa interação das componentes que formam o estado estacionário. Neste trabalho, desenvolvemos sequências de pulsos tipo SSFP para RMN em alta e baixa resolução com alternância e incremento de fase. Em alta resolução desenvolvemos as sequências SSFPdx e SSFPdxdt com incremento de fase linear e quadrático respectivamente. Os resultados mostram que espectros de núcleos com baixa sensibilidade podem ser obtidos com mesma razão s/r em menor tempo experimental e as sequências desenvolvidas removem as anomalias espectrais. Em baixa resolução, os resultados mostram que a introdução de alternâncias de fase na Continuous Wave Free Precession (CWFP) possibilita a remoção da dependência da sequência com o offset de frequência e com o tempo entre pulsos. Além disso, mostramos que a sequência CP-CWFPx-x com ângulo de refocalização pequeno (5&deg; a 10&deg;) possibilita a estimativa rápida do tempos de relaxação longitudinal. Apresentamos também resultados dos estudos e desenvolvidos no estágio de pesquisa no exterior, onde as sequências de pulsos no estado estacionário &ndash; DECPMG e Split 180&deg; &ndash; foram estudas numericamente e implementadas nos sistemas magnéticos compactos: mini-Halbach e MOUSE-NMR. Por fim, são apresentados resultados com os métodos de processamento de dados Krylov Basis Diagonalization Method (KBDM) e a Transformada Inversa de Laplace aplicados na análise de sinais SSFP. Resultados mostram que KBDM é uma ferramenta útil no processamento de dados em alta e baixa resolução, tanto na obtenção de espectros como na determinação da distribuição dos tempos de relaxação. / The application of a pulse sequence with repetition time much smaller than the relaxation times, Tp << T2; T1, causes the magnetization to reach a steady state, described by H. Y. Carr as a Steady State Free Precession (SSFP). In this condition, the signal is composed of the complex overlapping of the FID and eco components. SSFP type sequences are used in fast acquisition of NMR signals, resulting in a good signal to noise ratio (s/r) in a short time interval, however, they introduce phase and amplitude anomalies due to the complex interaction between the components of the steady state. In this work, we develop SSFP type pulse sequences for NMR in high and low resolution, with alternation and increment of phase. In high resolution, we develop SSFPdx and SSFPdxdt sequences, with linear and quadratic phase increment respectively. Results show that the low sensitivity nuclei spectra can be obtained with the same s/r ratio in smaller experimental time, about an order of magnitude, and the developed sequences can remove the spectral anomalies. In low resolution, the results show that the introduction of a phase alternation in the Continuous Wave Free Precession (CWFP) allows the elimination of the dependence of the sequence with the offset frequency and the time between pulses. Besides, we show that the CP-CWFPx-x sequence with a small refocalization angle (5° to 10°) allows the fast estimative of the longitudinal relaxation time in a single experiment. The results of the studies conducted during an international research internship are also presented. Steady state pulse sequences &ndash; DECPMG and Split 180° &ndash; were studied and implemented in compact magnetic systems: mini-Halbach and MOUSE-NMR. Finally, the results of the application of the Krylov Basis Diagonalization Method (KBDM) and the Inverse Laplace Transform for the analysis of SSFP signals are presented. The results show that KBDM is a useful tool in data processing for low and high resolution, both for obtaining spectra and determining the relaxation times distribution.

Orientador: Edevar Luvizotto Junior / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-05T20:04:30Z (GMT). No. of bitstreams: 1 Palhares_JulianaBarbosa_M.pdf: 1136611 bytes, checksum: 85a62466425d6655acb5af5bcc414c66 (MD5) Previous issue date: 2005 / Resumo: Nos sistemas de transporte de fluido líquido, têm-se a preocupação em combater às fugas ou vazamentos. Dessa fonna, este trabalho tem como objetivo aperfeiçoar o método de detecção de fugas em tubulações pelo método de resposta nos domínios fteqüência e tempo, utilizando como ferramentas matemáticas o Método da Matriz Transferência / Resposta em Freqüência e o Método das Características / Transfonnada Rápida de Fourier, sendo demonstradas as vantagens e desvantagens de cada método. E, como contribuição original, propõe um método de detecção de fugas através da análise de pulso de Alta Freqüência, localizando as fugas através da detenninação do tempo que um pulso emitido pela válvula leva para percorrer toda a tubulação e retomar à esta, denominado como Pulso Refletido / Abstract: In liquid fluid transport systems, there is a concem about avoiding leaks. Thus, this work has as objective to improve the leak detection method in pipes by úequency and time domains response method, being used as mathematical tools the method ofTransfer-Matrix / by úequency response and the Method of Characteristics / the Fast Fourier Transform, being demonstrated the advantages and disadvantages of each method. And, as new contribution, propose a leak detection method through the analysis of high frequency pulse, detecting the leaks through determination of time that a pulse produced by the valve takes to go through all pipe and come back, is denominated as a reflected pulse / Mestrado / Recursos Hidricos / Mestre em Engenharia Civil

La méthode de minimisation de l'intégrale d'action (principe variationnel) permet d’obtenir les équations de propagation des ondes. Cette méthode a été généralisée aux milieux poreux de dimensions fractales, pour étudier la propagation acoustique dans le domaine temporel, en se basant sur le modèle du fluide équivalent. L'équation obtenue réécrite dans le domaine fréquentiel représente une généralisation de l'équation d'Helmholtz. Dans le cadre du modèle d'Allard-Johnson, l'équation de propagation a été résolue de manière analytique dans le domaine temporel, dans les régimes des hautes et des basses fréquences. La résolution a été faite par la méthode de la transformée de Laplace, et a porté sur un milieu poreux semi-infini. Il a été trouvé que la vitesse de propagation dépend de la dimension fractale. Pour un matériau poreux fractal d'épaisseur finie qui reçoit une onde acoustique en incidence normale, les conditions d’Euler ont été utilisées pour déterminer les champs réfléchi et transmis. La résolution du problème direct a été faite dans le domaine temporel, par la méthode de la transformée de Laplace, et par l’usage des fonctions de Mittag-Leffler. Le problème inverse a été résolu par la méthode de minimisation aux sens des moindres carrés. Des tests ont été effectués avec succès sur des données expérimentales, en utilisant des programmes numériques développés à partir du formalisme établi dans cette thèse. La résolution du problème inverse a permis de retrouver les paramètres acoustiques de mousses poreuses, dans les régimes des hautes et des basses fréquences. / The action integral minimization method (variational principle) provides the wave propagation equations. This method has been generalized to fractal dimensional porous media to study the acoustic propagation in the time domain, based on the equivalent fluid model. The resulting equation rewritten in the frequency domain represents a generalization for the Helmholtz equation. As part of the Allard-Johnson model, the propagation equation was solved analytically in the time domain, for both high and low frequencies fields. The resolution was made by the method of the Laplace transform, and focused on a semi-infinite porous medium. It was found that the wave velocity depends on the fractal dimension.For a fractal porous material of finite thickness which receives an acoustic wave at normal incidence, the Euler conditions were used to determine the reflected and transmitted fields. The resolution of the direct problem was made in the time domain by the method of the Laplace transform, and through the use of the Mittag-Leffler functions. The inverse problem was solved by the method of minimizing the least squares sense. Tests have been performed successfully on experimental data; programs written from the formalism developed in this work have allowed finding the acoustic parameters of porous foams, in the fields of high and low frequencies.

This study seeks to develop a method that generalises the use of Adams-Bashforth to solve or treat partial differential equations with local and non-local differentiation by deriving a two-step Adams-Bashforth numerical scheme in Laplace space. The resulting solution is then transformed back into the real space by using the inverse Laplace transform. This is a powerful numerical algorithm for fractional order derivative. The error analysis for the method is studied and presented. The numerical simulations of the method as applied to the four-dimensional model, Caputo-Lu-Chen model and the wave equation are presented. In the analysis, the bifurcation dynamics are discussed and the periodic doubling processes that eventually caused chaotic behaviour (butterfly attractor) are shown. The related graphical simulations that show the existence of fractal structure that is characterised by chaos and usually called strange attractors are provided. For the Caputo-Lu-Chen model, graphical simulations have been realised in both integer and fractional derivative orders. / Mathematical Sciences / M. Sc. (Applied Mathematics)

No description available.

By the help of several examples the interactive work with the ClassPad330 is considered. The student can solve difficult exercises of practical applications step by step using the symbolic calculation and the graphic possibilities of the calculator. Sometimes several fields of mathematics are combined to solve a problem. Let us consider the ClassPad330 (with the actual operating system OS 03.03) and discuss on some new exercises in analysis, e.g. solving a linear differential equation by the help of the Laplace transformation and using the inverse Laplace transformation or considering the Fourier transformation in discrete time (the Fast Fourier Transformation FFT and the inverse FFT). We use the FFT- and IFFT-function to study periodic signals, if we only have a sequence generated by sampling the time signal. We know several ways to get a solution. The techniques for studying practical applications fall into the following three categories: analytic, graphic and numeric. We can use the Classpad software in the handheld or in the PC (ClassPad emulator version of the handheld).

Cette thèse traite de la résolution du problème direct de propagation d'un champ élastodynamique rayonné par une source dans un milieu stratifié anisotrope. Le contexte applicatif visé est le contrôle non destructif par ondes ultrasonores guidées de plaques de matériaux composites. Aux basses fréquences, ces matériaux sont assimilables à des milieux homogènes, anisotropes et dissipatifs. Deux approches causales sont étudiées et mises en oeuvre pour résoudre l'équation d'onde, et leur intérêt vis-à-vis de la méthode modale harmonique - la plus couramment employée dans ce domaine applicatif - est discuté. L'une des méthodes est modale et est formulée directement dans le domaine temporel. Elle permet de traiter facilement l'anisotropie, y compris en 3D, mais souffre des écueils classiques concernant le régime non-établi ou le cas du guide ouvert. L'autre approche est une formulation dans le domaine de Laplace de la méthode dite par ondes partielles. Elle présente l'intérêt d'être extrêmement polyvalente tout en conduisant à des coûts numériques tout à fait raisonnables. Dans un second temps, la possibilité d'exploiter ces deux méthodes pour résoudre des problèmes de diffraction par des défauts est étudiée. Une approche par éléments finis de frontière basée sur la méthode par ondes partielles est considérée. Elle permet de traiter efficacement le cas de défauts plans. L'extension à des défauts plus généraux est brièvement discutée. / This work adresses the direct problem of the propagation of an elastodynamic field radiated by a source in an anisotropic layered medium. Applications concern non destructive evaluation of composite plates by ultrasonic guided waves. In the lower frequencies, these materials can be modeled as homogeneous, anisotropic and dissipative media. Two causal approaches are studied and developped to solve the wave equation, and their interest is discussed regarding to the widely used harmonic modal method. One of these methods is modal, and is formulated directly in the time domain. It allows to deal easily with anisotropy, even in 3D ; however it also suffers classical shortcomings such as the high cost of the unestablished regime or the difficulty to deal with open waveguides. The other method is a formulation of the so-called partial-waves method in the Laplace domain. Its attractiveness relies in its versatility and in the fact that computational costs can be very acceptable. In a second time, we consider using both methods to solve problems of diffraction by defects. A boundary element method based on the partial-waves approach is developped and leads to solve very efficiently the case of a planar defect. The possibility of treating more general defects is briefly discussed.

Le mouvement Brownien réfléchi de manière oblique dans le quadrant, introduit par Harrison, Reiman, Varadhan et Williams dans les années 80, est un objet largement analysé dans la littérature probabiliste. Cette thèse, qui présente l’étude complète de la mesure invariante de ce processus dans tous les cônes du plan, a pour objectif plus global d’étendre au cadre continu une méthode analytique développée initialement pour les marches aléatoires dans le quart de plan par Fayolle, Iasnogorodski et Malyshev dans les années 70. Cette approche est basée sur des équations fonctionnelles, reliant des fonctions génératrices dans le cas discret et des transformées de Laplace dans le cas continu. Ces équations permettent de déterminer et de résoudre des problèmes frontière satisfaits par ces fonctions génératrices. Dans le cas récurrent, cela permet de calculer explicitement la mesure invariante du processus avec rebonds orthogonaux, dans le chapitre 2, et avec rebonds quelconques, dans le chapitre 3. Les transformées de Laplace des mesures invariantes sont prolongées analytiquement sur une surface de Riemann induite par le noyau de l’équation fonctionnelle. L’étude des singularités et l’application de méthodes du point col sur cette surface permettent de déterminer l’asymptotique complète de la mesure invariante selon toutes les directions dans le chapitre 4. / Obliquely reflected Brownian motion in the quadrant, introduced by Harrison, Reiman, Varadhan and Williams in the eighties, has been studied a lot in the probabilistic literature. This thesis, which presents the complete study of the invariant measure of this process in all the cones of the plan, has for overall aim to extend to the continuous framework an analytic method initially developped for random walks in the quarter plane by Fayolle, Iasnogorodski and Malyshev in the seventies. This approach is based on functional equations which link generating functions in the discrete case and Laplace transform in the continuous case. These equations allow to determine and to solve boundary value problems satisfied by these generating functions. In the recurrent case, it permits to compute explicitly the invariant measure of the process with orthogonal reflexions, in the chapter 2, and with any reflexions, in the chapter 3. The Laplace transform of the invariant measure is analytically extended to a Riemann surface induced by the kernel of the functional equation. The study of singularities and the use of saddle point methods on this surface allows to determine the full asymptotics of the invariant measure along every directions in the chapter 4.

We present several methods that allow the exact computation of the exponential matrix etA. Methods that include computation of eigenvectors or Laplace transform are very well-known, and they are mentioned herefor completeness. We also present other methods, not well-known inthe literature, that do not need the computation of eigenvectors, and are easy to introduce in a classroom, thus providing us with general formulas that can be applied to any matrix. / Presentamos varios métodos que permiten el calculo exacto de la matriz exponencial etA. Los métodos que incluyen el calculo de autovectores y la transformada de Laplace son bien conocidos, y son mencionados aquí por completitud. Se mencionan otros métodos, no tan conocidos en la literatura, que no incluyen el calculo de autovectores, y que proveen de fórmulas genéricas aplicables a cualquier matriz.