by Wai-Shing Luk. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 104-113). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Functional Extension of Iterative Methods --- p.2 / Chapter 1.2 --- Applications in Circuit Simulation --- p.2 / Chapter 1.3 --- Multigrid Acceleration --- p.3 / Chapter 1.4 --- Why Hilbert Space? --- p.4 / Chapter 1.5 --- Parallel Implementation --- p.5 / Chapter 1.6 --- Domain Decomposition --- p.5 / Chapter 1.7 --- Contributions of This Thesis --- p.6 / Chapter 1.8 --- Outlines of the Thesis --- p.7 / Chapter 2 --- Waveform Relaxation Methods --- p.9 / Chapter 2.1 --- Basic Idea --- p.10 / Chapter 2.2 --- Linear Operators between Banach Spaces --- p.14 / Chapter 2.3 --- Waveform Relaxation Operators for ODE's --- p.16 / Chapter 2.4 --- Convergence Analysis --- p.19 / Chapter 2.4.1 --- Continuous-time Convergence Analysis --- p.20 / Chapter 2.4.2 --- Discrete-time Convergence Analysis --- p.21 / Chapter 2.5 --- Further references --- p.24 / Chapter 3 --- Waveform Krylov Subspace Methods --- p.25 / Chapter 3.1 --- Overview of Krylov Subspace Methods --- p.26 / Chapter 3.2 --- Krylov Subspace methods in Hilbert Space --- p.30 / Chapter 3.3 --- Waveform Krylov Subspace Methods --- p.31 / Chapter 3.4 --- Adjoint Operator for WBiCG and WQMR --- p.33 / Chapter 3.5 --- Numerical Experiments --- p.35 / Chapter 3.5.1 --- Test Circuits --- p.36 / Chapter 3.5.2 --- Unstructured Grid Problem --- p.39 / Chapter 4 --- Parallel Implementation Issues --- p.50 / Chapter 4.1 --- DECmpp 12000/Sx Computer and HPF --- p.50 / Chapter 4.2 --- Data Mapping Strategy --- p.55 / Chapter 4.3 --- Sparse Matrix Format --- p.55 / Chapter 4.4 --- Graph Coloring for Unstructured Grid Problems --- p.57 / Chapter 5 --- The Use of Inexact ODE Solver in Waveform Methods --- p.61 / Chapter 5.1 --- Inexact ODE Solver for Waveform Relaxation --- p.62 / Chapter 5.1.1 --- Convergence Analysis --- p.63 / Chapter 5.2 --- Inexact ODE Solver for Waveform Krylov Subspace Methods --- p.65 / Chapter 5.3 --- Experimental Results --- p.68 / Chapter 5.4 --- Concluding Remarks --- p.72 / Chapter 6 --- Domain Decomposition Technique --- p.80 / Chapter 6.1 --- Introduction --- p.80 / Chapter 6.2 --- Overlapped Schwarz Methods --- p.81 / Chapter 6.3 --- Numerical Experiments --- p.83 / Chapter 6.3.1 --- Delay Circuit --- p.83 / Chapter 6.3.2 --- Unstructured Grid Problem --- p.86 / Chapter 7 --- Conclusions --- p.90 / Chapter 7.1 --- Summary --- p.90 / Chapter 7.2 --- Future Works --- p.92 / Chapter A --- Pseudo Codes for Waveform Krylov Subspace Methods --- p.94 / Chapter B --- Overview of Recursive Spectral Bisection Method --- p.101 / Bibliography --- p.104

by Ho Yum Bun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 93-94). / Text in English; abstracts in English and Chinese. / by Ho Yum Bun. / List of Figures --- p.3 / Abstract --- p.9 / Chinese Abstract --- p.10 / Acknowledgement --- p.11 / Chapter 1 --- Introduction --- p.12 / Chapter 1.1 --- Motivation --- p.12 / Chapter 1.2 --- What is Sonoluminescence? --- p.13 / Chapter 1.3 --- The Main Task of this Project --- p.13 / Chapter 1.4 --- Organization of this Thesis --- p.13 / Chapter 2 --- Reviews on One-dimensional Dynamical Cavity Problem --- p.15 / Chapter 2.1 --- Introduction --- p.15 / Chapter 2.2 --- Formulation --- p.15 / Chapter 2.3 --- Moore's R Function Method --- p.18 / Chapter 2.4 --- Mode Expansion Method --- p.19 / Chapter 2.5 --- Transformation method --- p.20 / Chapter 2-6 --- Summary --- p.21 / Chapter 3 --- Numerical Results For One-dimensional Dynamical Cavity Prob- lem --- p.22 / Chapter 3.1 --- Introduction --- p.22 / Chapter 3.2 --- Evolution of a Cavity System --- p.23 / Chapter 3.3 --- Motion of the Moving Mirror --- p.23 / Chapter 3.4 --- R(z) Function --- p.24 / Chapter 3.4.1 --- Construction of R(z) Function --- p.24 / Chapter 3.4.2 --- Numerical R(z) Function --- p.27 / Chapter 3.5 --- Results --- p.27 / Chapter 3.5.1 --- Results with Moore's R(z) Function Method --- p.27 / Chapter 3.5.2 --- Results with the Mode Expansion Method --- p.29 / Chapter 3.5.3 --- Results with the Transformation Method --- p.36 / Chapter 3.6 --- Summary --- p.36 / Chapter 4 --- Spherical Dynamical Cavity Problem --- p.37 / Chapter 4.1 --- Introduction --- p.37 / Chapter 4.2 --- Formulation --- p.37 / Chapter 4.3 --- Motion of a Moving Spherical Mirror --- p.39 / Chapter 4.4 --- Summary --- p.40 / Chapter 5 --- The G(z) Function Method --- p.41 / Chapter 5.1 --- Introduction --- p.41 / Chapter 5.2 --- G(z) Function --- p.42 / Chapter 5.2.1 --- Ideas of Deriving the G(z) Function --- p.42 / Chapter 5.2.2 --- Formalism --- p.42 / Chapter 5.2.3 --- Initial G(z) Function --- p.45 / Chapter 5.3 --- Construction of the G(z) Function --- p.46 / Chapter 5.3.1 --- Case I : l=0 --- p.46 / Chapter 5.3.2 --- Case II : l > 0 --- p.49 / Chapter 5.4 --- Asymptotic Series Solution of G(z) --- p.50 / Chapter 5.5 --- Application to Resonant Mirror Motion --- p.52 / Chapter 5.6 --- Regularization of G(z) --- p.58 / Chapter 5.7 --- Behaviors of the Fields --- p.58 / Chapter 5.7.1 --- z vs tf Graph --- p.61 / Chapter 5.7.2 --- Case 1: l= 0 --- p.61 / Chapter 5.7.3 --- "Case2: l= 1,2" --- p.62 / Chapter 5.7.4 --- Case 3: l= 3 --- p.73 / Chapter 5.7.5 --- Section Summary --- p.73 / Chapter 5.8 --- Summary --- p.73 / Chapter 6 --- Three-dimensional Mode Expansion Method and Transforma- tion Method --- p.75 / Chapter 6.1 --- Introduction --- p.75 / Chapter 6.2 --- Mode Expansion Method --- p.75 / Chapter 6.2.1 --- Formalism --- p.75 / Chapter 6.2.2 --- Application of Floquet's Theory --- p.78 / Chapter 6.2.3 --- Results --- p.80 / Chapter 6.3 --- The Transformation Method --- p.80 / Chapter 6.3.1 --- The Method --- p.80 / Chapter 6.3.2 --- Numerical Schemes --- p.86 / Chapter 6.3.3 --- Results --- p.89 / Chapter 6.4 --- Summary --- p.89 / Chapter 7 --- Conclusion --- p.90 / Chapter 7.1 --- The One-dimensional Dynamical Cavity Problem --- p.90 / Chapter 7.2 --- The Dynamical Spherical Cavity Problem --- p.91 / Chapter 7.3 --- Numerical Methods --- p.91 / Chapter 7.4 --- Further Investigation --- p.92 / Bibliography --- p.93

A number of high performance fibres (aramid, PBZT and PBO) spun from liquid crystal polymer solutions were examined in this work. In particular, a thorough investigation of the mechanical response of these fibres under tensile and compressive deformations was carried out. The major experimental tool employed was the technique of Laser Raman Spectroscopy. It was found that stress-induced changes of these fibres at molecular level are proportional to the macroscopic deformation applied. This correlation is unique for the fibres. A method for converting spectroscopic data to predicted stress-strain curves in tension and compression was proposed. An estimation of their compressive strength was derived and an understanding of the nature of their compressive failure was discussed. The adhesion of these fibres to epoxy resin was also investigated by monitoring in situ the interfacial stresses developed along the interface/interphaseo f model single fibre composite coupons. The strength of the interfacial bond was measured. The effect of various parameters such as fibre modulus, fibre diameter and fibre nature upon the interfacial strength of the various systems was evaluated. The mechanisms of stress transfer along with the nature of interfacial damage was examined accurately. It was found that the major parameter controlling the above mechanisms was interfacial yielding in shear. A numerical appoximation (using Finite Element Analysis) was employed in order to evaluate the experimental results. Finally, general conclusions concerning the performance of these fibres were drawn.

Mak, Tsz Fan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 33-36). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.

Wang Yuliang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 70-75). / Abstracts in English and Chinese. / Chapter 1 --- Introduction to Inverse Problems --- p.1 / Chapter 1.1 --- Typical Examples --- p.1 / Chapter 1.2 --- Major Properties --- p.3 / Chapter 1.3 --- Solution Methods --- p.4 / Chapter 1.4 --- Thesis Outline --- p.4 / Chapter 2 --- Review of the Theory --- p.6 / Chapter 2.1 --- Basic Concepts --- p.6 / Chapter 2.1.1 --- Ill-posedness --- p.6 / Chapter 2.1.2 --- Generalized Inverse --- p.7 / Chapter 2.1.3 --- Compact Operators and SVE --- p.8 / Chapter 2.2 --- Regularization Methods --- p.10 / Chapter 2.2.1 --- An Overview --- p.11 / Chapter 2.2.2 --- Convergence Rates --- p.12 / Chapter 2.2.3 --- Parameter Choice Rules --- p.15 / Chapter 2.2.4 --- Classical Regularization Methods --- p.18 / Chapter 3 --- Ill-posedenss of Typical Inverse Problems --- p.23 / Chapter 3.1 --- Integral Equations --- p.24 / Chapter 3.2 --- Inverse Source Problems --- p.26 / Chapter 3.3 --- Parameter Identification --- p.34 / Chapter 3.4 --- Backward Heat Conduction --- p.37 / Chapter 4 --- Error Estimates for Parameter Identification --- p.39 / Chapter 4.1 --- Overview of Numerical Methods --- p.40 / Chapter 4.2 --- Finite Element Spaces and Standard Estimates --- p.43 / Chapter 4.3 --- Output Least-square Methods --- p.43 / Chapter 4.4 --- Equation Error Methods --- p.50 / Chapter 4.5 --- Hybrid Methods --- p.50 / Chapter 5 --- Numerical Experiments --- p.52 / Chapter 5.1 --- Formulate the Linear Systems --- p.53 / Chapter 5.2 --- Test Problems and Observations --- p.55 / Bibliography --- p.70

心臟表面電位能夠真實反映心肌的活動，因此以重建心臟表面電位為目標的心臟電生理反問題被廣泛研究。心臟電生理反問題是一個不適定問題，因此輸入數據中一個小的噪聲也有可能導致一個高度不穩定的解。因此，通常基於2 範數的規則化方法被用於解決這個病態問題。但是2 範數的懲罰函數會導致一定程度的模糊，使得分辨和定位心臟表面一些不正常或者病變部位不準確。而直接使用1 範數的懲罰函數，會由於其不可微分而增加計算復雜度。 / 我們首先提出一種基於 1 範數的方法來減少計算復雜度和能夠快速收斂。在這個方法中，使用變量分離技術使得1 範數的懲罰函數可微分。然後這個反問題被構造成一個有界約束二次優化問題，從而可以很容易地利用梯度映射法叠代求解。在試驗中，使用合成數據和真實數據來評估提出的方法。實驗表明，提出的方法可以很好地處理測量噪聲和幾何噪聲，而且能夠獲得比以前的1、2 範數方法更準確的實驗結果。 / 盡管提出的 1 範數方法能夠有效克服2 範數存在的問題，但是1 範數方法仍然只是0 範數的近似。因此我們采用了一種平滑0 範數的方法來求解心臟電生理反問題。平滑0 範數使用平滑函數，使得0 範數連續，從而能夠直接求解0 範數的反問題。實驗結果表明，使用平滑0範數方法可以獲得比1、2 範數更好、更準確的心臟表面電位。 / 在以往的心臟反問題研究中，使用的心臟幾何模型都是靜態的，與實際跳動的心臟不符，從而使得反問題方法難以進入臨床。因此我們提出了從動態心臟模型中重建心臟表面電位。動態心臟模型是從一系列核磁共振圖像中重建得到的。體表電位也同步獲得。仿真實驗獲得了很好的心臟表面電位結果。 / 在論文最後，我們提出一個基於心臟電生理反問題的系統，來輔助束支傳導阻滯的治療。在這個系統中，心臟模型和體表模型都從病人的數據中重建獲得，體表電位也得到收集。通過電生理反問題方法，在心臟表面重建電位及其分布。醫生通過觀察重建結果來輔助束支傳導阻滯的診斷和治療。 / The epicardial potentials (EPs) targeted inverse problem of electrocardiography (ECG) has been widely investigated as it is demonstrated that EPs reflect underlying myocardial activity. It is a wellknown ill-posed problem as small noises in input data may yield a highly unstable solution. Traditionally, L2-norm regularization methods have been proposed to solve this ill-posed problem. But L2-norm penalty function inherently leads to considerable smoothing of the solution, which reduces the accuracy of distinguishing abnormalities and locating diseased regions. In this thesis, we propose three new techniques in order to achieve more accurate reconstruction results of EPs and applied these techniques to a clinical application. We first propose a L1-norm regularization method in order to reduce the computational complexity and make rapid convergence possible. Variable splitting is employed to make the L1- norm penalty function differentiable based on the observation that both positive and negative potentials exist on the epicardial surface. Then, the inverse problem of ECG is further formulated as a boundconstrained quadratic problem, which can be efficiently solved by gradient projection in an iterative manner. Extensive experiments conducted on both synthetic data and real data demonstrate that the proposed method can handle both measurement noise and geometry noise and obtain more accurate results than previous L2- and L1- norm regularization methods, especially when the noises are large. / Although L1 norm regularization achieves better reconstructed results compared with L2 norm regularization, L1 norm is still an approximation of L0 norm which is more accurate than L1 norm. We further presented a smoothed L0 norm technique in order to directly solve the L0 norm constrained problem. Our method employs a smoothing function to make the L0 norm continuous. Extensive experiments showed that the proposed method reconstructs more accurate epicardial potentials compared with L1 norm and L2 norm. / In current research of ECG inverse problem, epicardial potentials are reconstructed from a static heart model which blocks the techniques to clinic applications. A novel strategy is presented to recovii er epicardial potentials using a dynamic heart model built from MRI image sequences and ECG data. We used MRI images to estimate the current density and visualize it on the surface of the heart model. The ECG data also be used to achieve the time synchronization when the propagation of the current density. Experiments are conducted on a set of real time MRI images, also with the real ECG data, and we get favorable results. / Finally, a non-invasive system is presented for enhancing the diagnosis of Bundle Branch Block (BBB). In this system, epicardial potential is estimated and visualized in the 3D heart model to improve the diagnosis of BBB. Using patient CT and BSPM data, the system is able to reconstruct details of the complete electrical activity of BBB on the 3D heart model. Through the analysis of the epicardial potential mapping in this system, patients with BBB are easily and accurately distinguished instead of from empirically checking ECG. Therefore the diagnosis of BBB is improved using this system. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Wang, Liansheng. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 103-124). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Inverse Problem of ECG --- p.6 / Chapter 2.1 --- Background --- p.6 / Chapter 2.2 --- Problem Formulations --- p.8 / Chapter 2.2.1 --- Potential Reconstruction Problem --- p.8 / Chapter 2.2.2 --- Coefficient Reconstruction Problem --- p.11 / Chapter 2.3 --- Solving Methods --- p.11 / Chapter 2.3.1 --- Regularization Methods --- p.11 / Chapter 2.3.2 --- Non-quadratic Regularization --- p.12 / Chapter 2.3.3 --- Activation Wavefronts Solution --- p.14 / Chapter 3 --- L1-Norm to EPs Reconstruction --- p.16 / Chapter 3.1 --- Related Work --- p.16 / Chapter 3.2 --- Method --- p.21 / Chapter 3.3 --- Experimental Results and Validation --- p.24 / Chapter 3.3.1 --- Error Evaluation --- p.26 / Chapter 3.3.2 --- Synthetic Data Cases --- p.26 / Chapter 3.3.3 --- Real Data Cases --- p.32 / Chapter 3.4 --- Discussion --- p.44 / Chapter 3.5 --- Summary --- p.48 / Chapter 4 --- L0-Norm to EPs Reconstruction --- p.49 / Chapter 4.1 --- Related Work --- p.49 / Chapter 4.2 --- Smoothed L0-norm Method --- p.54 / Chapter 4.3 --- Experimental Results and Protocols --- p.57 / Chapter 4.3.1 --- Data --- p.57 / Chapter 4.3.2 --- Evaluation Protocol --- p.60 / Chapter 4.3.3 --- Experiments and Results --- p.60 / Chapter 4.4 --- Discussion --- p.68 / Chapter 4.5 --- Summary --- p.69 / Chapter 5 --- EPs Reconstruction in A Dynamic Model --- p.71 / Chapter 5.1 --- Related Work --- p.71 / Chapter 5.2 --- Forward Model --- p.73 / Chapter 5.3 --- Parameters Estimation for Inverse Problem of ECG --- p.75 / Chapter 5.4 --- Experiments and Results --- p.77 / Chapter 5.5 --- Summary --- p.80 / Chapter 6 --- Diagnosis of BBB: an Application --- p.82 / Chapter 6.1 --- Related Work --- p.82 / Chapter 6.2 --- Method --- p.84 / Chapter 6.2.1 --- Data --- p.85 / Chapter 6.2.2 --- Signal Preprocessing of BSPM --- p.87 / Chapter 6.2.3 --- Epicardial Potential Estimation and Imaging --- p.88 / Chapter 6.3 --- Experiments and Results --- p.89 / Chapter 6.3.1 --- Population Under Study --- p.89 / Chapter 6.3.2 --- Results --- p.89 / Chapter 6.4 --- Summary --- p.92 / Chapter 7 --- Conclusion --- p.94 / Chapter 7.1 --- Summary of Contributions --- p.94 / Chapter 7.2 --- Future Works --- p.96 / Chapter A --- Barzilai and Borwein Approach --- p.97 / Chapter B --- List of Publications --- p.99 / Bibliography --- p.103

We address the problem of identifying the neighborhood structure of an undirected graph, whose nodes are labeled with the elements of a multivariate normal (MVN) random vector. A semi-definite program is given for estimating the information matrix under arbitrary constraints on its elements. More importantly, a closed-form expression is given for the maximum likelihood (ML) estimator of the information matrix, under the constraint that the information matrix has pre-specified elements in a given pattern (e.g., in a principal submatrix). The results apply to the identification of dependency labels in a graphical model with neighborhood constraints. This neighborhood structure excludes nodes which are conditionally independent of a given node and the graph is determined by the non- zero elements in the information matrix for the random vector. A cross-validation principle is given for determining whether the constrained information matrix returned from this procedure is an acceptable model for the information matrix, and as a consequence for the neighborhood structure of the Markov Random Field (MRF) that is identified with the MVN random vector.

Ai Jun. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (p. 100-103). / 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.

Photocopy of typescript. / Digitized by Kansas Correctional Industries

Este trabalho tem como objetivo a obtenção de soluções analíticas e semi-analíticas para o problema de transferência de calor em filmes de água líquida escoando sobre aerofólios. O problema da transferência de calor em filmes já foi abordado na literatura, no entanto, não foram encontradas, na bibliografia aberta, soluções analíticas aplicáveis ao problema da formação de gelo em filmes escoando sobre aerofólios de aeronaves. Este fato se deve à presença de um termo de transferência de calor por convecção na interface filme-escoamento de ar, que não foi considerado nas soluções analíticas encontradas na literatura. Para os problemas estudados, a obtenção da distribuição de temperaturas no filme é fundamental, pois, com ela, é possível prever a iminência da formação de gelo, ou seja, quando a temperatura de solidificação é atingida no filme. Nos caos de superfícies com proteção térmica, deve ser especificado um fluxo de calor na superfície de contato entre o filme e o aerofólio, enquanto nos casos nos quais a superfície do aerofólio está desprotegida, deve ser considerada uma temperatura fixa. Neste trabalho, para cada um destes casos, foram considerados gradientes de pressão nulos e constantes no filme dágua. Assim, ao total, quatro casos foram gerados e analisados. O método da separação de variáveis e expansões em séries de autofunções foi utilizado na obtenção das soluções analíticas e o de Galerkin na obtenção das soluções semi-analíticas. Este último método, apesar de não ser exato, não apresenta alguns dos desvios intrínsecos aos métodos numéricos usuais, pois não depende da discretização do espaço em forma de malha e das interpolações decorrentes. Foi feita uma comparação entre as soluções para gradiente de pressão nulo obtidas pelo método de Galerkin e as soluções obtidas por separação de variáveis. Desta maneira, encontraram-se os desvios da soluções semi-analíticas em relação às soluções exatas. Finalmente, foram encontradas estimativas simplificadas para a distribuição de temperaturas no filme, além de variáveis adimensionais que generalizam o problema, podendo ser traçadas, então, uma série de curvas válidas para uma extensa gama de parâmetros. / This work aims to obtain analytical and semi-analytical solutions to the airfoil film heat transfer problem. The film heat transfer problem has been already solved in the literature. Nevertheless, no consistent solution with the airfoil ice accretion problem is known. This issue is due to the presence of a convective term in the interface between the film and the airflow, which has not been taken into account in the analytical studies available in the literature. Solving the temperature distribution in the film is essential for predicting the ice growth onset, i.e., the location where the solidification temperature is reached in the film. In the cases corresponding to thermally protected surfaces, the heat flow at the airfoil surface has to be specified, while, on the other hand, for the non-protected surfaces, the surface temperature has to be specified. In this work, for each of these cases, it has been considered both zero pressure gradient and a non-zero constant pressure gradient at the water and air flow. In this way, four cases were generated and analyzed. Separation of variables and eigenfunction expansion methods were used in the analytical solutions, whereas the Galerkin method was used to obtain the semi-analytical solutions. The latter, despite being approximate, does not produce some of the numerical errors associated with the space discretization and interpolation. The zero pressure solutions were compared in order to find the deviation between the analytical and semi-analytical solutions. Finally, estimates for the film temperature distribution were found, besides dimensionless variables that generalize the problem, enabling the creation of a family of curves valid for a wide range of parameters.