Cette thèse se compose de deux projets. Le premier concerne la structure des fonctions multiplicatives dont les moyennes sont petites. En particulier, dans ce projet, nous établissons le comportement moyen des valeurs \(f(p)\) de \(f\) aux nombres premiers pour des fonctions \(f\) multiplicatives appropriées lorsque leurs sommes partielles \(\sum_{n\leqslant x}f(n)\) sont plus petites que leur borne supérieure triviale par un facteur d′une puissance de \(\log x\). Ce résultat poursuit un travail antérieur de Koukoulopoulos et Soundararajan et il est construit sur des idées provenant du traitement plus soigné de Koukoulopoulos sur le cas special des fonctions multiplicatives bornées. Le deuxième projet de la thèse est inspiré par un analogue d’une estimation que Linnik a déduit dans sa tentative de prouver son célèbre théorème concernant la taille du plus petit nombre premier d’une progression arithmétique. Cette estimation fournit une formule asymptotique fortement uniforme pour les sommes de la fonction de von Mangoldt \(\Lambda\) sur les progressions arithmétiques. Dans la littérature, ses preuves existantes utilisent des informations non triviales sur les zéros des fonctions \(L\) de Dirichlet \(L(\cdot,\chi)\) et le but du deuxième projet est de présenter une approche différente, plus élémentaire qui récupère cette estimation en évitant la “langue” de ces zéros. Pour le développement de cette méthode alternative, nous utilisons des idées qui apparaissent dans le grand crible prétentieux (pretentious large sieve) de Granville, Harper et Soundararajan. De plus, comme dans le cas du premier projet, nous empruntons également des idées du travail de Koukoulopoulos sur la structure des fonctions multiplicatives bornées à petites moyennes. / This thesis consists of two projects. The first one is concerned with the structure of multiplicative functions whose averages are small. In particular, in this project, we establish the average behaviour of the prime values \(f(p)\) for suitable multiplicative functions \(f\) when their partial sums \(\sum_{n\leqslant x}f(n)\) admit logarithmic cancellations over their trivial upper bound. This result extends previous related work of Koukoulopoulos and Soundararajan and it is built upon ideas coming from the more careful treatment of Koukoulopoulos on the special case of bounded multiplicative functions. The second project of the dissertation is inspired by an analogue of an estimate that Linnik deduced in his attempt to prove his celebrated theorem regarding the size of the smallest prime number of an arithmetic progression. This estimate provides a strongly uniform asymptotic formula for the sums of the von Mangoldt function \(\Lambda\) on arithmetic progressions. In the literature, its existing proofs involve non-trivial information about the zeroes of Dirichlet \(L\)-functions \(L(\cdot,\chi)\) and the purpose of the second project is to present a different, more elementary approach which recovers this estimate by avoiding the “language” of those zeroes. For the development of this alternative method, we make use of ideas that appear in the pretentious large sieve of Granville, Harper and Soundararajan. Moreover, as in the case of the first project, we also borrow insights from the work of Koukoulopoulos on the structure of bounded multiplicative functions with small averages.

The current economic strategy of the European Union - the Europe 2020 Strategy - has defined five measurable Headline Targets to enhance economic growth and allowed the Member States to set their own national numerical values for these targets. This thesis analyses quality of this target setting process. First, it tries to figure out whether the targets have been set better than in the preceding Lisbon Strategy. Second, it examines whether the National Targets have been defined clearly and unequivocally. Third and the most important, based on original empirical analysis, the thesis evaluates whether the National Targets have been determined reasonably with respect to general capacities of individual European economies. The main results reveal that some learning from the Lisbon Strategy has been made, but the quality of the National Targets is insufficient and should be increased. JEL Classification E61, F55, O52 Keywords Europe 2020, strategy, European Union, national targets, empirical analysis, MULTIMOORA, Ratio System of MOORA, Reference point of MOORA, Full Multiplicative Form, Lisbon Strategy Author's e-mail PavlaBrizova@seznam.cz Supervisor's e-mail katerina.smidkova@cnb.cz

In this thesis, we study the existence of pathwise random periodic solutions to both the semilinear stochastic differential equations with linear multiplicative noise and the semilinear stochastic partial differential equations with linear multiplicative noise in a Hilbert space. We identify them as the solutions of coupled forward-backward infinite horizon stochastic integral equations in general cases, and then perform the argument of the relative compactness of Wiener-Sobolev spaces in C([0, T],L2Ω,Rd)) or C([0, T],L2(Ω x O)) and Schauder's fixed point theorem to show the existence of a solution of the coupled stochastic forward-backward infinite horizon integral equations.

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.

Diese Dissertation behandelt die ökonometrische Analyse von hochfrequenten Finanzmarktdaten. Kapitel 1 stellt einen neuen Ansatz zur Modellierung von seriell abhängigen positiven Variablen, die einen nichttrivialen Anteil an Nullwerten aufweisen, vor. Letzteres ist ein weitverbreitetes Phänomen in hochfrequenten Finanzmarktzeitreihen. Eingeführt wird eine flexible Punktmassenmischverteilung, ein maßgeschneiderter semiparametrischer Spezifikationstest sowie eine neue Art von multiplikativem Fehlermodell (MEM). Kapitel 2 beschäftigt sich mit dem Umstand, dass feste symmetrische Kerndichteschätzer eine geringe Präzision aufweisen, falls eine positive Zufallsvariable mit erheblicher Wahrscheinlichkeitsmasse nahe Null gegeben ist. Wir legen dar, dass Gammakernschätzer überlegen sind, wobei ihre relative Präzision von der genauen Form der Dichte sowie des Kerns abhängt. Wir führen einen verbesserten Gammakernschätzer sowie eine datengetriebene Methodik für die Wahl des geeigneten Typs von Gammakern ein. Kapitel 3 wendet sich der Frage nach dem Nutzen von Hochfrequenzdaten für hochdimensionale Portfolioallokationsanwendungen zu. Wir betrachten das Problem der Konstruktion von globalen Minimum-Varianz-Portfolios auf der Grundlage der Konstituenten des S&P 500. Wir zeigen auf, dass Prognosen, welche auf Hochfrequenzdaten basieren, im Vergleich zu Methoden, die tägliche Renditen verwenden, eine signifikant geringere Portfoliovolatilität implizieren. Letzteres geht mit spürbaren Nutzengewinnen aus der Sicht eines Investors mit hoher Risikoaversion einher. / In three essays, this thesis deals with the econometric analysis of financial market data sampled at intraday frequencies. Chapter 1 presents a novel approach to model serially dependent positive-valued variables realizing a nontrivial proportion of zero outcomes. This is a typical phenomenon in financial high-frequency time series. We introduce a flexible point-mass mixture distribution, a tailor-made semiparametric specification test and a new type of multiplicative error model (MEM). Chapter 2 addresses the problem that fixed symmetric kernel density estimators exhibit low precision for positive-valued variables with a large probability mass near zero, which is common in high-frequency data. We show that gamma kernel estimators are superior, while their relative performance depends on the specific density and kernel shape. We suggest a refined gamma kernel and a data-driven method for choosing the appropriate type of gamma kernel estimator. Chapter 3 turns to the debate about the merits of high-frequency data in large-scale portfolio allocation. We consider the problem of constructing global minimum variance portfolios based on the constituents of the S&P 500. We show that forecasts based on high-frequency data can yield a significantly lower portfolio volatility than approaches using daily returns, implying noticeable utility gains for a risk-averse investor.

Un entier est dit y-friable si tous ses facteurs premiers n'excèdent pas y. Les valeurs friables de formes binaires interviennent de manière essentielle dans l'algorithme de factorisation du crible algébrique (NFS). Dans cette thèse, nous obtenons des formules asymptotiques pour le nombre de représentations des entiers friables par différentes familles de polynômes. Nous considérons dans la première partie les formes binaires qui se décomposent comme produit d'une forme linéaire et d'une forme quadratique. Nous combinons pour cela le principe d'inclusion-exclusion à des idées issues de travaux sur la distribution multiplicative de certaines suites d'entiers représentés par des formes quadratiques développés par Fouvry et Iwaniec, puis Balog, Blomer, Dartyge et Tenenbaum. Dans un second temps, nous nous concentrons sur les valeurs friables de formes cubiques irréductibles. En adaptant les travaux de Heath-Brown et Moroz sur les nombres premiers représentés par de tels polynômes, nous obtenons des formules asymptotiques valides dans un vaste domaine de friabilité. Notre méthode permet également d'évaluer des moyennes sur les valeurs d'une forme cubique pour d'autres fonctions arithmétiques comprenant en particulier les fonctions de Möbius et de Liouville. Dans le dernier chapitre, nous étudions les corrélations de l'indicatrice des friables avec les nilsuites. En employant la méthode nilpotente de Green et Tao, nous en déduisons une formule pour le nombre de valeurs friables d'un produit de formes affines deux à deux affinement indépendantes / An integer is called y-friable if its largest prime factor does not exceed y. Friable values of binary forms play a central role in the integer factoring algorithm NFS (Number Field Sieve). In this thesis, we obtain some asymptotic formulas for the number of representations of friable integers by various classes of polynomials. In the first part, we focus on binary forms which split as a product of a linear form and a quadratic form. To achieve this, we combine the inclusion-exclusion principle with ideas based on works of Fouvry and Iwaniec and Balog, Blomer, Dartyge and Tenenbaum related to the distribution of some sequences of integers represented by quadratic forms. We then take a closer look at friable values of irreducible cubic forms. Extending some previous works of Heath-Brown and Moroz concerning primes represented by such polynomials, we provide some asymptotic formulas which hold in a large range of friability. With this method, we also evaluate some means over the values of an irreducible cubic form for other multiplicative functions including the Möbius function and the Liouville function. In the last chapter, we investigate the correlations between nilsequences and the characteristic function of friable integers. By using the nilpotent method of Green and Tao, our work provides a formula for the number of friable integers represented by a product of affine forms such that any two forms are affinely independent

Made available in DSpace on 2016-04-29T14:32:24Z (GMT). No. of bitstreams: 1 dissertacao_isva_maria_barreto.pdf: 1131602 bytes, checksum: b5407d21a22f83e8675e6af818fabe1f (MD5) Previous issue date: 2001-12-10 / Este trabalho tem por objetivo analisar os procedimentos de resolução de problemas verbais multiplicativos elementares mobilizados por uma população de alunos de 5ª série, de uma Escola Estadual da cidade de São Paulo. Nessa análise, buscamos ressaltar o modo como esses procedimentos se expressam, bem como as características das situações-problema sob as quais eles emergem. Em particular, focalizamos a reflexão sobre os procedimentos não canônicos em problemas de quarta- proporcional com números naturais, tomando como referência a proposta de Gerard Vergnaud sobre Campo Conceitual. Para essa pesquisa, fizemos um período de observação nas referidas classes; em seguida, aplicamos um instrumento diagnóstico seguido da realização de entrevistas. Constatamos um elevado grau de dificuldade na resolução desses problemas, bem como a mobilização de procedimentos não canônicos diversificados expressando operações cognitivas de diferentes naturezas. Os fenômenos observados revelaram aspectos específicos na evolução de concepções pré-multiplicativas para multiplicativas, com forte incidência de procedimentos aditivos nas situações consideradas. Essas constatações mostram a importância de se considerar, no ensino, a riqueza das produções individuais possíveis de serem estabelecidas pelos alunos em uma situação multiplicativa, divergindo de uma institucionalização precoce de procedimentos uniformes valorizados no âmbito escolar

Made available in DSpace on 2016-04-29T14:32:25Z (GMT). No. of bitstreams: 1 dissertacao_claudinei_aparecido_costa.pdf: 1031829 bytes, checksum: 6adce8373f4beaac22f6dc6200758706 (MD5) Previous issue date: 2003-10-13 / In the development of this researth we tried to study and analyze the available instruments for the Mathematics professor to teach Combinatory in the Fundamental Education for process of Modeling, as well as their knowledge on the mathematical object in game. The researth was developed close to teachers of Fundamental and Secundary Education of the public school, participants of the project of continuous formation in the course of year 2002 for the agreement PUC-SP/SEE. In this direction, we analyzed the Mathematics Parameters National Curriculum (PCN-EF) of Fundamental Education, the Curriculum for Matematics Teathing of São Paulo 1th level, and two collections of didactic books adopted now by teachers of the public school. To follow in the analysis of the questionnaires, above all in questionnaire 2, it grew in a qualitative perspective. For that, it was used five questions, of the whith three of them were applied in the research accomplished by ESTEVES (2001) and their results validated by us. With the obtained data we could verify difficulties of establishing a systematic procedure, to formation of the groupings if the order is relevant or not. Concluiding, some considerations were made here about the research developed and given suggestions for future researches / No desenvolvimento desta pesquisa procuramos estudar e analisar os instrumentos disponíveis para o professor de Matemática ensinar Combinatória no Ensino Fundamental por processo de Modelagem, bem como seus conhecimentos sobre o objeto matemático em jogo. A pesquisa foi desenvolvida junto à professores da Ensino fundamental e Médio da rede pública de ensino, participantes do projeto de formação continuada no correr do ano de 2002 pelo convênio PUC-SP/SEE. Neste sentido, analisamos os Parâmetros Curriculares Nacionais de Matemática do Ensino Fundamental, a Proposta Curricular para o Ensino da Matemática do Estado de São Paulo 1º grau, e duas coleções de livros didáticos adotados atualmente por professores da rede pública. A seguir na análise dos questionários, sobretudo no questionário 2 se desenvolveu numa perspectiva qualitativa. Para tanto, utilizou-se de cinco questões, das quais três delas foram aplicadas na pesquisa realizada por ESTEVES (2001) e seus resultados validados por nós. Com os dados obtidos pudemos constatar dificuldades de ; estabelecer um procedimento sistemático, justificar as respostas, não uso ou pouco uso de representações e dificuldades para reconhecer na formação dos agrupamentos se a ordem é relevante ou não. Finalizando, foram feitas algumas considerações sobre a pesquisa aqui desenvolvida e sugestões para pesquisas futuras

Made available in DSpace on 2016-04-27T16:59:02Z (GMT). No. of bitstreams: 1 Ariovaldo Guinther.pdf: 4387488 bytes, checksum: 00c33e26cf124a101cb7456b78e19eb7 (MD5) Previous issue date: 2009-11-12 / Secretaria da Educação do Estado de São Paulo / This research aims to investigate what teaching strategies, considering the use of a calculator in the classroom can become more efficient perception of mistakes in handling additive and multiplicative between students in a 7th grade of elementary school, in the afternoon shift of a State School in Osasco city S.P. (Brazil). This study consisted of a qualitative research as a tool with the use of two mathematical games: MAZE and HEX OF MULTIPLICATION. To achieve these games have used two hours/class of instruction for each one, the first without using the calculator. Thus, students enrolled in a sheet of paper paths (played) chosen using the additive and multiplicative. In our analysis, we point out that the mistakes made by most students when it comes to work with structures additive and multiplicative with decimal numbers were: a) adding or subtracting the decimal part of the whole, b) errors in the algorithm of division and multiplication c) errors in the positioning or absence of the comma d) subtracting tenths of hundredths. In the second hour of instruction, students played using the calculator, seeing their mistakes, beyond giving the results, providing opportunities for understanding the steps taken and opening new paths to knowledge. By assessing the strategies used in research on the foundations of Bianchini (2001) and Cunha (2002) and Bonanno (2007) and Rasi (2009) on the issue involving decimals, and additive and multiplicative, in the case of the use of games, we rely on research Grando (1995, 2000) and realize that such use involving the calculator, we allowed for greater efficiency in the perception of mistakes, and as our theoretical research by Penteado (2001) and Rubio (2003) and Borba ( 2005) and Schiffl (2006) and Borba et al (2008) and Sampaio and Leite (2008). Although these authors support the use of a mediator, there are various forms of resistance from many teachers in relation to such use. The argument used is that the student will not learn more mathematics, because no longer think, will do more calculations, nor shall the algorithms. Accordingly, we raised some discussions, which could help to illustrate the potential use of calculators and games in mathematics lessons. However, the analysis of collected data shows us that the practice of teaching mathematics gains new ground with the aid of games and calculator, which can facilitate teachers in their work to promote a more meaningful teaching of mathematics and the students a different view of use the calculator in the classroom / A presente pesquisa tem por objetivo investigar quais estratégias pedagógicas, considerando o uso da calculadora em sala de aula, podem tornar mais eficiente a percepção dos erros cometidos na manipulação de estruturas aditivas e multiplicativas entre alunos de um 7º ano do Ensino Fundamental, do período da tarde de uma Escola Estadual, na cidade de Osasco - São Paulo. Esse estudo se constituiu em uma pesquisa qualitativa tendo como instrumento a utilização de dois jogos matemáticos: MAZE e HEX DA MULTIPLICAÇÃO. Para a realização desses jogos foram utilizadas duas horas/aula para cada um, sendo a primeira sem o uso da calculadora. Dessa forma, os alunos registraram numa folha de papel que caminhos (jogadas) escolheram, utilizando as estruturas aditivas e multiplicativas. Em nossas análises, apontamos que os erros mais cometidos pelos alunos no que tange trabalhar com estruturas aditivas e multiplicativas com números decimais foram: a) somar ou subtrair a parte decimal da parte inteira; b) erros no algoritmo da divisão e multiplicação; c) erros no posicionamento ou ausência da vírgula; d) subtrair décimos de centésimos. Na segunda hora/aula, os alunos jogaram utilizando a calculadora, percebendo os erros cometidos, indo além de conferir os resultados obtidos, oferecendo possibilidades de compreensão das etapas realizadas e abrindo caminhos para novos saberes. Ao analizarmos as estratégias utilizadas, nos alicerçamos nas pesquisas de Bianchini (2001), Cunha (2002), Bonanno (2007) e Rasi (2009) quanto ao tema envolvendo números decimais e estruturas aditivas e multiplicativas; em se tratando do recurso aos jogos, nos baseamos nas pesquisas de Grando (1995, 2000) e percebemos que essa utilização envolvendo a calculadora, nos permitiu maior eficiência na percepção dos erros cometidos, tendo como nosso referencial teórico as pesquisas de Penteado (2001), Rubio (2003), Borba (2005), Schiffl (2006), Borba et al (2008) e Sampaio e Leite (2008). Embora esses autores apóiem o uso desse elemento mediador, ainda existem várias formas de resistências por parte de muitos professores em relação a tal uso. O argumento utilizado é de que o aluno não vai mais aprender Matemática, pois deixará de pensar, não fará mais cálculos e nem fixará os algoritmos. Nesse sentido, levantamos algumas discussões, que poderão contribuir para ilustrar as potencialidades da utilização das calculadoras e dos jogos nas aulas de Matemática. Contudo, a análise dos dados coletados nos aponta que, a prática docente da Matemática ganha novos horizontes com o auxílio dos jogos e da calculadora, podendo facilitar aos professores nas suas tarefas de promover um ensino mais significativo da Matemática e dos alunos uma visão diferente do uso da calculadora em sala de aula

Understanding the functional impact of physical interactions between proteins and DNA on gene expression is important for developing approaches to correct disease-associated gene dysregulation. I conducted a systematic, functional genetic analysis of protein-DNA interactions in the promoter region of the yeast ribonucleotide reductase subunit gene RNR3. I measured the transcriptional impact of systematically perturbing the major transcriptional regulator, Crt1, and three X-box sites on the DNA known to physically bind Crt1. This analysis revealed interactions between two of the three X-boxes in the presence of Crt1, and unexpectedly, a significant functional role of the X-boxes in the absence of Crt1. Further analysis revealed Crt1- independent regulators of RNR3 that were impacted by X-box perturbation. Taken together, these results support the notion that higher-order X-box-mediated interactions are important for RNR3 transcription, and that the X-boxes have unexpected roles in the regulation of RNR3 transcription that extend beyond their interaction with Crt1.