Yip Chi Ming = 守恆及開放系統的能譜反問題 / 葉志明. / Thesis submitted in 2000. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves [244]-247). / Text in English; abstracts in English and Chinese. / Yip Chi Ming = Shou heng ji kai fang xi tong de neng pu fan wen ti / Ye Zhiming. / Abstract --- p.i / Acknowledgements --- p.ii / Contents --- p.iii / List of Figures --- p.viii / List of Tables --- p.xxi / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- The Sturm-Liouville Problem --- p.3 / Chapter 1.2 --- Historical review of inverse problems --- p.7 / Chapter 1.3 --- Conservative systems --- p.10 / Chapter 1.4 --- Open systems --- p.10 / Chapter 1.5 --- Organization of the following chapters --- p.11 / Chapter Chapter 2. --- Conservative Spectral Problem --- p.12 / Chapter 2.1 --- The system --- p.12 / Chapter 2.2 --- Properties of conservative systems --- p.13 / Chapter 2.2.1 --- Asymptotic expansion of eigenvalues --- p.14 / Chapter 2.3 --- Forward spectral problem --- p.16 / Chapter 2.3.1 --- FDM and FEM --- p.17 / Chapter 2.3.2 --- Solving transcendental equation --- p.20 / Chapter 2.4 --- Phase shift problem --- p.20 / Chapter 2.4.1 --- Square well potential --- p.22 / Chapter Chapter 3. --- Forward Spectral Problem for Open Systems --- p.25 / Chapter 3.1 --- The system --- p.26 / Chapter 3.2 --- Properties of open systems --- p.28 / Chapter 3.2.1 --- Asymptotic behaviour of QNM eigenvalues --- p.28 / Chapter 3.2.2 --- Doubling of modes --- p.33 / Chapter 3.2.3 --- Generalized norm of QNMs --- p.34 / Chapter 3.2.4 --- Completeness --- p.37 / Chapter 3.2.5 --- Eigenfunction expansion for QNMs - two component formalism --- p.39 / Chapter 3.3 --- Forward spectral problem --- p.45 / Chapter Chapter 4. --- Conservative Inverse Problem --- p.50 / Chapter 4.1 --- Sun-Young-Zou (SYZ) method --- p.51 / Chapter 4.1.1 --- Perturbative inversion --- p.53 / Chapter 4.1.2 --- The regulators (δn) --- p.54 / Chapter 4.1.3 --- Total inversion (TI) --- p.59 / Chapter 4.1.4 --- Numerical results --- p.60 / Chapter 4.2 --- Rundell and Sacks method (RS method) --- p.74 / Chapter 4.2.1 --- Completeness --- p.75 / Chapter 4.2.2 --- The integral equation --- p.78 / Chapter 4.2.3 --- Uniqueness --- p.82 / Chapter 4.2.4 --- RS formalism --- p.84 / Chapter 4.2.5 --- Numerical results and difficulties --- p.89 / Chapter 4.2.6 --- Summary --- p.110 / Chapter 4.3 --- Phase shift problem --- p.112 / Chapter 4.3.1 --- Reduction to spectral problem --- p.113 / Chapter 4.3.2 --- Modified RS algorithm for finite-range phase shift problem --- p.116 / Chapter 4.3.3 --- Discussion --- p.130 / Chapter 4.4 --- Bound states --- p.131 / Chapter Chapter 5. --- Open Inverse Problem --- p.136 / Chapter 5.1 --- SYZ method --- p.136 / Chapter 5.1.1 --- Perturbative Inversion (PI) and Total Inversion (TI) --- p.137 / Chapter 5.1.2 --- Numerical results --- p.138 / Chapter 5.1.3 --- Other choices of (δn) --- p.156 / Chapter 5.2 --- RS method --- p.158 / Chapter 5.2.1 --- The integral equation --- p.159 / Chapter 5.2.2 --- Cauchy data --- p.160 / Chapter 5.2.3 --- Completeness conjecture --- p.162 / Chapter 5.2.4 --- Numerical verification of completeness condition --- p.163 / Chapter 5.2.5 --- Inversion for Cauchy data --- p.166 / Chapter 5.2.6 --- Cauchy data on 0 < x≤ α --- p.167 / Chapter 5.2.7 --- Comparison system --- p.169 / Chapter Chapter 6. --- Conclusions and Further Studies --- p.188 / Chapter 6.1 --- Conclusions of this thesis --- p.188 / Chapter 6.2 --- Further studies --- p.189 / Chapter Appendix A. --- Singular Value Decomposition --- p.199 / Chapter Appendix B. --- Asymptotic Behaviour of Phase Shifts --- p.203 / Chapter B.1 --- Asymptotic behaviour of phase shift data --- p.203 / Chapter B.2 --- Levinson's theorem --- p.204 / Chapter Appendix C. --- Forward Problem for Conservative Systems --- p.207 / Chapter C.1 --- Finite difference method --- p.207 / Chapter C.2 --- Finite element method --- p.209 / Chapter C.2.1 --- Solving transcendental equation --- p.215 / Chapter Appendix D. --- FDM and FEM for Open Systems --- p.220 / Chapter D.1 --- Finite difference method --- p.220 / Chapter D.2 --- Finite element method --- p.222 / Chapter Appendix E. --- Asymptotic Behaviour of NM Eigenvalues --- p.226 / Chapter Appendix F. --- Asymptotic Behaviour of QNM Eigenvalues --- p.232 / Chapter Appendix G. --- QNM Forward Problem 一 Transcendental Equation --- p.239 / Chapter Appendix H. --- Forward Problem - Calculation of Phase Shifts --- p.243 / Bibliography --- p.245

by Hau-Leung Chung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 41-42). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 1.1 --- Paper I --- p.5 / Chapter 1.2 --- Paper II --- p.6 / Chapter 2 --- The Inexact Newton-Like Method for Inverse Eigen- value Problem --- p.8 / Chapter 2.1 --- Introduction --- p.8 / Chapter 2.2 --- The Newton-Like Method --- p.9 / Chapter 2.3 --- The Inexact Newton-Like Method --- p.11 / Chapter 2.4 --- Convergence Analysis --- p.14 / Chapter 2.5 --- Numerical Experiments --- p.22 / Chapter 3 --- A DCT Based Watermarking Scheme for Copyright Protection of Images --- p.26 / Chapter 3.1 --- Introduction --- p.26 / Chapter 3.2 --- Preliminary --- p.28 / Chapter 3.2.1 --- Gray-level image --- p.28 / Chapter 3.2.2 --- Color image --- p.29 / Chapter 3.2.3 --- The Discrete Cosine transform --- p.30 / Chapter 3.3 --- Watermarking Approaches --- p.31 / Chapter 3.3.1 --- Insertion procedures --- p.31 / Chapter 3.3.2 --- Retrieval procedures --- p.33 / Chapter 3.4 --- Experimental results --- p.34 / Chapter 3.5 --- Other Applications --- p.38 / Chapter 3.5.1 --- Data Hiding --- p.38 / Chapter 3.5.2 --- Authentication --- p.39 / Chapter 3.5.3 --- Fingerprinting --- p.39 / Chapter 3.5.4 --- Copy Control --- p.39 / Chapter 3.6 --- Conclusion --- p.40 / Bibliography --- p.41

by Foon-Yip Ng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 111-115). / Abstract also in Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Main Problems --- p.1 / Chapter 1.2 --- The Basic Concept of Decision Theory --- p.4 / Chapter 1.3 --- The Class of Orthogonally Invariant Estimators --- p.6 / Chapter 1.4 --- Related Works --- p.8 / Chapter 1.5 --- Summary --- p.10 / Chapter Chapter 2 --- Estimation of the Scale Matrix in a Wishart Distribution --- p.12 / Chapter 2.1 --- Review of the Previous Works --- p.13 / Chapter 2.2 --- Some Useful Statistical and Mathematical Results --- p.15 / Chapter 2.3 --- Improved Estimation of Σ under the Loss L1 --- p.18 / Chapter 2.4 --- Simulation Study for Wishart Distribution under the Loss L1 --- p.22 / Chapter 2.5 --- Improved Estimation of Σ under the Loss L2 --- p.25 / Chapter 2.6 --- Simulation Study for Wishart Distribution under the Loss L2 --- p.28 / Chapter Chapter 3 --- Estimation of the Scale Matrix in a Multivariate F Distribution --- p.31 / Chapter 3.1 --- Review of the Previous Works --- p.32 / Chapter 3.2 --- Some Useful Statistical and Mathematical Results --- p.35 / Chapter 3.3 --- Improved Estimation of Δ under the Loss L1____ --- p.38 / Chapter 3.4 --- Simulation Study for Multivariate F Distribution under the Loss L1 --- p.42 / Chapter 3.5 --- Improved Estimation of Δ under the Loss L2 ________ --- p.46 / Chapter 3.6 --- Relationship between Wishart Distribution and Multivariate F Distribution --- p.51 / Chapter 3.7 --- Simulation Study for Multivariate F Distribution under the Loss L2 --- p.52 / Chapter Chapter 4 --- Estimation of the Scale Matrix in an Elliptically Contoured Matrix Distribution --- p.57 / Chapter 4.1 --- Some Properties of Elliptically Contoured Matrix Distributions --- p.58 / Chapter 4.2 --- Review of the Previous Works --- p.60 / Chapter 4.3 --- Some Useful Statistical and Mathematical Results --- p.62 / Chapter 4.4 --- Improved Estimation of Σ under the Loss L3 --- p.63 / Chapter 4.5 --- Simulation Study for Multivariate-Elliptical t Distributions under the Loss L3 --- p.67 / Chapter 4.5.1 --- Properties of Multivariate-Elliptical t Distribution --- p.67 / Chapter 4.5.2 --- Simulation Study for Multivariate- Elliptical t Distributions --- p.70 / Chapter 4.6 --- Simulation Study for ε-Contaminated Normal Distributions under the Loss L3 --- p.74 / Chapter 4.6.1 --- Properties of ε-Contaminated Normal Distributions --- p.74 / Chapter 4.6.2 --- Simulation Study for 2-Contaminated Normal Distributions --- p.76 / Chapter 4.7 --- Discussions --- p.79 / APPENDIX --- p.81 / BIBLIOGRAPHY --- p.111

The frame tube buildings have been the most efficient structural system used for building which is in the range of 40-100storey. The soaring heights and the demanding structural efficiency have led to them having smaller reserves of stiffness and consequently stability. In this thesis a Non-linear analysis and stability check of frame-tube building is done. Nonlinear analysis offers several options for addressing problems of nonlinearity and in this work focus is on Geometric Non-linearity. The main sources can be identified as P-Æ’´ effect of gravity loading acting on a transversely displaced structure due to lateral loading and can also be due to member imperfections, such as member camber and out of plumb erection of the frame. During analysis the element response keep continuously changing as a function of the applied load so simple step computing methods have been employed instead of direct analytical methods. The problem here is dealt in a piece wise linear way and solved. In this thesis a program using the matrix approach has been developed. The program developed can calculate the buckling load and can do Linear and Non-linear analysis using the Mat-lab as the computing platform. Numerical results obtained from the program have been compared with the Finite Element software Mastan2. The comparative solutions presented later on in the report clearly prove the accuracy of the program and go on to show, how exploiting simple matrix equation can help solve the most complex structures in fraction of seconds. The program is modular in structure. It provides opportunity for user to make minor manipulation or can append his own module to make it work for his specific needs and will get reliable results.

by Bai Zheng Jian. / "May 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references. / 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.

by Wai-Yin Chan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 42-45). / Chapter Chapter 1 --- Introduction / Chapter 1.1 --- Main Problems --- p.1 / Chapter 1.2 --- Class of Regularized Estimator --- p.4 / Chapter 1.3 --- Preliminaries --- p.6 / Chapter 1.4 --- Related Works --- p.9 / Chapter 1.5 --- Brief Summary --- p.10 / Chapter Chapter 2 --- Estimation of the Covariance Matrix and its Eigenvalues in a Wishart Distribution / Chapter 2.1 --- Significance of The Problem --- p.12 / Chapter 2.2 --- Review of the Previous Work --- p.13 / Chapter 2.3 --- Properties of the Wishart Distribution --- p.18 / Chapter 2.4 --- Main Results --- p.20 / Chapter 2.5 --- Simulation Study --- p.23 / Chapter Chapter 3 --- Estimation of the Scale Matrix and its Eigenvalues in a Multivariate F Distribution / Chapter 3.1 --- Formulation and significance of the Problem --- p.26 / Chapter 3.2 --- Review of the Previous Works --- p.28 / Chapter 3.3 --- Properties of Multivariate F Distribution --- p.30 / Chapter 3.4 --- Main Results --- p.33 / Chapter 3.5 --- Simulation Study --- p.38 / Chapter Chapter 4 --- Further research --- p.40 / Reference --- p.42 / Appendix --- p.46

by Hao-min Zhou. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references. / Abstract --- p.1 / Introduction --- p.3 / Paper I --- p.8 / Paper II --- p.28

Inicialmente, estudamos alguns resultados clássicos da teoria dos núcleos positivos definidos e alguns resultados pertinentes. Estudamos em seguida, o Teorema de Mercer e algumas de suas generalizações e conseqüências, incluindo a caracterização da transformada de Fourier de um núcleo positivo definido com domínio Rm£Rm, m ¸ 1. O trabalho traz um enfoque especial nos núcleos cujo domínio é um subconjunto não-compacto de Rm £ Rm, uma vez que os demais casos são considerados de maneira extensiva na literatura. Aplicamos esses estudos na análise do decaimento dos autovalores de operadores integrais gerados por núcleos positivos definidos / Firstly, we study some classical results from the theory of positive definite kernels along with some related results. Secondly, we focus on generalizations of Mercer\'s theorem and some of their implications. Special attention is given to the cases where the domain of the kernel is not compact, once the other cases are considered consistently in the literature. We include a characterization for the Fourier transform of a positive definite kernel on Rm£Rm, m ¸ 1. Finally, we apply the previous study in the analysis of decay rates for eigenvalues of integral operators generated by positive definite kernels

Ab-initio methods for calculating electronic structure represent an important field of material physics. The aim of this theses - within the project focused on developing the new method for calculating electronic states in non-periodic structures based on density functional theory, pseudopotentials, and finite elements methods - is to convert Kohn-Sham equations into the form suitable for discretisation, to suggest apropriate method for solving generalized eigenproblem resulting from this discretisation and to implement an eigenvalue solver (or to modify existing one). The thesis describes a procedure for converting the many-particle Schrödinger equation into generalized rank-k-update eigenvalue problem and discusses various methods for its solution. Eigensolver Blzpack, which makes use of the block Lanczos method, has been modified, integrated into the Sfepy framework (a tool for the finite element method calculation) and resulting code has been successfully tested.

The primary objective of this study is to develop new computational methods for solving a general random eigenvalue problem (REP) commonly encountered in modeling and simulation of high-dimensional, complex dynamic systems. Four major research directions, all anchored in polynomial dimensional decomposition (PDD), have been defined to meet the objective. They involve: (1) a rigorous comparison of accuracy, efficiency, and convergence properties of the polynomial chaos expansion (PCE) and PDD methods; (2) development of two novel multiplicative PDD methods for addressing multiplicative structures in REPs; (3) development of a new hybrid PDD method to account for the combined effects of the multiplicative and additive structures in REPs; and (4) development of adaptive and sparse algorithms in conjunction with the PDD methods. The major findings are as follows. First, a rigorous comparison of the PCE and PDD methods indicates that the infinite series from the two expansions are equivalent but their truncations endow contrasting dimensional structures, creating significant difference between the two approximations. When the cooperative effects of input variables on an eigenvalue attenuate rapidly or vanish altogether, the PDD approximation commits smaller error than does the PCE approximation for identical expansion orders. Numerical analysis reveal higher convergence rates and significantly higher efficiency of the PDD approximation than the PCE approximation. Second, two novel multiplicative PDD methods, factorized PDD and logarithmic PDD, were developed to exploit the hidden multiplicative structure of an REP, if it exists. Since a multiplicative PDD recycles the same component functions of the additive PDD, no additional cost is incurred. Numerical results show that indeed both the multiplicative PDD methods are capable of effectively utilizing the multiplicative structure of a random response. Third, a new hybrid PDD method was constructed for uncertainty quantification of high-dimensional complex systems. The method is based on a linear combination of an additive and a multiplicative PDD approximation. Numerical results indicate that the univariate hybrid PDD method, which is slightly more expensive than the univariate additive or multiplicative PDD approximations, yields more accurate stochastic solutions than the latter two methods. Last, two novel adaptive-sparse PDD methods were developed that entail global sensitivity analysis for defining the relevant pruning criteria. Compared with the past developments, the adaptive-sparse PDD methods do not require its truncation parameter(s) to be assigned a priori or arbitrarily. Numerical results reveal that an adaptive-sparse PDD method achieves a desired level of accuracy with considerably fewer coefficients compared with existing PDD approximations.