Chen, Chao. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 43-46). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Preliminaries --- p.7 / Chapter 3 --- The mathematical formulation of the problem and main results --- p.11 / Chapter 4 --- Reformulation of the problem --- p.17 / Chapter 5 --- Proof of the main theorems --- p.23 / Chapter 5.1 --- Proof of uniqueness --- p.23 / Chapter 5.2 --- Proof of non-existence --- p.31 / Chapter 6 --- Work in future --- p.40 / Chapter 7 --- Appendix --- p.41 / Bibliography --- p.43

Lee Chun Sing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 64-68). / Abstracts in English and Chinese. / Abstract --- p.i-ii / Acknowledgment --- p.iii / Contents --- p.iv / Lists of Tables --- p.vi / Lists of Figures --- p.vii / Chapter Chapter One --- Introduction --- p.1 / Chapter Chapter Two --- The Basic Model with Exogeneous Real Interest Rate --- p.6 / Chapter 2.1 --- Introduction --- p.6 / Chapter 2.2 --- Benchmark Model --- p.9 / Chapter 2.3 --- Discussion of Results --- p.18 / Chapter 2.3.1 --- Agent Behaviour --- p.19 / Chapter 2.4 --- Numerical Examples --- p.23 / Chapter 2.4.1 --- Base Results --- p.25 / Chapter Chapter Three --- The Basic Model with Endogeneous Real Interest Rate --- p.28 / Chapter 3.1 --- Numerical Examples --- p.30 / Chapter 3.1.1 --- Base Results --- p.30 / Chapter 3.2 --- Government Policy Evaluation --- p.33 / Chapter 3.2.1 --- Education Subsidies --- p.35 / Chapter 3.2.2 --- Wage Subsidy --- p.35 / Chapter 3.2.3 --- Base Case Outcome --- p.36 / Chapter Chapter Four --- Conclusions --- p.40 / Appendix A --- p.41 / Appendix B --- p.42 / Appendix C --- p.42 / Tables --- p.47 / Figures --- p.58 / References --- p.64

Ip Tak Sang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 65-67). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Data and Methodology --- p.4 / Chapter Chapter 3 --- Results / Chapter 3.1 --- Performance of Long/Short Strategies --- p.11 / Chapter 3.2 --- Subsample and Sensitivity Analysis --- p.17 / Chapter 3.3 --- Autocorrelation Analysis --- p.25 / Chapter Chapter 4 --- Discussion and Conclusion --- p.27 / Appendices / Chapter A.1 --- Exchange Rates Figures --- p.28 / Chapter A.2 --- Tables --- p.32 / References --- p.65

Li Zimu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 65-68). / Abstracts in English and Chinese. / Abstract --- p.ii / 中文摘要 --- p.iii / Acknowledgements --- p.iv / Contents --- p.v / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Literature Review --- p.5 / Chapter 2.1 --- Duration Dependence in Business Cycles --- p.5 / Chapter 2.2 --- Duration Dependence in Stock Market Cycles --- p.7 / Chapter 2.3 --- Definition of Bull and Bear Markets --- p.10 / Chapter Chapter 3. --- Nonparametric Tests for Duration Dependence --- p.12 / Chapter 3.1 --- Duration Dependence --- p.12 / Chapter 3.2 --- Stock Market Cycle Periodicity --- p.15 / Chapter 3.3 --- W and W (t0 =a) Tests --- p.18 / Chapter 3.4 --- Z and Z (t0 =a) Tests --- p.20 / Chapter Chapter 4. --- Data Analysis --- p.21 / Chapter 4.1 --- Dow Jones Industrial Average Index --- p.23 / Chapter 4.2 --- NASDAQ Composite Index --- p.29 / Chapter 4.3 --- Shanghai A Share Index --- p.33 / Chapter 4.4 --- Shenzhen B Share Index --- p.38 / Chapter Chapter 5. --- Empirical Results --- p.42 / Chapter 5.1 --- Dow Jones Industrial Average Index --- p.45 / Chapter 5.2 --- NASDAQ Composite Index --- p.47 / Chapter 5.3 --- Shanghai A Share Index --- p.49 / Chapter 5.4 --- Shenzhen B Share Index --- p.51 / Chapter 5.5 --- Summary of Significant W and Z tests --- p.53 / Chapter Chapter 6. --- Sub-sample Analysis --- p.54 / Chapter 6.1 --- Sub-sample 1 of the Dow Jones Index´ؤ --- p.56 / Chapter 6.2 --- Sub-sample 2 of the Dow Jones Index´ؤ --- p.57 / Chapter 6.3 --- Comparison of Sub-samples of the Dow Jones Index --- p.58 / Chapter 6.4 --- Comparison of the Dow Jones Index and the NASDAQ Composite Index --- p.60 / Chapter Chapter 7. --- Conclusion --- p.62 / References --- p.65

本論文討論了具有非平凡旋度的穩態亞音速流體的適定性問題。 / 首先，我們研究了通過無限長週期管道的二維亞音速流禮。當管道某一週期位置伯努利函數擾動很小，且質量數介於與適當的範圍時，有且僅有唯一的亞音速流禮。特別地，對於伯努利函數為常值的情形，我們還通過結構緊性的方法證明了亞音速-音速流體的存在性。此時，質量數可以達到一臨界值。謝春景和辛周平在處理二維司壓歐拉方程時曾引入了一個重要的處理方法一一流函數表達式。然而，對於週期流體的問題，伯努利函數和流函數的相互關係是無法事先確定的。為此，我們建立了一個關於流函數的非線性映射。該映射的不動點給出了相應歐拉方程的解。 / 其次，對於二維亞音速流體通過對稱障礙物的問題，當來流的伯努利函數關於y方向對稱，且擾動很小時，我們給出了流体的存在性和唯一性的証明。这里，我們利用歐拉方程的流函數方法，得到了對應于流函數的二階方程的解。能量方法以及動量場與來流動量場之差的L2可積性給出了流函數的漸進行為。這一漸進行為結合障礙物外無駐點的事實說明了流函數表示與原先歐拉方程是相容的。 / 最后，我們研究了當給定管道壁上法向动量時，三維穩態流體通過方體管道的問題。如果入口處伯努利函數的擾動和旋度的法向分量為零，則當邊界的法向動量不超過一臨界值時，無旋的亞音速流體存在。對於一般情形，若伯努利函數的擾動和旋度的法向分量很小時，我們利用將速度均分解均無旋部分和旋度部分的方法給出了流體存在性的證明。這裡，我們通過求解一加權的散旋系統得到了旋度部份的解:而無旋部份則由一擬線性橢圓方程的解給出。 / In this thesis, the wellposedness theory of steady subsonic flows with nontrivial vorticities is studied in various aspects. / First, we study 2-D subsonic flows through infinitely long periodic nozzles. It is showed that when mass flux lies in a suitable regime and the variation of Bernoulli's function at some given section is sufficiently small, there exists a unique global subsonic flow in the periodic nozzle. In particular, if Bernoulli's function is a constant, the existence of subsonic flow is also obtained when mass flux takes the critical number by a compensated compactness framework. One of the main tools to handle 2-D compressible Euler equations is the stream function formulation first established by Xie and Xin. The main difficulty in adapting this formulation in periodic nozzles is that the relation between Bernoulli's function and stream function cannot be fixed. We resolve this difficulty via setting up a nonlinear map from stream function at the given section to itself. The fixed point of this map induces a solution of corresponding Euler equations. / Second, the existence and uniqueness of 2-D subsonic flows past a symmetric body are established under the assumption that Bernoulli's function is given symmetrically in the upstream with small variation. By the stream function formulation for 2-D compressible Euler equations, one obtains the solution of the Euler equations via solving a quasilinear second order equation for stream function. This is achieved with the help of the theory of elliptic equations of two variables. Asymptotic behavior for the stream function is obtained via energy method and L²-integral of the difference between the momentum and its asymptotic behavior in the upstream. The asymptotic behavior, together with the property that stagnation points are absent outside the body, yields that the stream function formulation is consistent with the original Euler system. / Finally, we study the existence of 3-D steady subsonic flows in rectangular nozzles when prescribing the normal component of the momentum on the boundary. If, in addition, the normal component of the voriticity and the variation of Bernoulli's function at the exit vanish, then there exists a unique subsonic potential flow when the magnitude of the normal component of the momentum is less than a critical number. In general, if the normal component of the vorticity and the variation of Bernoulli's function are both sufficiently small, we prove the existence of Euler flows by decomposing the velocity into the vortical part and the potential part. A div-curl system with given weighted function is used to obtain the vortical part and the potential part is induced by the solution to a quasilinear elliptic equation. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Chen, Chao. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 111-120). / 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 --- Preliminaries --- p.12 / Chapter 3 --- 2-D subsonic flows through in finitely long periodic nozzles --- p.23 / Chapter 3.1 --- Introduction and main result --- p.23 / Chapter 3.2 --- Stream function formulation of potential flows --- p.27 / Chapter 3.2.1 --- Bernoulli's law and stream function formulation --- p.27 / Chapter 3.2.2 --- Potential flows and proof of Theorem 3.1.1 --- p.30 / Chapter 3.3 --- Analysis of the well-posedness of Euler flows --- p.32 / Chapter 3.3.1 --- Existence, uniqueness, and periodicity of truncated flows --- p.34 / Chapter 3.3.2 --- Existence and uniqueness of Euler flflows --- p.41 / Chapter 4 --- 2-D subsonic flows past a symmetric body --- p.47 / Chapter 4.1 --- Motivation and mathematical formulation --- p.47 / Chapter 4.2 --- Truncated problem --- p.53 / Chapter 4.3 --- Asymptotic behavior at upstream and downstream --- p.59 / Chapter 4.4 --- Existence and uniqueness of Euler flflows --- p.61 / Chapter 5 --- 3-D subsonic Euler flows through nitely long nozzles --- p.67 / Chapter 5.1 --- Mathematical formulation and main results --- p.67 / Chapter 5.2 --- Some preliminaries --- p.71 / Chapter 5.3 --- 3-D potential flows --- p.76 / Chapter 5.3.1 --- Apriori estimates for truncated potential flows --- p.77 / Chapter 5.3.2 --- Existence and uniqueness of potential flows --- p.91 / Chapter 5.4 --- General 3-D steady Euler systems --- p.94 / Chapter 6 --- Further discussions and future work --- p.109 / Bibliography --- p.111

這篇論文示主要討論在信息不完全情況下的無線網絡資源分配的兩個問題。傳輸節點不固定和信道狀態的不確定性將影響資源分配的選擇。因為不完整的信息，或在這些情況下可能無法確切獲得準確的信息，將對資源優化配置產生一定的影響。對於不完整信息對無線網路的影響，其中用戶的移動性和信道增益的不確定性，將是本論文中討論的兩個主要問題。 / 本論文的第一部分是關於移動傳輸節點的資源分配問題。我們主要分析上行系統的移動用戶，其中每個用戶會盡量優化他或她自己的功效函數，以達到最佳的性能。此外，我們提出對移動用戶的功率分配優化的方案當所有信道信息可用的時候。此外，我們提出了幫助每個用戶預測信道信息總幹擾來優化功效函數，當信息不完備的時候。這形成了一個不完全信息博弈。我們提出了預測的規則，幫助動態預測總幹擾。我們採用了卡爾曼濾波器來處理測量噪聲 我們也說明了利用預測來優化的功效函數和由完整的信息得出的之間的差異。此外，從動態規劃，我們在預測的基礎上給出一個動態的功率分配方案。 / 第二部分討論了在資源分配時，當有關信道增益是不完整時的不確定規劑。我們主要考慮認知無線電模型。在第二部分中，我們考慮，當二級用戶的干擾不會超過一定限制時，他們能夠使用共享的頻率的情況。我們首先利用約束幹擾的限制進行建模，使得二級用戶的干擾，即使在最壞的情況下，也不會超過限制，這將有助於他或她以避免不可行的解決方案。然後，我們擴展我們的概率約束條件來代表不確定性的干擾限制。由於概率約束一般都是難以解決的，而基於無線信道的衰落效應，有關變量的完整的信息是很難獲得。我們重新將概率約束條件轉化為隨機期望約束條件。利用樣本平均近似法，我們提出了隨機學習算法，以幫助次級用戶從主要用戶那裡獲得反饋信息，最大限度地提高自己的功效函數。此外，我們分析了在認知無線電網絡定價條件的頻譜共享方案。我們展示的聯合優化配置方案，幫助次級用戶從主要用戶購買頻譜和優化功率。當有信道增益的不確定性時，二級用戶希望最大限度地提高功效函數的期望值並且採用相對穩定的採購策略追求最佳平均收益。它是一個有鞍點的隨機優化問題。我們展示一個分佈式的隨機算法，以幫助二級用戶更新資源分配策略。在一些實際的情況下，為了減少計算複雜性和希望實施越來較為容易，我們利用迭代平均來為二級用戶進行資源配置。 / Two main issues of resource allocation in wireless networks with incomplete information are addressed in this thesis. Transmission node is not fixed in the wireless system and uncertainties of the channel states would also affect the choices of resource allocation, since full information cannot be provided or may not be exact under these scenarios. For incomplete information in wireless networks, mobility of the users and uncertainties of channel gains are two main issues that would be considered in this thesis. / The first part of this thesis is concerning the resource allocation problems with mobile trans- mission nodes. We consider mobile users in an up-link system. We analyze the mobile system where each user would try to maximize his or her own utility to achieve the best performance. Besides, we propose a power allocation scheme for the mobile users when all channel information is available. We show that our model can form a game. Moreover, we illustrate that each user would expect to predict the aggregate interference to maximize the utility when channel information is incomplete. It can be shown that this forms a game with incomplete information. We demonstrate the prediction rules which help predict the aggregate interference dynamically. We apply the Kalman filter to tackle measurement noises. We also illustrate the bound on the difference between the utility with prediction and that with complete information. Moreover, applying dynamic programming, we give a dynamic power allocation scheme based on the predictions. / The second part discusses the issue of uncertain programming in resource allocation when information about channel gains is incomplete. We mainly consider the model of cognitive radio networks. We introduce a resource allocation scheme for secondary users with spectrum sharing in a cognitive radio network. Secondary users can exploit the spectrum owned by primary links when their interference level does not exceed certain requirements. We first model the interfer- ence constraints as robust constraints such that secondary users would satisfy the interference constraints even under the worst cases, which would help him or her to avoid the unfeasible solutions. We then extend our consideration of the interference constraints as chance constraints to represent uncertainties. Since chance constraints are generally difficult to solve and full in- formation about the uncertain variables is not available due to the fading effects of wireless channels, we reformulate the constraints into stochastic expectation constraints. With sample average approximation method, we propose stochastic distributed learning algorithms to help secondary users satisfy the constraints with the feedback information from primary links when maximizing the utilities. Moreover, we introduce a resource allocation scheme for secondary users to share spectrum and optimize usage of power with pricing. Secondary users need to buy spectrum from primary users. In the process, secondary users also enhance the utilization of the unused bandwidth by primary users. We first demonstrate the resource allocation scheme when full information about channel gains is available. When there are uncertainties of channel gains, secondary users would like to maximize the expected value of the utilities to pursue the best benefits on average with relatively stable buying strategies. It can be shown that it is a stochastic optimization problem with saddle points. We demonstrate a Distributed Stochastic Algorithm to help secondary users update their resource allocation strategies. For some practical scenarios, to reduce computation complexity and make implementation easy, we illustrate an Iterate Average from Distributed Stochastic Algorithm for secondary users. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Zhou, Kenan. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 123-134). / 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 1.1 --- Motivations --- p.1 / Chapter 1.2 --- Contributions and Outline of the Thesis --- p.2 / Chapter 2 --- Background Study --- p.5 / Chapter 2.1 --- Slow and Flat Fading Wireless Channel --- p.5 / Chapter 2.2 --- Cognitive Radio Networks --- p.7 / Chapter 2.3 --- Multiple-Access Channel --- p.8 / Chapter 2.4 --- Mobility Model --- p.10 / Chapter 2.5 --- Convex Optimization --- p.12 / Chapter 2.6 --- Uncertain Programming --- p.13 / Chapter 2.7 --- Game Theory --- p.14 / Chapter Part I --- Resource Allocation in Wireless Networks with Mobility --- p.16 / Chapter 3 --- Resource Allocation with Mobile Users in an Up-link System --- p.19 / Chapter 3.1 --- System Model --- p.20 / Chapter 3.2 --- Power Allocation for Mobile Users with Complete Information --- p.22 / Chapter 3.3 --- Power Allocation with Incomplete Information --- p.26 / Chapter 3.3.1 --- Bound on the difference between the utility with prediction and that with complete information --- p.27 / Chapter 3.3.2 --- Prediction Scheme for Incomplete Channel Information --- p.30 / Chapter 3.3.3 --- Power Allocation with Dynamic Programming --- p.32 / Chapter 3.4 --- Numerical results and discussion --- p.35 / Chapter 3.4.1 --- Simulation Model --- p.35 / Chapter 3.4.2 --- Numerical Results --- p.36 / Chapter 3.5 --- Chapter Summary --- p.42 / Chapter 3.6 --- Appendices --- p.44 / Chapter 3.6.1 --- Proof of Theorem 3.1 --- p.44 / Chapter 3.6.2 --- Proof of Theorem 3.2 --- p.47 / Chapter Part II --- Resource Allocation inWireless Networks with Uncertain Programming --- p.48 / Chapter 4 --- Resource Allocation with Robust Optimization --- p.52 / Chapter 4.1 --- System Model --- p.52 / Chapter 4.2 --- Resource Allocation with Robust Optimization Approach --- p.54 / Chapter 4.3 --- Trade-Off Between Robustness and Performance --- p.59 / Chapter 4.4 --- Numerical results and discussion --- p.62 / Chapter 4.4.1 --- Choice of the Penalty Function --- p.62 / Chapter 4.4.2 --- Simulation Model --- p.63 / Chapter 4.4.3 --- Simulation Results --- p.64 / Chapter 4.5 --- Chapter Summary --- p.65 / Chapter 5 --- Resource Allocation with Chance Constraints --- p.67 / Chapter 5.1 --- System Model --- p.68 / Chapter 5.2 --- Power Allocation with Complete Information about Probabilistic Constraints --- p.69 / Chapter 5.3 --- A Stochastic Approximation Approach Based on the Outage Event --- p.72 / Chapter 5.3.1 --- Feasibility of the Stochastic Approximation Method --- p.74 / Chapter 5.3.2 --- Stochastic Distributed Learning Algorithm I (SDLA-I) --- p.76 / Chapter 5.3.3 --- Stochastic Distributed Learning Algorithm II (SDLA-II) --- p.80 / Chapter 5.4 --- Numerical Results and Discussion --- p.82 / Chapter 5.4.1 --- Examples of uk(.) for Simulation --- p.82 / Chapter 5.4.2 --- Simulation Model --- p.83 / Chapter 5.4.3 --- Simulation Results and Discussions --- p.84 / Chapter 5.5 --- Chapter Summary --- p.86 / Chapter 5.6 --- Appendices --- p.88 / Chapter 5.6.1 --- Proof of Lemma 5.3 --- p.88 / Chapter 6 --- Priced Resource Allocation with Stochastic Optimization --- p.90 / Chapter 6.1 --- System Model --- p.91 / Chapter 6.2 --- Price-Based Optimization with Complete Information --- p.94 / Chapter 6.3 --- Price-Based Stochastic Optimization with Uncertainties --- p.96 / Chapter 6.4 --- Distributed Stochastic Algorithms for the Price-Based Stochastic Optimization --- p.100 / Chapter 6.4.1 --- Iterate Averages of DSA --- p.104 / Chapter 6.5 --- Numerical Results and Discussion --- p.106 / Chapter 6.5.1 --- Simulation Model --- p.106 / Chapter 6.5.2 --- Numerical Results --- p.107 / Chapter 6.6 --- Chapter Summary --- p.112 / Chapter 6.7 --- Appendices --- p.113 / Chapter 6.7.1 --- Proof of Lemma 6.1 --- p.113 / Chapter 6.7.2 --- Proof of Proposition 6.1 --- p.114 / Chapter 6.7.3 --- Proof of Lemma 6.3 --- p.114 / Chapter 6.7.4 --- Proof of Lemma 6.4 --- p.115 / Chapter 6.7.5 --- Proof of Proposition 6.2 --- p.116 / Chapter 7 --- Conclusion and Future Work --- p.117 / Chapter 7.1 --- Conclusion --- p.117 / Chapter 7.2 --- Future Work --- p.119 / Chapter 7.2.1 --- Joint Power and Channel Access Scheduling for Mobile Users --- p.119 / Chapter 7.2.2 --- Power Control for Heterogeneous Mobile Users --- p.120 / Chapter 7.2.3 --- More on Uncertain Programming in Cognitive Radios --- p.120 / Chapter 7.2.4 --- Transmissions in Complex Networks with Uncertainties --- p.121 / Chapter 7.2.5 --- Secure Transmissions in Wireless Networks with Uncertainties --- p.122 / Bibliography --- p.123

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Thesis (M.S.)--Massachusetts Institute of Technology, Alfred P. Sloan School of Management, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND DEWEY / Bibliography: leaves 74-75. / by Peter Manning Guadagni. / M.S.

Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Economics. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND DEWEY. / Bibliography: leaves 105-109. / Ph.D.

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