Thesis (Ph. D.)--Johns Hopkins University, 1925. / Vita.

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2008. / Includes bibliographical references (leaves 43-45). Also available in electronic version.

Thesis (Ph. D.)--Johns Hopkins University, 1925. / Vita.

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2005. / Includes bibliographical references (leaves 77-80). Also available in electronic version.

: Soit E→P1 une surface elliptique sur Q de base P1 non triviale. On s’intéresse à la Zariski-densité des points rationnels de E . Il est conjecturé que le signe de l’équation fonctionnelle d’une courbe elliptique est relié à la parité du rang de celle-ci. Modulo cette conjecture, il est suffisant de démontrer que le signe des fibres de E varie pour démontrer la Zariski-densité de E (Q). Un théorème conditionnel de Helfgott garantit que le signe moyen d’une surface non isotriviale est strictement compris entre -1 et 1. Dans le cas où E possède une place générique de réduction multiplicative, le signe moyen serait nul. Ce travail est conditionnel à deux conjectures de théorie analytique des nombres : la conjecture sans facteur carré et la conjecture de Chowla. L’objectif principal de cette thèse est d’éviter les conjectures utilisées par Helfgott pour démontrer la variation du signe sur les surfaces elliptiques non triviales. On réussit à se passer de la conjecture sans facteur carré sous certaines hypothèses techniques. On démontre ainsi (sous l’hypothèse de la conjecture de parité) la densité des points rationnels sur certaines surfaces elliptiques dont les coefficients sont des polynômes de degré arbitraire. Une surface de Del Pezzo de degré 1 est reliée par l’éclatement d’un point canonique à une surface elliptique rationnelle. On démontre inconditionnellement la densité des points rationnels dans plusieurs cas par des arguments géométriques. On étudie aussi la variation du signe de l’équation fonctionnelle pour des surfaces elliptiques rationnelles isotriviales et on cerne des conditions pour que le signe soit fixé. Dans le cas où le signe est +1, on en déduit des exemples de surfaces elliptiques non triviales dont les points rationnels pourraient ne pas être denses. / Let E→P1 be an non-trivial elliptic surface over Q with base P1. We are interested in the Zariski density of the rational points of E. It is conjectured that the root number of an elliptic curve E has the same parity as its rank. Assuming this conjecture, it is enough to show that the root number of the fibre of E varies to prove the Zariski density of E(Q). A conditional theorem of Helfgott garanties that the average root number of a non-isotrivial elliptic surface is strictly between -1 et 1. In the case where E has a generic place of multiplicative reduction, the average root number should be zero. This work is conditional to two analytic number theory conjectures : the squarefree conjecture and the Chowla conjecture. The main aim of this Ph.D thesis is to avoid the conjectures used by Helfgott when proving the variation of the root number on non-trivial elliptic surfaces. We manage to drop the squarefree conjecture assumption under some technical hypothesis. We show thus (under the parity conjecture) the density of the rational points on some elliptic surfaces whose coefficients have arbitrary large degree. Blowing up the anticanonical point on a del Pezzo surface of degree 1, one obtains a rational elliptic surface. We show unconditionally the density of the rational points in many cases by means of geometric arguments. We also study the variation of the root number on some isotrivial rational elliptic surfaces and we state the conditions under which it is constant. When it is +1, we deduce examples of non trivial elliptic surfaces whose rational points might not be dense.

A model is constructed which views regolith evolution on asteroids as a stochastic process. Average values are shown to be poor descriptors of regolith depth. Large deviations from the average are expected to occur due both to variations in the depth over the surface of a body and to stochastic fluctuations in the variables which determine regolith depth, e.g. the number of craters produced on an asteroid. The utility of the average depth is not significantly increased by avoiding large craters of thick ejecta deposits; a procedure adopted in previous regolith studies. The statistical uncertainty associated with regolith depth severely limits the power of regolith models in predicting parent-body size for brecciated meteorites. Virtually any rocky asteroid larger than 100-200 km in diameter could have produced the abundance of brecciated material observed in the achondritic meteorites. Bodies which are composed of weaker materials and which have diameters greater than 20 km could have produced the abundance of breccias observed in the chondrites. A Monte Carlo algorithm is used to simulate the random walks and corresponding changed-particle irradiation histories of grains in regoliths. On rocky asteroids, only about 20% of the grains are exposed to solar cosmic ray ions. These grains typically spend a few thousand years in the upper 100 microns of the regolith and acquire particle track densities of 10⁷-10⁹/cm² at their surfaces. Only about 5% of the grains acquire track densities greater than 10⁸/cm². Grains which reach the surface are exposed to galactic cosmic rays for roughly 10⁶y. Weak asteroids with diameters less than a few tens of kilometers have very immature regoliths because of short collisional lifetimes and the ejection of heavily irradiated grains to space. Only a few percent of the grains are exposed at the surface and these acquire track densities of 10⁷-10⁸/cm². Exposure times and the fraction of grains irradiated should increase for larger weak bodies due to longer collisional lifetimes. These results, which are based on present-day conditions in the asteroid belt, agree well with irradiation features observed in gas-rich meteorites; an origin during epochs of early solar system evolution is not required.

Thesis (D.Sc.D.)-- - Boston University School of Graduate Dentistry, 1976 (Periodontology). / Bibliography included.

Cheung Leung-Fu. / Bibliography: leaves [51]-[53] / Thesis (M.Ph.)--Chinese University of Hong Kong, 1984

by Pun Shu Hoi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1990. / Bibliography: leaves 124-128. / Abstract --- p.1 / Acknowledgement --- p.2 / Introduction --- p.3 / Chapter I --- On the omitted values of the Gauss map of complete minimal surfaces --- p.8 / Chapter 1 --- Weierstrass Representation of minimal surface --- p.9 / Chapter 1.1 --- The generalized Gauss Map --- p.9 / Chapter 1.2 --- Gauss map in R3 --- p.13 / Chapter 1.3 --- Gauss map in R4 --- p.18 / Chapter 2 --- An optimal result on the omitted values --- p.23 / Chapter 2.1 --- Xavier's result --- p.23 / Chapter 2.2 --- A lower bound for Poincare metric --- p.32 / Chapter 2.3 --- A function-theoretic lemma --- p.37 / Chapter 2.4 --- The optimal result --- p.43 / Chapter 3 --- The relation between omitted values and total curvature --- p.57 / Chapter 3.1 --- An extension of Xavier's result --- p.57 / Chapter 3.2 --- An extension of Fujimoto's Theorem --- p.65 / Chapter II --- On geometry of complete minimal surfaces with finite Morse index in 3-manifold of non-negative scalar curvature --- p.75 / Chapter 4 --- The structure of complete stable minimal surfaces in3- manifolds of non-negative scalar curvature --- p.76 / Chapter 4.1 --- Preliminary results on λi of the operator Δ ´ؤ q --- p.76 / Chapter 4.2 --- Some results on the operator Δ ´ؤ ak for conformal metrics on the disk --- p.81 / Chapter 4.3 --- Classification Theorem --- p.86 / Chapter 4.4 --- Complete stable minimal surfaces in complete scalar flat 3- manifolds --- p.92 / Chapter 5 --- On complete minimal surfaces with finite Morse index in 3-manifolds of non-negative scalar curvature --- p.96 / Chapter 5.1 --- On properties of the operator L --- p.96 / Chapter 5.2 --- The geometry of minimal surfaces of finite index --- p.110 / Chapter 5.3 --- Finite index minimal sufrace in R3 --- p.120 / Bibliography --- p.124

Thesis (Ph. D.)--University of Chicago, 1915. / Vita. "Reprinted from the Transactions of the American mathematical society, October, 1915." Includes bibliographical references. Also available on the Internet.