La présente thèse porte sur le développement d'une théorie d'algèbre linéaire, de géométrie et d'analyse basée sur les algèbres (Z2)n-commutatives, c'est-à-dire des algèbres (Z2)n-graduées associatives unitaires satisfaisant ab = (-1)<deg(a),deg(b)>ba, pour tout couple d'éléments homogènes a, b de degrés deg(a), deg(b) où <.,.> est le produit scalaire usuel). Cette généralisation de la supergéométrie a de nombreuses applications : en mathématiques (l'algèbre de Deligne des superformes différentielles, l'algèbre des quaternions et les algèbres de Clifford en sont des exemples) et même en physique (paraparticules). Dans ce travail, les notions de trace et de (super)déterminant pour des matrices à coefficients dans une algèbre gradué-commutative sont définies et étudiés. Une attention particulière est portée au cas des algèbres de Clifford : ce point de vue gradué fournit une nouvelle approche au problème classique du « bon » déterminant pour des matrices à coefficient non-commutatifs (quaternioniques). En outre, nous entreprenons l'étude de la géométrie différentielle (Z2)n-graduée. Privilégiant l'approche par les espaces annelés, les (Z2)n-supervariétés sont définies en choisissant l'algèbre (Z2)n-commutative des séries formelles en variables graduées comme modèle pour le faisceau de fonctions. Les résultats les plus marquants ainsi obtenus sont : le Berezinien gradué et son interprétation cohomologique (essentielle pour établir une théorie de l'intégration) ; le théorème des morphismes, attestant qu'on peut rétablir un morphisme entre (Z2)n-supervariétés à partir de sa seule expression sur les coordonnées ; le théorème de Batchelor-Gawedzki pour les (Z2)n-supervariétés lisses / The present thesis deals with a development of linear algebra, geometry and analysis based on (Z2)n-superalgebras ; associative unital algebras which are (Z2)n-graded and graded-commutative, i.e. statisfying ab=(-1)<deg(a),deg(b)>ba, for all homogeneous elements a, b of respective degrees deg(a), deg(b) in (Z2)n (<.,.> denoting the usual scalar product). This generalization widens the range of applications of supergeometry to many mathematical structures (quaternions and more generally Clifford algebras, Deligne algebra of superdifferential forms, higher vector bundles) and appears also in physics (for describing paraparticles) proving its worth and relevance. In this dissertation, we first focus on (Z2)n-superalgebra theory ; we define and characterize the notions of trace and (super)determinant of matrices over graded-commutative algebras. Special attention is given to the case of Clifford algebras, where our study gives a new approach to treat the classical problem of finding a “good” determinant for matrices with noncommuting (quaternionic) entries. Further, we undertake the study of (Z2)n-graded differential geometry. Privileging the ringed space approach, we define (smooth) (Z2)n-supermanifolds modeling their algebras of functions on the (Z2)n-commutative algebra of formal power series in graded variables, and develop the theory along the lines of supergeometry. Notable results are : the graded Berezinian and its cohomological interpretation (essential to establish integration theory) ; the theorem of morphism, which states that a morphism of (Z2)n-supermanifolds can be recovered from its coordinate expression ; Batchelor-Gawedzki theorem for (Z2)n-supermanifolds

<p>The main result in this thesis is the generalisation of Bergman's diamond lemma for ring theory to power series rings. This generalisation makes it possible to treat problems in which there arise infinite descending chains. Several results in the literature are shown to be special cases of this diamond lemma and examples are given of interesting problems which could not previously be treated. One of these examples provides a general construction of a normed skew field in which a custom commutation relation holds.</p><p>There is also a general result on the structure of totally ordered semigroups, demonstrating that all semigroups with an archimedean element has a (up to a scaling factor) unique order-preserving homomorphism to the real numbers. This helps analyse the concept of filtered structure. It is shown that whereas filtered structures can be used to induce pretty much any zero-dimensional linear topology, a real-valued norm suffices for the definition of those topologies that have a reasonable relation to the multiplication operation.</p><p>The thesis also contains elementary results on degree (as of polynomials) functions, norms on algebras (in particular ultranorms), (Birkhoff) orthogonality in modules, and construction of semigroup partial orders from ditto quasiorders.</p>

The main result in this thesis is the generalisation of Bergman's diamond lemma for ring theory to power series rings. This generalisation makes it possible to treat problems in which there arise infinite descending chains. Several results in the literature are shown to be special cases of this diamond lemma and examples are given of interesting problems which could not previously be treated. One of these examples provides a general construction of a normed skew field in which a custom commutation relation holds. There is also a general result on the structure of totally ordered semigroups, demonstrating that all semigroups with an archimedean element has a (up to a scaling factor) unique order-preserving homomorphism to the real numbers. This helps analyse the concept of filtered structure. It is shown that whereas filtered structures can be used to induce pretty much any zero-dimensional linear topology, a real-valued norm suffices for the definition of those topologies that have a reasonable relation to the multiplication operation. The thesis also contains elementary results on degree (as of polynomials) functions, norms on algebras (in particular ultranorms), (Birkhoff) orthogonality in modules, and construction of semigroup partial orders from ditto quasiorders.

This paper investigates four important methods of solving summation and product problems in mathematics competitions. Chapter 1 presents the basic concepts of sequence and series, including arithmetic sequence (series), geometric sequence (series) and infinite geometric sequence (series). Chapter 2 handles the binomial coefficients and binomial theorem and show they how can be applied to compute series sum. Chapter 3 deals with power series, including interchanging summation and differentiation; interchanging summation and integration; and generating function which expresses a sequence as coefficients arising from a power series in variables. Chapter 4 provides four methods of telescoping sum, including antidifference, partial fractions, trigonometric functions, and factorial functions. Chapter 5 discusses the telescoping product which the main ideas and techniques are analogous to telescoping sum. Two types of telescoping product including difference of two squares and trigonometric functions are investigated.

Ultra narrow-band filters and the use of two loops in a cascade configuration dominate current clock conditioners based on phase-locked-loop (PLL) schemes. Since a PLL exhibits a low-pass transfer function with respect to the reference clock, the noise performance at very close-to-carrier offset frequencies is still determined by the input signal. Although better cleaning can be achieved with extremely narrow loops, an ultra low cut-off frequency could not be selected since the stability of the configuration deteriorates as the filter bandwidth is reduced. This fact suggests that a full-spectrum clock conditioning is not possible using traditional PLL architectures, and an alternative scheme is necessary to attenuate the very-close-to-carrier phase noise (PN). In addition, ultra-narrow loop filters can compromise on-chip integration because of the large size capacitors needed when chosen as passive. Input signal attenuation with relaxed bandwidth requirements becomes the main aspect that a comprehensive clock cleaner must address to effectively regenerate a reference signal. This dissertation describes the Band-Reject Nested-PLL (BRN-PLL) scheme, a modified PLL-based architecture that provides an effective signal cleaning procedure by introducing a notch in the input transfer function through inner and outer loops and a high-pass filter (HPF). This modified response attenuates the reference-signal PN and reduces the size of the loop-filter capacitors substantially. Ultra narrow loops are no longer required because the notch size is related to the system bandwidth. The associated transfer function for the constitutive blocks (phase detectors and local oscillators) show that the output close-to-carrier and far-from-carrier PN sections are mainly dominated by the noise from the inner-PLL phase detector (PD) and local oscillator (LO) located in the outer loop, respectively. The inner-PLL PD transfer function maintains a low-pass characteristic with a passband gain inversely proportional to the PD gain becoming the main contribution around the carrier signal. On the other hand, the PN around the transition frequency is determined mainly by the reference and the inner-PLL LO. Their noise contributions to the output will depend on the associated passband local maxima, which is located at the BRN-PLL transition frequency. Hence, in this region, the inner-PLL LO is selected so that its effect can be held below that of the outer-PLL PD. The BRN-PLL can use a high-Q MEMS-based VCO to further improve the transition region of the output PN profile and an LC-VCO as outer-PLL LO to reduce the noise floor of the output signal. In particular, two tuning mechanisms are explored for the MEMS-VCO: series tuning using varactors and phase shifting of a resonator operating in nonlinear regime. Both schemes are implemented to generate a tunable oscillator with no PN-performance degradation.

Eine der stärksten Erweiterungen der klassischen Theorie formaler Sprachen und Automaten ist die Einbeziehung von Gewichten oder Vielfachheiten aus einem Halbring. Diese Dissertation untersucht gewichtete Automaten über Strukturen mit Nebenläufigkeit. Wir erweitern die Arbeit von Lodaya und Weil und erhalten so ein Modell gewichteter verzweigender Automaten, in dem die Berechnung des Gewichts einer parallelen Komposition anders als die einer sequentiellen Komposition gehandhabt wird. Die von Lodaya und Weil eingeführten Automaten modellieren Nebenläufigkeit durch Verzweigen. Ein verzweigender Automat ist ein endlicher Automat mit drei verschiedenen Typen von Transitionen. Sequentielle Transitionen überführen durch Ausführen eines Ereignisses einen Zustand in einen anderen. Dagegen sind Gabel- und Binde-Transitionen für das Verzweigen verantwortlich. Läufe dieser Automaten werden beschrieben durch sequentiell-parallele posets, kurz sp-posets. Alle Transitionen des Automaten werden in unserem Modell mit Gewichten versehen. Neben dem Nichtdeterminismus und der sequentiellen Komposition wollen wir nun auch die parallele Komposition quantitativ behandeln. Dafür benötigen wir eine Gewichtsstruktur mit einer Addition, einer sequentiellen und einer parallelen Multiplikation. Solch eine Struktur, genannt Bihalbring, besteht damit de facto aus zwei Halbringen mit derselben additiven Struktur. Weiterhin muss die parallele Multiplikation kommutativ sein. Das Verhalten eines gewichteten verzweigenden Automaten ist dann eine Funktion, die jeder sp-poset ein Element eines Bihalbrings zuordnet. Das Hauptresultat charakterisiert das Verhalten dieser Automaten im Sinne von Kleenes und Schützenbergers Sätzen über das Zusammenfallen der Klassen der erkennbaren und der rationalen Sprachen bzw. formalen Potenzreihen. Darüber hinaus untersuchen wir den Abschluss dieser Verhalten unter allen rationalen Operationen und unter dem Hadamard-Produkt. Letztlich diskutieren wir Zusammenhänge zwischen Reihen und Sprachen im Rahmen verzweigender Automaten. / One of the most powerful extensions of classical formal language and automata theory is the consideration of weights or multiplicities from a semiring. This thesis investigates weighted automata over structures incorporating concurrency. Extending work by Lodaya and Weil, we propose a model of weighted branching automata in which the calculation of the weight of a parallel composition is handled differently from the calculation of the weight of a sequential composition. The automata as proposed by Lodaya and Weil model concurrency by branching. A branching automaton is a finite-state device with three different types of transitions. Sequential transitions transform a state into another one by executing an action. In contrast, fork and join transitions are responsible for branching. Executions of such systems can be described by sequential-parallel posets, or sp-posets for short. In the model considered here all kinds of transitions are equipped with weights. Beside non-determinism and sequential composition we would like to deal with the parallel composition in a quantitative way. Therefore, we are in need of a weight structure equipped with addition, a sequential, and, moreover, a parallel multiplication. Such a structure, called a bisemiring, is actually composed of two semirings with the same additive structure. Moreover, the parallel multiplication has to be commutative. Now, the behavior of a weighted branching automaton is a function that associates with every sp-poset an element from the bisemiring. The main result characterizes the behavior of these automata in the spirit of Kleene's and Schützenberger's theorems about the coincidence of recognizable and rational languages, and formal power series, respectively. Moreover, we investigate the closure of behaviors under all rational operations and under Hadamard-product. Finally, we discuss connections between series and languages within our setting.

Made available in DSpace on 2016-06-02T20:06:03Z (GMT). No. of bitstreams: 1 2510.pdf: 1878422 bytes, checksum: 882e21e70271b7a106e3a27a080da004 (MD5) Previous issue date: 2009-04-06 / This work has as central theme the Inflated Modified Power Series Distributions, where the objective is to study its main properties and the applicability in the bayesian context. This class of models includes the generalized Poisson, binomial and negative binomial distributions. These probability distributions are very helpful to models discrete data with inflated values. As particular case the - zero inflated Poisson models (ZIP) is studied, where the main purpose was to verify the effectiveness of it when compared to the Poisson distribution. The same methodology was considered for the negative binomial inflated distribution, but comparing it with the Poisson, negative binomial and ZIP distributions. The Bayes factor and full bayesian significance test were considered for selecting models. / Este trabalho tem como tema central a classe de distribuições série de potências inflacionadas, em que o intuito é estudar suas principais propriedades e a aplicabilidade no contexto bayesiano. Esta classe de modelos engloba as distribuições de Poisson, binomial e binomial negativa simples e as generalizadas e, por isso é muito aplicada na modelagem de dados discretos com valores excessivos. Como caso particular propôs-se explorar a distribuição de Poisson zero inflacionada (ZIP), em que o objetivo principal foi verificar a eficácia de sua modelagem quando comparada à distribuição de Poisson. A mesma metodologia foi considerada para a distribuição binomial negativa inflacionada, mas comparando-a com as distribuições de Poisson, binomial negativa e ZIP. Como critérios formais para seleção de modelos foram considerados o fator de Bayes e o teste de significância completamente bayesiano.

Submitted by Livia Mello (liviacmello@yahoo.com.br) on 2016-09-23T19:10:12Z No. of bitstreams: 1 TeseEBS.pdf: 936379 bytes, checksum: a7cd0812b331249755b7a9df5447e035 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-10T14:48:37Z (GMT) No. of bitstreams: 1 TeseEBS.pdf: 936379 bytes, checksum: a7cd0812b331249755b7a9df5447e035 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-10T14:48:44Z (GMT) No. of bitstreams: 1 TeseEBS.pdf: 936379 bytes, checksum: a7cd0812b331249755b7a9df5447e035 (MD5) / Made available in DSpace on 2016-10-10T14:48:50Z (GMT). No. of bitstreams: 1 TeseEBS.pdf: 936379 bytes, checksum: a7cd0812b331249755b7a9df5447e035 (MD5) Previous issue date: 2016-02-04 / Não recebi financiamento / In regression models in which a covariate is measured with error, 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 literature there are several interesting works that deal with regression models having an additive measurement 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 present 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 the response variable belongs to the exponential family, the model of beta regression with multiplicative measurement error is presented. All proposed models were analysed through simulation studies and applied to real data sets. / 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 multiplicativo, 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 estudos de simulação e aplicados a conjuntos de dados reais.

Submitted by Aelson Maciera (aelsoncm@terra.com.br) on 2017-06-23T18:57:54Z No. of bitstreams: 1 TeseKECZ.pdf: 1800356 bytes, checksum: a555e52c04756515d694387c471b4030 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-06-28T08:32:51Z (GMT) No. of bitstreams: 1 TeseKECZ.pdf: 1800356 bytes, checksum: a555e52c04756515d694387c471b4030 (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-06-28T08:33:00Z (GMT) No. of bitstreams: 1 TeseKECZ.pdf: 1800356 bytes, checksum: a555e52c04756515d694387c471b4030 (MD5) / Made available in DSpace on 2017-06-28T08:41:16Z (GMT). No. of bitstreams: 1 TeseKECZ.pdf: 1800356 bytes, checksum: a555e52c04756515d694387c471b4030 (MD5) Previous issue date: 2016-09-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / The present work's main objective is to study the significance of zeros in an observable and latent data. In observable data set that occur excess of zeros, its common to have sobredispersion. In this sense, the models zero-inflated power series (ZISP) were proposed to accommodate these excesses. Specifically for the analysis of observed data, it was made a study of gradient statistic, proposed by Terrell (2002), to test the hypotheses in relation to inflation parameter ZISP models. This test is based on evaluation of the performance of gradient statistic compared with the classical likelihood ratio (Wilks, 1938), score (Rao, 1948) and Wald (Wald, 1943) statistics. In addition, recently, fragility has being modeled by discrete distributions using non-negative integers values that allows zero fragility, which means, individuals who do not present the event of interest (fraction of zero risk). For this type of latent data, we have proposed a new survival model induced by discrete frailty with ZISP distribution. This proposal brings a real description of individuals without risk, because individuals cured due to genetic factors (immune) are modeled by fraction of deterministic zero risk, while the cured by treatment are modeled by fraction of random zero risk. In this context, we also developed the gradient statistic to verify parameter significance of zero risk for data modeled by fraction of deterministic zero risk. To show our proposals, we present the results of simulation studies and applications using real data. / O presente trabalho teve como objetivo principal, estudar a significância de zeros numa análise de dados observáveis e latentes. Nos conjuntos de dados observáveis que ocorrem excessos de zeros, é comum a existência de sobredispersão. Neste sentido os modelos Zero-Inflacionados Série de Potência (ZISP) foram propostos para acomodar o excesso de zeros. Especifcamente para a análise de dados observáveis com excesso de zeros desenvolvemos um estudo da estatística gradiente, proposta por Terrell (2002), para testar as hipóteses em relação ao parâmetro de inflação do modelo ZISP, baseado na avaliação da performance da estatística gradiente em comparação com as estatísticas clássicas da razão de verossimilhan ça (Wilks, 1938), escore (Rao, 1948) e Wald (Wald, 1943). Por outro lado, recentemente a fragilidade é modelada por distribuições discretas sob os inteiros não negativos e permite fragilidade zero, isto é, indivíduos que não apresentam o evento de interesse (fração de risco zero). Para este tipo dados de latentes, propusemos um novo modelo de sobrevivência induzida por fragilidade discreta com distribuição ZISP. Essa proposta traz uma descrição mais real dos indivíduos sem risco, pois inclui indivíduos curados devido aos fatores genéticos (imunes) modelados como a fração de risco zero determinístico, enquanto que, os indivíduos curados por tratamento são modelados pela fração de risco zero aleatório. Neste contexto desenvolvemos também a estatística gradiente para verificar a significância do parâmetro de risco zero para dados modelados pela fração de risco zero determinístico. E para completar o desenvolvimento das propostas, apresentamos os resultados de estudos de simulação e exemplos de aplicação com uso de dados reais.

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