A finalidade deste trabalho e calcular a composição de modelos no FBST (the Full Bayesian Signicance Test) descrito por Borges e Stern [6]. Nosso objetivo foi encontrar um método de aproximação numérica mais eficiente que consiga substituir o método de condensação descrita por Kaplan. Três técnicas foram comparadas: a primeira é a aproximação da convolução de Mellin usando discretização e condensação descrita por Kaplan [11], a segunda é a aproximação da convolução de Mellin usando mistura de exponenciais, descrita por Dufresne [8], para calcular a convolução de Fourier mediante a aproximação de mistura de convoluções exponenciais, usando a estrutura algébrica descrita por Hogg [10], mais a aplicação do operador descrito por Collins [7], para transformar a convolução de Fourier para a convolução de Mellin, a terceira é a aproximação da convolução de Mellin usando mistura de exponenciais, descrita por Dufresne [8], para aproximar diretamente via mistura de exponenciais a convolução de Fourier, mais a aplicação do operador descrito por Collins [7], para transformar a convolução de Fourier para a convolução de Mellin. / The purpose of this work is to calculate the compositional models of FBST (the Full Bayesian Signicance Test) studied by Borges and Stern [6]. The objective of this work was to find an approximation method numerically eficient that can replace the condensation methods described by Kaplan. Three techniques were compared: First, the approximation of Mellin convolution using discretization and condensation described by Kaplan [11], second, the approximation of Mellin convolution using mixtures of exponentials, described by Dufresne [8], to calculate the Fourier convolution by approximation of mixtures of exponential convolutions, using the algebraic structure described by Hogg [10], and then to apply the operator described by Collins [7], to transform the usual convolution to Mellin convolution, third, the approximation of Mellin convolution using mixtures of exponentials, described by Dufresne [8], to calculate the Fourier convolution by direct approximation of mixtures of exponentials, and then to apply the operator described by Collins [7], to transform the usual convolution to Mellin convolution.

This thesis provides an introduction to and analysis of the problem of determining nuclear magnetic resonance (NMR) relaxation times of porous media by using the so-called Carr-Purcell-Meiboom-Gill (CPMG) technique. We introduce the principles of NMR, the CPMG technique and the signals produced, porous effects on the NMR relaxation times and discuss various numerical methods for the inverse problem of extracting the relaxation times from CPMG signals. The numerical methods for solving Fredholm integral equations of the first kind are sketched from a series expansion perspective. A method of using arbitrary constituent functions for improving the performance of non-negative least squares (NNLS) is developed and applied to several synthesized data sets and real experimental data sets of saturated porous glass gels. The data sets were obtained by the author of this thesis and the experimental procedure will be presented. We discuss the imperfections in the assumptions on the physical and numerical models, the numerical schemes, and the experimental results, which may lead to new research possibilities.

This thesis provides an introduction to and analysis of the problem of determining nuclear magnetic resonance (NMR) relaxation times of porous media by using the so-called Carr-Purcell-Meiboom-Gill (CPMG) technique. We introduce the principles of NMR, the CPMG technique and the signals produced, porous effects on the NMR relaxation times and discuss various numerical methods for the inverse problem of extracting the relaxation times from CPMG signals. The numerical methods for solving Fredholm integral equations of the first kind are sketched from a series expansion perspective. A method of using arbitrary constituent functions for improving the performance of non-negative least squares (NNLS) is developed and applied to several synthesized data sets and real experimental data sets of saturated porous glass gels. The data sets were obtained by the author of this thesis and the experimental procedure will be presented. We discuss the imperfections in the assumptions on the physical and numerical models, the numerical schemes, and the experimental results, which may lead to new research possibilities.

In this dissertation we consider several problems in classical complex analysis and operator theory. In the first part we study basis properties of a system of complex exponentials with a given frequency sequence. We show that most of these basis properties can be characterized in terms of the invertibility properties of certain Toeplitz operators. We use this reformulation to give a metric description of the radius of l2-dependence. Using similar methods we solve the classical Beurling gap problem in the case of separated real sequences. In the second part we consider the classical Polýa-Levinson problem asking for a description of all real sequences with the property that every zero type entire function which is bounded on such a sequence must be a constant function. We first give a description in terms of injectivity of certain Toeplitz operators and then use this to give a metric description of all such sequences. In the last part we study the spectral changes of a partial isometry under unitary perturbations. We show that all the spectra can be described in terms of the characteristic function of the partial isometry that is being perturbed. Our main tool in the proofs is a Herglotz-type representation for generalized spectral measures. We furthermore use this representation to give a new proof of the classical Naimark's dilation theorem and to generalize Aleksandrov's disintegration theorem.

A finalidade deste trabalho e calcular a composição de modelos no FBST (the Full Bayesian Signicance Test) descrito por Borges e Stern [6]. Nosso objetivo foi encontrar um método de aproximação numérica mais eficiente que consiga substituir o método de condensação descrita por Kaplan. Três técnicas foram comparadas: a primeira é a aproximação da convolução de Mellin usando discretização e condensação descrita por Kaplan [11], a segunda é a aproximação da convolução de Mellin usando mistura de exponenciais, descrita por Dufresne [8], para calcular a convolução de Fourier mediante a aproximação de mistura de convoluções exponenciais, usando a estrutura algébrica descrita por Hogg [10], mais a aplicação do operador descrito por Collins [7], para transformar a convolução de Fourier para a convolução de Mellin, a terceira é a aproximação da convolução de Mellin usando mistura de exponenciais, descrita por Dufresne [8], para aproximar diretamente via mistura de exponenciais a convolução de Fourier, mais a aplicação do operador descrito por Collins [7], para transformar a convolução de Fourier para a convolução de Mellin. / The purpose of this work is to calculate the compositional models of FBST (the Full Bayesian Signicance Test) studied by Borges and Stern [6]. The objective of this work was to find an approximation method numerically eficient that can replace the condensation methods described by Kaplan. Three techniques were compared: First, the approximation of Mellin convolution using discretization and condensation described by Kaplan [11], second, the approximation of Mellin convolution using mixtures of exponentials, described by Dufresne [8], to calculate the Fourier convolution by approximation of mixtures of exponential convolutions, using the algebraic structure described by Hogg [10], and then to apply the operator described by Collins [7], to transform the usual convolution to Mellin convolution, third, the approximation of Mellin convolution using mixtures of exponentials, described by Dufresne [8], to calculate the Fourier convolution by direct approximation of mixtures of exponentials, and then to apply the operator described by Collins [7], to transform the usual convolution to Mellin convolution.

In the 1980s and 1990s, Joyal and Street developed a graphical notation for various flavours of monoidal category using graphs drawn in the plane, commonly known as string diagrams. In particular, their work comprised a rigorous topological foundation of the notation. In 2007, Harmer, Hyland and Melliès gave a formal mathematical foundation for game semantics using a notions they called ⊸-schedules, ⊗-schedules and heaps. Schedules described interleavings of plays in games formed using ⊸ and ⊗, and heaps provided pointers used for backtracking. Their definitions were combinatorial in nature, but researchers often draw certain pictures when working in practice. In this thesis, we extend the framework of Joyal and Street to give a formal account of the graphical methods already informally employed by researchers in game semantics. We give a geometric formulation of ⊸-schedules and ⊗-schedules, and prove that the games they describe are isomorphic to those described in Harmer et al.’s terms, and also those given by a more general graphical representation of interleaving across games of multiple components. We further illustrate the value of the geometric methods by demonstrating that several proofs of key properties (such as that the composition of ⊸-schedules is associative) can be made straightforward, reflecting the geometry of the plane, and overstepping some of the cumbersome combinatorial detail of proofs in Harmer et al.’s terms. We further extend the framework of formal plane diagrams to account for the heaps and pointer structures used in the backtracking functors for O and P.

Submitted by isabela.moljf@hotmail.com (isabela.moljf@hotmail.com) on 2016-08-18T13:39:26Z No. of bitstreams: 1 andersonferrari.pdf: 467006 bytes, checksum: 4288009b4363cd5f47f256c0b8c4657c (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-08-19T11:55:49Z (GMT) No. of bitstreams: 1 andersonferrari.pdf: 467006 bytes, checksum: 4288009b4363cd5f47f256c0b8c4657c (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-08-19T11:56:10Z (GMT) No. of bitstreams: 1 andersonferrari.pdf: 467006 bytes, checksum: 4288009b4363cd5f47f256c0b8c4657c (MD5) / Made available in DSpace on 2016-08-19T11:56:10Z (GMT). No. of bitstreams: 1 andersonferrari.pdf: 467006 bytes, checksum: 4288009b4363cd5f47f256c0b8c4657c (MD5) Previous issue date: 2013-03-22 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho versa sobre uma proposta de aprofundamento na abordagem e aplicação de Logaritmos Naturais para alunos do ensino médio, de como são deduzidas as expressões matemáticas (fórmulas) que modelam os fenômenos como, por exemplo, crescimento e decrescimento de uma população de bactérias e crescimento e decaimento radioativo. Inicialmente, faremos uma revisão dos tópicos necessários. / This paper discusses a proposal for deepening the approach and application of Natural Logarithms for high school students, how the Mathematical expressions are deduced (formulas) shaping phenomena such as, for example, growth and decrease of a population of bacteria and growth and radioactive decay. Initially, we will revise the necessary topics.

No description available.

This thesis presents a robust method for estimating the relaxations of a metallic object from its electromagnetic induction (EMI) response. The EMI response of a metallic object can be accurately modeled by a sum of real decaying exponentials. However, it is diffcult to obtain the model parameters from measurements when the number of exponentials in the sum is unknown or the terms are strongly correlated. Traditionally, the time constants and residues are estimated by nonlinear iterative search that often leads to unsatisfactory results. In this thesis, a constrained linear method of estimating the parameters is formulated by enumerating the relaxation parameter space and imposing a nonnegative constraint on the parameters. The resulting algorithm does not depend on a good initial guess to converge to a solution. Using tests on synthetic data and laboratory measurement of known targets the proposed method is shown to provide accurate and stable estimates of the model parameters.

No description available.