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Pulino, Filho Athail Rangel 1949. "Diferenças finitas para malhas arbitrarias : via serie de Taylor". [s.n.], 1989. http://repositorio.unicamp.br/jspui/handle/REPOSIP/264687.
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Orientador : Fernando IgutiDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia de Campinas
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Resumo: Este trabalho apresenta duas técnicas para obtenção de equações discretas de diferenças finitas para a solução numérica de problemas de valor de contorno e de auto-valor, bidimensionais, descritos por equações diferenciais parciais de ordem igual ou inferior a 2. As duas técnicas baseiam-se na expansão em série de Taylor da função solução do problema em estudo, diferindo apenas no numero de pontos escolhidos para a montagem das moléculas (esquemas) de diferenças e no correspondente desenvolvimento algébrico para obtenção das equações discretas. A possibilidade de escolha arbitrária da localização dos pontos que compõem o domínio discreto de solução permite a elaboração de algoritmos para cálculo automático com a mesma versatilidade de algoritmos baseados no método dos elementos finitos, quer no que se refere ao tratamento de contornos curvos, quer na possibilidade de adensamento da malha em regiões em que o gradiente da função solução varie muito rapidamente. São apresentados exemplos de aplicação em condução de calor em regime permanente, Torção livre de hastes retas e vibração livre de membranas
Abstract: This work presents two procedures for obtaining discrete finite-difference equations for the numerical solution of two-dimensional second order boundary value and eigenvalue problems. These two procedures are based on the Taylor's series expansion of the solution function, and they differ from each other by the number of nodes of the difference scheme (star) and the corresponding algebraic derivation of the difference equations. A completely geometrically irregular array of nodal points opens the possibility for developing computational algorithms with the same flexibility as those based on the Finite Element Method for dealing with irregular boundaries and mesh refinement. Three example problems (Heat Conduction, Torsion of a Rod and Free Vibration of Flat Membranes) are presented
Mestrado
Mestre em Engenharia Mecânica
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Perugini, Stefania. "Le funzioni circolari ed esponenziali". Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/8694/.
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Nei capitoli I e II ho costruito rigorosamente le funzioni circolari ed esponenziali rispettivamente attraverso un procedimento analitico tratto dal libro Analisi Matematica di Giovanni Prodi. Nel III capitolo, dopo aver introdotto il numero di Nepero e come limite di una particolare successione monotona, ho calcolato i limiti notevoli dell'esponenziale e della sua inversa, che sono alla base del calcolo differenziale di queste funzioni, concludendo poi la sezione dimostrando l'irrazionalità del numero e, base dei logaritmi naturali. Nel capitolo successivo ho dato, delle funzioni circolari ed esponenziali, i rispettivi sviluppi in serie di Taylor ma solamente nel V capitolo potremo renderci veramente conto di come i risultati ottenuti siano fra loro dipendenti.
In particolare verrà messa in evidenza come il legame del tutto naturale che si osserva fra le funzioni circolari e le funzioni esponenziali rappresenta le fondamenta di argomenti molto notevoli e pieni di significato, come l'estensione ai numeri complessi dell'esponenziale o le celebri identità di Eulero. L'ultimo capitolo vedrà come protagonista pi greco, così misterioso quanto affascinante, che per secoli ha smosso gli animi dei matematici intenzionati a volerne svelare la natura. Come per il numero di Nepero, non potrà mancare un paragrafo dedicato alla dimostrazione della sua non razionalità.
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Davólio, Alessandra 1980. "Aproximações para os coeficientes de reflexão e analise de AVO". [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307608.
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Orientador: Lucio Tunes dos SantosDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: O estudo dos coeficientes de reflexão, de suas aproximações e consequentemente da análise de AVO (do inglês, Amplitude Variation with Offset) desenvolve um papel bastante importante na indústria do petróleo, por auxiliar na descrição litológica da região de interesse. Neste trabalho, inicialmente abordamos as principais idéias envolvidas na dedução das equações dos coeficientes de reflexão PP (ondas P incidente e P refletida) e PS (ondas P incidente e S refletida). Na sequência, são apresentadas diferentes aproximações para estas equações, seguidas de uma análise do comportamento das mesmas quando comparadas entre si e entre suas respectivas expressões exatas. Introduzimos uma nova aproximação para o coeficiente de reflexão PS similar à impedância de reflexão do coeficiente PP proposta recentemente. Finalizamos o trabalho discutindo o conceito de inversão de dados, avaliando a precisão dos indicadores apresentados, e fazendo um breve sumário da tradicional análise de AVO
Abstract: The study of the reflection coefficients, their approximations and the AVO (Amplitude Variation with Offset) analysis plays an important role in the oil industry as they can help to describe the interest region lithology. The first part of this work deals with the main ideas of the deduction of the reflection coefficients PP (P incident and P reflected waves) and PS (P incident and S reflected waves). Then, different approximations for these equations are presented, followed by a discussion of their behavior when compared among them and with their exact expressions. We introduce a new approximation for the reflection coefficient PS similar to the reflection impedance of PP coefficient proposed recently. To conclude, some indicators and their accuracy are discussed and a brief summary about the traditional AVO analysis is presented.
Mestrado
Mestre em Matemática Aplicada
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Munkhammar, Joakim. "Riemann-Liouville Fractional Derivatives and the Taylor-Riemann Series". Thesis, Uppsala University, Department of Mathematics, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-121418.
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Seo, Dong-Won. "Performance analysis of queueing networks via Taylor series expansions". Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/25098.
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Tian, Haitao. "Taylor meshless method for thin plates". Thesis, Paris, ENSAM, 2019. http://www.theses.fr/2019ENAM0036.
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Une nouvelle classe de méthodes sans maillage - Taylor Meshless Method (TMM) - a été introduite. Elle repose sur une solution explicite des équations aux dérivées partielles dans le domaine à l’aide des extensions de séries de Taylor. Parce que la PDE est résolue analytiquement dans le domaine, on est réduit à un problème de frontière discret dont la taille est plutôt petite.L’efficacité de TMM a été vérifiée en résolvant certaines équations aux dérivées partielles. Dans les cas étudiés, TMM est robuste et efficace. Pour les problèmes linéaires 2D, un domaine suffit pour résoudre les problèmes de valeurs limites.TMM est utilisé pour résoudre les problèmes de plaques de Kirchhoff. Les techniques de TMM permettent de réduire considérablement le degré de liberté, de manière à augmenter le degré de polynôme à un niveau très élevé. Les plaques sandwich laminées sont étudiées à l'aide de TMM. Différents cas sont considérés pour tester l'efficacité et le rendement de la méthode. L'erreur montre une convergence exponentielle avec l'augmentation du degré de polynômes.TMM est combiné à la méthode asymptotique-numérique (ANM) pour résoudre les problèmes de déviation importante des plaques minces. Les équations non linéaires sont développées sous la forme de séries de puissances, ce qui conduit le problème à une série d'équations linéaires. La longueur de l'étape est déterminée automatiquement par une technique de suivi de chemin fiable. La précision et l'efficacité de ANM-TMM sont vérifiées à l'aide de ces exemples et la méthode peut facilement être étendue à d'autres problèmes non linéaires.Basé sur le travail des problèmes de flexion, le flambement des plaques minces est étudié. Cette approche tire pleinement parti de la technique de suivi de chemin. Ainsi, le processus de flambement peut être illustré de manière beaucoup plus précise que celle d'autres méthodes. La performance de l'approche est examinée par une série de problèmes de flambement de référence.Les problèmes de plissement de la membrane sont étudiés. Différentes tensions et imperfections sont imposées pour tester leur influence sur les motifs de rides finaux. Les résultats montrent que TMM peut réaliser des simulations convergentes avec de très petites imperfections et des charges de tension comparées aux méthodes par éléments finis. L’approche de l’analyse de la membrane ridée par la TMM est bien établieA new class of meshless method – Taylor Meshless Method (TMM) - has been introduced that relies on an explicit solution of the Partial Differential Equations inside the domain with the help of Taylor series expansions. Because the PDE is solved analytically in the domain, one is reduced to a discrete boundary problem whose size is rather small.The effectiveness and efficiency of TMM have been verified by solving some partial differential equations. In the cases that have been studied, TMM is robust and effective. For 2D linear problems, one domain is sufficient to solve boundary value problems.TMM is used to solve Kirchhoff plate problems. Techniques in TMM help to reduce the degree of freedoms significantly so that one can increase the degree of the polynomials to a very high level. Laminated sandwich plates are studied by using TMM. Different cases are considered to test the effectiveness and efficiency of the method. The error shows exponential convergence with the increase of degree of polynomials.TMM is combined with asymptotic-numerical method (ANM) to solve large deflection problems of thin plates. The nonlinear equations are expanded in the form of power series, which leads the problem to a series of linear equations. The step length is determined automatically by a reliable path following technique. The accuracy and efficiency of ANM-TMM is verified through these examples and the method can be easily extended to other nonlinear problems.Based on the work of bending problems, the buckling of thin plates are studied. This approach fully takes the advantage of the path following technique. Thus the buckling process can be illustrated much more accurate than that by other methods. The performance of the approach is investigated by a series of benchmark buckling problems.The membrane wrinkling problems are studied. Different tension loads and imperfections are imposed to test their influence on final wrinkle patterns. The results show that TMM can accomplish convergent simulations with very small imperfections and tension loads in comparison with finite element methods. The approach of wrinkled membrane analysis by TMM has been well established
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Bastos, Claudinei Martins. "Um breve estudo sobre funções e séries de Taylor". reponame:Repositório Institucional da UFABC, 2016.
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Orientador: Prof. Dr. Vinicius Cifú LopesDissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional, 2016.
Inicia-se o presente trabalho apresentando ao leitor a necessidade de se apropriar profundamente dos conceitos relacionados às funções lineares e quadráticas, seu crescimento e decrescimento, estudos dos sinais e construção de seus respectivos gráficos, da resolução pelo método do varal para inequações-produto e inequações-quociente, que auxiliam na construção de gráficos de funções de graus maiores que dois, das variáveis e substituição de variáveis, bem como calcular e operar com polinômios, especialmente a divisão euclidiana e o algoritmo de Briot-Ruffini, para então estudar as sequências e séries numéricas. O estudo das séries de potências, desenvolvido no capítulo 5, é de fundamental importância na expansão do polinômio de Taylor, com suas aproximações sucessivas para as funções seno, cosseno entre outras, definidas por séries de potências e para a perfeita compreensão dos resultados presentes no capítulo final.
The present work begins by presenting to the reader the need to take a firm hold of the concepts related to linear and quadratic functions, their growth and decrement, studies of their signal and construction of their respective graphs, resolution by the factor method for product inequalities and quotient inequalities, which help constructing graphs of functions of degrees greater than two, variables and variable substitution, as well as to calculate and operate with polynomials, especially the Euclidean division and the Briot-Ruffini algorithm, and then to study the sequences and series numbers. The study of power series, developed in Chapter 5, has fundamental importance for the expansion of the Taylor polynomial, with its successive approximations for the functions sine, cosine among others, defined by power series, and for the perfect understanding of the results shown in the final chapter.
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santos, Eduardo Isidoro dos. "O Polinômio e Série de Taylor: Um estudo com aplicações". Universidade Federal da Paraíba, 2017. http://tede.biblioteca.ufpb.br:8080/handle/tede/9833.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this work,we present two important concepts: Taylor Polynomialand Taylor Series. We discus show theTaylor Polynomial can be used toapproximate the value of Analytic function sin the neighbor hoodo fagiven point, an destimate the precision of the approximation obtained. Subsequently,we study the possibility oflocallyre- presenting functions through a power system,called theTaylor Serie. We concludeby presenting some application sof the result sobtained.
Neste trabalho,abordamos dois conceitos importantes:o Polinômiode Taylor e a Série de Taylor. Apresentamos como o Polinômio de Taylor pode ser usado para aproximar o valor de funções analíticas na vizinhança de um ponto determinado e esti- mamos a precisão da aproximação obtida.Posteriormente,estudamos a possibilidade de representar,localmente,funções através de uma serie de potências,chamadas série de Taylor Finalizamos apresentando algumas aplicações dos resultados obtidos.
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Dula, Mark, Eunice Mogusu, Sheryl Strasser, Ying Liu y Shimin Zheng. "Median and Mode Approximation for Skewed Unimodal Continuous Distributions using Taylor Series Expansion". Digital Commons @ East Tennessee State University, 2016. https://dc.etsu.edu/etsu-works/112.
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Background: Measures of central tendency are one of the foundational concepts of statistics, with the most commonly used measures being mean, median, and mode. While these are all very simple to calculate when data conform to a unimodal symmetric distribution, either discrete or continuous, measures of central tendency are more challenging to calculate for data distributed asymmetrically. There is a gap in the current statistical literature on computing median and mode for most skewed unimodal continuous distributions. For example, for a standardized normal distribution, mean, median, and mode are all equal to 0. The mean, median, and mode are all equal to each other. For a more general normal distribution, the mode and median are still equal to the mean. Unfortunately, the mean is highly affected by extreme values. If the distribution is skewed either positively or negatively, the mean is pulled in the direction of the skew; however, the median and mode are more robust statistics and are not pulled as far as the mean. The traditional response is to provide an estimate of the median and mode as current methodological approaches are limited in determining their exact value once the mean is pulled away. Methods: The purpose of this study is to test a new statistical method, utilizing the first order and second order partial derivatives in Taylor series expansion, for approximating the median and mode of skewed unimodal continuous distributions. Specifically, to compute the approximated mode, the first order derivatives of the sum of the first three terms in the Taylor series expansion is set to zero and then the equation is solved to find the unknown. To compute the approximated median, the integration from negative infinity to the median is set to be one half and then the equation is solved for the median. Finally, to evaluate the accuracy of our derived formulae for computing the mode and median of the skewed unimodal continuous distributions, simulation study will be conducted with respect to skew normal distributions, skew t-distributions, skew exponential distributions, and others, with various parameters. Conclusions: The potential of this study may have a great impact on the advancement of current central tendency measurement, the gold standard used in public health and social science research. The study may answer an important question concerning the precision of median and mode estimates for skewed unimodal continuous distributions of data. If this method proves to be an accurate approximation of the median and mode, then it should become the method of choice when measures of central tendency are required.
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Abraao, York Mark. "Exploring the phase diagram with Taylor series: epic voyage or just another bad trip". Thesis, McGill University, 2010. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=95229.
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The phase transition at the QCD critical end point is believed to be in the 3D Ising universality class. A recently proposed method of using low order Taylor series coefficients to pinpoint the location of the QCD critical end point is tested with the Ising Model. The finding is that one cannot rely solely on the lowest order series coefficients to accurately locate the Ising critical point, and moreover, the values of higher order coefficients are clouded with statistical uncertainty. The method does manage to qualitatively capture the features of the Ising Model phase diagram.La transition de phase au point critique de la chromodynamique quantique est censé d'appartenir à la classe d'universalité d'Ising à 3D. Une méthode récemment proposée qui emploie la série de Taylor de certaines fonctions thermodynamiques pour déduire l'emplacement de ce point critique est testée avec le modèle d'Ising. La conclusion est qu'on ne peut pas compter uniquement sur les coefficients d'ordre bas de cette série pour localiser avec précision le point critique. D'ailleurs, les coefficients d'ordre supérieur sont difficiles à calculer à cause de l'incertitude statistique. Néanmoins, on trouve que la méthode décrit avec succès les caractèristiques qualitatives du diagramme des phases du modèle d'Ising. fr
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Biazotti, Herbert Antonio. "Soluções solitônicas por aproximantes de Padé via método iterativo de Taylor /". Guaratinguetá, 2018. http://hdl.handle.net/11449/157328.
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Orientador: Denis DalmaziCoorientador: Álvaro de Souza Dutra
Banca: Julio Marny Hoff da Silva
Banca: Rafael Augusto Couceiro Corrêa
Resumo: Certos sistemas físicos podem ser descritos por uma classe de equações não-lineares. Essas equações descrevem pacotes de onda chamado de sólitons que tem aplicações em diversas áreas, por exemplo, Óptica, Cosmologia, Matéria Condensada e Física de Partículas. Alguns métodos foram desenvolvidos ao longo dos anos para encontrar as soluções dessas equações. Buscaremos essas soluções usando o que chamamos de Método Iterativo de Taylor (MIT), que fornece uma solução aproximada em polinômio de Taylor de forma distinta do que se tem na literatura. Usaremos o MIT para calcular soluções por aproximantes de Padé que são razões entre dois polinômios e fornecem soluções melhores que o polinômio de Taylor que o gerou. Inicialmente resolveremos a equação de um modelo de um campo denominado λφ4 . Em seguida resolveremos um modelo com dois campos escalares acoplados e encontraremos uma solução analítica aproximada em casos onde não existe solução analítica, explorando a diversidade das soluções do modelo. Usando essa abordagem por aproximantes de Padé veremos que há algumas vantagens em relação a outros métodos
Abstract: Certain physical systems can be described by a class of non-linear differential equations. Those equations describe wave packets called solitons which have applications in several areas, for example, Optics, Cosmology, Condensed Matter, and Particle Physics. Some methods have been developed over the years to find solutions to these equations. We will look for those solutions using what we call the Taylor Iterative Method (TIM), which provides an approximate solution in terms of a Taylor's polynomial in a unusual way, regarding the present literature. We will use TIM to calculate solutions by Padé approximants, which are ratios between two polynomials and provide better solutions than the Taylor polynomial itself. We first solve the field equation of a model called λφ4 . Then we will solve a model with two coupled scalar fields and find an approximate analytic solution in cases where there is no known analytical solution, exploring the diversity of the solutions of the model. We will see that there are some advantages in using the Padè approximants as compared to other methods
Mestre
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Viola, Denise Nunes. "Redução no vício da distribuição da deviance para dados de contagem". Universidade de São Paulo, 2001. http://www.teses.usp.br/teses/disponiveis/11/11134/tde-26032002-113122/.
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Dados de contagem podem ser considerados, em geral, como provenientes de uma distribuição de Poisson. Neste contexto, a análise de tais dados apresenta certas dificuldades, pois não segue algumas pressuposições básicas para o ajuste de um modelo matemático. Desse modo, algumas transformações são sugeridas, mas nem sempre bons resultados são obtidos. No enfoque de Modelos Lineares Generalizados, a estatística que mede a qualidade do ajuste do modelo para os dados é chamada deviance. Porém, a distribuição da deviance é, em geral, desconhecida. No entanto, para dados com distribuição de Poisson, pode-se mostrar que a distribuição da deviance se aproxima de uma distribuição ?2, mas tal aproximação não é boa para tamanhos pequenos de amostra. Para melhorar essa aproximação, alguns fatores de correção para os dados são sugeridos, mas os resultados obtidos ainda não são satisfatórios. Assim, o objetivo deste trabalho é propor um novo fator de correção para os dados seguindo uma distribuição de Poisson, de modo a se obter uma melhora na distribuição da deviance para qualquer tamanho de amostra. Para isto, será adicionada uma constante à variável resposta e, através do valor esperado da deviance, calcula-se tal constante de modo a reduzir o erro cometido na aproximação. Para verificar a melhora na aproximação da distribuição da deviance a uma distribuição qui-quadrado, dados de uma distribuição de Poisson são simulados e o valor da deviance é calculado. QQ-plots são construídos para a comparação com a distribuição qui-quadrado.Analysis of count data presents, in general, can be supposed coming from a Poisson distribution. The analysis of such data have some problems once the underlying distribution of them does not follow the basic assumptions to fit a model. Some tranformations can be suggested, but good results are not always obtained. In the approach of the Generalized Linear Models, the deviance is the statistics that measures the goodness of fit, but its distribution is unknown. Furthermore, considering Poisson distribution data, it is possible to approximate the distribution of the deviance for a chi-square distribution, but such approximation is not good for small sample size. In order of improve this approximation, corrections for the data are suggested, but the results are not good yet. Then, the aim of this work is to propose a new correction factor for data following a Poisson distribution in order to obtain an improvement in the distribution of the deviance for any sample size. For this, just adding a constant at the response variable and, through the expected value of the deviance, such constant is obtained in order to reduce the error in the aproximation. Simulated data from the Poisson distribution were made to calculate the deviance with and without the correction and QQ-plots were used to compare the values of the deviance with the chi-square distribution.
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Saunders, Robert P. y Charles Natale Calvano. "An investigation of the resistance properties of a modern trimaran combatant ship based on Taylor Standard Series and Series 64". Thesis, Monterey, California. Naval Postgraduate School, 1995. http://hdl.handle.net/10945/7477.
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Braga, Márcio Feliciano 1983. "Discretização e controle por rede de sistemas politópicos com taxa de amostragem incerta e atraso". [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/261057.
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Orientadores: Pedro Luis Dias Peres, Ricardo Coração de Leão Fontoura de OliveiraTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação
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Resumo: Esta tese investiga o problema de discretização de sistemas lineares incertos em dois cenários distintos. O primeiro supõe que as matrizes do sistema e a taxa de amostragem são incertas e invariantes no tempo, descritas em termos de politopos. No segundo caso supõe-se que todos os parâmetros incertos, incluindo o intervalo de amostragem, podem variar no tempo; que os parâmetros do sistema possuem limitantes conhecidos para a taxa de variação e são continuamente monitorados, de forma que uma nova amostra é coletada sempre que ocorrer uma mudança significativa nos parâmetros ou quando um intervalo máximo desde a última amostragem for atingido, caracterizando-se assim a chamada amostragem baseada em eventos. O objetivo é projetar controladores digitais para o sistema discretizado e garantir teoricamente a estabilidade robusta em malha fechada do sistema contínuo original. Considera-se também um atraso induzido pela rede no modelo discreto. Do ponto de vista da discretização, propõem-se extensões da expansão em série de Taylor até um grau arbitrário l aplicada ao sistema original como uma solução para tratar as expressões envolvendo exponenciais de matrizes incertas. O modelo discreto resultante é composto por matrizes polinomiais homogêneas de grau l com parâmetros pertencentes ao produto cartesiano de simplexos unitários, chamado multi-simplex, mais um termo aditivo limitado em norma que representa o erro residual de aproximação. Modelos mais acurados são obtidos com o aumento do grau l que, consequentemente, produz resíduos com menor norma, possibilitando resultados de síntese menos conservadores. Também são propostas condições na forma de desigualdade matriciais lineares para a síntese de controladores digitais robustos por realimentação de estados e de saída, cômputo de norma H2 e análise de estabilidade para sistemas discretos polinomiais com incertezas aditivas limitadas em norma. As condições empregam funções de Lyapunov com dependência polinomial nos parâmetros incertos para certificar a estabilidade em malha fechada do sistema controlado. Em alguns casos, as desigualdades matriciais possuem um parâmetro escalar, tornando-se lineares para valores fixos desse parâmetro. Os resultados obtidos são gradativamente menos conservadores com o aumento do grau da matriz de Lyapunov, podendo ainda ser melhorados com o auxílio de uma busca linear no parâmetro escalar. Experimentos numéricos são apresentados para ilustrar a versatilidade da metodologia proposta, aplicável a uma classe mais geral de problemas de controle por rede que os métodos existentes na literatura
Abstract: This thesis investigates the problem of discretization of uncertain linear systems in two distinct scenarios. The first one supposes that the matrices of the system and the sampling rate are uncertain and time-invariant, described in terms of polytopes. The second case considers that all uncertain parameters, including the sampling interval, can vary in time and that the parameters of the system have known bounds for the rate of variation and are continuously monitored, in such a way that a new sample is collected whenever a significant change in the parameters occurs or when a maximum time interval since the previous sample is reached, thus characterizing the so-called event-based sampling. The aim is to design digital controllers for the discretized system and to guarantee the closed-loop robust stability of the original continuous-time system. A network-induced delay is also considered in the discretetime model. From the discretization point of view, extensions of the Taylor series expansion of an arbitrary degree ℓ applied to the original system are proposed as a solution to deal with expressions involving the exponential of uncertain matrices. The resulting discrete-time model consists of homogeneous polynomial matrices of degree ℓ with parameters belonging to the Cartesian product of unit simplexes, called multi-simplex, plus an additive norm-bounded term which represents the approximation residual error. More accurate models are obtained with the increase in the degree ℓ which, consequently, yields residues with lower norms, allowing to produce less conservative synthesis results. Conditions based on linear matrix inequalities for the synthesis of robust state-feedback and output-feedback digital controllers, H2 norm computation, and stability analysis for polynomial discrete-time systems with additive norm-bounded terms are also proposed. The conditions employ Lyapunov functions with polynomial dependency on the uncertain parameters to certify the closed-loop stability of the controlled system. In some cases, the matrix inequalities have a scalar parameter, becoming linear for fixed values of the parameter. The obtained results are gradually less conservative with the increase of the degree of the Lyapunov matrix and can be further enhanced with the help of a line search in the scalar parameter. Numerical experiments are presented to illustrate the versatility of the proposed methodology, applicable to a more general class of networked control problems than the existing methods in the literature.
Doutorado
Automação
Doutor em Engenharia Elétrica
15
Awuah, E. B. "The feasibility of Taylor series methods on digital continuous systems described as networks of interconnected boxes". Thesis, University of Reading, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.374696.
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Khajotia, Burzin. "Cased based reasoning Taylor series model to predict corrosion rate in oil and gas wells and pipelines /". Ohio : Ohio University, 2007. http://www.ohiolink.edu/etd/view.cgi?ohiou1173828758.
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Yang, Jie. "Solving Partial Differential Equations by Taylor Meshless Method". Thesis, Université de Lorraine, 2018. http://www.theses.fr/2018LORR0032/document.
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Le but de cette thèse est de développer une méthode numérique simple, robuste, efficace et précise pour résoudre des problèmes d'ingénierie de grande taille à partir de la méthode Taylor Meshless (TMM) et fournir de nouvelles idées principales de TMM est d'utiliser comme fonctions de forme des polynômes d'ordre élevé qui sont des solutions approchées de l'EDP. Ainsi la discrétisation ne concerne que la frontière. Les coefficients de ces fonctions de forme sont obtenus en discrétisant les conditions aux limites par des procédures de collocation associées à la méthode des moindres carrés. TMM est alors une véritable méthode sans maillage sans processus d'intégration, les conditions aux limites étant obtenues par collocation. Les principales contributions de cette thèse sont les suivantes: 1) Basé sur TMM, un algorithme général et efficace a été développé pour résoudre des EDP elliptiques tridimensionnelles; 2) Trois techniques de couplage pour des résolutions par morceaux ont été discutées dans des cas de problèmes à grande échelle: la méthode de collocation par les moindres carrés et deux méthodes de couplage basées sur les multiplicateurs de Lagrange; 3) Une méthode numérique générale pour résoudre les EDP non-linéaires a été proposée en combinant la méthode de Newton, la TMM et la technique de différentiation automatique. 4) Pour résoudre des problèmes avec un bord non régulier, des solutions singulières satisfaisant l'équation de contrôle sont introduites comme des fonctions de forme complémentaires, ce qui fournit une base théorique pour la résolution de problèmes singuliersBased on Taylor Meshless Method (TMM), the aim of this thesis is to develop a simple, robust, efficient and accurate numerical method which is capable of solving large scale engineering problems and to provide a new idea for the follow-up study on meshless methods. To this end, the influence of the key factors in TMM has been studied by solving three-dimensional and non-linear Partial Differential Equations (PDEs). The main idea of TMM is to use high order polynomials as shape functions which are approximated solutions of the PDE and the discretization concerns only the boundary. To solve the unknown coefficients, boundary conditions are accounted by collocation procedures associated with least-square method. TMM that needs only boundary collocation without integration process, is a true meshless method. The main contributions of this thesis are as following: 1) Based on TMM, a general and efficient algorithm has been developed for solving three-dimensional PDEs; 2) Three coupling techniques in piecewise resolutions have been discussed and tested in cases of large-scale problems, including least-square collocation method and two coupling methods based on Lagrange multipliers; 3) A general numerical method for solving non-linear PDEs has been proposed by combining Newton Method, TMM and Automatic Differentiation technique; 4) To apply TMM for solving problems with singularities, the singular solutions satisfying the control equation are introduced as complementary shape functions, which provides a theoretical basis for solving singular problems
18
Khajotia, Burzin K. "CASE BASED REASONING – TAYLOR SERIES MODEL TO PREDICT CORROSION RATE IN OIL AND GAS WELLS AND PIPELINES". Ohio University / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1173828758.
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Hottois, JoAnn. "Albert Davis Taylor: his impact on 20th century American landscape architecture combined with a bibliographical compilation to serve as a resource to encourage further research on A. D. Taylor". The Ohio State University, 1991. http://rave.ohiolink.edu/etdc/view?acc_num=osu1347647794.
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Kratky, Joseph J. "SERIES EXPANSION FOR SEMI-SPDES WITH REMARKS ON HYPERBOLIC SPDES ON THE LATTICE". Kent State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=kent1310614464.
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Schneider, Eduardo da Silva. "Exact Calculations for the Lagrangian Velocity". Bowling Green State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1555086598198833.
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22
Richter, Birgit. "Taylorapproximationen und kubische Konstruktionen von [gamma]-Moduln". Bonn : [Druck : Rheinische Friedrich-Wilhelms-Universität Bonn], 2000. http://catalog.hathitrust.org/api/volumes/oclc/47306421.html.
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23
Pang, Yu. "Optimization of fixed-point circuits represented by Taylor Series and real-valued polynomials including analysis of precision and range". Thesis, McGill University, 2010. http://digitool.Library.McGill.CA:8881/R/?func=dbin-jump-full&object_id=92401.
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24
Reis, Daniel de Brito. "Abordagem semi-paramétrica para cópulas variantes no tempo em séries temporais financeiras". Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-22082017-004041/.
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Neste trabalho foram utilizadas cópulas bivariadas variantes no tempo para modelar a dependência entre séries de retornos financeiros. O objetivo deste trabalho é apresentar uma abordagem de estimação semi-paramétrica de cópulas variantes no tempo a partir de uma função de cópula paramétrica na qual o parâmetro varia no tempo. A função do parâmetro desconhecido será estimada pela aproximação de ondaleta Haar, polinômio de Taylor e Kernel. O desempenho dos três métodos de aproximação será comparado via estudos de simulação. Uma aplicação aos dados reais será apresentada para ilustrar a metodologia estudada.In this work the bivariate Time-varying copula models have been used to model the dependence between payback. The aim of this work is to present an approach of semiparametric estimation of Time-varying copula models from a parametric copula function in which the parameter varies with the time. The function of the unknown parameter will be estimated by Haar wavelet approach, Taylor series and smoothing Kernel approximation. The measured performance of the three estimation method will be compared by simulation study. An application of the data will be presented to illustrate the studied methodology.
25
Quintanilha, Laura de Mesquita. "Análise do modelo de fluxo de potência retangular intervalar baseado na expansão completa da série de Taylor". Universidade Federal de Juiz de Fora (UFJF), 2018. https://repositorio.ufjf.br/jspui/handle/ufjf/7554.
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A análise de fluxo de potência visa calcular as tensões nas barras e as correntes nos ramos, para um dado cenário pré-estabelecido de geração e carga. É uma ferramenta essencial na operação e no controle dos sistemas elétricos de potência. Na análise tradicional, os parâmetros são tratados como quantidades determinísticas. Contudo, na prática, esses parâmetros podem apresentar incertezas associadas à medição ou à variação inerente ao longo do tempo. Em adição, o crescimento da participação de fontes intermitentes, como eólica e solar, em redes elétricas, aumenta o grau de incerteza e, portanto, estudos específicos de fluxo de potência devem ser desenvolvidos no sentido de tratar esta possível variabilidade de dados. Neste contexto, este trabalho investiga um método, publicado na literatura, que modela o fluxo de potência sujeito a incertezas associadas às cargas ativa e reativa das barras. A idéia básica deste método é proceder a expansão completa, em termos da série de Taylor, das equações de potência expressas em coordenadas retangulares das tensões nas barras. O método é implementado em MATLAB, considerando diferentes incertezas aplicadas aos sistemas IEEE 57 barras e brasileiro de 107 barras. Os resultados são, então, comparados com aqueles gerados pela matemática intervalar e pela simulação de Monte Carlo. De forma geral, a qualidade dos intervalos gerados pelo método em estudo é melhor que aquela apresentada pela matemática intervalar.
The power flow analysis aims to calculate bus voltage and current in branches, for a given pre-established scenario of generation and load. It is an essential tool in electrical power systems operation and control In traditional analysis, the parameters are treated as deterministic values. However, in practice, these parameters may present uncertainties associated with measurement as well as their inherent variation over the time. In addition, the growth of intermittent sources participation, such as wind and solar, into power grids has increased the uncertainties level, which demands the development of specific power flow studies in order to deal with data variability. In this context, this work investigates a method published in literature, that models the power flow subject to uncertainties associated with active and reactive bus loads. The basic idea of this method is to carry out the complete expansion of power equations, in terms of Taylor series, expressed in rectangular coordinates of bus voltages. The method is implemented in MATLAB, considering different uncertainties applied to IEEE 57 bus and Brazilian 107 bus. The results are then compared with those generated by interval mathematics and Monte Carlo simulation. In general, the quality of this method generated intervals is better than that presented by interval mathematics.
26
Humená, Patrícia. "Adaptivní metody řešení eliptických parciálních diferenciálních rovnic". Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2013. http://www.nusl.cz/ntk/nusl-236199.
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The objective of this project is to get familiar with the numerical solution of partial differential equations. This solution will be implemented by using a grid refinement based on the aposteriory error estimation.
27
Nečasová, Gabriela. "Paralelní numerické řešení parciálních diferenciálních rovnic". Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2014. http://www.nusl.cz/ntk/nusl-236119.
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This thesis deals with the topic of partial differential equations parallel solutions. First, it focuses on ordinary differential equations (ODE) and their solution methods using Taylor polynomial. Another part is devoted to partial differential equations (PDE). There are several types of PDE, there are parabolic, hyperbolic and eliptic PDE. There is also explained how to use TKSL system for PDE computing. Another part focuses on solution methods of PDE, these methods are forward, backward and combined methods. There was explained, how to solve these methods in TKSL and Matlab systems. Computing accuracy and time complexity are also discussed. Another part of thesis is PDE parallel solutions. Thanks to the possibility of PDE convertion to ODE systems it is possible to represent each ODE equation by independent operation unit. These units enable parallel computing. The last chapter is devoted to implementation. Application enables generation of ODE systems for TKSL system. These ODE systems represent given hyperbolic PDE.
28
Ciydem, Mehmet. "Ray Based Finite Difference Method For Time Domain Electromagnetics". Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12606633/index.pdf.
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In this study, novel Ray Based finite difference method for Time Domain electromagnetics(RBTD) has been developed. Instead of solving Maxwell&rsquos hyperbolic partial differential equations directly, Geometrical Optics tools (wavefronts, rays) and Taylor series have been utilized. Discontinuities of electromagnetic fields lie on wavefronts and propagate along rays. They are transported in the computational domain by transport equations which are ordinary differential equations. Then time dependent field solutions at a point are constructed by using Taylor series expansion in time whose coefficients are these transported distincontinuties. RBTD utilizes grid structure conforming to wave fronts and rays and treats all electromagnetic problems, regardless of their dimensions, as one dimensional problem along the rays. Hence CFL stability condition is implemented always at one dimensional eqaulity case on the ray. Accuracy of RBTD depends on the accuracy of grid generation and numerical solution of transport equations. Simulations for isotropic medium (homogeneous/inhomogeneous) have been conducted. Basic electromagnetic phenomena such as propagation, reflection and refraction have been implemented. Simulation results prove that RBTD eliminates numerical dispersion inherent to FDTD and is promising to be a novel method for computational electromagnetics.
29
Capanni, Niccolo Francesco. "The functionality of spatial and time domain artificial neural models". Thesis, Robert Gordon University, 2006. http://hdl.handle.net/10059/241.
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This thesis investigates the functionality of the units used in connectionist Artificial Intelligence systems. Artificial Neural Networks form the foundation of the research and their units, Artificial Neurons, are first compared with alternative models. This initial work is mainly in the spatial-domain and introduces a new neural model, termed a Taylor Series neuron. This is designed to be flexible enough to assume most mathematical functions. The unit is based on Power Series theory and a specifically implemented Taylor Series neuron is demonstrated. These neurons are of particular usefulness in evolutionary networks as they allow the complexity to increase without adding units. Training is achieved via various traditiona and derived methods based on the Delta Rule, Backpropagation, Genetic Algorithms and associated evolutionary techniques. This new neural unit has been presented as a controllable and more highly functional alternative to previous models. The work on the Taylor Series neuron moved into time-domain behaviour and through the investigation of neural oscillators led to an examination of single-celled intelligence from which the later work developed. Connectionist approaches to Artificial Intelligence are almost always based on Artificial Neural Networks. However, another route towards Parallel Distributed Processing was introduced. This was inspired by the intelligence displayed by single-celled creatures called Protoctists (Protists). A new system based on networks of interacting proteins was introduced. These networks were tested in pattern-recognition and control tasks in the time-domain and proved more flexible than most neuron models. They were trained using a Genetic Algorithm and a derived Backpropagation Algorithm. Termed "Artificial BioChemical Networks" (ABN) they have been presented as an alternative approach to connectionist systems.
30
Anderson, Travis V. "Efficient, Accurate, and Non-Gaussian Error Propagation Through Nonlinear, Closed-Form, Analytical System Models". BYU ScholarsArchive, 2011. https://scholarsarchive.byu.edu/etd/2675.
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Uncertainty analysis is an important part of system design. The formula for error propagation through a system model that is most-often cited in literature is based on a first-order Taylor series. This formula makes several important assumptions and has several important limitations that are often ignored. This thesis explores these assumptions and addresses two of the major limitations. First, the results obtained from propagating error through nonlinear systems can be wrong by one or more orders of magnitude, due to the linearization inherent in a first-order Taylor series. This thesis presents a method for overcoming that inaccuracy that is capable of achieving fourth-order accuracy without significant additional computational cost. Second, system designers using a Taylor series to propagate error typically only propagate a mean and variance and ignore all higher-order statistics. Consequently, a Gaussian output distribution must be assumed, which often does not reflect reality. This thesis presents a proof that nonlinear systems do not produce Gaussian output distributions, even when inputs are Gaussian. A second-order Taylor series is then used to propagate both skewness and kurtosis through a system model. This allows the system designer to obtain a fully-described non-Gaussian output distribution. The benefits of having a fully-described output distribution are demonstrated using the examples of both a flat rolling metalworking process and the propeller component of a solar-powered unmanned aerial vehicle.
31
Kraus, Michal. "Paralelní výpočetní architektury založené na numerické integraci". Doctoral thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2013. http://www.nusl.cz/ntk/nusl-261227.
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This thesis deals with continuous system simulation. The systems can be described by system of differential equations or block diagram. Differential equations are usually solved by numerical methods that are integrated into simulation software such as Matlab, Maple or TKSL. Taylor series method has been used for numerical solutions of differential equations. The presented method has been proved to be both very accurate and fast and also procesed in parallel systems. The aim of the thesis is to design, implement and compare a few versions of the parallel system.
32
Iša, Radek. "Efektivní výpočty vícenásobných integrálů". Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2017. http://www.nusl.cz/ntk/nusl-363877.
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This thesis deals with the design system for multiple integrals for diferential expression with space variables. Today, integration is one of engineering problems. Reader is acquainted with different method of integration, then with numerican integration and Taylor series. The practical aim of this work is to design software and hardware system of numerican integration multiple integrals.
33
Vopěnka, Václav. "Vývojové prostředí numerických integrátorů". Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2011. http://www.nusl.cz/ntk/nusl-412852.
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This term project describes transformation of system of diferential equations into polynomial form. Such transformed systems of diferential equations can be subsequently solved using Taylor series. This method enables computing of initial problem's numeric solution using dynamical order selection in order to achieve required accuracy. The work mathematically proves, that transformed systems of diferential equations have the same solution as the original systems. This transformation can be used for all mathematic functions commonly used in technical applications. The work also focuses on optimization of given problem and implements it in programme taylor. This progamme enables user to solve given diferential equations with chosen parameters.
34
Janko, Roman. "Modelování elektrických obvodů ve specializovaném paralelním systému". Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2013. http://www.nusl.cz/ntk/nusl-236416.
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This work provides an overview of methods for the numerical solution of differential equations. Options of their parallelization, a division of computational operations on multiple microprocessors, are provided with emphasis placed on the Taylor series. The next part of the work is devoted to the description of a specialized parallel system, which was design to fast solving of these equations. Differential equations are appropriate to describe electrical circuits. An important characteristic of each circuit is its behavior in the frequency domain. The aim of this thesis was to design and implement a program which investigate frequency characteristics of AC circuits. A method for analyzing a circuit and automatically assembling corresponding equations is presented. These differential equations are then solved in TKSL. At the end of this work a time consumption is evaluated and compared with Matlab.
35
Matečný, František. "Hardwarová realizace numerického integrátoru s metodou vyššího řádu". Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2018. http://www.nusl.cz/ntk/nusl-385907.
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This work describes numerical integration and solution for ordinary differential equations by the Taylor series by different types of integrators. The next part is a description of floating point and fixed point arithmetic. Subsequently, we are presenting designs and calculation methods for parallels multiplication and division integrators in floating point and fixed point arithmetic. The designs were realized in VHDL and implemented on FPGA. Finally we summarizes the proposed solution and compare time complexity with another numerical methods.
36
Gradinaru, Mihai. "Fonctions de Green et support de diffusions hypoelliptiques". Phd thesis, Université Paris Sud - Paris XI, 1995. http://tel.archives-ouvertes.fr/tel-00011820.
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La première partie contient une description précise de la singularité près de la diagonale de la fonction de Green
associée à un opérateur hypoelliptique. L'approche est
probabiliste et repose sur le développement de Taylor
stochastique des trajectoires de la diffusion associée
et sur les estimations à priori de la fonction de Green.
On donne des exemples et des applications à la théorie du
potentiel.
Dans la deuxième partie on étend le théorème de support
de Stroock-Varadhan pour la norme hölderienne. L'outil central
est l'estimation de la probabilité pour que le mouvement brownien
ait une grande norme hölderienne, conditionnellement au fait
qu'il ait une petite norme uniforme.
37
Naeem, Muhammad Farhan. "Analysis of an Ill-posed Problem of Estimating the Trend Derivative Using Maximum Likelihood Estimation and the Cramér-Rao Lower Bound". Thesis, Linnéuniversitetet, Institutionen för fysik och elektroteknik (IFE), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-95163.
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The amount of carbon dioxide in the Earth’s atmosphere has significantly increased in the last few decades as compared to the last 80,000 years approximately. The increase in carbon dioxide levels are affecting the temperature and therefore need to be understood better. In order to study the effects of global events on the carbon dioxide levels, one need to properly estimate the trends in carbon dioxide in the previous years. In this project, we will perform the task of estimating the trend in carbon dioxide measurements taken in Mauna Loa for the last 46 years, also known as the Keeling Curve, using estimation techniques based on a Taylor and Fourier series model equation. To perform the estimation, we will employ Maximum Likelihood Estimation (MLE) and the Cramér-Rao Lower Bound (CRLB) and review our results by comparing it to other estimation techniques. The estimation of the trend in Keeling Curve is well-posed however, the estimation for the first derivative of the trend is an ill-posed problem. We will further calculate if the estimation error is under a suitable limit and conduct statistical analyses for our estimated results.
38
Doan, Van Tu. "Modèles réduits pour des analyses paramètriques du flambement de structures : application à la fabrication additive". Thesis, Valenciennes, 2018. http://www.theses.fr/2018VALE0017/document.
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Le développement de la fabrication additive permet d'élaborer des pièces de forme extrêmement complexes, en particulier des structures alvéolaires ou "lattices", où l'allégement est recherché. Toutefois, cette technologie, en très forte croissance dans de nombreux secteurs d'activités, n'est pas encore totalement mature, ce qui ne facilite pas les corrélations entre les mesures expérimentales et les simulations déterministes. Afin de prendre en compte les variations de comportement, les approches multiparamétriques sont, de nos jours, des solutions pour tendre vers des conceptions fiables et robustes. L'objectif de cette thèse est d'intégrer des incertitudes matérielles et géométriques, quantifiées expérimentalement, dans des analyses de flambement. Pour y parvenir, nous avons, dans un premier temps, évalué différentes méthodes de substitution, basées sur des régressions et corrélations, et différentes réductions de modèles afin de réduire les temps de calcul prohibitifs. Les projections utilisent des modes issus soit de la décomposition orthogonale aux valeurs propres, soit de développements homotopiques ou encore des développements de Taylor. Dans un second temps, le modèle mathématique, ainsi créé, est exploité dans des analyses ensemblistes et probabilistes pour estimer les évolutions de la charge critique de flambement de structures latticesThe development of additive manufacturing allows structures with highly complex shapes to be produced. Complex lattice shapes are particularly interesting in the context of lightweight structures. However, although the use of this technology is growing in numerous engineering domains, this one is not enough matured and the correlations between the experimental data and deterministic simulations are not obvious. To take into account observed variations of behavior, multiparametric approaches are nowadays efficient solutions to tend to robust and reliable designs. The aim of this thesis is to integrate material and geometric uncertainty, experimentally quantified, in buckling analyses. To achieve this objective, different surrogate models, based on regression and correlation techniques as well as different reduced order models have been first evaluated to reduce the prohibitive computational time. The selected projections rely on modes calculated either from Proper Orthogonal Decomposition, from homotopy developments or from Taylor series expansion. Second, the proposed mathematical model is integrated in fuzzy and probabilistic analyses to estimate the evolution of the critical buckling load for lattice structures
39
Šátek, Václav. "Analýza stiff soustav diferenciálních rovnic". Doctoral thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2012. http://www.nusl.cz/ntk/nusl-261258.
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The solving of stiff systems is still a contemporary sophisticated problem. The basic problem is the absence of precise definition of stiff systems. A question is also how to detect the stiffness in a given system of differential equations. Implicit numerical methods are commonly used for solving stiff systems. The stability domains of these methods are relatively large but the order of them is low. The thesis deals with numerical solution of ordinary differential equations, especially numerical calculations using Taylor series methods. The source of stiffness is analyzed and the possibility how to reduce stiffness in systems of ordinary differential equations (ODEs) is introduced. The possibility of detection stiff systems using explicit Taylor series terms is analyzed. The stability domains of explicit and implicit Taylor series are presented. The solutions of stiff systems using implicit Taylor series method are presented in many examples. The multiple arithmetic must be used in many cases. The new suitable parallel algorithm based on implicit Taylor series method with recurrent calculation of Taylor series terms and Newton iteration method (ITMRN) is proposed.
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Du, Plessis Irma. "Narrating the "nation" : cultural production, political community and young Afrikaans readers". Thesis, University of Pretoria, 2004. http://hdl.handle.net/2263/28861.
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This study explores the relationship between literature and society against the background of the emergence in the 1930s and 1940s in South Africa of a form of Afrikaner nationalism that was spearheaded by members of the Afrikaner petty bourgeoisie and intelligentsia and a subsequent expansion in Afrikaans literary production. It addresses problems of explanation in Afrikaner nationalism by focusing attention on the question of culture, the field of imagination and the domain of everyday life. In particular, the study examines the Keurboslaan series - a series of schoolboy stories aimed at juvenile readers - by Stella Blakemore, and traces the production, circulation and critical reception of the twenty titles in the series. The first title in this series was published in 1941 and the series has been reprinted several times over a number of decades and as recently as 1997. Drawing on the work of Benedict Anderson, this study illuminates the link between the emergence of print capitalism and the production of popular fiction on the one hand and nationalism on the other. Whilst this is a link that is not often explored, an analysis of the Keurboslaan series illustrates that the study of popular fiction can illuminate the practices through which nationalism gains popular support. It is argued that the Keurboslaan series produced a narrative of the Afrikaner ‘nation’ in popular fiction, but that this narrative was not authenticated by the intelligentsia and petty bourgeoisie who were the driving forces behind Afrikaner nationalism and its contents. It is further argued that this ‘narrative of nation’ circulated alongside more official narratives of the ‘nation’ espoused in discourses of religion, science and literature published in Afrikaans. The narrative of ‘nation’ in Keurboslaan – whilst sharing many similarities with official narratives in other discourses – but also differs from those discourses in important respects. It is argued that the popular series was influential precisely because it imagined the Afrikaner ‘nation’ in very different ways and on different terms from those discourses. Moreover, the form in which this narrative was produced, that is popular youth literature, appealed to readers of Afrikaans who were in search of escapist fiction. For these readers, the Keurboslaan series helped to give shape to and created new possibilities for interpreting the world that they inhabited. Reading the school as a corollary of the ‘nation’, it is argued that the narrative of the nation in Keurboslaan series explores the boundaries between the self and the other and posits the self as a danger to the self, resulting in an emphasis on the need to discipline the self. This kind of analysis also creates the space for examining in what ways ideas and identities about ‘race’, gender, sexuality, class and ‘nation’ are constructed in the texts. Yet, the study maintains that whilst the Keurboslaan series contributed to creating a space in which a particular understanding of the self and the world becomes possible, and whereas the reader is not conceived of as a completely free agent that can derive simply any meaning from the text, the study and its theoretical underpinnings do not fully account for individual readers’ engagement with popular texts and the ways in which reading strategies and habits can generate different, ambiguous or inconclusive meanings for readers. It is suggested that a study of popular texts and Afrikaner nationalism employing theories of reading and the reader will complement this analysis.Thesis (DLitt (Literary Theory))--University of Pretoria, 2004.
Afrikaans
unrestricted
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Kadák, Michal. "Vizuální editor elektrických schemat". Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2009. http://www.nusl.cz/ntk/nusl-235502.
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This work deals with the possibilities of modeling electrical circuits and methods of solving these models. It focuses on the analysis of today's systems, so that their features can be used in our graphic editor design.
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Čambor, Michal. "Paralelní řešení parciálních diferenciálnich rovnic". Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2011. http://www.nusl.cz/ntk/nusl-412855.
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This thesis deals with the concepts of numerical integrator using floating point arithmetic for solving partial differential equations. The integrator uses Euler method and Taylor series. Thesis shows parallel and serial approach to computing with exponents and significands. There is also a comparison between modern parallel systems and the proposed concepts.
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Al-Mohy, Awad. "Algorithms for the matrix exponential and its Fréchet derivative". Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/algorithms-for-the-matrix-exponential-and-its-frechet-derivative(4de9bdbd-6d79-4e43-814a-197668694b8e).html.
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New algorithms for the matrix exponential and its Fréchet derivative are presented. First, we derive a new scaling and squaring algorithm (denoted expm[new]) for computing eA, where A is any square matrix, that mitigates the overscaling problem. The algorithm is built on the algorithm of Higham [SIAM J.Matrix Anal. Appl., 26(4): 1179-1193, 2005] but improves on it by two key features. The first, specific to triangular matrices, is to compute the diagonal elements in the squaring phase as exponentials instead of powering them. The second is to base the backward error analysis that underlies the algorithm on members of the sequence {||Ak||1/k} instead of ||A||. The terms ||Ak||1/k are estimated without computing powers of A by using a matrix 1-norm estimator. Second, a new algorithm is developed for computing the action of the matrix exponential on a matrix, etAB, where A is an n x n matrix and B is n x n₀ with n₀ << n. The algorithm works for any A, its computational cost is dominated by the formation of products of A with n x n₀ matrices, and the only input parameter is a backward error tolerance. The algorithm can return a single matrix etAB or a sequence etkAB on an equally spaced grid of points tk. It uses the scaling part of the scaling and squaring method together with a truncated Taylor series approximation to the exponential. It determines the amount of scaling and the Taylor degree using the strategy of expm[new].Preprocessing steps are used to reduce the cost of the algorithm. An important application of the algorithm is to exponential integrators for ordinary differential equations. It is shown that the sums of the form $\sum_{k=0}^p\varphi_k(A)u_k$ that arise in exponential integrators, where the $\varphi_k$ are related to the exponential function, can be expressed in terms of a single exponential of a matrix of dimension $n+p$ built by augmenting $A$ with additional rows and columns. Third, a general framework for simultaneously computing a matrix function, $f(A)$, and its Fréchet derivative in the direction $E$, $L_f(A,E)$, is established for a wide range of matrix functions. In particular, we extend the algorithm of Higham and $\mathrm{expm_{new}}$ to two algorithms that intertwine the evaluation of both $e^A$ and $L(A,E)$ at a cost about three times that for computing $e^A$ alone. These two extended algorithms are then adapted to algorithms that simultaneously calculate $e^A$ together with an estimate of its condition number. Finally, we show that $L_f(A,E)$, where $f$ is a real-valued matrix function and $A$ and $E$ are real matrices, can be approximated by $\Im f(A+ihE)/h$ for some suitably small $h$. This approximation generalizes the complex step approximation known in the scalar case, and is proved to be of second order in $h$ for analytic functions $f$ and also for the matrix sign function. It is shown that it does not suffer the inherent cancellation that limits the accuracy of finite difference approximations in floating point arithmetic. However, cancellation does nevertheless vitiate the approximation when the underlying method for evaluating $f$ employs complex arithmetic. The complex step approximation is attractive when specialized methods for evaluating the Fréchet derivative are not available.
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Oqielat, Moa'ath Nasser. "Modelling water droplet movement on a leaf surface". Queensland University of Technology, 2009. http://eprints.qut.edu.au/30232/.
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The central aim for the research undertaken in this PhD thesis is the development of a model for simulating water droplet movement on a leaf surface and to compare the model behavior with experimental observations. A series of five papers has been presented to explain systematically the way in which this droplet modelling work has been realised. Knowing the path of the droplet on the leaf surface is important for understanding how a droplet of water, pesticide, or nutrient will be absorbed through the leaf surface. An important aspect of the research is the generation of a leaf surface representation that acts as the foundation of the droplet model. Initially a laser scanner is used to capture the surface characteristics for two types of leaves in the form of a large scattered data set. After the identification of the leaf surface boundary, a set of internal points is chosen over which a triangulation of the surface is constructed. We present a novel hybrid approach for leaf surface fitting on this triangulation that combines Clough-Tocher (CT) and radial basis function (RBF) methods to achieve a surface with a continuously turning normal. The accuracy of the hybrid technique is assessed using numerical experimentation. The hybrid CT-RBF method is shown to give good representations of Frangipani and Anthurium leaves. Such leaf models facilitate an understanding of plant development and permit the modelling of the interaction of plants with their environment. The motion of a droplet traversing this virtual leaf surface is affected by various forces including gravity, friction and resistance between the surface and the droplet. The innovation of our model is the use of thin-film theory in the context of droplet movement to determine the thickness of the droplet as it moves on the surface. Experimental verification shows that the droplet model captures reality quite well and produces realistic droplet motion on the leaf surface. Most importantly, we observed that the simulated droplet motion follows the contours of the surface and spreads as a thin film. In the future, the model may be applied to determine the path of a droplet of pesticide along a leaf surface before it falls from or comes to a standstill on the surface. It will also be used to study the paths of many droplets of water or pesticide moving and colliding on the surface.
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Ashu, Tom A. Ashu. "Non-Smooth SDEs and Hyperbolic Lattice SPDEs Expansions via the Quadratic Covariation Differentiation Theory and Applications". Kent State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=kent1500334062680747.
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Joldes, Mioara Maria. "Approximations polynomiales rigoureuses et applications". Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2011. http://tel.archives-ouvertes.fr/tel-00657843.
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Quand on veut évaluer ou manipuler une fonction mathématique f, il est fréquent de la remplacer par une approximation polynomiale p. On le fait, par exemple, pour implanter des fonctions élémentaires en machine, pour la quadrature ou la résolution d'équations différentielles ordinaires (ODE). De nombreuses méthodes numériques existent pour l'ensemble de ces questions et nous nous proposons de les aborder dans le cadre du calcul rigoureux, au sein duquel on exige des garanties sur la précision des résultats, tant pour l'erreur de méthode que l'erreur d'arrondi.Une approximation polynomiale rigoureuse (RPA) pour une fonction f définie sur un intervalle [a,b], est un couple (P, Delta) formé par un polynôme P et un intervalle Delta, tel que f(x)-P(x) appartienne à Delta pour tout x dans [a,b].Dans ce travail, nous analysons et introduisons plusieurs procédés de calcul de RPAs dans le cas de fonctions univariées. Nous analysons et raffinons une approche existante à base de développements de Taylor.Puis nous les remplaçons par des approximants plus fins, tels que les polynômes minimax, les séries tronquées de Chebyshev ou les interpolants de Chebyshev.Nous présentons aussi plusieurs applications: une relative à l'implantation de fonctions standard dans une bibliothèque mathématique (libm), une portant sur le calcul de développements tronqués en séries de Chebyshev de solutions d'ODE linéaires à coefficients polynômiaux et, enfin, un processus automatique d'évaluation de fonction à précision garantie sur une puce reconfigurable.
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Šťastná, Hilda. "Simulace CMOS VLSI obvodů". Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2017. http://www.nusl.cz/ntk/nusl-363732.
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This diploma thesis deals with processes of electrical circuits calculations in the last years' worldwide standards like Dymola, MATLAB, Maple or SPICE applications. Circuits calculations are linked with methods for solving linear differential equations, used in this work also by verification of functionality of designed models for CMOS inverter, CMOS NAND, CMOS NOR. Numerical integration method in combination with Taylor series is a suitable method also for parallel calculations of CMOS VLSI circuits. CMOS circuits simulation was implemented with this method in applications in MATLAB language, solving circuits, represented by differential equations. Functionality of the applications was verified by some real examples. Significant acceleration of calculations using Taylor series compared to other methods is an important factor in choosing methods used in circuit simulations.
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Opálka, Jan. "Automatické řízení výpočtu ve specializovaném výpočetním systému". Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2016. http://www.nusl.cz/ntk/nusl-363728.
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This work deals with the automatic control of calculations of specialized system. The reader is acquainted with the numerical solution of differential equations by Taylor series method and numerical integrators. The practical aim of this work is to analyze parallel characteristics of Taylor series method, specification of parallel math operations and design of control of this operations.
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Krajčíková, Lucia. "Komplexná analýza požívaných výnosových vzťahov u dlhopisov". Master's thesis, Vysoká škola ekonomická v Praze, 2015. http://www.nusl.cz/ntk/nusl-201567.
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This thesis covers detailed analysis of bond pricing function. It focuses on connections between mathematical definitions and financial practice and it points out advantages and drawbacks of currently used function. Well known properties of this function are extended to negative internal rate of return values. This topic is further discussed with internal rate of return polynomial equations solving. Taylor series approximation is also shown regarding duration and convexity of bonds.
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Minárik, Michal. "Modelování elektrických obvodů s využitím diferenciálního počtu". Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2010. http://www.nusl.cz/ntk/nusl-237269.
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This master's thesis deals with modeling of linear electrical circuits through the differential algebraical equation systems. It describes methods of numerical solving, discusses the need of algebraical conversions and possibility of minimalization through the use of parasitic components. In addition, it involves the design and implementation of extension of available simulation tool.