Submitted by PEDRO VALIM SAMPAIO null (pedrovalimsampaio@gmail.com) on 2018-01-11T01:06:31Z No. of bitstreams: 1 pedro-sampaio-dissertacao-pgmat-dezembro-2017-com-ficha.pdf: 8235020 bytes, checksum: 58adc9b07110ff0e572b49fd9bc15579 (MD5) / Rejected by Marcia Correa Bueno Degasperi null (mcbueno@rc.unesp.br), reason: Prezado Pedro Valim Sampaio, Solicitamos que realize uma nova submissão seguindo as orientações abaixo: - capa (faltou a capa que é elemento obrigatório no seu programa de pós-graduação. Agradecemos a compreensão e aguardamos o envio do novo arquivo. Atenciosamente, Biblioteca câmpus Rio Claro Repositório institucional Unesp on 2018-01-11T12:47:44Z (GMT) / Submitted by PEDRO VALIM SAMPAIO null (pedrovalimsampaio@gmail.com) on 2018-01-11T13:35:32Z No. of bitstreams: 2 pedro-sampaio-dissertacao-pgmat-dezembro-2017-com-ficha.pdf: 8235020 bytes, checksum: 58adc9b07110ff0e572b49fd9bc15579 (MD5) pedro-sampaio-dissertacao-pgmat-dezembro-2017-com-ficha-e-capa.pdf: 8377820 bytes, checksum: 3d6af025594125f81c9f43dc70d7b7f8 (MD5) / Approved for entry into archive by Adriana Aparecida Puerta null (dripuerta@rc.unesp.br) on 2018-01-11T16:45:12Z (GMT) No. of bitstreams: 1 sampaio_pv_me_rcla.pdf: 8271293 bytes, checksum: 10bf9858fb1a38ce127cb3c9b992f9df (MD5) / Made available in DSpace on 2018-01-11T16:45:12Z (GMT). No. of bitstreams: 1 sampaio_pv_me_rcla.pdf: 8271293 bytes, checksum: 10bf9858fb1a38ce127cb3c9b992f9df (MD5) Previous issue date: 2017-12-18 / Esta dissertação explora fundamentos comuns de dois temas, Música e Matemática, que são desenvolvidos lado a lado. Noções musicais e matemáticas são reunidas, como escalas e aritmética modular, intervalos e logaritmos, música de doze tons e aritmética modular, timbre e análise de Fourier. Quando possível, as discussões de noções musicais e matemáticas estão diretamente interligadas. Ocasionalmente o texto permanece por um tempo sobre um assunto e não sobre o outro, mas finalmente a conexão é estabelecida, tornando este um tratamento integrador dos dois assuntos. É uma tradução matematicamente comentada de uma grande parte de Mathematics and Music de David Wright. / This dissertation explores the common foundations of the two subjects, Music and Mathematics, which are developed side by side. Musical and mathematical notions are brought together, such as scales and modular arithmetic, intervals and logarithms, twelve tone music and modular arithmetic, timbre and Fourier analysis. When possible, discussions of musical and mathematical notions are directly interwoven. Occasionally the text stays for a while on one subject and not the other, but eventually the connection is established, making this an integrative treatment of the two subjects. It is a mathematically commented translation (to portuguese) of a major part of David Wright’s Mathematics and Music.

Made available in DSpace on 2014-06-11T19:22:34Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-07-20Bitstream added on 2014-06-13T20:09:48Z : No. of bitstreams: 1 costa_llh_me_bauru.pdf: 1092988 bytes, checksum: 490b62551f9555ff7b869527de5680f6 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Este trabalho apresenta um estudo dos fenômenos de desequilíbrio e assimetria que podem ocorrer em sistemas trifásicos, no qual foram estudadas duas abordagens. A primeira delas é a abordagem tradicional de análise de fenômenos de desequilíbrio e assimetria, proposta por Fortescue, denominadas Componentes Simétricas ou Componentes de Sequência. Essa proposta desenvolvida no domínio da frequência foi estudada também no domínio do tempo, após sua adaptação. Isso porque as componentes simétricas generalizadas, nova abordagem de análise de desequilíbrio, está desenvolvida no domínio do tempo. Ambas as propostas de análise do desequilíbrio e assimetria trifásicos são aplicadas à sistemas trifásicos periódicos não senoidais. Enquanto que as componentes simétricas de Fortescue, para serem calculadas, necessitam que o sistema trifásico não senoidal seja decomposto nas harmônicas da série de Fourier, as componentes simétricas generalizadas podem ser aplicadas diretamente ao sistema não senoidal. O desenvolvimento de ambas as abordagens para um sistema periódico não senoidal resulta em relação entre ambas as propostas de análise de desequilíbrio e assimetria As relações entre as componentes simétricas generalizadas e as componentes simétricas de Fortescue são a principal contribuição deste trabalho. Baseado nas componentes simétricas generalizadas, novos indicadores de desequilíbrio são propostos. Os novos indicadores são comparados com os indicadores de desequilíbrio clássicos, os quais foram desenvolvidos a partir da proposta de Fortescue. Por fim, uma aplicação é desenvolvida na qual foram aplicados os conceitos estudados. Nesta aplicação, uma tensão trifásica não senoidal desequilibrada alimenta um motor de indução trifásico / This work presents a study of the phenomena of unbalance and asymmetry which may occur in three-phase systems which two approaches were studied. The first one is the traditional approach of analysis of phenomena of unbalance and asymmetry, proposed by Fortescue, called Symmetrical Components or Sequence Components. This proposal developed in the frequency domain was also studied in the time domain after adaptation. This because of the generalized symmetrical components, new approach to the analysis of unbalance and asymmetry is developed in the time domain. Both proposals for analysis if the unbalance and asymmetry in three-phase systems are applied to the periodic non-sinusoidal three-phase systems. While the symmetrical components of Fortescue, to be calculated, require that the non-sinusoidal three-phase system is decomposed into harmonic Fourier series, the generalized symmetrical components can be applied directly to the non-sinusoidal system. The development of both approaches to a periodic non-sinusoidal system results in relationships between both proposals for analysis of unbalance and asymmetry. The relationships between the symmetrical components and the generalized symmetrical components of Fortescue are the main contribution of this work. Based on the generalized symmetrical components, new indicators of unbalance are proposed. The new new indicators are compared with the classical indicators of unbalance, which were developed from the proposed Fortescue. Finally, an application is developed with the concepts studied. In this application, an unbalanced non-sinusoidal three-phase voltage supplies a three-phase induction motor

Orientador: Alvaro Rodolfo De Pierro / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-05T18:58:18Z (GMT). No. of bitstreams: 1 Martinez_AnaGabriela_D.pdf: 800274 bytes, checksum: 9d484ffeb59df3623e4bb55d8c8fb1a1 (MD5) Previous issue date: 2006 / Resumo: A detecção de descontinuidades e um problema que aparece em muitas áreas de aplicação. Exemplos disto são os métodos de Fourier em tomografia computa dorizada, inversão em ressonância magnetica e as leis de conservação em qua»c~oes diferenciais. A determina»c~ao precisa dos pontos de descontinuidade e essencial para obter converg^encia exponencial da serie de Fourier para fun»c~oes cont³nuas por partes e evitar assim os efeitos do conhecido fen^omeno de Gibbs. Nos trabalhos de Wei et al. de 1999 e 2004 foram desenvolvidos ¯ltros polinomiais para reconstruir funções a partir de seus coeficientes de Fourier. No trabalho de Wei et al. do 2005 estes filtros foram usados para construir metodos iterativos rapidos para a detecção de de- scontinuidades. Nesta tese são introduzidos filtros mais gerais baseados em fun»c~oes splines, que conseguem maior precis~ao que aqueles apresentados em esses trabalhos e também são apresentados os correspondentes metodos iterativos para as descon- tinuidades. S~ao obtidas tambem estimativas para os erros assim como experi^encias numericas que validam os algoritmos. Mostra-se tambem um novo metodo que ap- resenta um melhor desempenho que aqueles baseados na serie parcial conjugada de Fourier usados nos trabalhos de Gelb e Tadmor / Abstract: Detecting discontinuities from Fourier coefficients is a problem that arises in several areas of application. Important examples are Fourier methods in Computed Tomography, Nuclear Magnetic Resonance Inversion and Conservation Law Differential Equations. Also, the knowledge of the precise location of the discontinuity points is essential to obtain exponential convergence of the Fourier series for a piecewise continuous function, avoiding the well known Gibbs phenomenon. In the work of Wei et al. (1999, 2004), polynomial filters were developed to reconstruct functions from their Fourier coefficients. In the work of Wei et. al. (2005), these fillters were used to develop fast iterative methods for discontinuity detection. In this thesis we introduce more general spline based filters, that achieve higher accuracy than those works, and the corresponding iterative methods for the discontinuities. Estimates for the errors are presented as well as many numerical experiments validating the algorithms. Also, we show that a new and simple method, not using any nonlinear solver, performs better than those based on the conjugate Fourier series as in the work of Gelb and tadmor / Doutorado / Analise Numerica / Doutor em Matemática Aplicada

O método das matrizes operacionais é expandido para o corpo complexo a ordens arbitrárias pela abordagem de Riemann-Liouville e Caputo com ênfase nas séries de Fourier complexas. Elabora-se uma adaptação do formalismo bra-ket de Dirac à linguagem tensorial no espaço de Hilbert de funções com expansões finitas para uso específico na teoria de equações diferenciais e matrizes operacionais, denominado \\Formalismo Coadjunto\". Estende-se o tratamento aos operadores fracionais de Weyl para períodos genéricos a fim de determinar as matrizes operacionais de derivação e integração de ordem arbitrária na base complexa de Fourier. Introduz-se um novo método de resolução de equações diferenciais ordinárias lineares e fracionais não-homogêneas, denominado \\Modelagem Operacional\", que permite a obtenção de soluções de equações de alta ordem com grande precisão sem a necessidade de imposição de condições iniciais ou de contorno. O método apresentado é aperfeiçoado por meio de um novo tipo de expansão, que denominamos \"Séries Associadas de Fourier\", a qual apresenta convergência mais rápida que a série de Fourier original numa restrição de domínio, possibilitando soluções de EDOs e EDFs de alta ordem com maior precis~ao e ampliando a esfera de casos passíveis de resolução. / Operational matrices method is expanded to complex field and arbitrary orders by using the Riemann-Liouville and Caputo approach with emphasis on complex Fourier series. Dirac\'s bra-ket notation is associated to tensor procedures in Hilbert spaces for finite function expansions to be applied specifically to dfferential equations and operational matrices, being called \\Coadjoint Formalism\". This treatment is extended to Weyl fractional operators for generic periods in order to establish the integral and derivative operational matrices of fractional order to complex Fourier basis. A new method to solve linear non-homogeneous ODEs and FDEs, called \\Operational Modelling\"is introduced. It yields high precision solutions on high order dfferential equations without assumption of boundary or initial conditions. The presented method is improved by a new kind of function expansion, called \\Fourier Associated Series\", which yields a faster convergence than original Fourier in a restrict domain, enabling to obtain solutions of high order ODEs and FDEs with excellent precision and broadening the set of solvable equations.

This thesis presents how Tikhonov’s regularization can be used to solve an inverse problem of Helmholtz equation inside of a rectangle. The rectangle will be met with both Neumann and Dirichlet boundary conditions. A linear operator containing a Fourier series will be derived from the Helmholtz equation. Using this linear operator, an expression for the inverse operator can be formulated to solve the inverse problem. However, the inverse problem will be found to be ill-posed according to Hadamard’s definition. The regularization used to overcome this ill-posedness (in this thesis) is Tikhonov’s regularization. To compare the efficiency of this inverse operator with Tikhonov’s regularization, another inverse operator will be derived from Helmholtz equation in the partial frequency domain. The inverse operator from the frequency domain will also be regularized with Tikhonov’s regularization. Plots and error measurements will be given to understand how accurate the Tikhonov’s regularization is for both inverse operators. The main focus in this thesis is the inverse operator containing the Fourier series. A series of examples will also be given to strengthen the definitions, theorems and proofs that are made in this work.

Pratima Sadangi in a Ph.D. thesis submitted to Utkal University proved results on degree of approximation of functions by operators associated with their Fourier series. In this dissertation, we consider degree of approximation of functions in Hα,ρ by different operators. In Chapter 1 we mention basic definitions needed for our work. In Chapter 2 we discuss different methods of summation. In Chapter 3 we define the Hα,ρ metric and present the degree of approximation problem relating to Fourier series and conjugate series of functions in the Hα,ρ metric using Karamata (Κλ) means. In Chapter 4 we present the degree of approximation of an integral associated with the conjugate series by the Euler, Borel and (e,c) means of a series analogous to the Hardy-Littlewood series in the Hα,ρ metric. In Chapter 5 we propose problems to be solved in the future.

This thesis addresses the question of mathematical involvement in music, a topic long discussed going all the way back to Plato. It details the mathematical construction of the three main tuning systems (Pythagorean, just intonation, and equal temperament), the methods by which they were built and the mathematics that drives them through the lens of a historical perspective. It also briefly touches on the philosophical aspects of the tuning systems and whether their differences affect listeners. It further details the invention of the Fourier Series and their relation to the sound wave to explain the concept of overtones within the tuning systems.

We study the behavior of trigonometric Fourier series in classes φ(L) close to L. We prove that recent Fillipov's result on the convergence of trigonometric Fourier series in classes φ(L) containing L cannot be improved. In the case when the function φ(u) defining the class φ(L) grows at infinity slower than up for all p>1, we that a famous result on the convergence of trigonometric Fourier series in the classes φ(L) containing in L cannot be improved. / Изучается поведение тригонометрических рядов Фурье в пространствах φ(L), близких к L. Доказана неулучшаемость недавнего результата В.И.Филиппова о сходимости тригонометрического ряда Фурье в пространствах φ(L), содержащих в L. В случае, когда функция φ(u), задающая класс φ(L), на бесконечности растёт медленнее, чем up при всех p>1, показана неулучшаемость известного результата о сходимости тригонометрического ряда Фурье в пространстве φ(L), содержащемся в L.

The purpose of this thesis is to formulate and proof some theorems about convergences of Fourier series. In essence, we shall formulate and proof Wiener's lemma and Wiener-Lévy theorem which give us weaker conditions for absolute convergence of Fourier series. This thesis follows the classical Fourier analysis approach in a straightforward and detailed way suitable for undergraduate science students.

Yes / Physics-based skin deformation methods can greatly improve the realism of character animation, but require non-trivial training, intensive manual intervention, and heavy numerical calculations. Due to these limitations, it is generally time-consuming to implement them, and difficult to achieve a high runtime efficiency. In order to tackle the above limitations caused by numerical calculations of physics-based skin deformation, we propose a simple and efficient analytical approach for physics-based skin deformations. Specifically, we (1) employ Fourier series to convert 3D mesh models into continuous parametric representations through a conversion algorithm, which largely reduces data size and computing time but still keeps high realism, (2) introduce a partial differential equation (PDE)-based skin deformation model and successfully obtain the first analytical solution to physics-based skin deformations which overcomes the limitations of numerical calculations. Our approach is easy to use, highly efficient, and capable to create physically realistic skin deformations. / This research is supported by the PDE-GIR project which has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement (No.778035), the National Natural Science Foundation of China (Grant No.51475394), and Innovate UK (Knowledge Transfer Partnerships KTP.010860). Shaojun Bian is also supported by Chinese Scholar Council. Xiaogang Jin is supported by the Key Research and Development Program of Zhejiang Province (No.2018C01090) and the National Natural Science Foundation of China (No.61732015).