Orientadora: Profa. Dra. Ana Carolina Boero / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional, 2017. / Este trabalho acadêmico cobrirá alguns dos aspectos mais relevantes sobre o número p, desde o contexto histórico no qual está inserido até a demonstração de uma de suas características marcantes: a sua irracionalidade. O trabalho também terá como escopo aspectos teóricos da formação de professores, como a construção dos conjuntos numéricos, a obtenção de alguns métodos numéricos para a determinação de aproximações do valor numérico de p e, por último, sobre a aplicação do número p nas salas de aula da Educação Básica. / This academic work will cover some of the most relevant aspects of the p number, from the historical context in which it is inserted to the demonstration of one of its defining characteristics: its irrationality. The work will also have as scope theoretical aspects of teacher training, such as the construction of numerical sets, the obtainment of some numerical methods to determine approximations of the numerical value of p and, finally, on the application of the number p in the Secondary School classrooms.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2014-11-21T14:25:51Z No. of bitstreams: 2 Dissertação - Túlio Guimarães Marques - 2013.pdf: 3490137 bytes, checksum: a39789fad1b421e22443faee08545072 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2014-11-24T10:17:57Z (GMT) No. of bitstreams: 2 Dissertação - Túlio Guimarães Marques - 2013.pdf: 3490137 bytes, checksum: a39789fad1b421e22443faee08545072 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-11-24T10:17:57Z (GMT). No. of bitstreams: 2 Dissertação - Túlio Guimarães Marques - 2013.pdf: 3490137 bytes, checksum: a39789fad1b421e22443faee08545072 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-03-01 / Outras / This paper aims at introducing the science which is behind the most intriguing number known to history, the number . It has challenged generations of researchers who have tried to determine its value and articulate several areas of Mathematics such as Geometry, Algebra and Analysis. The quotient of ratio between the measure of the length of a circumference and the measure of its diameter are what de ne . Some historical references such as Archimedes, Euler, Leibniz and Lindemann have signi cantly contributed with the methods to precise . The rst real academic approach to this ratio was studied by the greatest mathematician of antiquity, Archimedes, when he created an instructive process for the study of the limits. With the unsolvable problem of the quadrature of the circle, ingenious geometrical constructions are born, in order to allow the drawing, with a ruler and compass, of a square having the same area as a previous given circle. The evolution of the forms employed in order to calculate have become more evident with the introduction of Analysis applied under the foundations of Calculus. At that time, the Series come to life, indispensable tools allowing the study of the behaviour of its decimal places. Along with the advances brought by them, the investigations turned towards the classi cation concerning the rationality or the irrationality of the number. In the end, we will present some contextualization and propose exercises with the aim of stimulating the search for knowledge. / O trabalho a seguir apresenta a ciência por trás do número mais intrigante da história, o número . Ele tem desa ado gerações de pesquisadores a determinar o seu valor e articular as várias áreas da matemática, como a Geometria, a Álgebra e a Análise. O quociente da razão entre a medida do comprimento de uma circunferência e a medida de seu diâmetro de ne . Algumas referências históricas, entre eles, Arquimedes, Euler, Leibniz e Lindemann, contribuíram signi cantemente nos métodos para precisar . A primeira abordagem realmente acadêmica dessa razão foi estudada pelo maior matemático da antiguidade, Arquimedes, quando ele criou um processo instrutivo no estudo dos limites. Com o insolúvel problema da quadratura do círculo, surgem construções geométricas engenhosas na tentativa de desenhar, com régua e compasso, um quadrado de mesma área de um círculo dado. A evolução das formas utilizadas para o cálculo do tornou-se mais evidente com a introdução da Análise aplicada nos fundamentos do Cálculo. Neste momento, surgem as Séries, ferramentas indispensáveis para estudar o comportamento de suas casas decimais. Com os avanços obtidos por estas, as investigações voltaram-se para classi cação quanto a racionalidade ou irracionalidade do número . Inicialmente a irracionalidade foi provada e mais tarde sua transcendência. Por m, são apresentadas algumas contextualizações e propostas de exercícios com a tentativa de estimular a busca por conhecimento.

Abstract This dissertation consists of four articles on irrationality measures. In the first paper we derive explicit irrationality measures by using the simple continued fraction expansions in a completely new way. In the second and third articles we use Padé approximations to construct irrationality measures. In the second paper we obtain an explicit irrationality measure for the values of q-exponential series, for which the earlier corresponding results are not as explicit. Furthermore, we construct a restricted irrationality measure for the values of q-exponential series, which is an improvement on the earlier results in the restricted case. In the third article we derive the best possible asymptotic restricted irrationality exponent for the values of Jacobi's triple product. In the last paper we consider Cantor series. We generalize the earlier results by deriving Sondow's irrationality measure for some Cantor series. / Tiivistelmä Tämä väitöskirja koostuu neljästä artikkelista, jotka kaikki käsittelevät irrationaalisuusmittoja. Ensimmäisessä artikkelissa irrationaalisuusmittoja johdetaan uudella tavalla irrationaalilukujen yksinkertaisista ketjumurtolukuesityksistä. Toisessa ja kolmannessa artikkelissa irrationaalisuusmitat konstruoidaan Padé-approksimaatioiden avulla. Toisessa artikkelissa saadaan eksplisiittinen irrationaalisuusmitta q-eksponenttisarjan arvoille, joiden vastaavat aikaisemmat irrationaalisuusmitat eivät ole näin eksplisiittisiä. Lisäksi samassa artikkelissa konstruoidaan q-eksponenttisarjan arvoille rajoitettu eksplisiittinen irrationaalisuusmitta, mikä parantaa aikaisempia tuloksia rajoitetussa tapauksessa. Kolmannessa artikkelissa johdetaan paras mahdollinen asymptoottinen irrationaalisuuseksponentti Jacobin kolmitulon arvoille. Viimeisessä artikkelissa käsitellään Cantorin sarjoja. Siinä yleistetään aikaisempia tuloksia johtamalla Sondowin irrationaalisuusmitta tietylle joukolle Cantorin sarjoja.

Avsikten med denna studie har varit att studera det nya fenomenet börsinfluencers och deras samexistens med professionella licensierade rådgivare samt beskriva på vilket sätt betydelsen av den finansiella rådgivarrollen kan ha förändrats, något som inte har behandlats av tidigare forskning. Studiens genomförande utgår från det teoretiska ramverkets nyckelbegrepp Det klassiska ekonomiska finansparadigmet, beteendevetenskaplig finans, den rationella investeraren, den irrationella investeraren, egna fundamentala analyser, flockbeteende & tillgänglighetsheuristik, professionella rådgivare, börsinfluencers och postmodernism som tillsammans bildar analysmodellen. Modellen visar på hur de två rådgivningstrenderna samexisterar och den är indelad i två delar, en “rationell” sida och en “irrationell” sida för att slutligen visa att existensen av båda sidorna tillåts i det postmoderna samhället. Denna studie hade ett postmodernistiskt synsätt vilket medförde att resultatet endast ska betraktas som en av flera versioner av den yttre verkligheten. För att på bästa möjliga sätt kunna uppfylla syftet och besvara frågeställningarna användes dels en innehållsanalys av en dokumentstudie och dels en tematisk analys av sex semistrukturerade intervjuer där kriteriet vid urval av respondenter var att ha ett intresse för aktiemarknaden samt följa minst en börsinfluencer på Instagram. Studien använde dessa två olika metoder för att både kunna beskriva börsinfluencers agerande på sociala plattformar samt för att kunna analysera deras följares uppfattningar och upplevelser av fenomenet. Studien visade att börsinfluencers fyller olika behov hos respondenterna, där vissa ser på fenomenet som en typ av rådgivare vars åsikter och indirekta råd värderas högt vid investeringsbeslut medan andra vänder sig till börsinfluencers för inspiration i sin investeringsprocess. De tidigare tydliga gränsdragningarna och definitionerna av vad en finansiell rådgivare är har luckrats upp och istället lämnat plats för börsinfluencers, fenomenet kan betraktas som produkten av individers pragmatiska behov av lättillgänglig finansiell rådgivning. Där resultatet är börsinfluencers, den hyperrealistiska rådgivaren. / The purpose of this study has been to examine the new phenomenon of stock market influencers and their coexistence with professionally licensed advisers and to describe in what way the significance of the financial adviser role may have changed, something that has not been addressed by previous research. The implementation of the study is based on the theoretical framework's key concepts The classic economic finance paradigm, behavioral finance, the rational investor, the irrational investor, own fundamental analyzes, herd behavior & accessibility heuristics, professional advisors, stock market influencers and postmodernism that together form the analysis model. The model shows how the two advisory trends coexist and it is divided into two parts, one “rational” side and one “irrational” side, to finally show that the existence of both sides is allowed in the postmodern society. This study had a postmodernist approach, which meant that the result should only be considered as one of several versions of the external reality. In order to best fulfill the purpose and answer the questions, a content analysis of a document study and a thematic analysis of six semi-structured interviews were used, where the criterion when selecting respondents was to have an interest in the stock market and follow at least one stock market influencer on Instagram. The study used these two different methods to both be able to describe the actions of stock market influencers on social platforms and to be able to analyze their followers' perceptions and experiences of the phenomenon. The study showed that stock market influencers meet different needs of the respondents, where some see the phenomenon as a type of advisor whose opinions and indirect advice are highly valued in investment decisions while others use stock market influencers for inspiration in their investment process. The previously clear boundaries and definitions of what a financial adviser is have loosened up and instead left room for stock market influencers, the phenomenon can be considered as the product of individuals' pragmatic need for easily accessible financial advice. Where the result is stock market influencers, the hyperrealistic advisor.

Det senaste decenniet har användandet av sociala medier exploderat och blivit en plattformdär information och tips om aktier och investeringar delas ut. Unga personer är de störstaanvändarna av sociala medier, och tidigare studier visar att denna åldersgrupp uppvisar ettmer riskfyllt beteende på aktiemarknaden. Syftet med denna studie var således att undersökahuruvida det finns ett samband mellan aktivitet på sociala medier och riskbenägenhet. Vidareundersöktes om tre variabler - överdrivet självförtroende, ångeraversion och kognitivdissonans - hade en medierande effekt i sambandet mellan aktivitet på sociala medier ochriskbenägenhet. En kvantitativ metod med en enkätstudie användes för studiensdatainsamling. Statistiska mått, däribland regressionsanalys och medieringsanalys, användesför att besvara forskningsfrågan. Resultaten visade att sociala medier har en statistisktsignifikant effekt på riskbenägenhet på aktiemarknaden, och att överdrivet självförtroende haren statistiskt signifikant medierande effekt på relationen. Det fanns inga belägg ellerindikationer på att kognitiv dissonans och ångeraversion har en medierande effekt.Sammanfattningsvis visade studien att aktivitet på sociala medier i investeringssyfte kanbidra till ökad riskbenägenhet, och att överdrivet självförtroende har en viktig roll sommedierande variabel i förhållandet. / The last decade, the use of social media has escalated and become a platform whereinformation and tips about stocks and investments are shared. Young individuals aregenerally the most frequent users of social media, and studies also show that the same agegroup displays a more risk-prone behavior in financial markets. Therefore, the purpose of thisstudy was to examine the potential effect of social media activity on risk propensity on thestock market. Furthermore, the study investigated whether the three variables -overconfidence, regret aversion, and cognitive dissonance - could be classified as a mediatingvariable between social media activity and risk propensity. The study was conducted using aquantitative method, employing a survey, where 130 people responded. Statistical measuressuch as regression analysis and mediation analysis were used to answer the research question.The results showed that social media has a statistically significant effect on risk propensity onthe stock market, and that overconfidence has a statistically significant mediating effect onthe relationship. There was no evidence or indication that cognitive dissonance or regretaversion has a mediating effect. In summary, the study demonstrated that use of social mediain investment purposes can increase risk willingness, and that overconfidence plays animportant role as a mediating variable in this relationship.

No description available.

Diese Dissertation beschäftigt sich mit asymptotischen Syzygien und Gleichungen Abelscher Varietäten, sowie mit deren Anwendung auf zyklische Überdeckungen von Kurven von Geschlecht zwei. Was asymptotischen Syzygien angeht, zeigen wir für beliebige Geradenbündel auf projektiven Schemata: Wenn die asymptotischen Syzygien von Grad p eines Geradenbündels verschwinden, dann ist das Geradenbündel p-sehr ampel. Darüber hinaus verwenden wir die Bridgeland-King-Reid-Haiman Korrespondenz, um zu zeigen, dass dieses Ergebnis auch umgekehrt wahr ist, wenn es um eine glatte Fläche und kleine p geht. Dies dehnt Ergebnisse von Ein-Lazarsfeld und Ein-Lazarsfeld-Yang aus. Wir verwenden unsere Ergebnisse, um zu untersuchen, wie Syzygien verwendet werden können, um den Grad der Irrationalität einer Varietät zu begrenzen. Ferner, beweisen wir eine Vermutung von Gross and Popescu über Abelsche Flächen, deren Ideal durch Quadriken und Kubiken erzeugt wird. Außerdem verwenden wir die projektive Normalität einer Abelschen Fläche, um die Prym Abbildung, die mit zyklischen Überdeckungen von Geschlecht zwei Kurven assoziert ist, zu untersuchen. Wir zeigen, dass das Differential der Abbildung generisch injektiv ist, wenn der Grad der Überdeckung mindestens sieben ist. Wir dehnen damit Ergebnisse von Lange und Ortega aus. Abschließend zeigen wir, dass das Differential genau für bielliptische Überdeckungen nicht injectiv ist. / In this thesis we study asymptotic syzygies of algebraic varieties and equations of abelian surfaces, with applications to cyclic covers of genus two curves. First, we show that vanishing of asymptotic p-th syzygies implies p-very ampleness for line bundles on arbitrary projective schemes. For smooth surfaces we prove that the converse holds, when p is small, by studying the Bridgeland-King-Reid-Haiman correspondence for the Hilbert scheme of points. This extends previous results of Ein-Lazarsfeld and Ein-Lazarsfeld-Yang. As an application of our results, we show how to use syzygies to bound the irrationality of a variety. Furthermore, we confirm a conjecture of Gross and Popescu about abelian surfaces whose ideal is generated by quadrics and cubics. In addition, we use projective normality of abelian surfaces to study the Prym map associated to cyclic covers of genus two curves. We show that the differential of the map is generically injective as soon as the degree of the cover is at least seven, extending a previous result of Lange and Ortega. Moreover, we show that the differentials fails to be injective precisely at bielliptic covers.

La part de l’irrationnel dans les processus de sélection des futurs dirigeants des grandes entreprises françaises. Cette thèse explore la part d’irrationalité intervenant dans les processus de sélection des futurs dirigeants français. Examinant les profils des dirigeants français du début du 21ème siècle, elle souligne la persistance d’une doxa cartésienne, c’est-à-dire la croyance en l’autorité de la conscience et de la raison dans la détection, la sélection ou la génération d’élites et plus particulièrement de dirigeants dans les organisations, réalisant en particulier un biais de sélection sociale précoce pour l’accès à la direction des grandes entreprises. Combinant les apports des théories de l’agence, des échelons supérieurs, et de la rationalité limitée, ce travail construit une vision intégrative des enjeux et paramètres de la sélection des futurs dirigeants à plusieurs niveaux (individus, systèmes, réseaux, organisation, culture), et analyse comment des processus rationnels peuvent être modifiés par des formes d’irrationalité, des premiers moments de détection et de fabrique des talents à celle, à la fois plus symbolique et signifiante, de la dirigeance. Le cadre conceptuel du leader transcendant permet de représenter une vision intégrative du leadership, et d’explorer les « nouvelles » qualités que les processus de sélection devront identifier, illustrant l’inadéquation des processus traditionnels aux enjeux des entreprises modernes. Ce travail met en lumière la nécessité de réévaluer les pratiques de la sélection des dirigeants au travers d’une rationalité procédurale plus en adéquation avec la réalité opératoire, à la fois sur le plan de la rationalité sous-jacente (les valeurs et critères du leadership), de ses outils (les méthodes d’évaluation), et de son objet (une articulation intégrative et continue du développement et de la sélection assumant une part d’irrationnel). / The purpose of this research work is to investigate how irrationality plays a significant role in selecting top executives in French corporates. Upon an in-depth review of the making of top executives in France at the beginning of the 21st century, it appears that a Cartesian rationale still prevails, based on the sheer belief that conscience and reason must be the unique dimensions used in selecting, promoting, and thus, perpetuating elites, from the early school years to the appointment of the C-suite in large organisations. Three theories are central in this research work: the agency theory, the upper echelon theory, as well as the bounded rationality theory. Combining them in an integrative conceptual framework allows to understand how strong rational patterns might be affected by forms and mechanisms of irrationality all along the process of identifying and developing future leaders to the more significant moment when they are appointed. Ultimately, the outcome of this research work shows that the model of « transcendent leadership » seems more effective than others to address the challenges of identifying and selecting executives in modern organisations. This leads to examining how to build more robust systems of executive selection at three levels of progress: (a) underlying values and patterns of leadership, (b) assessment tools and processes and (c) conscious acceptance of irrationality as a significant part of talent and executive spotting and development.

Made available in DSpace on 2016-04-29T13:30:56Z (GMT). No. of bitstreams: 1 Alekssey Marcos Di Piero Sobral.pdf: 407855 bytes, checksum: 52f26e73224261f55429c5fe0e0dbb95 (MD5) Previous issue date: 2012-05-18 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / The object of this investigation was to study the possibly notions of irrationality in the theories of some pioneers authors of Social Psychology, named Psychology of The Masses. Is believed that the presence of irrationality s notions in this theories could be an indication of a larger historic movement, described as a lurch to irrationality, whereby all the philosophical-scientific enterprise of the XIX century s end and XX century s beginning has crossed. This research is dedicated, therefore, to search for the underlying irracional element in the theories of Gabriel Tarde, Scipio Sighele and Gustave Le Bon, for the purpose of understand their coincidences and nuances and to scribe anything of their possible fate in the psychology s history. To accomplish this proposal, the work was unfolded in two ways of analysis: the first, lexical, in witch was investigated the plot of meanings in the theories that could point to a irracionality notion, and the second one, historical, that proposes to understand the way and the meaning of the trajectory of the irrationality s notions in the psychology and in the contemporary science in general. In the first analysis, the afterthought of Ludwig Wittgestein was used, upon the language-games. In the second one, the theories of Adorno and Horkheimer developed mainly in the Dialectic of Enlightment were the basis to a historical interpretation of history. When the analysis reach the end, is concluded in favor of the highlighted notion of the irrationality in each of the investigated authors, which notions are part of the veiled irrational subject in general, that had been posteriorly adduced to the psychoanalysis and, ultimately, popularized. This turning point toward irrationality observed in the sciences of mind had parallel in the natural science, as in the case of the emergency of quantum physics, one of the examples discussed. Far from imagine the irracionality notion as an threat to rationality and science, we can see it, in a dialetical perspective, as a sign of openness toward the study of the concret world and man / A presente investigação teve por objeto o estudo de possíveis noções de irracionalidade nas teorias de alguns dos autores pioneiros da Psicologia Social, então nomeada Psicologia das Massas. Supô-se que a presença de uma noção de irracionalidade nessas teorias poderia ser indício de um movimento histórico mais amplo, descrito como uma guinada em direção à irracionalidade, pelo qual teria passado todo o empreendimento filosófico-científico no fim do século XIX e começo do século XX. A pesquisa se dedica, assim, a procurar pelo elemento irracional subjacente às teorias de Gabriel Tarde, Scipio Sighele e Gustave Le Bon a fim de entender suas coincidências e nuances e traçar algo de seu possível destino na história da psicologia. Para a realização da proposta, o trabalho desdobrou-se em duas formas de análise: a primeira, léxica, em que se investigou a trama de significantes nas teorias que poderiam apontar para uma noção de irracionalidade, e a segunda, histórica, que se propôs a entender o caminho e o significado da trajetória das noções de irracionalidade na psicologia e na ciência contemporânea, de uma forma geral. Na primeira análise, fez-se uso do pensamento tardio de Ludwig Wittgenstein acerca dos jogos de linguagem. Na segunda, as teses de Adorno e Horkheimer desenvolvidas principalmente na Dialética do Esclarecimento foram a base para uma interpretação da história. Quando as análises chegam a termo, conclui-se em favor da presença bem destacada de uma noção de irracionalidade em cada um dos autores investigados, noções estas constituidoras das formas gerais de um sujeito irracional velado, que teria sido posteriormente carreado para a psicanálise e enfim, popularizado. Tal virada em direção à irracionalidade observada nas ciências do espírito teve paralelos nas ciências naturais, como no caso da emergência da Física Quântica, um dos exemplos abordados. Longe de imaginarmos a noção de irracionalidade como uma ameaça à razão e a ciência, podemos vê-la, numa perspectiva dialética, como um sinal de abertura em direção ao estudo do mundo e do homem concretos

One could argue that the most discussed topic in finance is whether or not it is possible to “beat the market”. Even though many people claim to do this, there is little evidence to support the idea that one can consistently beat the market over a long period of time. There are indeed several examples of investors who have managed to outperform the market consistently for a long time, but the efforts of these individuals or institutions could by many be considered to be pure luck. One of the many strategies that have been evaluated by several researchers and is said to generate a risk adjusted return greater than that of the market, is one based on the P/E-effect. This strategy is based on the financial ratio P/E – price divided by earnings – and used by constructing portfolios consisting of stocks with low P/E ratios. Several studies have confirmed the existence of the P/E-effect on various stock markets around the world and over different time periods. On the Swedish market, however, few studies have generated the same results. Most of these studies can be considered to be insufficient with regards to sample sizes and methods, spawning a need for more extensive studies. We have examined the P/E strategy on the Swedish Stock Exchange (SSE) between 2004 and 2012. The sample included 358 companies (excluding financial companies) with available necessary data. The stocks were divided into five portfolios based on their yearly P/E ratios (low to high), upon which the monthly returns of the individual stocks were calculated using a logarithmic formula. The returns were also risk adjusted using the Capital Asset Pricing Model (CAPM), followed by a regression analysis to see if possible abnormal returns could be considered to be statistically significant for the examined time period. The results of our study indicate that the P/E effect is not present on the Swedish Stock Exchange during the examined time period, and we therefore conclude that it was not possible to utilize a strategy based on the P/E effect between 2004 and 2012 in order to achieve an abnormal return. The results can be used to argue that the Swedish stock market is more efficient than for example the U.S. stock market where the P/E effect has been found to exist.