by Yubao Zhang. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (p. 138-146). / 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.

Dai, Zhuojun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references. / Abstracts in English and Chinese. / 摘要 --- p.i / ABSTRACT --- p.iii / ACKNOWLEDGEMENT --- p.v / Chapter Chapter 1 --- Introduction and Background --- p.-1- / Chapter 1.1 --- General introduction to internal motions --- p.-1- / Chapter 1.1.1 --- Definition of translational diffusion and internal motions --- p.-1- / Chapter 1.1.2 --- Theoretical background of internal motions --- p.-1- / Chapter 1.2 --- Investigation of internal motions on LLS --- p.-4- / Chapter 1.2.1 --- General introduction on investigation of internal motion by LLS --- p.-4- / Chapter 1.2.2 --- Theory on internal motion detected by LLS --- p.-5- / Chapter 1.3 --- Laser light scattering --- p.-6- / Chapter 1.3.1 --- General introduction to laser light scattering --- p.-6- / Chapter 1.3.2 --- Data process about internal motions in LLS --- p.-9- / Chapter 1.4 --- Notes and References --- p.-12- / Chapter Chapter 2 --- Internal motions of PNIPAM chains in 6 and bad solvent --- p.-15- / Chapter 2.1 --- Introduction --- p.-15- / Chapter 2.2 --- Experimental section --- p.-15- / Chapter 2.2.1 --- Sample preparation --- p.-15- / Chapter 2.2.2 --- Dynamic laser light scattering --- p.-16- / Chapter 2.3 --- Result and discussion --- p.-16- / Chapter 2.4 --- Conclusion --- p.-23- / Chapter 2.5 --- Notes and References --- p.-25- / Chapter Chapter 3 --- Internal motions of PNIPAM microgels in 6 and bad solvent --- p.-26- / Chapter 3.1 --- Introduction --- p.-26- / Chapter 3.2 --- Experimental section --- p.-26- / Chapter 3.2.1 --- Sample preparation --- p.-26- / Chapter 3.2.2 --- Dynamic laser light scattering --- p.-21- / Chapter 3.3 --- Result and discussion --- p.-27- / Chapter 3.4 --- Conclusion --- p.-30- / Chapter 3.5 --- Notes and References --- p.-31- / Chapter Chapter 4 --- Examination on the internal motions variations with solvent quality of Polystyrene chains --- p.-32- / Chapter 4.1 --- Introduction --- p.-32- / Chapter 4.2 --- Experimental Section --- p.-32- / Chapter 4.2.1 --- Sample preparation --- p.-32- / Chapter 4.2.2 --- Dynamic laser light scattering --- p.-33- / Chapter 4.3 --- Result and discussion --- p.-33- / Chapter 4.4 --- Conclusion --- p.-36- / Chapter 4.5 --- Notes and References --- p.-38- / Chapter Chapter 5 --- Examination on the internal motions variations with solvent quality of Poly(methyl methacrylate) chains --- p.-40- / Chapter 5.1 --- Introduction --- p.-40- / Chapter 5.2 --- Experimental Section --- p.-40- / Chapter 5.2.1 --- Sample preparation --- p.-40- / Chapter 5.2.2 --- Dynamic laser light scattering --- p.-41- / Chapter 5.3 --- Result and discussion --- p.-41- / Chapter 5.4 --- Conclusion --- p.-45- / Chapter 5.5 --- Notes and References --- p.-46-

Digitized by Kansas Correctional Industries

Orientador: Alvaro de Souza Dutra / Banca: Julio Marny Hoff da Silva / Banca: Bruto Max Pimentel Escobar / Resumo: Neste trabalho, apresentamos uma breve introdução ao estudo dos sólitons. Além disso, introduzimos uma nova classe de configurações oscilantes do tipo lump e do tipo kink. Tais configurações são obtidas de forma analítica e exata, como conseqüência somos capazes de fazer a análise da estabilidade das soluções apresentadas. Por fim, apresentamos no último capítulo soluções de estados ligados de férmions na presença das novas configurações de campo que estamos apresentando neste trabalho / Abstract: In this work we present a brief introduction to the study of solitons. Furthermore, we introduce a new class of oscillating Lorentz covariant configurations for the evolution of the domain walls which are analytically obtained in diverse dimensions. As a consequence, we are able to perform the analysis of the stability of the presented solutions. Finally, in the last chapter, we present analytical solutions of fermion bound states on the background of kinks of a class of asymmetrical scalar field / Mestre

No description available.

Maxwell’s equations are a set of partial differential equations that describe the classic electromagnetic problems, electrodynamics etc. Effective numerical methods are derived to solve the equations in the past decades, and continued to be of great interest to be developed to its completion. In this thesis, we introduce and propose numerical methods using staggered meshes that deal with both two dimensional and three dimensional space problem in polygonal and general curved domains. / Finite difference method, finite volume method, spectral method and staggered discontinuous Galerkin method are discussed in the thesis. A forth order finite difference method using Taylor expansion technic is proposed. The integral form of the original Maxwell’s equations give rise to methods based on more general domain. For the finite volume method, covolume methods both on the cyclic polygon elements and noncyclic polygon elements are derived. To derive a higher order accurate method, staggered discontinuous Galerkin method based on the same domain decomposition present in the finite volume method use Nedelec elements is derived in two dimensional space, and spectral method using nodal high-order method operate on a general domain in 3D with flexible domain geometry is introduced. Numerical results are shown to show the performance oft he above mentioned approximation methods in 2D case. / 麥克斯韋方程組是一組描述經典電磁問題，電磁力學的偏微分方程。在過去數十年，行之有效的偏微分方程數值解已經被推導出並用於求解該方程，該問題現在仍然吸引著學者極大的興趣，並日臻完善。在這篇論文中，我們介紹並提出一些運用曲域交錯網格數值方法在二維和三維的多面體和更一般幾何體處理麥克斯韋方程組問題。 / 本論文對有限差分法，有限體積法，光譜法和交錯間斷有限元方法進行了討論。利用泰勒展開式這一方法推導出一個二維的四階有限差分方法。基於原來的麥克斯韋方程組的積分形式所得到的數值方法更適用於更普遍的域。對於有限體積法，對循環多邊形元素和非環狀多邊形元素的有限體積方法都將被導出。為了得到一個更高階準確的方法，基於有限體積法中使用的域分解方法，使用Nedelec元素，推導了二維空間的高階有限元方法。基於頂點高階數值方法的光譜法對於三維一般定義域的幾何形態更為靈活適用。在二維的定義域中，數值模擬結果驗證上述數值方法的精確性。 / Jian, Fangqiong. / Thesis M.Phil. Chinese University of Hong Kong 2014. / Includes bibliographical references (leaves 62-65). / Abstracts also in Chinese. / Title from PDF title page (viewed on 07, October, 2016). / Detailed summary in vernacular field only. / Detailed summary in vernacular field only.

Cheung, Man Wah. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 89-91). / Abstracts in English and Chinese. / Chapter 1 --- Introduction to Inverse Problems --- p.1 / Chapter 1.1 --- Major properties --- p.1 / Chapter 1.2 --- Typical examples --- p.3 / Chapter 1.3 --- Thesis outline --- p.5 / Chapter 2 --- Some Operator Theory --- p.6 / Chapter 2.1 --- Fredholm integral equation of the first kind --- p.6 / Chapter 2.2 --- Compact operator theory --- p.8 / Chapter 2.3 --- Singular system --- p.12 / Chapter 2.4 --- Moore-Penrose generalized inverse --- p.14 / Chapter 3 --- Regularization Theory for First Kind Equations --- p.19 / Chapter 3.1 --- General regularization theory --- p.19 / Chapter 3.2 --- Tikhonov regularization --- p.24 / Chapter 3.3 --- Landweber iteration --- p.26 / Chapter 3.4 --- TSVD --- p.28 / Chapter 4 --- Multilevel Algorithms for Ill-posed Problems --- p.30 / Chapter 4.1 --- Basic assumptions and definitions --- p.31 / Chapter 4.2 --- Multilevel analysis --- p.33 / Chapter 4.3 --- Applications --- p.37 / Chapter 4.3.1 --- Preconditioned iterative methods with nonzero regularization parameter --- p.38 / Chapter 4.3.2 --- Preconditioned iterative methods with zero regularization parameter --- p.38 / Chapter 4.3.3 --- Full multilevel algorithm --- p.40 / Chapter 5 --- Numerical Experiments --- p.41 / Chapter 5.1 --- Integral equations --- p.41 / Chapter 5.1.1 --- Discretization --- p.42 / Chapter 5.1.2 --- Test problems --- p.43 / Chapter 5.1.3 --- "Singular values, singular vectors and condition numbers" --- p.45 / Chapter 5.1.4 --- Effect of condition numbers on numerical accuracies --- p.49 / Chapter 5.2 --- Differential equations --- p.50 / Chapter 5.2.1 --- Discretization --- p.51 / Chapter 5.2.2 --- "Singular values, singular vectors and condition numbers" --- p.53 / Chapter 5.3 --- Numerical experiments by classical methods --- p.55 / Chapter 5.3.1 --- Tikhonov regularization --- p.55 / Chapter 5.3.2 --- TSVD --- p.56 / Chapter 5.3.3 --- Landweber iteration --- p.63 / Chapter 5.4 --- Numerical experiments by multilevel methods --- p.63 / Chapter 5.4.1 --- General convergence --- p.63 / Chapter 5.4.2 --- Numerical results --- p.65 / Chapter 5.4.3 --- Effect of multilevel parameters on convergence --- p.76 / Bibliography --- p.89

Estágio realizado na Wipro Retail e orientado pelo Eng.ª Cláudia Bartolo Araújo / Tese de mestrado integrado. Engenharia Informática e Computação. Faculdade de Engenharia. Universidade do Porto. 2009

Burgers’ Equation ut + cuux = νuxx is a nonlinear partial differential equation which arises in models of traffic and fluid flow. It is perhaps the simplest equation describing waves under the influence of diffusion. We consider the large time behavior of solutions with exponentially localized initial conditions, analyzing the rate of convergence to a known self similar single-hump solution. We use the Cole-Hopf Transformation to convert the problem into a heat equation problem with exponentially localized initial conditions. The solution to this problem converges to a Gaussian. We then find an optimal Gaussian approximation which is accurate to order t−2. Transforming back to Burgers’ Equation yields a solution accurate to order t−2.

In this paper we prove that div(|x|β∇u)+|x|αf(u)=0, inB u = 0 on ∂B has infinitely many solutions when f is superlinear and grows subcritically for u ≥ 0 and up to critically for u less than 0 with 10, 13 N+β−2 N+β−2 We make extensive use of Pohozaev identities and phase plane and energy arguments.