Yeung Wai Kong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 51-55). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Some Preliminaries --- p.13 / Chapter 3 --- "Approximate Function we,p" --- p.17 / Chapter 4 --- "The Computation Of Je[we,p]" --- p.21 / Chapter 5 --- The Signs of c1 And c3 --- p.30 / Chapter 6 --- The Asymptotic Behavior of ue and Je[ue] --- p.35 / Chapter 7 --- "The Proofs Of Theorem 1.1, Theorem 1.2 And Corol- lary 11" --- p.40 / Appendix --- p.43 / Bibliography --- p.51

It is well-known that del Pezzo surfaces of degree 9 -- n. are in one-to-one correspondence to flat En bundles over elliptic curves which are anti-canonical curves of such surfaces. In my thesis, we study a broader class of rational surfaces which are called ADE surfaces. We construct Lie algebra bundles of any type on these surfaces, and extend the above correspondence to flat G bundles over elliptic curves, where G is a simple, compact and simply-connected Lie group of any type. Concretely, we establish a natural identification between the following two very different moduli spaces for a Lie group G of any type: the moduli space of rational surfaces with G-configurations and the moduli space of flat G-bundles over a fixed elliptic curve. / Zhang, Jiajin. / "July 2007." / Adviser: Leung Nai Chung Conan. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0357. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 77-79). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Ng, Chit Yu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 89-90). / Abstracts in English and Chinese.

Thesis (M.S.)--University of Nevada, Reno, 2005. / "May 2005." Includes bibliographical references (leaves 27-28). Online version available on the World Wide Web.

The elliptic equation $Delta u+K(|x|)|u|^{p-1}u=0,xin mathbf{R}^{n}$ is studied, where $p>1$, $n>2$, $K(r)$ is smooth and positive on $(0,infty)$, and $rK(r)in L^{1}(0,1)$. It is known that the radial solution either oscillates infinitely, or $lim_{r ightarrow infty}r^{n-2}u(r;al) in Rsetminus {0}$ (rapidly decaying), or $lim_{r ightarrow infty}r^{n-2}u(r;al) = infty (or -infty)$ (slowly decaying). Let $u=u(r;al)$ is a solution satisfying $u(0)=al$. In this thesis, we classify all the radial solutions into three types: Type R($i$): $u$ has exactly $i$ zeros on $(0,infty)$, and is rapidly decaying at $r=infty$. Type S($i$): $u$ has exactly $i$ zeros on $(0,infty)$, and is slowly decaying at $r=infty$. Type O: $u$ has infinitely many zeros on $(0,infty)$. If $rK_{r}(r)/K(r)$ satisfies some conditions, then the structure of radial solutions is determined completely. In particular, there exists $0<al_{0}<al_{1}<al_{2}<cdots<infty$ such that $u(r;al_{i})$ is of Type R($i$), and $u(r;al)$ is of Type S($i$) for all $al in (al_{i-1},al_{i})$, where $al_{-1}:=0$. These works are due to Yanagida and Yotsutani. Their main tools are Kelvin transformation, Pr"{u}fer transformation, and a Pohozaev identity. Here we give a concise account. Also, I impose a concept so called $r-mu graph$, and give two proofs of the Pohozaev identity.

Thesis (M.S.)--Brigham Young University. Dept. of Mathematics, 2008. / Includes bibliographical references (p. 45-46).

published_or_final_version / Mathematics / Master / Master of Philosophy

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Thesis (M.S.) -- Worcester Polytechnic Institute. / Keywords: low power; montgomery multiplication; elliptic curve crytography; modulus scaling; unified architecture; inversion; redundant signed digit. Includes bibliographical references (p.55-59).