Leung, Lai Lai = 利用譜表示法設計隱形超材料 / 梁麗儷. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 63-64). / Abstracts in English and Chinese. / Leung, Lai Lai = Li yong pu biao shi fa she ji yin xing chao cai liao / Liang Lili. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Control Electromagnetic Field by Transformation Media Concept --- p.1 / Chapter 1.2 --- The invariance of Maxwell's equations under coordinate transformation --- p.2 / Chapter 1.3 --- Spatially dependent material parameters --- p.3 / Chapter 1.4 --- Objectives of the thesis --- p.4 / Chapter 2 --- Spectral Representation --- p.6 / Chapter 2.1 --- The Maxwell-Garnett approximation --- p.7 / Chapter 2.2 --- The Bruggeman theory --- p.10 / Chapter 2.3 --- The Bergman-Milton spectral representation theory --- p.11 / Chapter 2.4 --- Spectral representation of the effective dielectric constant of graded composites --- p.13 / Chapter 3 --- Design of perfect cloaking --- p.17 / Chapter 3.1 --- Pendry´ةs profile --- p.17 / Chapter 3.2 --- Slhalaev's profile --- p.21 / Chapter 4 --- Imperfect cloaking --- p.27 / Chapter 4.1 --- Sensitivity to loss effect --- p.27 / Chapter 4.2 --- Sensitivity to dispersion effect --- p.31 / Chapter 5 --- Ray Tracing --- p.38 / Chapter 5.1 --- Hamiltonian and ray equations --- p.39 / Chapter 5.2 --- Refraction --- p.41 / Chapter 5.3 --- Ray tracing of perfect spherical cloaking --- p.42 / Chapter 5.4 --- Ray tracing for imperfect spherical cloaking --- p.46 / Chapter 6 --- Other applications of the concept of transformation media --- p.52 / Chapter 6.1 --- Spherical concentrators --- p.52 / Chapter 6.2 --- Cylindrical concentrators --- p.55 / Chapter 6.3 --- Graded Drude model design --- p.58 / Chapter 7 --- Conclusion --- p.60 / A Scaling of ε and μ for a general coordinate transformation --- p.61 / Bibliography --- p.63

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 156-164). Available also in a digital version from Dissertation Abstracts.

No description available.

The purpose of this thesis is to investigate how "spect ralness" properties of a torsion theory T on R - Mod are reflected by properties of the ring R and its ring of quotients R,.. The development of "spectral" torsion theory owes much to Zelmanowitz [50] and Gomez-Pardo [23] . Gomez-Pardo proved that there exists a bijective correspondence between the set of spectral torsion theories on R - Modand rings of quotients of R that are Von Neumann regular and left self-injective. Chapter 1 is concerning with the notation used in the thesis and a summary of main results which are needed for understanding the sequel. Chapter 2 is concerned with the construction of a maximal ring of quotients of an arbitrary ring R by using the notion of denseness and relative injective hull. In Chapter 3, we survey the three equivalent ways of formulating Torsion Theory: by means of preradical functors on the category R- Mod, pairs of torsion / torsion-free classes and topologizing filters on rings. We shall show that Golan's approach to Torsion Theory via equivalence classes of injectives; and Dickson's one (as presented by Stenstrom) are equivalent. With a torsion theory T defined on R-Mod we associate R,. a ring of quotients of R. The full subcategory (R, T) - Mod of R- Mod whose objects are the T-torsion-free r-injective left R-modules is a Grothendieck category called the quotient category of R - Mod with respect to T. A left R,.-module that is r-torsion-free T-injective as a left R-module is injective if and only if it is injective as a left R-module (Proposition 3.6.4). Because of its use in the sequel , particular attention is paid to the lattice isomorphism that exists between the lattice of .r-pure submodules of a left Rmodule M and the lattice of subobjects of the quotient module M; in the category (R , T) - Mod. Chapter 4 introduces the definition of a spectral torsion theory: a Vll torsion theory r on R - Mod is said to be spectral if the Grothendieck category (R, r) - Mod is spectral. Using the notion of relative essential submodule, one can construct a spectral torsion theory from an arbitrary torsion theory on R - Mod. We shall show how an investigation of a general spectral torsion theory on R - Mod reduces to the Goldie torsion theory on R/tT (R) - Mod. Moreover, we shall exhibit necessary and sufficient conditions for R; to be a regular left self-injective ring (Theorem 4.2.10). In Chapter 5, after constructing the torsion functor Soce(-) which is associated with the pseudocomplement r.l of r in R - tors, we show how semiartinian rings can be characterized by means of spectral torsion theories: if a spectral torsion theory r on R - Mod is generated by the class of r-torsion simple left R-modules or, equivalently, cogenerated by the class of r-torsion-free simple left R-modules, then R is a left semiartinian ring (Proposition 5.3.2). Chapter 6 gives Zelmanowitz' important result [50]: R; is a semisimple artinian ring if and only if the torsion theory r is spectral and the associated left Gabriel topology has a basis of finitely generated left ideals. We also exhibit results due to M.J. Arroyo and J. Rios ([4] and [5]) which illustrate how spectral torsion theories can be used to describe when R; is (1) prime regular and left self-injective, (2) a left full linear ring, and (3) a direct product of left full linear rings. We also study the relationship between the flatness of the ring of quotients R; and the r- coherence of the ring R when r is a spectral torsion theory. It is proved that if r is a spectral torsion theory on R - Mod then the following conditions are equivalent: (1) R is left r-coherent; (2) (Rr)R is flat; (3) every right Rr-module is flat as a right R-module (Proposition 6.3.9). This result is an extension of Cateforis' results. / Thesis (M.Sc) - University of Natal, Pietermaritzburg, 2003

Thesis (M.S.)--Rochester Institute of Technology, 1990. / Includes bibliographical references.

Thesis (Dr. rer. nat.)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2001. / "11 Februar 2001." Includes bibliographical references (p. 123-124).

Spectral moment formulae of various shapes have proven to be very successful in studying the statistics of central 𝐿-values. In this article, we establish, in a completely explicit fashion, such formulae for the family of 𝐺𝐿(3) × 𝐺𝐿(2) Rankin-Selberg 𝐿-functions using the period integral method. The Kuznetsov and the Voronoi formulae are not needed in our argument. We also prove the essential analytic properties and explicit formulae for the integral transform of our moment formulae. It is hoped that our method will provide insights into moments of 𝐿-functions for higher-rank groups.

Ph.D. (Applied Mathematics) / In this thesis we introduce new numerical methods for solving nonlinear ordinary and partial differential equations. These methods solve differential equations in a manner similar to the Gauss Seidel approach of solving linear systems of algebraic equations. First the nonlinear differential equations are linearized by simply evaluating nonlinear terms at previous iterations. To solve the linearized iteration schemes obtained we use either the spectral method or higher order compact finite difference schemes and we call the resulting methods the spectral relaxation method (SRM) and the compact finite difference relaxation method (CFD-RM) respectively. We test the applicability of these methods in a wide variety of ODEs and PDEs. The accuracy and computational efficiency in terms of CPU time is compared against other methods as well as other results from literature. We solve a range of chaotic and hyperchaotic systems of equations. Chaotic and hyperchaotic are complex dynamical systems which are characterised by rapidly changing solutions and high sensitivity to small perturbations of the initial data. As a result finding their solutions is a challenging task. We modify the proposed SRM to be able to deal with such systems of equations. We also consider chaos control and synchronization between too identical chaotic systems. We also make a comparison between the SRM and CFD-RM and between the spectral quasilinearization method (SQLM) and the compact finite difference quasilinearization method (CFD-QLM). The aim is to compare the performance between the spectral and the compact finite difference approaches in solving similarity boundary layer problems. We consider two examples. First, we consider the flow of a viscous incompressible electrically conducting fluid over a continuously shrinking sheet. We also consider a three-equation system that models the problem of unsteady free convective heat and mass transfer on a stretching surface in a porous medium in the presence of a chemical reaction. We extend the application of the SRMand SQLMto PDEs. In particular we consider two unsteady boundary layer flow problems modelled by a PDE or a system of PDEs. We solve a one dimensional unsteady boundary layer flow due to an impulsively stretching surface and the problem of unsteady three-dimensional MHD flow and mass transfer in a porous space. Results are compared with results obtained using the Keller-box method which is popular in solving unsteady boundary layer problems. We also extend the application of the CFD-RM to PDEs modelling unsteady boundary layer flows and again compare results to Keller-box results. We consider two examples, the unsteady one dimensional MHD laminar boundary layer flow due to an impulsively stretching surface, and the unsteady three-dimensional MHD flow and heat transfer over an impulsively stretching plate.

We consider on the interval [0; a], rstly fourth-order di erential operators with eigenvalue parameter dependent boundary conditions and secondly a sixth-order di erential operator with eigenvalue parameter dependent boundary conditions. We associate to each of these problems a quadratic operator pencil with self-adjoint operators. We investigate the spectral proprieties of these problems, the location of the eigenvalues and we explicitly derive the rst four terms of the eigenvalue asymptotics.

by Li Jian Lin. / "November 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 85-90) / 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.