926 resultados para Elementary Methods In Number Theory


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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 $1/9$.

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In this work, we show how number theoretical problems can be fruitfully approached with the tools of statistical physics. We focus on g-Sidon sets, which describe sequences of integers whose pairwise sums are different, and propose a random decision problem which addresses the probability of a random set of k integers to be g-Sidon. First, we provide numerical evidence showing that there is a crossover between satisfiable and unsatisfiable phases which converts to an abrupt phase transition in a properly defined thermodynamic limit. Initially assuming independence, we then develop a mean-field theory for the g-Sidon decision problem. We further improve the mean-field theory, which is only qualitatively correct, by incorporating deviations from independence, yielding results in good quantitative agreement with the numerics for both finite systems and in the thermodynamic limit. Connections between the generalized birthday problem in probability theory, the number theory of Sidon sets and the properties of q-Potts models in condensed matter physics are briefly discussed

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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).

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∗ This research is partially supported by the Bulgarian National Science Fund under contract MM-403/9

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INTRODUCTION: The aim of this study was to evaluate the frequency of anti-Toxocara antibodies in serum from 7-year-old children attending elementary school in Vitória-ES, Brazil and to correlate these antibodies with socio-demographic factors, the presence of intestinal helminths, blood eosinophil numbers, past history of allergy or asthma, and clinical manifestations of helminth infections. METHODS: The detection of anti-Toxocara antibodies was performed using an ELISA (Cellabs Pty Ltd)on serum from 391 children who had already been examined by fecal examination and blood cell counts. Data from clinical and physical examinations were obtained for all children. RESULTS: The prevalence of anti-Toxocara antibodies was 51.6%, with no gender differences. No significant differences were observed between positive serology and the presence or absence of intestinal worms (60.3 and 51.7%, respectively; p = 0.286). The only variables significantly related to positive serology were onycophagy and the use of unfiltered water. Although eosinophilia (blood eosinophil count higher than 600/mm³) was significantly related to the presence of a positive ELISA result, this significance disappeared when we considered only children without worms or without a past history of allergy or asthma. No clinical symptoms related to Toxocara infection were observed. CONCLUSIONS: There is a high prevalence of anti-Toxocara antibodies in children attending elementary schools in Vitória, which may be partially related to cross-reactivity with intestinal helminths or to a high frequency of infection with a small number of Toxocara eggs.

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Recent theoretical developments and case study evidence suggests a relationship between the military in politics and corruption. This study contributes to this literature by analyzing theoretically and empirically the role of the military in politics and corruption for the first time. By drawing on a cross sectional and panel data set covering a large number of countries, over the period 1984-2007, and using a variety of econometric methods substantial empirical support is found for a positive relationship between the military in politics and corruption. In sum, our results reveal that a one standard deviation increase in the military in politics leads to a 0.22 unit increase in corruption index. This relationship is shown to be robust to a variety of specification changes, different econometric techniques, different sample sizes, alternative corruption indices and the exclusion of outliers. This study suggests that the explanatory power of the military in politics is at least as important as the conventionally accepted causes of corruption, such as economic development.

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Mode of access: Internet.

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2000 Mathematics Subject Classification: 11D75, 11D85, 11L20, 11N05, 11N35, 11N36, 11P05, 11P32, 11P55.

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This article considers the place of qualitative research in psychoanalysis and child psychotherapy. It discusses why research methodology for many years occupied so small a place in these fields, and examines the cultural and social developments since the 1960s which have changed this situation, giving formal methods of research much greater significance. It reflects on the different pressures to develop formal research methods which arise both from outside the psychoanalytic field, as a condition of its continued professional survival, and from within it, where its main aim is the development of fundamental psychoanalytic knowledge, It suggests that the conduct of mainly quantitative research into treatment outcomes is largely a response to these external pressures, whilst the main benefits to be gained from the development of qualitative research methods, such as Grounded Theory, are in facilitating the knowledge-generating capacities and achievements of child psychotherapists themselves. The paper describes Grounded Theory methods, and explains how they can be valuable in the recognition of hitherto unrecognised meanings and patterns as these are made visible in clinical practice. Finally, it briefly describes five different examples of completed doctoral studies, all of which have added significantly to the knowledge-base of child psychotherapy, and which demonstrate how much can be accomplished using this method of research.

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This thesis considers non-perturbative methods in quantum field theory with applications to gravity and cosmology. In particular, there are chapters on black hole holography, inflationary model building, and the conformal bootstrap.

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Experimental geophysical fluid dynamics often examines regimes of fluid flow infeasible for computer simulations. Velocimetry of zonal flows present in these regimes brings many challenges when the fluid is opaque and vigorously rotating; spherical Couette flows with molten metals are one such example. The fine structure of the acoustic spectrum can be related to the fluid’s velocity field, and inverse spectral methods can be used to predict and, with sufficient acoustic data, mathematically reconstruct the velocity field. The methods are to some extent inherited from helioseismology. This work develops a Finite Element Method suitable to matching the geometries of experimental setups, as well as modelling the acoustics based on that geometry and zonal flows therein. As an application, this work uses the 60-cm setup Dynamo 3.5 at the University of Maryland Nonlinear Dynamics Laboratory. Additionally, results obtained using a small acoustic data set from recent experiments in air are provided.