This body of work examines the plausibility of applying partial di erential equations and time-fractional partial di erential equations to images. The standard di usion equation is coupled with a nonlinear cubic source term of the Fitzhugh-Nagumo type to obtain a model with di usive properties and a binarizing e ect due to the source term. We examine the e ects of applying this model to a class of images known as document images; images that largely comprise text. The e ects of this model result in a binarization process that is competitive with the state-of-the-art techniques. Further to this application, we provide a stability analysis of the method as well as high-performance implementation on general purpose graphical processing units. The model is extended to include time derivatives to a fractional order which a ords us another degree of control over this process and the nature of the fractionality is discussed indicating the change in dynamics brought about by this generalization. We apply a semi-discrete method derived by hybridizing the Laplace transform and two discretization methods: nite-di erences and Chebyshev collocation. These hybrid techniques are coupled with a quasi-linearization process to allow for the application of the Laplace transform, a linear operator, to a nonlinear equation of fractional order in the temporal domain. A thorough analysis of these methods is provided giving rise to conditions for solvability. The merits and demerits of the methods are discussed indicating the appropriateness of each method.

A research report submitted to the Faculty of Science, University of the Witwatersrand, in ful lment of the requirements for the degree of Master of Science. School of Mathematics Johannesburg February 15, 2016 / We obtain a solution of the Black-Scholes equation with a non-smooth bound- ary condition using symmetry methods. The Black-Scholes equation along with its boundary condition are rst transformed into the one dimensional heat equation and an initial condition respectively. We then nd an appro- priate general symmetry generator of the heat equation using symmetries of the heat equation and the fundamental solution of the heat equation. The method we use to nd the symmetry generator is such that the boundary condition is left invariant and yet the symmetry can still be used to solve the heat equation. We then use the help of Mathematica to nd the solution to the heat equation. Then the solution is then transformed backwards to a solution of the Black-Scholes equation using the same change of variables that were used for the forward transformations. The solution is then nally checked if it satis es the boundary condition of the Black-Scholes equation.

Zhou, Qianwen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 80-87). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.

Digitized by Kansas Correctional Industries

Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1909. / "Estratto dal tomo XXVIII (2 sem. 1909)del Rendiconti del Circolo matematico di Palermo"--P. 1. Vita.

Inaug.-Diss.-Bonn.

No description available.

No description available.

Thesis ( Ph.D. ) -- McMaster University, 1997. / Includes bibliographical references (leaves 63-66). Also available via World Wide Web.

Thesis (Ph.D.)--McMaster University (Canada), 1996. / Source: Dissertation Abstracts International, Volume: 57-10, Section: B, page: 6300. Adviser: H. P. Heinig.