Thesis (D. Min.)--Trinity International University, 2004. / Abstract. Includes bibliographical references (leaves 180-185).

Thesis (D. Min.)--Trinity International University, 2004. / Abstract. Includes bibliographical references (leaves 180-185).

Thesis (D. Min.)--Trinity International University, 2004. / Abstract. Includes bibliographical references (leaves 180-185).

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Made available in DSpace on 2016-04-28T14:16:15Z (GMT). No. of bitstreams: 1 Rodrigo Andrade da Cruz.pdf: 1629158 bytes, checksum: 3ec8cff79cd51d70c0323e3aae016b09 (MD5) Previous issue date: 2012-06-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The present study focused on the development and institutionalization of the science of eugenics in the United States during the first decades of the 20th century. For this purpose, we focused on the ideas of Charles B. Davenport (1866-1944), his work team, and the institutional networks he contributed to establish. Davenport initially learned the notions and methods developed for eugenic research by Francis Galton (1822-1911) and Karl Pearson (1857-1936), who essentially applied statistical methods. However, by the same time the studies by Gregor Mendel (1822-1884) were rediscovered giving impetus to the incipient field of genetics and were also assimilated by Davenport into his eugenic project. Together with a discussion of the overall historical context that favored the development of eugenics in the US, we analyzed the works by Davenport as well as by some of his main collaborators, such as psychologist Henry Goddard (1866-1957) and eugenicist Harry Laughlin (1880-1943), as well as the repercussions of eugenics in US society in the early decades of the 20th century / A presente pesquisa abordou o desenvolvimento e institucionalização da ciência eugenista nos Estados Unidos nas primeiras décadas do século XX. Para tanto, focou-se nos trabalhos de Charles B. Davenport (1866-1944), seu grupo de trabalho e as redes institucionais que estabeleceu. Inicialmente, Davenport assimilou os conceitos e métodos de pesquisa eugenista desenvolvidos por Francis Galton (1822-1911) e Karl Pearson (1857-1936), que aplicaram basicamente uma abordagem estatística. No entanto, no mesmo período, são redescobertos os trabalhos de Gregor Mendel (1822-1884), associados à incipiente pesquisa genética, também assimilados por Davenport no seu projeto eugenista. Junto de uma discussão do contexto histórico geral que favoreceu as teses eugenistas nos EUA no período sob consideração, foram analisadas as publicações científicas de Davenport e de alguns de seus principais colaboradores, como o psicólogo Henry Goddard (1866-1957) e o eugenista Harry Laughlin (1880-1943), assim como as repercussões desse desenvolvimento na sociedade norte-americana nas três primeiras décadas do século XX

Un entier naturel est dit $y$-friable lorsque son plus grand facteur premier n'excède pas $y$. Ce travail est consacré à l'étude des entiers friables dans le cadre de la théorie analytique et probabiliste des nombres. La première partie est dévolue à un problème posé par Davenport en 1937, qui consiste à déterminer les conditions de validité de diverses généralisations de son développement de la fonction sinus en série de parties fractionnaires. Ces généralisations peuvent être décrites par un couple de fonctions arithmétiques, liées par la relation de convolution $f=g*\1$. Nous traitons le cas où $g$ est la fonction de Piltz d'ordre $z\in\CC$. La deuxième partie est consacrée à l'étude du comportement asymptotique de la constante optimale dans une version friable de l'inégalité de Turán-Kubilius. Précisant des résultats récents de La Bretèche et Tenenbaum, nous généralisons au cas friable une formule asymptotique de la variance d'une fonction arithmétique additive, établie par Hildebrand en 1983.

Cette thèse est divisée en deux parties : la partie I traite de combinatoire additive, la partie II s’est portée sur des questions de théorie élémentaire des nombres. Dans le chapitre 1, on généralise la transformée de Davenport pour prouver que si S\mathbb A=(A, +)S est un demi-groupe cancellatif (éventuellement non commutatif) et SX, YS sont des sous-ensembles non vides de SAS tels que le sous semi groupe engendré par SYS est commutatif, on a SS|X+Y|\gc\min(\gamma(Y, |X|+|Y|-I)SS, où S\gamma(\ctlot)S dénote la constante de Cauchy-Davenport d’un ensemble. On en obtient une extension des théorèmes de Chowla et Pillai pour les groupes cycliques et une version plus forte d’un théorème additif de Karolyi et Hamidoune. Dans le chapitre 2, on montre que si S(A,+)S est un semi-groupe cancellatif et si SX, Y\subsetcq AS alors SS|X+Y|\gc\min(\gammaX+Y), |X|+|Y|-I)SS. Cela donne une généralisation de l’inégalité de Kemperman pour les groupes sans torsion et une version plus forte du théorème d’Hamidoune-Karolyi. Dans le chapitre 3, on généralise des résultats par Freiman et al., en prouvant que si S(A,\ctlot)S est un semi-groupe linéairement ordonnable et SSS est un sous-ensemble fini de SAS engendrant un sous-semi-groupe non-abélien, alors S|S^2-\gc3|S|-2S. Dans le chapitre 4, on prouve des résultats liés à une conjecture par Gyorgy et Smyth sur la finitude des entiers Sn\gc1S tels que Sn^kS divise Sa^a \pmb^nS pour des entiers fixés SaS, SbS et SkS avec Sk\gc3S, S|ab|\gc2Set S\gcd(a,b) = 1S. Enfin, dans le chapitre 5, on considère une question de divisibilité dans les entiers, en quelque sorte liée au problème de Znam et à la conjecture d’Agoh-Giuga / This thesis is divided into two parts. Part I is about additive combinatorics. Part II deals with questions in elementary number theory. In Chapter 1, we generalize the Davenport transform to prove that if si S\mathbb A=(A, +)S is acancellative semigroup (either abelian or not) and SX, YS are non-empty subsets of SAS such that the subsemigroup generated by SYS is abelian, then SS|X+Y|\gc\min(\gamma(Y, |X|+|Y|-I)SS, where for SZ\subsetcq AS we let S\gamma(Z):=\sup_{z_0\in Z^\times}\in f_(z_0\nc z\inZ) (vm ord)(z-z_0)S. This implies an extension of Chowla’s and Pillai’s theorems for cyclic groups and a stronger version of an addition theorem by Hamidoune and Karolyi for arbitrary groups. In Chapter 2, we show that if S(A, +) is a cancellative semigroup and SX, Y\subsetcq AS then SS|X+Y|\gc\min(\gammaX+Y), |X|+|Y|-I)SS. This gives a generalization of Kemperman’s inequality for torsion free groups and a stronger version of the Hamidoune-Karolyi theorem. In Chapter 3, we generalize results by Freiman et al. by proving that if S(A,\ctlot)S is a linearly orderable semigroup and SSS is a finite subset of SAS generating a non-abelian subsemigroup, then S|S^2-\gc3|S|-2S. In Chapter 4, we prove results related to conjecture by Gyory and Smyth on the sets SR_k^\pm(a,b)S of all positive integers SnS such that Sn^kS divides Sa^a \pmb^nS for fixed integers SaS, SbS and SkS with Sk\gc3S, S|ab|\gc2Set S\gcd(a,b) = 1S. In particular, we show that SR_k^pm(a,b)S is finite if Sk\gc\max(|a|.|b|)S. In Chapter 5, we consider a question on primes and divisibility somchow related to Znam’s problem and the Agoh-Giuga conjecture

This thesis is divided into two parts. Part I is about additive combinatorics. Part II deals with questions in elementary number theory. In Chapter 1, we generalize the Davenport transform to prove that if si S\mathbb A=(A, +)S is acancellative semigroup (either abelian or not) and SX, YS are non-empty subsets of SAS such that the subsemigroup generated by SYS is abelian, then SS|X+Y|\gc\min(\gamma(Y, |X|+|Y|-I)SS, where for SZ\subsetcq AS we let S\gamma(Z):=\sup_{z_0\in Z^\times}\in f_(z_0\nc z\inZ) (vm ord)(z-z_0)S. This implies an extension of Chowla's and Pillai's theorems for cyclic groups and a stronger version of an addition theorem by Hamidoune and Karolyi for arbitrary groups. In Chapter 2, we show that if S(A, +) is a cancellative semigroup and SX, Y\subsetcq AS then SS|X+Y|\gc\min(\gammaX+Y), |X|+|Y|-I)SS. This gives a generalization of Kemperman's inequality for torsion free groups and a stronger version of the Hamidoune-Karolyi theorem. In Chapter 3, we generalize results by Freiman et al. by proving that if S(A,\ctlot)S is a linearly orderable semigroup and SSS is a finite subset of SAS generating a non-abelian subsemigroup, then S|S^2-\gc3|S|-2S. In Chapter 4, we prove results related to conjecture by Gyory and Smyth on the sets SR_k^\pm(a,b)S of all positive integers SnS such that Sn^kS divides Sa^a \pmb^nS for fixed integers SaS, SbS and SkS with Sk\gc3S, S|ab|\gc2Set S\gcd(a,b) = 1S. In particular, we show that SR_k^pm(a,b)S is finite if Sk\gc\max(|a|.|b|)S. In Chapter 5, we consider a question on primes and divisibility somchow related to Znam's problem and the Agoh-Giuga conjecture