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published_or_final_version / Mathematics / Master / Master of Philosophy

published_or_final_version / Physics / Master / Master of Philosophy

Shu-jia Wang. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 94-101). / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Estimation of Structural Equation Models --- p.7 / Chapter Chapter 3 --- Statistical Curvatures in Structural Equation Models --- p.11 / Chapter 3.1 --- The Intrinsic and Parameter-effects Curvatures --- p.12 / Chapter 3.2 --- The Three Dimensional Curvature Arrays --- p.16 / Chapter Chapter 4 --- Bias and Covariance Matrix of the GLS Estimates --- p.20 / Chapter 4.1 --- Stochastic Expansion of the GLS Estimates --- p.20 / Chapter 4.2 --- The Second Order Approximation of the Bias --- p.23 / Chapter 4.3 --- The Second Order Approximation of Covariance Matrix of the GLS Estimates --- p.25 / Chapter 4.4 --- An Artificial Example --- p.29 / Chapter 4.5 --- Discussion --- p.33 / Chapter Chapter 5 --- Information Loss of the Estimators Under Assumption of Multivariate Normality --- p.35 / Chapter Chapter 6 --- Sensitivity Analysis of Structural Equation Models --- p.44 / Chapter 6.1 --- Introduction --- p.44 / Chapter 6.2 --- General Theory of Local Influence Analysisin Structural Equation Models --- p.46 / Chapter 6.3 --- Perturbation to the Case Weights in the GLS Estimation --- p.50 / Chapter 6.4 --- Cook's Distance in the Case Deletion Approach --- p.54 / Chapter 6.5 --- Relationship of Local Influence and Influence Function --- p.59 / Chapter 6.6 --- Illustrative Examples --- p.61 / Chapter 6.7 --- Sensitivity Analysis of Parameters --- p.63 / Chapter 6.8 --- Discussion --- p.68 / Chapter Chapter 7 --- Sensitivity Analysis of Structural Equation Models with Equality Functional Constraints --- p.70 / Chapter 7.1 --- Introduction --- p.70 / Chapter 7.2 --- Local Influence of Structural Equation Models With Constraints --- p.71 / Chapter 7.2.1 --- General Theory --- p.72 / Chapter 7.2.2 --- Perturbation to Case Weights in Constrained GLS Estimation --- p.77 / Chapter 7.2.3 --- Relationship of Local Influence and Influence Function --- p.79 / Chapter 7.3 --- Generalized Cook's Distance: Case Deletion Approach --- p.81 / Chapter 7.4 --- An Illustrative Example --- p.84 / Chapter 7.5 --- Sensitivity Analysis of Parameters With Constraints --- p.86 / Chapter 7.6 --- Discussion --- p.89 / Chapter Chapter 8 --- Summary and Discussion --- p.91 / References --- p.94 / Tables --- p.102 / Figures --- p.111

by Mong Kai Cheong. / Bibliography: leaf 50 / Thesis (M.Phil.)--Chinese University of Hong Kong, 1983

by Leung Kwok Kei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 90-94). / Chapter 0 --- Introduction --- p.1 / Chapter 1 --- Comparison Theorems --- p.4 / Chapter 1.1 --- Introduction --- p.4 / Chapter 1.2 --- Bishop Comparison Theorem --- p.5 / Chapter 1.3 --- Hessian Comparison Theorem --- p.13 / Chapter 1.4 --- Applications of Laplacian comparison theorem --- p.16 / Chapter 2 --- "The first eigenvalue, gradient estimates and related inequalities" --- p.21 / Chapter 2.1 --- Lower bounds of the first eigenvalue --- p.21 / Chapter 2.2 --- Gradient estimate and Harnack inequality --- p.29 / Chapter 2.3 --- Mean value inequality --- p.33 / Chapter 2.4 --- Isoperimetric inequalities and Sobolev inequalities --- p.40 / Chapter 3 --- Harmonic mappings --- p.47 / Chapter 3.1 --- Definitions and notations --- p.47 / Chapter 3.2 --- Existence results --- p.50 / Chapter 3.3 --- Bochner technique --- p.54 / Chapter 3.4 --- Strong rigidity theorems --- p.58 / Chapter 3.5 --- Superrigidity and harmonic maps --- p.71 / Appendix --- p.75 / Chapter A --- Bochner formula and its integral form --- p.76 / Chapter A.1 --- Bochner formula --- p.76 / Chapter A.2 --- Reilly's formula and its applications --- p.82 / Bibliography --- p.90

by Lung Tak Yee. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1987. / Bibliography: leaves 80-82.

by Wong Wai Keung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 101-[102]). / Abstract also in Chinese. / Introduction --- p.1 / Chapter 1 --- CR Manifolds --- p.3 / Chapter 1.1 --- Abstract CR manifolds --- p.3 / Chapter 1.2 --- Embedded CR manifolds --- p.4 / Chapter 1.3 --- A normal form for generic embedded CR manifolds --- p.9 / Chapter 2 --- Differential Geometry of Strongly Pseudo-convex Manifolds --- p.18 / Chapter 2.1 --- Holomorphic vector bundles --- p.18 / Chapter 2.2 --- The cohomology groups Hq(M，E) --- p.20 / Chapter 2.3 --- "The spectral sequence {Erp,q(M)}" --- p.23 / Chapter 2.4 --- The Levi form --- p.31 / Chapter 2.5 --- Strongly pseudo-convex manifolds --- p.37 / Chapter 2.6 --- Strongly pseudo-convex real hypersurfaces --- p.40 / Chapter 2.7 --- Canonical affine connections --- p.44 / Chapter 2.8 --- Green's Theorem --- p.51 / Chapter 2.9 --- Canonical connections in holomorphic vector bundles --- p.53 / Chapter 3 --- The Harmonic Theory --- p.59 / Chapter 3.1 --- The fundamental operators --- p.59 / Chapter 3.2 --- The fundamental inequalities --- p.65 / Chapter 3.3 --- Kohn's harmonic theory --- p.67 / Chapter 3.4 --- The harmonic theory and the duality --- p.71 / Chapter 4 --- The Holomorphic Extension of CR Functions --- p.76 / Chapter 4.1 --- Approximation theorem --- p.76 / Chapter 4.2 --- The technique of analytic discs --- p.81 / Chapter 4.3 --- Holomorphic extension --- p.95 / Bibliography --- p.101

by Chen Bing-Long. / "August 2003." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 68-71). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.