by Yu Wai Kuen. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 71-76). / Preface --- p.1 / PART I / Chapter Chapter 1 --- Inverse Scattering Method / Chapter §1 --- Introduction --- p.5 / Chapter §2 --- Rapidly decreasing solutions of the GNLSE --- p.6 / Chapter Chapter 2 --- Modified Inverse Scattering Method / Chapter §1 --- Introduction --- p.25 / Chapter §2 --- Singular solutions of the KdV equation --- p.25 / PART II / Chapter Chapter 3 --- Backlund Transformation Method / Chapter §1 --- Introduction --- p.37 / Chapter §2 --- Solution by Backlund transformation --- p.37 / Chapter §3 --- Clairin's method for finding Backlund transformations --- p.46 / Chapter §4 --- Construction of multi-soliton solutions --- p.48 / Chapter Chapter 4 --- Dressing Method And Hirota Direct Method / Chapter §1 --- Introduction --- p.51 / Chapter §2 --- Zakharov-Shabat's dressing method --- p.52 / Chapter §3 --- Hirota direct method --- p.57 / Chapter Chapter 5 --- Group Reduction Method / Chapter §1 --- Introduction --- p.61 / Chapter §2 --- Method of group reduction --- p.61 / Bibliography --- p.71

Chan Yuet Tai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 107-111). / Chapter 1 --- Introduction to Sturm-Liouville Problem --- p.1 / Chapter 1.1 --- What are inverse problems? --- p.1 / Chapter 1.2 --- Introductory background --- p.2 / Chapter 1.3 --- The Liouville transformation --- p.3 / Chapter 1.4 --- The Sturm-Liouville problem 一 A historical look --- p.4 / Chapter 1.5 --- Where Sturm-Liouville problems come from? --- p.6 / Chapter 1.6 --- Inverse problems of interest --- p.8 / Chapter 2 --- Reconstruction Method I --- p.10 / Chapter 2.1 --- Perturbative inversion --- p.10 / Chapter 2.1.1 --- Inversion problem via Fredholm integral equation --- p.10 / Chapter 2.1.2 --- Output least squares method for ill-posed integral equations --- p.15 / Chapter 2.1.3 --- Numerical experiments --- p.17 / Chapter 2.2 --- Total inversion --- p.38 / Chapter 2.3 --- Summary --- p.45 / Chapter 3 --- Reconstruction Method II --- p.46 / Chapter 3.1 --- Computation of q --- p.47 / Chapter 3.2 --- Computation of the Cauchy data --- p.48 / Chapter 3.2.1 --- Recovery of Cauchy data for K --- p.51 / Chapter 3.2.2 --- Numerical implementation for computation of the Cauchy data . --- p.51 / Chapter 3.3 --- Recovery of q from Cauchy data --- p.52 / Chapter 3.4 --- Iterative procedure --- p.53 / Chapter 3.5 --- Numerical experiments --- p.60 / Chapter 3.5.1 --- Eigenvalues without noised data --- p.64 / Chapter 3.5.2 --- Eigenvalues with noised data --- p.69 / Chapter 4 --- Appendices --- p.79 / Chapter A --- Tikhonov regularization --- p.79 / Chapter B --- Basic properties of the Sturm-Liouville operator --- p.80 / Chapter C --- Asymptotic formulas for the eigenvalues --- p.86 / Chapter C.1 --- Case 1: h ≠ ∞ and H ≠ ∞ --- p.87 / Chapter C.2 --- Case 2: h= ∞ and H ≠∞ --- p.90 / Chapter C.3 --- Case 3: h = ∞ and H = ∞ --- p.91 / Chapter D --- Completeness of the eigenvalues --- p.92 / Chapter E --- d'Alembert solution formula for the wave equation --- p.97 / Chapter E.1 --- "The homogeneous solution uH(x,t)" --- p.98 / Chapter E.2 --- "The particular solution up(x, t)" --- p.99 / Chapter E.3 --- "The standard d'Alembert solution u(x,t)" --- p.101 / Chapter E.4 --- Applications to our problem --- p.101 / Chapter F --- Runge-Kutta method for solving eigenvalue problems --- p.104 / Bibliography --- p.107

by Chan Kam Wai Clifford. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 105-108). / Text in English; abstracts in English and Chinese. / by Chan Kam Wai Clifford. / Abstract --- p.i / Acknowledgements --- p.iii / Contents --- p.iv / List of Figures --- p.vii / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Motivations of the Project --- p.1 / Chapter 1.2 --- Historical Background --- p.1 / Chapter 1.3 --- Objective and Outline of Thesis --- p.3 / Chapter Chapter 2. --- Reviews on One-dimensional Dynamical Cavity --- p.4 / Chapter 2.1 --- Formalism --- p.4 / Chapter 2.2 --- Methods of Solution --- p.6 / Chapter 2.2.1 --- Phase Construction (R function) --- p.6 / Chapter 2.2.2 --- Instantaneous Mode Expansion --- p.12 / Chapter 2.2.3 --- Transformation Method --- p.15 / Chapter 2.3 --- Numerical Results --- p.15 / Chapter 2.3.1 --- Some Results using R function --- p.16 / Chapter 2.3.2 --- Some Results using Instantaneous Mode Decomposition --- p.24 / Chapter 2.3.3 --- Remarks on the Numerical Scheme used in Transformation Method --- p.28 / Chapter 2.3.4 --- "Comparisons of Results obtained by Phase Construction, In- stantaneous Mode Decomposition and Transformation" --- p.28 / Chapter 2.4 --- Conclusion --- p.30 / Chapter Chapter 3. --- Fixed-point Analysis for the One-dimensional Cavity --- p.31 / Chapter 3.1 --- Introduction --- p.31 / Chapter 3.2 --- What are the fixed-points? --- p.32 / Chapter 3.3 --- Characteristics of Fixed-points --- p.36 / Chapter 3.4 --- Fixed-points and Geometric Resonance --- p.39 / Chapter Chapter 4. --- Electromagnetic Field in an Undulating Spherical Cavity --- p.44 / Chapter 4.1 --- Classical Electromagnetic field theory --- p.44 / Chapter 4.2 --- Boundary Conditions --- p.46 / Chapter 4.3 --- The Motion of Cavity Surface --- p.47 / Chapter Chapter 5. --- Methods of Solution and Results to the Spherical Cavity --- p.48 / Chapter 5.1 --- Introduction --- p.48 / Chapter 5.2 --- Mode Decomposition and Transformation Method revisited --- p.49 / Chapter 5.2.1 --- Mode Decomposition --- p.49 / Chapter 5.2.2 --- Transformation Method --- p.50 / Chapter 5.2.3 --- Remarks on the use of Instantaneous Mode Expansion and Transformation Method --- p.51 / Chapter 5.3 --- The Ge(z) function --- p.52 / Chapter 5.3.1 --- The Ge(z) function as a solution of the scalar wave equation --- p.52 / Chapter 5.3.2 --- Numerical Results --- p.54 / Chapter 5.4 --- The Me(z) function --- p.60 / Chapter 5.4.1 --- Formalism --- p.60 / Chapter 5.4.2 --- Comparison of Me(z) with Ge(z) --- p.62 / Chapter 5.4.3 --- Numerical Results --- p.63 / Chapter 5.5 --- Conclusions and Discussions --- p.93 / Chapter 5.5.1 --- Geometric Resonances --- p.93 / Chapter 5.5.2 --- Harmonic Resonances --- p.94 / Chapter Chapter 6. --- Conclusion --- p.95 / Appendix A. Electromagnetic Field in Spherical Cavity --- p.97 / Chapter A.1 --- Field Strength --- p.97 / Chapter A.2 --- Field Energy --- p.98 / "Appendix B. Construction of Ψe(r,t) by G(z)" --- p.100 / Appendix C. The Arbitrary Part GH(z) of Ψe(r，t) --- p.103 / Bibliography --- p.105

Lau Chin Wa. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 77-78). / Abstracts in English and Chinese. / Abstract --- p.i / Chinese Abstract --- p.ii / Acknowledgement --- p.iv / Contents --- p.v / Abbreviations --- p.viii / List of Figures --- p.xiv / List of Tables --- p.xviii / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Basic Principle of Laser Light Scattering and Instrumentation --- p.7 / Chapter 2.1 --- Static laser light scattering (Static LLS) --- p.8 / Chapter 2.2 --- Dynamic laser light scattering (Dynamic LLS) --- p.9 / Chapter 2.3 --- Calibration between translational diffusion coefficient D and molar mass M --- p.10 / Chapter 2.3.1 --- Tranform G(D) to Molar Mass Distributionfw(M) --- p.10 / Chapter 2.3.2 --- Calibration between D and M- Using a set of narrowly distributed standards --- p.12 / Chapter 2.3.3 --- Calibration between D and M- Using two or more broadly distributed samples --- p.12 / Chapter 2.4 --- Data Analysis --- p.14 / Chapter 2.5 --- References --- p.16 / Chapter Chapter 3 --- Experimental --- p.17 / Chapter 3.1 --- Laser Light Scattering Instrumentation --- p.17 / Chapter 3.1.1 --- Overview of laser light scattering spectrometer --- p.17 / Chapter 3.1.2 --- Differential Refractometer --- p.18 / Chapter 3.2 --- References --- p.21 / Chapter Chapter 4 --- Thermally Sensitive and Biocompatible Poly(N-vinylcaprolactam): Synthesis and Characterization of High Molar Mass Linear Chains / Chapter 4.1 --- Introduction --- p.22 / Chapter 4.2 --- Sample Preparation --- p.23 / Chapter 4.3 --- Results and discussion --- p.24 / Chapter 4.4 --- Conclusion --- p.27 / Chapter 4.5 --- References --- p.29 / Chapter Chapter 5 --- Stabilization and destabilization of potassium persulfate (as an initiator) in an surfactant-free water/acetone mixture emulsion polymerization of styrene under microwave irradiation / Chapter 5.1 --- Introduction --- p.41 / Chapter 5.2 --- Experimental --- p.43 / Chapter 5.3 --- Results and discussion --- p.44 / Chapter 5.4 --- Conclusion --- p.51 / Chapter 5.5 --- References --- p.53 / Appendix / Chapter A.l --- Static Laser Light Scattering --- p.66 / Chapter A.1.1 --- Scattering from a small particles --- p.66 / Chapter A.1.2 --- Scattering from a large particles --- p.67 / Chapter A.1.3 --- Scattering by solutions of small molecules --- p.69 / Chapter A.1.3.1 --- Scattering from polymer solutions --- p.70 / Chapter A.2 --- Dynamic laser light scattering --- p.71 / Chapter A.2.1 --- Line-width measurement --- p.73 / Chapter A.2.2 --- Data analysis --- p.75

Wang, Xiaohui. / "November 1999." / Thesis (Ph.D.)--Chinese University of Hong Kong, 1999. / 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. / Abstracts in English and Chinese.

Thesis. 1976. Ph.D.--Massachusetts Institute of Technology. Dept. of Materials Science and Engineering. / Microfiche copy available in Archives and Science. / Vita. / Includes bibliographical references. / Ph.D.

Hung Kin Ting. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 126-129). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Inverse Problems --- p.1 / Chapter 1.2 --- Applications of Inverse Problems --- p.2 / Chapter 1.3 --- Least-squares Solutions --- p.4 / Chapter 1.4 --- Discrete Systems --- p.4 / Chapter 1.5 --- "Discretization, Regularization and Regularization Pa- rameters" --- p.5 / Chapter 1.6 --- Outline of the Thesis --- p.6 / Chapter 2 --- Some Basic Concepts and Mathematical Tools --- p.8 / Chapter 2.1 --- Singular Value Decomposition (SVD) --- p.8 / Chapter 2.2 --- Generalized Singular Value Decomposition (GSVD) --- p.13 / Chapter 2.3 --- White Noises --- p.16 / Chapter 3 --- Regularized Solutions --- p.18 / Chapter 3.1 --- Derivation of Regularized Solutions --- p.18 / Chapter 3.2 --- Discrete Picard Condition --- p.20 / Chapter 3.3 --- Relationship between Discrete Picard Condition and Regularized Solution --- p.21 / Chapter 3.4 --- Checking for the Discrete Picard Condition --- p.22 / Chapter 4 --- Different Discretization Approaches --- p.23 / Chapter 4.1 --- Problem 1 - Volterra Integral Equation of the First Kind --- p.25 / Chapter 4.2 --- Examples of Problem 1 --- p.30 / Chapter 4.3 --- Problem 2 - Fredholm Integral Equation of the First Kind --- p.49 / Chapter 4.4 --- Examples of Problem 2 --- p.53 / Chapter 4.5 --- Conclusion --- p.57 / Chapter 5 --- Effect of Different Kinds of Observation Data and Differential Operators on Accuracy --- p.59 / Chapter 5.1 --- Pointwise Observation Data --- p.60 / Chapter 5.2 --- Pointwise Observation Data of Heat Fluxes at the Boundary --- p.69 / Chapter 5.3 --- Observation Data with Heat Fluxes --- p.80 / Chapter 5.4 --- Conclusion --- p.89 / Chapter 6 --- L-curve --- p.90 / Chapter 6.1 --- Properties of L-curve --- p.93 / Chapter 6.2 --- L-curve in Log-Log Scale --- p.100 / Chapter 6.3 --- Disadvantages of the L-curve Method --- p.100 / Chapter 7 --- Algorithms of Finding the Corner of L-curve --- p.105 / Chapter 7.1 --- Cubic Spline Curve Fitting --- p.105 / Chapter 7.2 --- Conic Section Fitting --- p.106 / Chapter 7.3 --- Triangle Method --- p.109 / Chapter 8 --- Implementation of the L-curve Method --- p.111 / Chapter 8.1 --- Our Algorithm --- p.111 / Chapter 8.2 --- Numerical Experiments --- p.112 / Chapter 8.3 --- Conclusion --- p.124 / Bibliography --- p.126

這篇論文的目的是討論下述半線性橢圓方程的穩定解。 / -Δu = f (u) in Ω, / 這裡Ω是R{U+207F}中的光滑區域。對於非線性項f (u) = / [附圖]. / 我們得到了關於穩定解的Liouville-type結果。對於帶有更一般非線性項的半線性橢圓方程，在二到四維的情況下，我們得到一個關於穩定解的先驗估計。 / 最後，在維數很大的情形下，我們具體的給出一個關於以下雙調和方程的指數P的上界P，使得當P滿足 <1 P < Pc ‘下述雙調和方程不存在穩定解。 / Δ²u=u{U+1D56}, u>0 in R{U+207F} / The main aim of this thesis is to review recent results on stable solutions to the following semilinear elliptic equation / -Δu = f (u) in Ω, / where Ω ⊆ R{U+207F}.For the special case f (u) = / [With mathematic formula]. / For the general nonlinearity f in a bounded domain, we obtain a priori estimate for the stable solution when 2 ≤ n ≤ 4 / Finally, we give a explicit bound on the exponent for the nonexistence of stable solutions to the following biharmonic problem in large dimensions. / Δ²u=u{U+1D56}, u>0 in R{U+207F} / 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. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Yang, Wen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 66-69). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- On the Lane-Emden equation --- p.12 / Chapter 2.1 --- On stable solutions to the Lane-Emden equation --- p.12 / Chapter 2.2 --- On nite Morse index solutions to the Lane-Emden equation --- p.19 / Chapter 3 --- On general semilinear elliptic equation --- p.28 / Chapter 4 --- On the biharmonic equation --- p.44 / Chapter 4.1 --- The rst part of the proof of Theorem 1.6 --- p.44 / Chapter 4.2 --- The second part of the proof of Theorem 1.6 --- p.54 / Bibliography --- p.66

Lee, Chak Shing. / "August 2011." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 60-62). / Abstracts in English and Chinese. / Chapter 1 --- Model Problems --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- The curl-curl operator --- p.2 / Chapter 1.3 --- The convection-diffusion equation --- p.6 / Chapter 2 --- Staggered DG method for the Curl-Curl operator --- p.8 / Chapter 2.1 --- Introduction --- p.8 / Chapter 2.2 --- Discontinuous Galerkin discretization --- p.8 / Chapter 2.3 --- Stability for aligned fields --- p.14 / Chapter 2.4 --- Error estimates --- p.17 / Chapter 2.5 --- Numerical experiments --- p.21 / Chapter 2.6 --- Concluding Remarks --- p.32 / Chapter 3 --- Staggered DG method for the convection-diffusion equation --- p.33 / Chapter 3.1 --- Introduction --- p.33 / Chapter 3.2 --- Method description --- p.33 / Chapter 3.3 --- Preservation of physical structures --- p.38 / Chapter 3.4 --- Stability and convergence --- p.42 / Chapter 3.4.1 --- Static problem --- p.42 / Chapter 3.4.2 --- Time-dependent problem --- p.46 / Chapter 3.5 --- Fully discrete scheme --- p.49 / Chapter 3.6 --- Numerical examples --- p.55 / Chapter 3.6.1 --- The static problem --- p.55 / Chapter 3.6.2 --- Time dependent problem --- p.56 / Chapter 3.7 --- Concluding Remark --- p.59 / Bibliography --- p.60

Chapter 1 briefly introduces the theoretical background of the association and dissociation of polymer chains or colloidal particles are briefly introduced, including thermodynamic consideration and viscoelastic effect on the formation of mesoglobular phase in dilute polymer solutions, as well as some basic theories and universal models of fractal aggregates. / Chapter 2 details the theories of static and dynamic laser light scattering (LLS) as well as the instrumental set-up. In addition, the invention and set-up of differential refractometer are briefly discussed. / Chapter 3 summarizes laser light-scattering (LLS) and stopped-flow studies of association of cyclic- and linear-poly( N-isopropylacrylamide) (c-PNIPAM and l-PNIPAM) chains in dilute aqueous solutions. Dynamic and static LLS results reveal that the heating leads to a microphase transition. Resultant structures of interchain aggregates depend on the heating rate and the chain structure. In comparison with l-PNIPAM chains, a slow heating of c-PNIPAM chains in the solution results in stable mesoglobules with a lower average aggregation number, a looser structure and a smaller average size (&sim;290 nm). The temperature-jump induced association of c -PNIPAM chains in the stopped-flow measurement reveals two kinetic stages; namely, the loose packing of contracted c-PNIPAM chains and further contraction-induced fragmentation of initially packed c-PNIPAM chains due to the lack of interchain entanglements. On the other hand, for l-PNIPAM chains, the intrachain contraction and interchain penetration/entanglement simultaneously occur as the temperatures increases, leading to larger and more compact aggregates whose size increases with the solution temperature. / Chapter 4 discusses the association of water-soluble PNIPAM-monolayer-protected gold particles in dilute dispersions induced by heating the dispersions to different final temperatures higher than the lower critical solution temperature (LCST) of PNIPAM chains via the slow and fast processes. LLS was used to trace and characterize the association process, supplemented by transmission electron microscopy (TEM) measurements. The slow heating-and-cooling cycle reveals that the association and dissociation of PNIPAM-protected gold nanoparticles can be easily induced by altering the solution temperatures and the association and dissociation are fully reversible. Fast heating the dispersion to three different temperatures reveals that both the aggregation rate and average aggregation number increase with the dispersion temperature. Furthermore, the fast heating leads to the formation of fractal aggregates. The fractal dimensions of such formed aggregates continuously increases as the time evolves, which can be ascribed to the simultaneous dissociation that leads to the restructuring and rearrangement of the aggregates, resulting in denser structures. It is interesting to note that the structure of aggregate always remains fractal during the whole process. / Chapter 5 shows how water-dispersible nanosized semiconductor CdS particles (quantum dots, QDs) can be synthesized with a protective layer of covalently grafting linear thermally sensitive PNIPAM chains as well as how these CdS particles can be induced into reversible association and dissociation via an alteration of the dispersion temperature. The formation and fragmentation of these QDs aggregates were systematically investigated by laser light scattering (LLS) and confirmed by transmission electron microscopy (TEM). There exists a hysteresis in one heating-and-cooling cycle. The CdS particles stabilized with shorter PNIPAM chains (Mn = 15,000 g/mol) can associate to form larger and denser spherical aggregates with a much higher aggregation number than those grafted with longer PNIPAM chains ( Mn = 31,000 g/mol) in the heating process. The dissociation (fragmentation) in the cooling process has two stages: initially, the aggregates dissociate as the temperature decreases, and then, the fragmentation stops over a wider temperature range before its final complete dissociation at a lower temperature. We attribute such a two-stage fragmentation to a balanced effect of inter- and intra-chain hydrogen bonding as well as to the hydrophobic interaction between PNIPAM chains and CdS particles. / In this Ph.D. thesis, temperature-induced association and dissociation of various polymeric systems were systematically investigated by a combination of static and dynamic laser light scattering (LLS), supplemented by other methods, such as stopped-flow temperature jump, transmission electron microscopy (TEM), and Fourier transform infrared spectroscopy (FTIR). / Ye, Jing. / Adviser: Wu Chi. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3533. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references. / 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.