Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2004.\ / Includes bibliographical references (p. 91-92).

by Ip Che-ho. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaf 136). / Covering Page --- p.i / Acknowledgement --- p.ii / Abstract --- p.iii / Table of Content --- p.v / Chapter 1. --- Fundamentals of Complex Analys --- p.is / Chapter 1.1 --- The extended complex plane --- p.1 / Chapter 1.2 --- Stereographic projection --- p.2 / Chapter 1.3 --- Analytic functions --- p.3 / Chapter 1.4 --- Rational functions --- p.5 / Chapter 1.5 --- Mobius transformation --- p.6 / Chapter 2. --- The Topology of the Extended Plane / Chapter 2.1 --- The topology of S2 and C ∞ --- p.9 / Chapter 2.2 --- Smooth map and manifolds --- p.10 / Chapter 2.3 --- Regular points --- p.11 / Chapter 2.4 --- Degree of maps --- p.13 / Chapter 2.5 --- Euler characteristics --- p.14 / Chapter 2.6 --- Covering space --- p.16 / Chapter 2.7 --- Riemann-Hurwritz formula --- p.17 / Chapter 3 --- The Montel Theorem / Chapter 3.1 --- Introduction --- p.21 / Chapter 3.2 --- Normality and Equicontinuous --- p.21 / Chapter 3.3 --- Local boundedness --- p.23 / Chapter 3.4 --- Covering and uniformization --- p.26 / Chapter 3.5 --- Montel's theorem --- p.28 / Chapter 4 --- Fatou Set and Julia Set / Chapter 4.1 --- Iteration of functions --- p.31 / Chapter 4.2 --- Fatou set and Julia set --- p.35 / Chapter 4.3 --- Iteration of Mobius transformtion --- p.39 / Chapter 4.4 --- Fixed points and their classification --- p.44 / Chapter 4.5 --- Periodic points and cycles --- p.45 / Chapter 4.6 --- Critical points --- p.47 / Chapter 4.7 --- Dlustractions of local behaviour of map near periodic points --- p.48 / Chapter 5 --- More about Julia Set / Chapter 5.1 --- Some examples of Julia set --- p.57 / Chapter 5.2 --- Completely invariant set --- p.58 / Chapter 5.3 --- Exceptional set --- p.61 / Chapter 5.4 --- Properties of Julia set --- p.63 / Chapter 5.5 --- Forward and backward convergence of sets --- p.66 / Chapter 6 --- More about Fatou Set / Chapter 6.1 --- Components of Fatou set --- p.97 / Chapter 6.2 --- Simply connected Fatou components --- p.98 / Chapter 6.3 --- Number of components in Fatou set --- p.100 / Chapter 6.4 --- Classification of forward invariant components of the Fatou set --- p.102 / Chapter 6.5 --- Examples illustrating the five possible forward invariant components --- p.104 / Chapter 7 --- Critical Points / Chapter 7.1 --- Introduction --- p.108 / Chapter 7.2 --- Some interesting results --- p.110 / Chapter 7.3 --- The Fatou set of polynomials --- p.114 / Chapter 7.4 --- Quadratic polynomial and Mandelbrot set --- p.116 / Appendix --- p.125 / Reference --- p.136

Thesis (Ph.D.)--Baylor University, 2007. / In abstract "n, ri1, and sj-1" are superscript. In abstract "1, k, n-k, k-1, and nk-1" are subscript. Includes bibliographical references (p. 82-84).

Thesis (M.S.)--University of Nevada, Reno, 2008. / "May, 2008." Includes bibliographical references (leaf 58). Online version available on the World Wide Web.

Thesis (M.Sc.) -- Memorial University of Newfoundland. 1973. / Typescript. Bibliography : leaves 69-76. Also available online.

Thesis (M.Sc.)--Memorial University of Newfoundland. / Bibliography : leaves 62-63. Also available online.

Thesis (B.S.)--Haverford College, Dept. of Mathematics, 2002. / Includes bibliographical references.

In recent decades, significant interest, based on physics and engineering applications, has developed on so-called anomalous diffusion processes that possess different spread functions with classical ones. The resulting differential equation whose fundamental solution matches this decay process is best modeled by an equation containing a fractional order derivative. This dissertation mainly focuses on some inverse problems for fractional diffusion equations. After some background introductions and preliminaries in Section 1 and 2, in the third section we consider our first inverse boundary problem. This is where an unknown boundary condition is to be determined from overposed data in a time- fractional diffusion equation. Based upon the fundamental solution in free space, we derive a representation for the unknown parameters as the solution of a nonlinear Volterra integral equation of second kind with a weakly singular kernel. We are able to make physically reasonable assumptions on our constraining functions (initial and given boundary values) to be able to prove a uniqueness and reconstruction result. This is achieved by an iterative process and is an immediate result of applying a certain fixed point theorem. Numerical examples are presented to illustrate the validity and effectiveness of the proposed method. In the fourth section a reaction-diffusion problem with an unknown nonlinear source function, which has to be determined from overposed data, is considered. A uniqueness result is proved and a numerical algorithm including convergence analysis under some physically reasonable assumptions is presented in the one-dimensional case. To show effectiveness of the proposed method, some results of numerical simulations are presented. In Section 5, we also attempted to reconstruct a nonlinear source in a heat equation from a number of known input sources. This represents a new research even for the case of classical diffusion and would be the first step in a solution method for the fractional diffusion case. While analytic work is still in progress on this problem, Newton and Quasi-Newton method are applied to show the feasibility of numerical reconstructions. In conclusion, the fractional diffusion equations have some different properties with the classical ones but there are some similarities between them. The classical tools like integral equations and fixed point theory still hold under slightly different assumptions. Inverse problems for fractional diffusion equations have applications in many engineering and physics areas such as material design, porous media. They are trickier than classical ones but there are also some advantages due to the mildly ill-conditioned singularity caused by the new kernel functions.

Author's `Characterization of subgradients: 1` (31 leaves) in pocket / Bibliography: leaves 229-231 / 231 leaves : 1 port ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, 1986

Thesis (Ph.D.)--Baylor University, 2007. / Includes bibliographical references (p. 64-66).