Soit p un polynôme d'une variable complexe z. On peut trouver plusieurs inégalités reliant le module maximum de p et une combinaison de ses coefficients. Dans ce mémoire, nous étudierons principalement les preuves connues de l'inégalité de Visser. Nous montrerons aussi quelques généralisations de cette inégalité. Finalement, nous obtiendrons quelques applications de l'inégalité de Visser à l'inégalité de Chebyshev. / Let p be a polynomial in the variable z. There exist several inequalities between the coefficents of p and its maximum modulus. In this work, we shall mainly study known proofs of the Visser inquality together with some extensions. We shall finally apply the inequality of Visser to obtain extensions of the Chebyshev inequality.

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.

Orientador: Prof. Dr. Vinicius Cifú Lopes / Dissertação (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.

Submitted by Daniele Amaral (daniee_ni@hotmail.com) on 2016-09-14T19:37:01Z No. of bitstreams: 1 TeseVAAM.pdf: 2213045 bytes, checksum: 7a27583f2dfac9c11da36b29050f4fe4 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-16T19:48:45Z (GMT) No. of bitstreams: 1 TeseVAAM.pdf: 2213045 bytes, checksum: 7a27583f2dfac9c11da36b29050f4fe4 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-16T19:48:49Z (GMT) No. of bitstreams: 1 TeseVAAM.pdf: 2213045 bytes, checksum: 7a27583f2dfac9c11da36b29050f4fe4 (MD5) / Made available in DSpace on 2016-09-16T19:48:53Z (GMT). No. of bitstreams: 1 TeseVAAM.pdf: 2213045 bytes, checksum: 7a27583f2dfac9c11da36b29050f4fe4 (MD5) Previous issue date: 2015-08-14 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / In this thesis, we construct distribution functions for analysis of lifetimes with the focus in scenes of latent risks inspired in models of the carcinogenesis process. Some properties of these distribution functions are presented and discussed as well as the viability front the models in literature. In some cases the models were describes as long-time model where a part of population presents infinite lifetime, i.e, on the population in study some objects are not susceptible (or immunes) for the event of interest. Some models present complexity in the maximization and was necessary the implementation of routines of maximization that allows us the control some variables that are not offered in routines in tradicional programs. The implemented routine is available in appendix. / Nesta tese apresentamos novas distribuições para o estudo do tempo de vida com foco no cenário de riscos latentes com interpretações das construções dos modelos direcionados com os estudos da carcinogênese. Várias propriedades das distribuições são apresentadas e discutidas bem como a viabilidade destes novos modelos frente a vários modelos na literatura. Alguns dos modelos são estendidos para modelos de longa duração, que são modelos que permitem que os tempos de vida sejam infinitos ou em outras palavras que existem indivíduos não suscetíveis (ou curados) ao evento de interesse. Pela complexidade de vários modelos obtidos foi necessário a implementação de rotinas de maximização para o controle de variáveis que não são oferecidos nas rotinas de maximização em programas tradicionais e esta rotina está disponibilizada em anexo.

Cette thèse est composée d'une partie sur la conjecture des familles stables par unions et de quatre autres chapitres consacrés aux sujets liés aux suites automatiques. Dans la première partie, on donne une condition suffisante pour qu'une version affaiblie de la conjecture soit vraie. On donne aussi un majorant de la fréquence maximale minimale dans une famille de taille $n$. Dans Chapitre 3 on démontre que la formule d'extraction des coefficients des séries algébriques connue pour les corps à caractéristique $0$ est une conséquence d'un théorème de Furstenberg qui permet d'écrire certaines séries algébriques comme les diagonales des fractions rationnelles à deux variables. Comme ce théorème est valide pour tous les corps, la formule l'est aussi. Dans Chapitre 4 on donne une généralisation des résultats de J.-P. Allouche et J. Shallit concernant certains produits infinis et les fonctions qui comptent le nombre d'occurrences d'un facteur dans l'expansion en base $B$ de $n$. Dans Chapitre 5 on donne une construction explicite d'un mot infini avec complexité en facteur de $\Theta(n^t)$ avec la valuation $p$-adique. Dans Chapitre 6 on donne une nouvelle démonstration de la transcendance de la série formelle $L(1,\chi_s)/\Pi$, où $L$ est un analogue des fonctions $L$ de Dirichlet en caractéristique finie défini par D. Goss et $\Pi$ l'analogue de $\pi$ défini par L. Carlitz. / This thesis comprises one part concerning the union-closed sets conjecture and four other chapters dedicated to subjects related to automatic sequences. In the first part, we give a sufficient condition for a weaker version of the conjecture ($\varepsilon$-union closed sets conjecture) to hold. We also give an upper bound of the minimal maximal frequency for a family of size $n$. In Chapter 3 we prove that the coefficient extraction formula for algebraic series known for fields of characteristic $0$ is a consequence of a theorem of Furstenberg that says certains algebraic series can be written as the diagonals of a rational fractions in two variables. As the theorem is true for all fields, so is the formula. In Chapter 4 we give a generalization of the result of J.-P. Allouche and J. Shallit concerning certain infinite products and block-counting functions. In Chapter 5 we give an explicit construction based on $p$-adic valuation of an infinite word with subword complexity $\Theta(n^t)$. In Chapter 6 we give a new proof of the transcendence of the power series $L(1,\chi_s)/\Pi$, where $L$ is an analogue in positive characteristics of Dirichlet $L$ functions defined by D. Goss and $\Pi$ the analogue of $\pi$ defined by L. Carlitz.

This thesis will focus on generating the probability mass function using Fibonacci sequenceas the coefficient of the power series. The discrete probability, named Fibonacci distribution,was formed by taking into consideration the recursive property of the Fibonacci sequence,the radius of convergence of the power series, and additive property of mutually exclusiveevents. This distribution satisfies the requisites of a legitimate probability mass function. It's cumulative distribution function and the moment generating function are then derived and the latter are used to generate moments of the distribution, specifically, the mean and the variance. The characteristics of some convergent sequences generated from the Fibonacci sequenceare found useful in showing that the limiting form of the Fibonacci distribution is a geometricdistribution. Lastly, the paper showcases applications and simulations of the Fibonacci distribution using MATLAB. / <p></p><p></p><p></p>

No description available.

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Em modelos de regressão em que uma covariável é medida com erro, é comum o uso de estruturas que relacionam a covariável observada com a verdadeira covariável não observada. Essas estruturas são usualmente aditivas ou multiplicativas. Na literatura existem diversos trabalhos interessantes que tratam de modelos de regressão com erro de medida aditivo, muitos dos quais são modelos lineares com covariáveis e erro de medida normalmente distribuídos. Para modelos em que o erro de medida é multipicativo, não se encontra na literatura o mesmo desenvolvimento teórico encontrado para modelos em que o erro de medida é aditivo. O mesmo vale para situações em que as suposições de normalidade para as covariáveis e erro de medida não se aplicam. Este trabalho propõe a construção, definição, métodos de estimação e análise de diagnóstico para modelos de regressão com erro de medida multiplicativo em uma das covariáveis. Para esses modelos, consideramos que a variável resposta possa pertencer ou à classe de modelos de regressão série de potências modificadas ou à família exponencial. O rol de distribuições pertencentes à família série de potências modificada é bem abrangente, portanto, neste trabalho, desenvolvemos a teoria de estimação e validação do modelo primeiramente de forma geral e, para exemplificar, apresentamos o modelo de regressão binomial negativa com erro de medida. para o caso em que a variável resposta pertença à família exponencial. apresentamos o modelo de regressão beta com erro de medida multiplicativo. Todos os modelos propostos foram analisados através de estados de simulação e aplicados a conjuntos de dados reais. / In regression models in which a covariate is measured with erros, it is common to use structures that correlate the observed covariate with the true non-observed covariate. Such structures are usually additive or multiplicative. In the literatue there are several interesting works that deal with regression models having an additive measuremsnt error, many of which are linear models with covariate and measurement error normally distributed. For models having a multiplicative measurement error, one does not find in the literature the same theoretical amount of works as one finds for models in which the measurement error is additive. The same happens in situations where the supositions of normality for the covariates and the measurement errors do not apply. The presente work proposes the construction,definition, estimation methods, and diagnostic analysis for the regression models with a multiplicative measurement error in one of the covariates. For these models it is considered that the response variable may belong either to the class of modified power series regression models or to the exponential family. The list of distributions belonging to the family modified power series is rather comprehensive; for this reason this work develops, firstly and in a general way, the models estimation and validation theory, and, as an example, presents the model of negative binomial regression with measurement error. In the case where response variable belongs to the exponential family, the model of beta regression with multiplicative measurement error is presented. All proposed models were analysed through simulationb studies and applied to real data sets.

Na literatura da área da análise de sobrevivência existem os modelos tradicionais, ou sem fração de cura, e os modelos de longa duração, ou com fração de cura. Recentemente tem sido proposto um modelo mais geral, conhecido como o modelo com fatores de risco latentes com esquemas de ativação. Nesta tese são deduzidas novas propriedades que possuem a função de sobrevivência, a função de taxa de risco e o valor esperado, quando e considerado o modelo com fatores de risco latentes. Estas propriedades são importantes, já que muitos outros modelos que tem aparecido na literatura recentemente podem ser considerados como casos particulares do modelo com fatores de risco latentes. Além disto, são propostos novos modelos de sobrevivência e estes são aplicados a conjuntos de dados reais. Também é realizado um estudo de simulação e uma análise de sensibilidade, para mostrar a qualidade destes modelos / In the survival literature we can find traditional models without cure fraction and longterm models with cure fraction. A more general risk factor model with latent activation scheme has been recently proposed. In this thesis we deduce new properties for the survival function, hazard function and expected value for this model. Since many recent survival models can be regarded as particular cases of the risk factor model with latent activation scheme these properties are of great relevance. In addition we propose new survival models that are applied to real data examples. A simulation and sensibility analysis are also performed to asses the goodness of fit of these models