Thesis (MSc (Mathematical Sciences. Physical and Mathematical Analysis))--University of Stellenbosch, 2006. / This work studies the regularity (or smoothness) of continuous finitely supported refinable functions which are mainly encountered in multiresolution analysis, iterative interpolation processes, signal analysis, etc. Here, we present various kinds of sufficient conditions on a given mask to guarantee the regularity class of the corresponding refinable function. First, we introduce and analyze the cardinal B-splines Nm, m ∈ N. In particular, we show that these functions are refinable and belong to the smoothness class Cm−2(R). As a generalization of the cardinal B-splines, we proceed to discuss refinable functions with positive mask coefficients. A standard result on the existence of a refinable function in the case of positive masks is quoted. Following [13], we extend the regularity result in [25], and we provide an example which illustrates the fact that the associated symbol to a given positive mask need not be a Hurwitz polynomial for its corresponding refinable function to be in a specified smoothness class. Furthermore, we apply our regularity result to an integral equation. An important tool for our work is Fourier analysis, from which we state some standard results and give the proof of a non-standard result. Next, we study the H¨older regularity of refinable functions, whose associated mask coefficients are not necessarily positive, by estimating the rate of decay of their Fourier transforms. After showing the embedding of certain Sobolev spaces into a H¨older regularity space, we proceed to discuss sufficient conditions for a given refinable function to be in such a H¨older space. We specifically express the minimum H¨older regularity of refinable functions as a function of the spectral radius of an associated transfer operator acting on a finite dimensional space of trigonometric polynomials. We apply our Fourier-based regularity results to the Daubechies and Dubuc-Deslauriers refinable functions, as well as to a one-parameter family of refinable functions, and then compare our regularity estimates with those obtained by means of a subdivision-based result from [28]. Moreover, we provide graphical examples to illustrate the theory developed.

No description available.

Made available in DSpace on 2014-10-09T12:43:51Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:10:10Z (GMT). No. of bitstreams: 1 06767.pdf: 4710608 bytes, checksum: 0df801946c2e3b5907a9d77d5ff698e5 (MD5) / Dissertacao (Mestrado) / IPEN/D / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP

O eletrocardiograma transMITe informações com relação à passagem do pulso elétrico pelo coração e, conseqüentemente, do funcionamento deste. Desde o início da sua utilização, possibilitada pelo trabalho de Willem Einthoven criando a primeira máquina capaz de medir o pulso elétrico de forma não invasiva e com sensibilidade forte o bastante para ser capaz de produzir um gráfico proveitoso, o eletrocardiograma é muito utilizado para avaliação clínica de pacientes. Entretanto a evolução das máquinas que o descrevem não foi muito além do que o elaborado por Einthoven no início do século 20. As máquinas capazes de captar o eletrocardiograma se tornaram menores (até portáteis para algumas aplicações), gráficos passaram a ser disponibilizados em telas de vídeo (ao invés das fitas de papel) e, como maior evolução, as máquinas que observam o eletrocardiograma passaram a conseguir captar a ocorrência de um ciclo cardíaco com alta confiabilidade e, atualmente, passaram a medir também o parâmetro ST com precisão deliMITada (necessitando ajuda do operador para ajuste em alguns casos). É baseado nestes fatos que esta dissertação procura estudar algoritmos matemáticos, de forma mais focada nos modelos do impulso elétrico durante os ciclos cardíacos, e avaliar suas capacidades de interpretar parâmetros do ciclo de ECG de forma precisa e rápida para que o médico tenha prontamente os dados necessários para realizar a avaliação clínica do paciente. Em primeira análise foram estudados os algoritmos para detecção do pulso de eletrocardiograma (detecção da onda R), em seguida feito o janelamento da curva de ECG a fim de separar os ciclos cardíacos. A partir deste ponto foram analisados os modelos matemáticos gerados por equações polinomiais, Transformada de Fourier e Transformada wavelet. E, com o intuito de filtrar ruídos e gerar derivações não medidas, foi implementado um filtro de kalman em um modelo vetorial do eletrocardiograma. Para avaliar os resultados obtidos foram utilizados requisitos de desempenho declarados pelo FDA norte americano e pela norma européia IEC60601-2-51. Essas análises foram feitas através da utilização dos algoritmos gerados nas curvas provindas do banco de dados do PhisioNet. O método polinomial não foi considerado interessante na medida em que não possibilita gerar uma equação para um ciclo cardíaco, mas sim várias equações (uma para cada ponto do ciclo). Os demais métodos apresentaram melhor eficiência na medida em que foram capazes de gerar parâmetros com significado físico e possibilitando melhor caracterização de pontos importantes da curva do eletrocardiograma. / The electrocardiogram gives information related to the passage of an electric pulse through the heart and, therefore, to his state function. Since the beginning of electrocardiogram utilization, thanks to the work of Willem Einthoven building the first machine capable of measuring the electric pulse non-invasively and with sensitivity enough to be able to provide a profitable graph, it is widely used for clinical evaluation of patients. However the evolution of the machines that describes the electrocardiogram hadn´t much more advances since the elaborated by Einthoven in the beginning of the 20th century. They become smaller (even portable for some applications), the graphs are now displayed in video screens (instead of the paper strip) and, taking place as the biggest evolutions, machines that observes the electrocardiogram became able to recognize a cardiac cycle with high reliability and, more recently, became able to measure the ST parameter with liMITed precision (it needs the help of the operator to set specific measuring points in some cases). It is based in these facts that this dissertation looks for analyzing mathematic algorithms, more specifically the mathematic models of the electric impulse during the cardiac cycles, and evaluate their capacities to expound ECG parameters in a fast and reliable way in order to the physician receive promptly the data needed for his clinical evaluation of the patient. For the first step were analyzed some algorithms for electrocardiogram pulse detection (detection of R wave), in the following step were done the windowing of the ECG wave in order to separate the cardiac cycles. In this step were analyzed the mathematic models generated by polynomial equations, Fourier Transform and Wavelet Transform. And, in order to filter noises and generate leads not measure, it was implemented a kalman´s filter at a vector model. To evaluate the obtained results were used the requirements of performance given by north-american FDA and by the European rule IEC60601-2-51. These evaluations were done by executing the generated algorithms in the waves supplied by the databank PhisioNet. The polynomial method weren´t considered interesting because it weren´t able to generate an equation for the cardiac cycle, but many equations (one for each point of the cycle). The other methods showed a better efficiency since they were capable of generate parameters with physical meaning and being able to do a better characterization of the important points of the electrocardiogram wave.

Made available in DSpace on 2014-10-09T12:43:51Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:10:10Z (GMT). No. of bitstreams: 1 06767.pdf: 4710608 bytes, checksum: 0df801946c2e3b5907a9d77d5ff698e5 (MD5) / Dissertacao (Mestrado) / IPEN/D / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP

Orientador: Ricardo Caetano Azevedo Biloti / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-13T04:58:29Z (GMT). No. of bitstreams: 1 Sousa_Nadsonde_M.pdf: 846587 bytes, checksum: 2e5832c38e969f5279654b4c89da83e3 (MD5) Previous issue date: 2009 / Resumo: O presente trabalho aborda os métodos de diferenças finitas com suas propriedades e aplicações. Iniciamos com uma revisão histórica, destacando alguns matemáticos que participaram do desenvolvimento da teoria de métodos de diferenças. Em seguida, apresentamos alguns modelos matemáticos compostos por equações diferenciais. Através da equação de advecção, estudamos métodos de diferenças explícitos, com especial enfoque para as propriedades de erro de truncamento, consistência, estabilidade e convergência dando ênfase ao Teorema de Lax. Estudamos a análise de Fourier e a condição de von Neumann para interpretar a amplitude, a dissipação e a dispersão das soluções numéricas. Abordamos os métodos Upwind, de Lax-Friedrichs e de Lax-Wendroff. Por fim, exemplificamos numericamente os conceitos e propriedades estudados com comparações entre os métodos, aplicados em um problema teste. / Abstract: The present work approaches finite-difference methods, their properties, and their applications. We present a historical review, including some mathematieians who participated in the development of the theory of differences. Furthermore, we present some mathematical models consisting of differential equatiolls. Through the advection equationl, we study explicit finite-difference methods, detailing their truncation error, consistency, stability and conlvergence properties. We employ Fourier analysis and the von Neumann condition to study the amplitude, dissipation and dispersion of numerical solutions. We compare three methods: Upwind, Lax-Friedrichs and Lax-Wendroff. Finally, we perform numerical tests to illustrate the concepts and properties studied in this work. / Mestrado / Analise Numerica / Mestre em Matemática

Orientador: Flávio Vasconcelos da Silva / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Química / Made available in DSpace on 2018-08-21T21:00:26Z (GMT). No. of bitstreams: 1 Rodrigues_Sergio_M.pdf: 4024499 bytes, checksum: 621b50dee12f09a22c121b01b7c3340b (MD5) Previous issue date: 2012 / Resumo: Neste trabalho foi utilizada uma série histórica de dados reais de danos sofridos na rede de distribuição de gás natural da concessionária Comgás, em sua área de concessão no estado de São Paulo abrangendo 177 municípios das regiões metropolitanas de São Paulo, Campinas, Baixada Santista e Vale do Paraíba. Com a análise desses dados foi observado que a ocorrência de danos na rede subterrânea de distribuição de gás natural é composta por harmônicas de diferentes frequências e amplitudes. Através da aplicação da transformada de Fourier a série histórica de dados de danos, identificou-se a presença de quatro harmônicas e seus respectivos períodos e magnitudes. De posse desses coeficientes de Fourier aplicou-se a eles a série de Fourier e construiu-se um modelo matemático que representou a função dano com um intervalo de confiança de 94% tornando assim possível prever sua intensidade no domínio do tempo / Abstract: This study used a real third party excavation damages time series data on a natural gas distribution network that belongs to Comgás in your concession area, Brazil, São Paulo state with 177 cities included in metropolitan areas as São Paulo, Campinas, Santos and Vale do Paraiba, demonstrates that this occurrence is droved by harmonic or cycled forces with different frequencies am magnitudes. Due to the application of Fourier transform at the historical damages time series data there was an identification of four harmonic forces and your periods and magnitudes. With this Fourier coefficients identified was applied to a Fourier series to model the third party damage function in time domain. This model gets a 94% of confidential interval and becomes able to prevent damages or time periods with more incidences of damages / Mestrado / Sistemas de Processos Quimicos e Informatica / Mestre em Engenharia Química

Orientador: Jose Roberto de França Arruda / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-07-31T18:15:00Z (GMT). No. of bitstreams: 1 Rossetto_GustavoDalben_M.pdf: 4484828 bytes, checksum: b149e9723524115d4c39c2ea81d0c5bc (MD5) Previous issue date: 2001 / Resumo: Neste trabalho uma geometria simples (cavidade retangular) é usada para o estudo da metodologia aplicada na análise modal acústica. Modelos analítico e numérico são desenvolvidos para a comparação com os resultados experimentais. Três tipos de dispositivos de excitação do sistema acústico foram construídos. Um baseado num pistão conectado a um shaker, e outros dois usando um alto-falante do tipo driver. O primeiro atuador usando o driver é similar ao modelo desenvolvido por um projeto europeu, onde um tubo flexível com uma terminação instrumentada com um microfone é usado para a condução da excitação acústica. O segundo atuador baseado no uso do driver também usa um tubo flexível, mas este é instrumentado com dois microfones em sua terminação. O comportamento destes dois últimos atuadores em termos de aceleração de volume (essencial para a análise modal acústica experimental) e de potência ativa (necessária para Análise Estatística de Energia Experimental) sendo injetados no meio são investigados. A análise modal experimental da cavidade retangular é realizada e um método que utiliza a transformada de Fourier espacial multidimensional do campo de pressão medido é proposto para-a construção do campo de deslocamento de partícula para a visualização do modo acústico / Abstract: In the present work, a simple geometry (rectangular shallow cavity) is used to investigate the acoustic modal analysis methodology. Analytical and numerical models are developed for the comparison with the experimental results. Three types of excitation devices were constructed. One based on a shaker-driven piston and the other two using a driver loudspeaker. The first actuator based on a driver loudspeaker is similar to a model developed by an EEC project, where a flexible tube with a socket, instrumented with one microphone, at its termination is used to conduct the sound excitation. The second actuator based on a driver loudspeaker alse uses a flexible tube, but it is instrumented with two microphones in its socket instead of one. The behavior of these last two actuators in terms of volume acceleration (essential in the acoustic modal analysis) and active power (necessary for the Experimental Statistical Energy Analysis) being injected into the medium are investigated. The experimental modal analysis of the rectangular cavity is performed and a method using multi-dimensional spatial Fourier transforms of the array of pressure measurements is proposed for the construction of the partic1e displacement field for acoustic mode shape visualization / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

The goal of this thesis is to apply the theory of multilinear weighted Fourier estimates to nonlinear dispersive equations in order to tackle problems in regularity, well-posedness, and pointwise convergence of solutions. Dispersion of waves is a ubiquitous physical phenomenon that arises, among others, from problems in shallow-water propagation, nonlinear optics, quantum mechanics, and plasma physics. A natural tool for understanding the related physics is to study waves/signals simultaneously from both physical and spectral perspectives. Specifically, we will treat nonlinearities as multilinear operator perturbations, which (by the method of spacetime Fourier transforms), exhibit smoothing properties in norms defined to reflect the dispersive natures of the solutions. Our model equation is the quantum Zakharov system, which can be viewed as a variation on the cubic nonlinear Schrödinger equation (NLS). We investigate the model in various contexts (adiabatic limits, nonlinear Schrödinger limits, semi-classical limits). We additionally study a variation of Carleson's Fourier convergence problem in the context of pointwise convergence of the full Schrödinger operator with non-zero potential.

Sexual dimorphism of the distal humerus has been used for the development of morphometric sex estimation methods in human identification. In particular, visual assessment of the olecranon fossa, trochlear shape, and medial epicondyle angle are variably successful in differentiating females and males in African, Asian, and European groups. However, the influence of other factors on the distal humerus has yet to be fully explored. This study utilizes elliptical Fourier analysis (EFA) to examine the shape of these three features for evidence of sexual dimorphism and the effects of age-at-death, stature, and humeral measurements in 261 modern Thai individuals (f=116; m=145), 20-97 years of age. Left humeri were measured, photographed, traced, and analyzed in SHAPE v. 1.3 for EFA. Chi-square, ANOVA, and principal component results indicate sexual dimorphism in the olecranon fossa and trochlear extension shapes, both of which are correlated with epicondylar breadth. Trochlear extension was also found to be correlated with minimum midshaft diameter, vertical head diameter, and stature. The medial epicondyle was not correlated with any of the other factors examined, and age was not correlated with any of the shapes. High rates of intra- and interobserver error were found in the tracings of the three features. While future research should assess methods that better capture the medial epicondyle and improve reliability, features of the distal humerus are sexually dimorphic and somewhat affected by stature and/or body size.