On some Density Theorems in Number Theory and Group Theory

Gowers, dans son article sur les matrices quasi-aléatoires, étudie la question, posée par Babai et Sos, de l'existence d'une constante $c>0$ telle que tout groupe fini possède un sous-ensemble sans produit de taille supérieure ou égale a $c|G|$. En prouvant que, pour tout nombre premier $p$ assez grand, le groupe $PSL_2(\mathbb{F}_p)$ (d'ordre noté $n$) ne posséde aucun sous-ensemble sans produit de taille $c n^{8/9}$, il y répond par la négative. Nous allons considérer le probléme dans le cas des groupes compacts finis, et plus particuliérement des groupes profinis $SL_k(\mathbb{Z}_p)$ et $Sp_{2k}(\mathbb{Z}_p)$. La premiére partie de cette thése est dédiée à l'obtention de bornes inférieures et supérieures exponentielles pour la mesure suprémale des ensembles sans produit. La preuve nécessite d'établir préalablement une borne inférieure sur la dimension des représentations non-triviales des groupes finis $SL_k(\mathbb{Z}/(p^n\mathbb{Z}))$ et $Sp_{2k}(\mathbb{Z}/(p^n\mathbb{Z}))$. Notre théoréme prolonge le travail de Landazuri et Seitz, qui considérent le degré minimal des représentations pour les groupes de Chevalley sur les corps finis, tout en offrant une preuve plus simple que la leur. La seconde partie de la thése à trait à la théorie algébrique des nombres. Un polynome monogéne $f$ est un polynome unitaire irréductible à coefficients entiers qui endengre un corps de nombres monogéne. Pour un nombre premier $q$ donné, nous allons montrer, en utilisant le théoréme de densité de Tchebotariov, que la densité des nombres premiers $p$ tels que $t^q -p$ soit monogéne est supérieure ou égale à $(q-1)/q$. Nous allons également démontrer que, quand $q=3$, la densité des nombres premiers $p$ tels que $\mathbb{Q}(\sqrt[3]{p})$ soit non monogéne est supérieure ou égale à $1/9$.

A practical grammar of the English language : in which the principles established by Lindley Murray, are inculcated, and the theory of modes clearly illustrated by diagrams, representing the number of tenses in each mode, their signs and the manner in which they are formed /

Williamson,

A practical grammar of the English language, in which the principles established by Lindley Murray, are inculcated, and his theory of the moods clearly illustrated by diagrams, representing the number of the tenses in each mood--their signs--and the manner in which they are formed.

"Recommendations": prelim. leaves 2-4.

Problems in number theory and hyperbolic geometry

In the first part of this thesis we generalize a theorem of Kiming and Olsson concerning the existence of Ramanujan-type congruences for a class of eta quotients. Specifically, we consider a class of generating functions analogous to the generating function of the partition function and establish a bound on the primes ℓ for which their coefficients c(n) obey congruences of the form c(ℓn + a) ≡ 0 (mod ℓ). We use this last result to answer a question of H.C. Chan. In the second part of this thesis [S2] we explore a natural analog of D. Calegari’s result that there are no hyperbolic once-punctured torus bundles over S^1 with trace field having a real place. We prove a contrasting theorem showing the existence of several infinite families of pairs (−χ, p) such that there exist hyperbolic surface bundles over S^1 with trace field of having a real place and with fiber having p punctures and Euler characteristic χ. This supports our conjecture that with finitely many known exceptions there exist such examples for each pair ( −χ, p).

Cooperation and game theory, free software or the #15m movement: Two examples for universities

Closing talk of the Open Access Week 2011 at the UOC, by Josep Jover. Why do altruistic strategies beat selfish ones in the spheres of both free software and the #15m movement? The #15m movement, like software but unlike tangible goods, cannot be owned. It can be used (by joining it) by an indeterminate number of people without depriving anyone else of the chance to do the same. And that turns everything on its head: how universities manage information and what their mission is in this new society. In the immediate future, universities will be valued not for the information they harbour, which will always be richer and more extensive beyond their walls, but rather for their capacity to create critical masses, whether of knowledge research, skill-building, or networks of peers... universities must implement the new model or risk becoming obsolete.

THE FORMAL AND THE FORMALIZED: THE CASES OF SYLLOGISTIC AND SUPPOSITION THEORY

As a discipline, logic is arguably constituted of two main sub-projects: formal theories of argument validity on the basis of a small number of patterns, and theories of how to reduce the multiplicity of arguments in non-logical, informal contexts to the small number of patterns whose validity is systematically studied (i.e. theories of formalization). Regrettably, we now tend to view logic 'proper' exclusively as what falls under the first sub-project, to the neglect of the second, equally important sub-project. In this paper, I discuss two historical theories of argument formalization: Aristotle's syllogistic theory as presented in the "Prior Analytics", and medieval theories of supposition. They both illustrate this two-fold nature of logic, containing in particular illuminating reflections on how to formalize arguments (i.e. the second sub-project). In both cases, the formal methods employed differ from the usual modern technique of translating an argument in ordinary language into a specially designed symbolism, a formal language. The upshot is thus a plea for a broader conceptualization of what it means to formalize.

Examining sport commitment and intentions to participate in intramural sports : application of the Sport Commitment Model and the Theory of Planned Behaviour in a campus recreational sport setting

Fifty-six percent of Canadians, 20 years of age and older, are inactive (Canadian Community Health Survey, 200012001). Research has indicated that one of the most dramatic declines in population physical activity occurs between adolescence and young adulthood (Melina, 2001; Stephens, Jacobs, & White, 1985), a time when individuals this age are entering or attending college or university. Colleges and universities have generally been seen as environments where physical activity and sport can be promoted and accommodated as a result of the available resources and facilities (Archer, Probert, & Gagne, 1987; Suminski, Petosa, Utter, & Zhang, 2002). Intramural sports, one of the most common campus recreational sports options available for post-secondary students, enable students to participate in activities that are suited for different levels of ability and interest (Lewis, Jones, Lamke, & Dunn, 1998). While intramural sports can positively affect the physical activity levels and sport participation rates of post-secondary students, their true value lies in their ability to encourage sport participation after school ends and during the post-school lives of graduates (Forrester, Ross, Geary, & Hall, 2007). This study used the Sport Commitment Model (Scanlan et aI., 1993a) and the Theory of Planned Behaviour (Ajzen, 1991) with post secondary intramural volleyball participants in an effort to examine students' commitment to intramural sport and 1 intentions to participate in intramural sports. More specifically, the research objectives of this study were to: (1.) test the Sport Commitment Model with a sample of postsecondary intramural sport participants(2.) determine the utility of the sixth construct, social support, in explaining the sport commitment of post-secondary intramural sport participants; (3.) determine if there are any significant differences in the six constructs of IV the SCM and sport commitment between: gender, level of competition (competitive A vs. B), and number of different intramural sports played; (4.) determine if there are any significant differences between sport commitment levels and constructs from the Theory of Planned Behaviour (attitudes, subjective norms, perceived behavioural control, and intentions); (5.) determine the relationship between sport commitment and intention to continue participation in intramural volleyball, continue participating in intramurals and continuing participating in sport and physical activity after graduation; and (6.) determine if the level of sport commitment changes the relationship between the constructs from the Theory of Planned Behaviour. Of the 318 surveys distributed, there were 302 partiCipants who completed a usable survey from the sample of post-secondary intramural sport participants. There was a fairly even split of males and females; the average age of the students was twenty-one; 90% were undergraduate students; for approximately 25% of the students, volleyball was the only intramural sport they participated in at Brock and most were part of the volleyball competitive B division. Based on the post-secondary students responses, there are indications of intent to continue participation in sport and physical activity. The participation of the students is predominantly influenced by subjective norms, high sport commitment, and high sport enjoyment. This implies students expect, intend and want to 1 participate in intramurals in the future, they are very dedicated to playing on an intramural team and would be willing to do a lot to keep playing and students want to participate when they perceive their pursuits as enjoyable and fun, and it makes them happy. These are key areas that should be targeted and pursued by sport practitioners.

Geometric Algebra and Einstein’s Electron

This thesis entitled Geometric algebra and einsteins electron: Deterministic field theories .The work in this thesis clarifies an important part of Koga’s theory.Koga also developed a theory of the electron incorporating its gravitational field, using his substitutes for Einstein’s equation.The third chapter deals with the application of geometric algebra to Koga’s approach of the Dirac equation. In chapter 4 we study some aspects of the work of mendel sachs (35,36,37,).Sachs stated aim is to show how quantum mechanics is a limiting case of a general relativistic unified field theory.Chapter 5 contains a critical study and comparison of the work of Koga and Sachs. In particular, we conclude that the incorporation of Mach’s principle is not necessary in Sachs’s treatment of the Dirac equation.

Some Problems In Algebra And Topology A Study Of Fuzzy Convexity With Special Reference To Separation Properties

This thesis is a study of abstract fuzzy convexity spaces and fuzzy topology fuzzy convexity spaces No attempt seems to have been made to develop a fuzzy convexity theoryin abstract situations. The purpose of this thesis is to introduce fuzzy convexity theory in abstract situations

Interpersonal interaction and economic theory: the case of public goods

Interpersonal interaction in public goods contexts is very different in character to its depiction in economic theory, despite the fact that the standard model is based on a small number of apparently plausible assumptions. Approaches to the problem are reviewed both from within and outside economics. It is argued that quick fixes such as a taste for giving do not provide a way forward. An improved understanding of why people contribute to such goods seems to require a different picture of the relationships between individuals than obtains in standard microeconomic theory, where they are usually depicted as asocial. No single economic model at present is consistent with all the relevant field and laboratory data. It is argued that there are defensible ideas from outside the discipline which ought to be explored, relying on different conceptions of rationality and/or more radically social agents. Three such suggestions are considered, one concerning the expressive/communicative aspect of behaviour, a second the possibility of a part-whole relationship between interacting agents and the third a version of conformism.

Analysing the factors that influence tag choice based on semiotic analysis and activity theory

Social tagging has become very popular around the Internet as well as in research. The main idea behind tagging is to allow users to provide metadata to the web content from their perspective to facilitate categorization and retrieval. There are many factors that influence users' tag choice. Many studies have been conducted to reveal these factors by analysing tagging data. This paper uses two theories to identify these factors, namely the semiotics theory and activity theory. The former treats tags as signs and the latter treats tagging as an activity. The paper uses both theories to analyse tagging behaviour by explaining all aspects of a tagging system, including tags, tagging system components and the tagging activity. The theoretical analysis produced a framework that was used to identify a number of factors. These factors can be considered as categories that can be consulted to redirect user tagging choice in order to support particular tagging behaviour, such as cross-lingual tagging.

ALGEBRAIC AND GEOMETRIC THEORY OF THE TOPOLOGICAL RING OF COLOMBEAU GENERALIZED FUNCTIONS

We continue the investigation of the algebraic and topological structure of the algebra of Colombeau generalized functions with the aim of building up the algebraic basis for the theory of these functions. This was started in a previous work of Aragona and Juriaans, where the algebraic and topological structure of the Colombeau generalized numbers were studied. Here, among other important things, we determine completely the minimal primes of (K) over bar and introduce several invariants of the ideals of 9(Q). The main tools we use are the algebraic results obtained by Aragona and Juriaans and the theory of differential calculus on generalized manifolds developed by Aragona and co-workers. The main achievement of the differential calculus is that all classical objects, such as distributions, become Cl-functions. Our purpose is to build an independent and intrinsic theory for Colombeau generalized functions and place them in a wider context.