Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 79-83). Also available on the Internet.

Thesis (M. Phil.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 55-59). Also available in print.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, August 2003. / Includes bibliographical references. Also available on the Internet.

This thesis present a new algorithm for creating high quality surfaces from large data sets of oriented points, sampled using a laser range scanner. This method works in two phases. In the first phase, using wavelet surface reconstruction method, we calculate a rough estimate of the surface in the form of Haar wavelet coefficients, stored in an Octree. In the second phase, we modify these coefficients to obtain a higher quality surface. We cast this method as a gradient minimization problem in the wavelet domain. We show that the solution to the gradient minimization problem, in the wavelet domain, is a sparse linear system with dimensionality roughly proportional to the surface of the model in question. We introduce a fast inplace method, which uses various properties of Haar wavelets, to solve the linear system and demonstrate the results of the algorithm.

Thesis (Ph.D.)--York University, 2008. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 102-108). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:NR51694

We establish the existence of radial solutions to the p-Laplacian equation ∆p u + f(u)=0 in RN, where f behaves like |u|q-1 u when u is large and f(u) < 0 for small positive u. We show that for each nonnegative integer n, there is a localized solution u which has exactly n zeros. Also, we look for radial solutions of a superlinear Dirichlet problem in a ball. We show that for each nonnegative integer n, there is a solution u which has exactly n zeros. Here we give an alternate proof to that which was given by Castro and Kurepa.

published_or_final_version / abstract / Mathematics / Doctoral / Doctor of Philosophy

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

There are numerous applications of mathematics, specifically spectral graph theory, within the sciences and many other fields. This paper is an exploration of recent applications of spectral graph theory, including the fields of chemistry, biology, and graph coloring. Topics such as the isomers of alkanes, the importance of eigenvalues in protein structures, and the aid that the spectra of a graph provides when coloring a graph are covered, as well as others.The key definitions and properties of graph theory are introduced. Important aspects of graphs, such as the walks and the adjacency matrix are explored. In addition, bipartite graphs are discussed along with properties that apply strictly to bipartite graphs. The main focus is on the characteristic polynomial and the eigenvalues that it produces, because most of the applications involve specific eigenvalues. For example, if isomers are organized according to their eigenvalues, a pattern comes to light. There is a parallel between the size of the eigenvalue (in comparison to the other eigenvalues) and the maximum degree of the graph. The maximum degree of the graph tells us the most carbon atoms attached to any given carbon atom within the structure. The Laplacian matrix and many of its properties are discussed at length, including the classical Matrix Tree Theorem and Cayley's Tree Theorem. Also, an alternative approach to defining the Laplacian is explored and compared to the traditional Laplacian.

Wong Chun Wai Carto. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 78-80). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.4 / Chapter 2 --- The Probabilistic Approach --- p.9 / Chapter 2.1 --- Diffusion on the Sierpinski gasket --- p.9 / Chapter 2.2 --- A Laplacian from the diffusion process --- p.18 / Chapter 2.3 --- Other ramifications --- p.24 / Chapter 3 --- The Analytic Approach --- p.28 / Chapter 3.1 --- Discrete Laplacians on finite sets --- p.28 / Chapter 3.2 --- Laplacian from a compatible sequence --- p.33 / Chapter 3.3 --- Compatible sequence from a harmonic structures --- p.40 / Chapter 3.4 --- Existence theorem for harmonic structures --- p.50 / Chapter 4 --- On Two Related Classes of Symmetric Polytopes --- p.55 / Chapter 4.1 --- Symmetries and regular polytopes --- p.56 / Chapter 4.2 --- Classification of highly symmetric polytopes --- p.62 / Chapter 4.3 --- Classification of strongly symmetric polytopes --- p.66 / Bibliography --- p.78