透過使用調和映射的Bochner技巧, Siu[15, 16]證明了對於複維數≥2 時不可約對稱域緊致商空間的複結構的強剛定理. 其後在[9]中, Mok 證明了在任何秩≥2 的不可約對稱域緊致商空間上, 所有具備非正全純雙截曲率的Hermitian 度量必然和典範度量相差一個常數因子. 由這個定理和Siu 的定理可以得出Mostow 剛性定理[14]在特殊情形下的推廣.本論文會對Mok的結果作出研究. / By using Bochner technique of harmonic maps, Siu[15, 16] proved a strong rigidity theorem concerning the complex structure of compact quotients of irreducible bounded symmetric domain of complex dimension≥ 2. Later in [9], Mok proved a metric rigidity theorem which asserts that any Hermitian metric of seminegative holomorphic bisectional curvature on a compact quotient of an irreducible bounded symmetric domain of rank≥ 2 is necessarily a constant multiple of the canonical metric. This theorem together with the theorem of Siu yields a generalization of a special case of Mostow's rigidity theorem[14]. This thesis is an exposition of Mok's results. / Detailed summary in vernacular field only. / Li, Ka Fai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 102-104). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Symmetric Space --- p.5 / Chapter 2.1 --- Riemannian Symmetric Spaces --- p.5 / Chapter 2.2 --- Lie Groups and Lie Algebras --- p.10 / Chapter 2.3 --- Riemannian Symmetric Spaces of Compact and Non-compact type --- p.11 / Chapter 2.4 --- Hermitian Symmetric Spaces --- p.16 / Chapter 2.5 --- Duality --- p.19 / Chapter 3 --- Some Embedding Theorems --- p.22 / Chapter 3.1 --- The Borel Embedding Theorem --- p.22 / Chapter 3.2 --- Root Space Decomposition and Root System --- p.24 / Chapter 3.3 --- The Polydisc Theorem --- p.28 / Chapter 3.4 --- The Harish-Chandra Embedding Theorem --- p.36 / Chapter 4 --- Bounded Symmetric Domains --- p.42 / Chapter 4.1 --- Classical Bounded Symmetric Domains --- p.42 / Chapter 4.2 --- The Bergman metric --- p.57 / Chapter 5 --- Projective and Characteristic Bundle --- p.65 / Chapter 5.1 --- Projectivization of Hermitian Vector Bundle --- p.65 / Chapter 5.2 --- Characteristic bundle --- p.69 / Chapter 6 --- The Hermitian Metric Rigidity Theorem --- p.83 / Chapter 7 --- Appendix --- p.100 / Bibliography --- p.102

In this thesis we introduce and study the (i) Grassmannian, (ii) Lagrangian Grassmannian, and (iii) double Lagrangian Grassmannian of subspaces in ( A ⊗ B )n, where A and B are normed division algebras, i.e. R,C,H or O . / This gives a simple and uniform description of all symmetric spaces. This is analogous to Tits magic square description for simple Lie algebras. / We show that every irreducible compact Riemannian symmetric space X must be one of these Grassmannian spaces (up to a finite cover) or a compact simple Lie group. Furthermore, its noncompact dual symmetric space is the open sub-manifold of X consisting of spacelike linear subspaces, at least in the classical cases. / Huang, Yongdong. / "July 2007." / Adviser: Naichung Conan Leung. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0353. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 64-65). / 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.

Chen, Yunxia. / "August 2010." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 54-56). / Abstracts in English and Chinese. / Chapter 1 --- Embedding in Hermitian case --- p.8 / Chapter 1.1 --- Basics on Riemannian symmetric spaces --- p.8 / Chapter 1.2 --- Embedding in Hermitian case --- p.11 / Chapter 1.2.1 --- Borel embedding theorem --- p.11 / Chapter 1.2.2 --- Harish-Chandra embedding theorem --- p.12 / Chapter 1.2.3 --- Hermann convexity theorem --- p.14 / Chapter 2 --- Embedding in generalized Grassmannian case --- p.15 / Chapter 2.1 --- Compact symmetric spaces as Grassmannians --- p.15 / Chapter 2.1.1 --- Preliminaries --- p.15 / Chapter 2.1.2 --- "Grassmannians, Lagrangian Grassmannians and Double Lagrangian Grassmannians" --- p.16 / Chapter 2.1.3 --- Compact simple Lie groups --- p.20 / Chapter 2.2 --- Embedding in generalized Grassmannian case --- p.23 / Chapter 2.2.1 --- Space-like Grassmannian --- p.23 / Chapter 2.2.2 --- Graph-like Grassmannian --- p.26 / Chapter 2.2.3 --- Convexity property --- p.27 / Chapter 3 --- Cut locus of Compact symmetric spaces --- p.29 / Chapter 3.1 --- Cut locus --- p.29 / Chapter 3.1.1 --- Cut locus of Riemannian manifold --- p.29 / Chapter 3.1.2 --- Lie algebra of compact symmetric space --- p.31 / Chapter 3.1.3 --- Tangent cut locus of compact symmetric spaces --- p.32 / Chapter 3.2 --- Hermitian case and generalized Grassmannian case --- p.36 / Chapter 3.2.1 --- The Hermitian case --- p.36 / Chapter 3.2.2 --- The generalized Grassmannian case --- p.38 / Chapter 4 --- Construction of the explicit embedding --- p.42 / Chapter 4.1 --- Regular symmetric spaces --- p.42 / Chapter 4.2 --- Embedding in Regular case --- p.45 / Chapter 4.2.1 --- Construction of the embedding --- p.45 / Chapter 4.2.2 --- The properties of the explicit embedding --- p.47 / Chapter 4.3 --- Generalization of the embedding --- p.51 / Bibliography --- p.54

So, Tse Leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 55-56). / Abstracts in English and Chinese. / Chapter 1 --- Geometric Quantization --- p.8 / Chapter 1.1 --- Motivation --- p.8 / Chapter 1.2 --- Prequantization --- p.10 / Chapter 1.3 --- Kahler Polarization --- p.14 / Chapter 1.4 --- Holomorphic Quantization and Fock Space --- p.17 / Chapter 1.4.1 --- Example: Fock Space --- p.19 / Chapter 2 --- Projectively Flat Connection --- p.21 / Chapter 2.1 --- Variation of Complex Structure --- p.21 / Chapter 2.2 --- Projectively Flat Connection on H --- p.24 / Chapter 2.2.1 --- Example of n= 1: --- p.30 / Chapter 3 --- Construction of Projectively Flat Connection --- p.34 / Chapter 3.1 --- Mechanism for Construction of Projectively Flat Con- nection --- p.34 / Chapter 3.2 --- K = C Case --- p.39 / Chapter 3.2.1 --- Identification of C´ؤlinear Complex Structures --- p.40 / Chapter 3.2.2 --- Projecitvely flat bundle on U(n)×U(n) --- p.43 / Chapter 3.2.3 --- Example of n=1 --- p.44 / Chapter 3.3 --- K = H Case --- p.45 / Chapter 3.3.1 --- Identification of H-linear Complex Structures --- p.46 / Chapter 3.3.2 --- Projecitvely flat bundle on SO*(4n) --- p.49 / Chapter 3.3.3 --- Example of n = 1 --- p.51 / Bibliography --- p.55

Optimal pick point location is discovered in order to have the full buckling capacity of a suspended, non-prismatic, singly symmetric plate girders. The results show that a significant increase in stability occurs at the pick point location of 0.25L, where L is the span length. This recommendation can be utilized in the field to save construction cost and time because of how simplistic it is to use. A finite element software, ABAQUS 6.14, is used to determine the buckling capacities at different pick point locations and of different cross sections. The dimension of the cross sections and span lengths for the research is based upon a case study.

In this thesis we have investigated permutation and monomial progenitors of the form p^*n:N (p=2,3,5,...) and p^*n:_m N (p=3,5,7,...) respectively. We have discovered new symmetric presentations of several finite nonabelian simple groups including linear groups, unitary groups, orthogonal groups, and sporadic groups. We have constructed interesting groups found using the technique of double coset enumeration and found the isomorphic types of the numerous groups that appeared as homorphic images. These include the sympletic group, S_4(5) and the Janko groups, J_2 and J_1 which were found using a variety of different control groups over finite fields.

We will examine progenitors. We begin with progenitors of the from $m^{*n} : N$ where $m^{*n}$ is a free group and $N$ is a permutation group of degree $n$. Now $m^{*n} : N$ is a group of infinite order so we will factor by the necessary relations to get the finite homomorphic images. We construct these groups through the method of double coset enumeration paying special attention to the proving of each relation.

The subject of the thesis is the study of operator functions in the setting of symmetric operator spaces. In this latter setting, it is of great importance to analyze the properties of so-called operator functions A --> f(A), where the variable A is a self-adjoint operator and f is a complex-valued Borel function on the real line. The thesis study the question of differentiability of this type of operator functions. The latter question is intimately related to the study of commutators. Text not only extends existing results to the setting of unbounded self-adjoint linear operators, but it is also shown that this can be obtained via a unified approach utilizing the left regular representation of von Neumann algebras.

Let S and T be numerical semigroups and let k be a positive integer. We say that S is the quotient of T by k if an integer x belongs to S if and only if kx belongs to T. Given any integer k larger than 1 (resp., larger than 2), every numerical semigroup S is the quotient T/k of infinitely many symmetric (resp., pseudo-symmetric) numerical semigroups T by k. Related examples, probabilistic results, and applications to ring theory are shown. Given an arbitrary positive integer k, it is not true in general that every numerical semigroup S is the quotient of infinitely many numerical semigroups of maximal embedding dimension by k. In fact, a numerical semigroup S is the quotient of infinitely many numerical semigroups of maximal embedding dimension by each positive integer k larger than 1 if and only if S is itself of maximal embedding dimension. Nevertheless, for each numerical semigroup S, for all sufficiently large positive integers k, S is the quotient of a numerical semigroup of maximal embedding dimension by k. Related results and examples are also given.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, August 1999. / Includes bibliographical references. Also available on the Internet.