Cho, Chi Lam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 63-65). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.

對流佔優擴散問題一直是一個俱有挑戰性的問題。眾所週知，解可能在邊界或者內部表現出局部斷層。傳統的數值解法在解決對流佔優擴散問題時不夠穩定和精確。因此有很多空間穩定技巧被提出和學習。 / 在這篇論文中，我們設計了一個全變分規則化方法來解對流佔優擴散方程。首先，選取一個較小的測試函數空間構造一個欠定模型。然後，通過附加條件最小化全變分來計算唯一解。這個想法是基於離散化解雙曲形偏微分方程的全變分遞減原理。為了實現這個全變分規則化方法，我們需要找出相應的拉格郎日方程的最優條件，並當做時間依賴方程進行求解。論文中涉及了三個運算符拆分方法，Peaceman-Rachford方法，Douglas-Rachford方法和Theta方法。數值實驗證明我們的方法可以準確的描繪出對流佔優擴散問題的邊界和內部斷層現象，因此可以在擴散系數很小的時候提供可靠的數值結果。 / The convection-dominated diffusion problem has been a challenge problem for a long time. It is well known that the solution may exhibit localized layer on the boundary or in the interior. Conventional numerical schemes for the convection-dominated diffusion problem are lacking in both stability and accuracy. Therefore many spatial stabilization techniques have been proposed and studied. / In this thesis, we devise a TV regularization method for solving convection-dominated diffusion equations. First, we form an underdetermined system by choosing a small test function space. Then, we find the unique solution by minimizing the total variation. The idea is based on the fact that total variation diminishing (TVD) is a property of certain discretization schemes used to solve hyperbolic partial differential equation. To implement this TV regularization approach, we find the optimality condition of the corresponding Lagrange function for the minimization problem, and then solve it as a time dependent problem. Three operator splitting methods, the Peaceman-Rachford method, the Douglas-Rachford method and the Theta scheme are studied. The numerical experiments demonstrate that our scheme can accurately capture the boundary and internal layer for the convection-dominated problem, and therefore provide reliable numerical result for small diffusivity. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Zhang, Qi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 56-[58]). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 2 --- TV scheme --- p.9 / Chapter 2.1 --- TV regularization --- p.9 / Chapter 2.1.1 --- The underdetermined system --- p.10 / Chapter 2.1.2 --- The minimization problem --- p.10 / Chapter 2.2 --- The optimality conditions --- p.11 / Chapter 2.3 --- Discrete version --- p.14 / Chapter 3 --- Numerical schemes --- p.17 / Chapter 3.1 --- Peachment-Rachford method --- p.17 / Chapter 3.2 --- Douglas-Rachford method --- p.18 / Chapter 3.3 --- Theta scheme --- p.19 / Chapter 3.4 --- Two systems --- p.22 / Chapter 3.4.1 --- System 1 --- p.23 / Chapter 3.4.2 --- System 2 --- p.25 / Chapter 3.5 --- Matrix representation --- p.26 / Chapter 4 --- Numerical examples --- p.29 / Chapter 4.1 --- Scenario --- p.30 / Chapter 4.1.1 --- Initial condition --- p.30 / Chapter 4.1.2 --- Notation --- p.30 / Chapter 4.1.3 --- Parameter --- p.31 / Chapter 4.2 --- Experiment 1 --- p.32 / Chapter 4.3 --- Experiment 2 --- p.38 / Chapter 4.4 --- Experiment 3 --- p.42 / Chapter 4.5 --- Experiment 4 --- p.48 / Chapter 5 --- Conclusion --- p.55

We are interested in solving the time-harmonic inverse acoustic scattering problem for planar sound-soft obstacles. In this work, we introduce four methods for solving inverse scattering problems. The first method is a variation of the method introduced by Johansson and Sleeman. This method solves the inverse problem when we have the far field pattern given for only one incident wave. It is an iterative method based on a pair of integral equations used to obtain the far field pattern of a known single object. The method proposed in this thesis has a better computational performance than the method of Johansson and Sleeman. The second method we present is a multi-frequency method called the recursive linearization algorithm. This method solves the inverse problem when the far field pattern is given for multiple frequencies. The idea of this method is that from an initial guess, we solve the single frequency inverse problem for the lowest frequency. We use the result obtained as the initial guess to solve the problem for the next highest frequency. We repeat this process until we use the data from all frequencies. To solve the problem at each frequency, we use the first method proposed. To improve the quality of the reconstruction of the shadowed part of the object, we solve the inverse scattering problem of reconstructing an unknown sound-soft obstacle in the presence of known scatterers. We show that depending on the position of the scatterers, we may be able to obtain very accurate reconstructions of the entire unknown object. Next, we introduce a method for solving the inverse problem of reconstructing a convex sound-soft obstacle, given measures of the far field pattern at two frequencies that are not in the resonance region of the object. This method is based on the use of an approximation formula for the far field pattern using geometric optics. We are able to prove that for the reconstruction of the circle of radius $R$ and center at the origin, the size of the interval of convergence of this method is proportional to the inverse of the wavenumber. This procedure is effective at reconstructing the illuminated part of the object; however, it requires an initial guess close to the object for frequencies out of the resonance region. Finally, we propose a globalization technique to obtain a better initial guess to solve the inverse problem at frequencies out of the resonance region. In this technique, given the far field pattern of a convex object at two frequencies out of the resonance region, we use our extrapolation operator to generate synthetic data for low frequencies. We apply the recursive linearization algorithm, using as a single frequency solver the method that is based on geometric optics. We obtain an approximation of the object that can be used as the initial guess to apply the recursive linearization algorithm using the first method introduced as the single frequency solver.

by Cheng Ting. / "August 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 103-107). / 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.

After the Boxing Day 2004 Sumatran Tsunami, a review of tsunami hazard and risk for New Zealand identified Gisborne as the urban area with the greatest risk. Gisborne could experience gt;500 fatalities and extensive damage to infrastructure during a severe tsunami. The severity of a tsunami is likely to be low for distance sources given the effectiveness of the Pacific Tsunami Warning System. However, there is a substantial risk from local sources, as no local warning system of any kind exists. Prompt evacuation is probably the most cost-effective tsunami mitigation strategy available for New Zealand coastal locations, including Gisborne. This requires both knowledge of the extent of tsunami inundation, and sufficient warning of the tsunami arrival. Hence, there are two main objectives for this investigation: 1. Determine the likely extent of tsunami inundation for Gisborne City and surrounding populated coastal locations in Poverty Bay, using a combination of hydrodynamic tsunami modelling and GIS. The modelling will simulate historical events, particularly the largest historical tsunami, the May 1947 local tsunami. Modelling will consider potential events based on the Maximum Credible Earthquake for local sources associated with the Hikurangi Deformation Front. 2. Create inundation maps of Poverty Bay that can be used for future town planning and emergency plans.

<p>In this thesis a new method for the option pricing will be introduced with</p><p>the help of the Mellin transforms. Firstly, the Mellin transform techniques for</p><p>options on a single underlying stock is presented. After that basket options</p><p>will be considered. Finally, an improvement of existing numerical results</p><p>applied to Mellin transforms for 1-basket and 2-basket American Put Option</p><p>will be discussed concisely. Our approach does not require either variable</p><p>transformations or solving diusion equations.</p>

Study of the impact of early visual deprivation and its following experience with numbers and numerosities on the elaboration of the semantic numerical representation with the same properties to those postulated in sighted people.

Thesis (Ph. D.)--University of Texas at Dallas, 2006. / Includes vita. Includes bibliographical references (leaves 138-149).

Thesis (Ph. D.)--Ohio State University, 1984. / Includes bibliographical references (leaves 146-149). Available online via OhioLINK's ETD Center.

Thesis (Ph.D.)--York University, 2004. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 160-165). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ99262