Liu Chun-Lung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 98-100). / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Fundamentals of thickness --- p.7 / Chapter 2.1 --- Definition of thickness --- p.9 / Chapter 2.2 --- Basic theorem and corollaries --- p.10 / Chapter 2.3 --- Equivalent definitions --- p.17 / Chapter 3 --- Ropelength minimizer --- p.19 / Chapter 3.1 --- Existence of ropelength minimizer --- p.20 / Chapter 3.2 --- Some ropelength minimizers --- p.23 / Chapter 4 --- Thickness computation --- p.27 / Chapter 4.1 --- Definitions --- p.28 / Chapter 4.2 --- Octrope algorithm --- p.33 / Chapter 4.3 --- Minor improvements --- p.45 / Chapter 5 --- Arc presentation --- p.54 / Chapter 5.1 --- Definitions --- p.55 / Chapter 5.2 --- Basic Theorems --- p.57 / Chapter 5.3 --- Ropelength upper bound --- p.64 / Chapter 6 --- Hamiltonian knot projection --- p.74 / Chapter 6.1 --- Hamiltonian RPG --- p.75 / Chapter 6.2 --- Embedding of RPG --- p.78 / Chapter 6.3 --- Ropelength upper bound --- p.95 / Bibliography --- p.98

本論文考慮對於二值輸入廣播信道在沒有公共信息要求的情況下，如何評估Marton 內界。對於雙用戶廣播信道而言，該內界是最好的，而最好的外界是UV 外界。最近我們證明了UV 外界不是容量區域，但是Marton 內界是否是容量區域尚未可知。 / 在論文的第一部份，我們介紹了一個由Jog 和Nair 獲得的基於二值輸入斜對稱廣播信道的不等式，該不等式被用於首次證明Marton 內界嚴格包含在UV 外界里。我們將該不等式推廣到任意二值輸入廣播信道。在證明中，我們採用擾動分析的方法，幫助刻劃了不等式在非平凡情況下的性質。 / 在第二部份，我們專注于研究輸出對稱的二值輸入廣播信道。我們證明了Marton 內界是否嚴格包含于UV 外界里是與特定偏序密切相關的，同時找到了另一個嚴格包含的例子。 / 對於評估內界而不僅僅是其中的總傳輸率，我們考慮邊界的支撐超平面，然後提出一個猜想，利用凸包的概念推廣了之前提及的不等式。對於大部份情況，我們證明了該猜想。 / 本論文的主要貢獻在於，我們拓展了評估特定可達傳輸率的新工具和方法，同時證明了某些非基於凸性質的不等式。 / This thesis concerns the evaluation of Marton's inner bound for binary input broadcast channel without common message.This inner bound is the best one for two-receiver broadcast channel, while the best outer bound is UV outer bound. Recently we have shown that UV outer bound is not optimal, however the optimality of Marton's inner bound is still unknown. / In the first part, we introduce a binary inequality obtained by Jog and Nair for binary-skew symmetric broadcast channel, which helps to show for the first time that Marton's inner bound is strictly included in UV outer bound. We generalize this inequality to be true for arbitrary binary input broadcast channel. The method applied here is perturbation analysis, which helps to characterize the properties of non-trivial cases in the proof. / In the second part, we study a class of broadcast channel consisting of binary input symmetric-output channels. We show that whether Marton's inner bound is strictly included in UV outer bound is closely related to the more capable partial order, and we find a second example that demonstrates the strict inclusion. / To evaluate the inner bound beyond the sum-rate, we consider the supporting hyperplanes of the boundary points and conjecture the binary inequality to a stronger one, where we utilize the notion of concave envelope. We prove the extended inequality for certain cases. / The main contribution of the thesis is in the development of new tools and techniques for evaluating certain achievable regions as well as for proving certain information inequalities that are not based on convexity. / 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. / Geng, Yanlin. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 64-66). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Broadcast channel and capacity region --- p.2 / Chapter 1.2 --- Inner bounds to capacity region --- p.3 / Chapter 1.3 --- Outer bounds to capacity region --- p.6 / Chapter 1.4 --- Partial orders --- p.7 / Chapter 1.5 --- Examples where inner and outer bounds differ --- p.11 / Chapter 2 --- A binary inequality --- p.14 / Chapter 2.1 --- Proof of special settings --- p.20 / Chapter 2.2 --- Two nontrivial cases --- p.20 / Chapter 2.3 --- Proof of XOR case --- p.22 / Chapter 2.4 --- Proof of AND case --- p.26 / Chapter 3 --- BISO broadcast channel --- p.30 / Chapter 3.1 --- BISO channel --- p.32 / Chapter 3.2 --- Partial orders on BISO broadcast channel --- p.34 / Chapter 3.2.1 --- More capable comparability --- p.34 / Chapter 3.2.2 --- More capable and essentially less noisy --- p.39 / Chapter 3.3 --- Comparison of bounds for BISO broadcast channel --- p.42 / Chapter 3.4 --- A new partial order --- p.46 / Chapter 4 --- Extended binary inequality --- p.56 / Chapter 4.1 --- Proof of XOR case --- p.57 / Chapter 4.2 --- A conjecture on extending the inequality --- p.61 / Chapter 5 --- Conclusion --- p.62 / Bibliography --- p.64

我們研究與圖的擴張值相關的問題。圖的擴張值反映了一個圖的連通程度。很多不同的應用問題都可以轉換成在圖中找一個不擴張的點集，而這亦跟近似理論中的唯一遊戲猜想(unique games conjecture) 有密切的關係。故此，圖的擴張值在應用和理論上均有研究動機。 / 我們介紹有關圖的擴張值的新發現。這些發現包括設計和分析找不擴張的子集的算法、近似算法的困難結論，以及擴張圖的算法應用： / 我們用更多的特徵值去證明一個Cheeger 不等式的推廣，從而較好地分析譜分割算法(spectral graph partitioning algorithm)。 / 我們分析圖上的隨機漫走來設計一個局部的圖分割算法。此算法跟Cheeger 不等式的保證相合。 / 我們給出圖冪的擴張值的緊下界，並用以得到一個關於找小的不擴張子集的困難結論(hardness result)。 / 我們利用擴張圖來設計一個快而簡單的算法來計算矩陣的秩，新算法顯著地改進了以往的算法。 / We study problems related to graph expansions, which measure how well a graph is connected. Various practical problems can be modelled as finding a small non-expanding subset of vertices, and this is also closely related to the unique games conjecture in the theory of approximation algorithms. Hence our study of graph expansions is both practically and theoretically motivated. / We present our new results about graph expansions. The results include the design and analysis of algorithms for finding non-expanding subsets, hardness of approximation results and algorithmic applications of expanders: / We prove a generalization of Cheeger's inequality using higher eigenvalues, providing a better analysis of the spectral graph partitioning algorithm. / We design a local graph partitioning algorithm using random walks on graph, matching the performance guaranteed by Cheeger's inequality. / We give a tight lower bound for the expansion of graph powers and use it to prove hardness results for small set expansions. / We use expanders to design fast and simple algorithms for computing matrix ranks, significantly improving over previous works. / 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. / Kwok, Tsz Chiu. / Thesis (Ph.D.) Chinese University of Hong Kong, 2015. / Includes bibliographical references (leaves 104-109). / Abstracts also in Chinese.

by Wong Chi-hang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 86-87). / Acknowledgment --- p.i / Abstract --- p.ii / Introduction --- p.1 / Chapter 1 --- Preliminaries --- p.2 / Chapter 1.1 --- Hilbert C*-modules --- p.2 / Chapter 1.2 --- Some Constructions with Hilbert C*-modules --- p.10 / Chapter 1.3 --- Graded C*-algebras --- p.14 / Chapter 1.4 --- Graded Tensor Products --- p.19 / Chapter 1.5 --- Kasparov's Technical Theorem --- p.24 / Chapter 2 --- The KK-groups --- p.31 / Chapter 2.1 --- Basic Definition --- p.31 / Chapter 2.2 --- The Relation of KK-groups and K-groups --- p.43 / Chapter 2.3 --- "KKoh(C,C)" --- p.47 / Chapter 2.4 --- Basic Properties of KK-groups --- p.50 / Chapter 3 --- The Kasparov Products --- p.55 / Chapter 3.1 --- Kasparov Products --- p.55 / Chapter 3.2 --- The associativity of Kasparov product --- p.73 / Bibliography --- p.86

Yuen Kwun Wan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves [91]-93). / Text in English; abstracts in English and Chinese. / Yuen Kwun Wan. / Abstract --- p.i / Acknowledgements --- p.ii / Contents --- p.iii / List of Figures --- p.vi / List of Tables --- p.ix / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Formalism of Geometrical Phase --- p.4 / Chapter 2.1 --- Adiabatic cyclic evolution in the parameter space --- p.4 / Chapter 2.2 --- Cyclic evolution of a quantum state on the projective Hilbert space --- p.8 / Chapter 2.3 --- General setting for Berry's phase --- p.11 / Chapter Chapter 3. --- Geometric Phases in Physical Systemms --- p.16 / Chapter 3.1 --- The Aharonov-Bohm Effect --- p.16 / Chapter 3.2 --- An Electron a in Magnetic Field --- p.20 / Chapter 3.2.1 --- The Geometrical Phase in The Adiabatic Limit --- p.22 / Chapter 3.2.2 --- The Geometrical Phases for Other Special Cases --- p.25 / Chapter 3.2.2.1 --- Cyclic Evolution --- p.26 / Chapter 3.2.2.2 --- The Pancharatnam Phase Difference Between ̐ưجψ(t)〉〉〉 and ̐ưجψ(t-pr)〉 --- p.27 / Chapter Chapter 4. --- Review on The Dynamical Cavity Problems --- p.34 / Chapter 4.1 --- Scalar Electrodynamics in a 1-D Cavity with Moving Boundaries --- p.34 / Chapter 4.1.1 --- The Method of Moore's R Function --- p.36 / Chapter 4.1.2 --- Method of Transformation --- p.37 / Chapter 4.2 --- Scalar Electrodynamics in a 1-D Cavity with Oscillating Boundaries --- p.38 / Chapter 4.3 --- Scalar Electrodynamics in a Spherical Cavity with Moving Boundary --- p.39 / Chapter Chapter 5. --- The quantum mechanical phase of a particle in vibrating cavity --- p.41 / Chapter 5.1 --- SU(2) method --- p.48 / Chapter 5.1.1 --- Formalism --- p.48 / Chapter 5.1.2 --- Calculation --- p.51 / Chapter 5.2 --- Rotating Wave Approximation(RWA) --- p.52 / Chapter 5.2.1 --- Formalism --- p.52 / Chapter 5.2.2 --- Behaviors of the system --- p.54 / Chapter 5.2.3 --- Energy --- p.56 / Chapter 5.2.4 --- Geometrical Phases of The System at Resonances --- p.58 / Chapter 5.3 --- Results --- p.63 / Chapter 5.3.1 --- For a Cylindrical Cavity --- p.63 / Chapter 5.4 --- For a Spherical Cavity --- p.70 / Chapter 5.5 --- Conclusion and Discussion --- p.74 / Chapter Chapter 6. --- Summary --- p.76 / Chapter Appendix A. --- Energy Eigenfunctions and Eigenvalues of a Statics Cavity --- p.79 / Chapter A.1 --- For the Case of Cylindrical Cavity --- p.79 / Chapter A.1.1 --- The Energy Eigenfunctions and Corresponding Eigenvalues --- p.81 / Chapter A.2 --- For the Case of Spherical Cavity --- p.81 / Chapter A.2.1 --- The Radial Equation --- p.82 / Chapter A.2.2 --- The Angular Equation --- p.83 / Chapter A.2.3 --- The Energy Eigenfunctions and Corresponding Eigenvalues --- p.84 / Chapter Appendix B. --- The Schrodinger Equation for The Transformed System --- p.85 / Chapter B.1 --- The Schrodinger Equation --- p.85 / Chapter B.2 --- Radial Part of The Schrodinger Equation --- p.86 / Chapter B.2.1 --- For The Case of Cylindrical Cavity --- p.86 / Chapter B.2.2 --- For The Case of Spherical Cavity --- p.87 / Chapter Appendix C. --- Method of Rotating Wave Approximation --- p.88 / Bibliography --- p.91

No description available.

This programme of research focused on incorporating Behavioural Analysis (BA) within the digital forensics investigation process. A review of previously developed digital forensics investigation models indicated a lack of sufficient consideration of the behavioural and motivational dimensions of offending, and the way in which digital evidence can be used to address these issues during the investigation process. This programme of research aimed to build on previous work by scientific researchers and investigators by developing a digital forensics investigation model which incorporates greater consideration of the behavioural and motivational implications of case-related digital evidence based on current theoretical understandings of these aspects of offending from forensic psychology. This can aid with understanding of the crime events and reconstruction, and lead to the development of more detailed models and guidelines for examining computer-facilitated interpersonal crimes. The first study employed an abductive approach to forensically analyse individual cases (real cases obtained from the Dubai Police archives) applying BA to the online Sexually Exploitative Imagery of Children (SEIC) and cyberstalking. Its aim was to investigate what BA could contribute to the digital forensics investigation of cases within these crime categories. It identified five benefits: (1) providing focus, speed and investigative directions, (2) inferring victim/offender behaviours, (3) inferring offender motivation(s), (4) identifying potential victims, and (5) eliminating suspects. This was followed by a survey study empirically examining the perceptions of national and international digital forensics practitioners regarding the use and utility of BA during the process of investigating SEIC and cyberstalking cases. The results indicated that while the majority believed that BA has potential to contribute to many aspects of digital forensics investigations, their daily investigative activities involved a limited use of this technique. The implications of the study were outlined, and emphasised the need to design a digital forensics investigation model that provides guiding steps and illustrations on how to utilise BA in digital forensics investigations. Based on the findings from the conducted studies, a digital forensics investigation model that incorporates aspects of BA was designed. It aimed to provide a pragmatic, structured, multidisciplinary approach to performing a post mortem examination, analysis, and interpretation of the content of the digital devices associated with computer-facilitated interpersonal crimes. Two comprehensive case studies were also used to illustrate the investigative importance of the model in investigating computer-facilitated interpersonal crimes.

Ku, Wai Lim. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 97-100). / Abstracts in English and Chinese. / Ku, Wai Lim. / Chapter 1 --- Review of Entanglement --- p.1 / Chapter 1.1 --- Schmidt Decomposition --- p.1 / Chapter 1.1.1 --- Schmidt Decomposition in Continuous Systems --- p.3 / Chapter 1.2 --- Detecting the Quantum Entanglement of Pure States --- p.5 / Chapter 1.3 --- Quantifying the Quantum Entanglement of Pure States --- p.6 / Chapter 1.3.1 --- Von Neumann entropy --- p.8 / Chapter 1.3.2 --- Purity --- p.8 / Chapter 1.3.3 --- Logarithmic Negativity --- p.9 / Chapter 1.3.4 --- Concurrence --- p.10 / Chapter 2 --- Review of Entanglement in the Relativistic Framework --- p.11 / Chapter 2.1 --- Lorentz Transformation of a Quantum State --- p.11 / Chapter 2.2 --- Unruh effect --- p.14 / Chapter 2.2.1 --- The Rindler Spacetime --- p.14 / Chapter 2.2.2 --- Quantum field theory in Rindler Spacetime --- p.18 / Chapter 2.2.3 --- Lightcone Mode Expansion --- p.21 / Chapter 2.3 --- Entanglement Measured by Uniformly Accelerating Detectors --- p.25 / Chapter 2.3.1 --- Number of States in Rindler Spacetime --- p.26 / Chapter 2.3.2 --- Entanglement in an non-inertial frame --- p.29 / Chapter 2.4 --- Entanglement in an Expanding Universe --- p.32 / Chapter 2.5 --- Summary --- p.36 / Chapter 3 --- Some Topics in Entanglement --- p.37 / Chapter 3.1 --- Introduction --- p.37 / Chapter 3.2 --- Accelerating Schrodinger particles --- p.40 / Chapter 3.3 --- Entanglement of Two-body Wavefuction --- p.43 / Chapter 3.4 --- Accelerating the Relativistic Particles --- p.47 / Chapter 3.4.1 --- Quantization of Fields --- p.47 / Chapter 3.5 --- Accelerating Fermions --- p.51 / Chapter 3.6 --- Accelerating scalar particles --- p.55 / Chapter 3.6.1 --- Spectrum --- p.55 / Chapter 3.6.2 --- Entanglement --- p.55 / Chapter 3.6.3 --- Entanglements if the Number of Produced Pairs is Restricted --- p.57 / Chapter 3.7 --- Discussion of the Accelerating Particles --- p.60 / Chapter 3.8 --- Entanglement in de Sitter space --- p.63 / Chapter 3.8.1 --- Pair Creation in de Sitter space --- p.63 / Chapter 3.8.2 --- Entanglement in the de Sitter space --- p.65 / Chapter 4 --- Review of Geometric Phase --- p.67 / Chapter 4.1 --- Magnetic Aharonov-Bohm Effect --- p.68 / Chapter 4.2 --- Berry Phase --- p.69 / Chapter 4.3 --- Aharonov-Anandan Phase --- p.72 / Chapter 4.4 --- Pancharatnam Phase --- p.73 / Chapter 4.5 --- Geometric Phase in a two-level atom --- p.75 / Chapter 5 --- Relationship Between Entanglement and Geometric Phase --- p.78 / Chapter 5.1 --- Relationship Between Berry's Phase and Concurrence --- p.78 / Chapter 5.2 --- Jaynes-Cummings model --- p.82 / Chapter 5.3 --- Projective Phase in the Jaynes-Cummings model --- p.86 / Chapter A --- The Bogoliubov coefficients in the scalar case --- p.91 / Chapter B --- Reducing the Dirac equations to two Klein-Gordon equations --- p.94 / Bibliography --- p.97

Digitized by Kansas Correctional Industries

It has often been said that the problem of creating timetables for scheduling university courses is hard, even as hard as solving an NP-Complete problem. There are many papers in the literature that make this assertion but rarely are precise problem definitions provided and no papers were found which offered proofs that the university course scheduling problem being discussed is NP-Complete. This thesis defines a scheduling problem that has realistic constraints. It schedules professors to sections of courses they are willing to teach at times when they are available without overloading them. Both decision and optimization versions are precisely defined. An algorithm is then provided which solves the optimization problem in polynomial time. From this it is concluded that the decision problem is unlikely to be NP-Complete because indeed it is in P. A second more complex timetable design problem, that additionally seeks to assign appropriate rooms in which the professors can teach the courses, is then introduced. Here too both decision and optimization versions are defined. The second major contribution of this thesis is to prove that this decision problem is NP-Complete and hence the corresponding optimization problem is NP-Hard.