Thesis (Ph.D.)--Flinders University, School of Informatics and Engineering. / Typescript bound. Includes bibliographical references: (leaves 174-180) and index. Also available online.

Thesis (doctoral)--Technische Universiteit Delft, 1997. / Also published in the series: Communications on hydraulic and geotechnical engineering ; no. 97-4. Vita. Includes bibliographical references (p. [127]-136).

Thesis (Ph.D.) - University of Glasgow, 2000. / Ph.D. thesis submitted to the Department of Mathematics, University of Glasgow, 2000. Includes bibliographical references. Print version also available.

Thesis (M.S.)--Rochester Institute of Technology, 1994. / Typescript. Bibliography: leaf 59.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

M.Sc. (Applied Mathematics) / A comparison between the recently developed spectral relaxation method (SRM) and the spectral local linearisation method (SLLM) is done for the first time in this work. Both spectral hybrid methods are employed in finding the solution to the non isothermal mass and heat balance model of a catalytic pellet boundary value problem (BVP) with finite mass and heat transfer resistance, which is a coupled system of singular nonlinear ordinary differential equations (ODEs). The SRM and the SLLM are applied, for the first time, to solve a problem with singularities. The solution by the SRM and the SLLM are validated against the results by bvp4c, a well known matlab built-in procedure for solving BVPs. Tables and graphs are used to show the comparison. The SRM and the SLLM are exceptionally accurate with the SLLM being the fastest to converge to the correct solution. We then construct a new spectral hybrid method which we named the spectral Adomian decomposition method (SADM). The SADM is used concurrently with the standard Adomian decomposition method (ADM) to solve well known models arising in fluid mechanics. These problems are the magneto hydrodynamic (MHD) Jeffery-Hamel flow model and the Darcy-Brinkman- Forchheimer momentum equations. The validity of the results by the SADM and ADM are verified by the exact solution and bvp4c solution where applicable. A simple alteration of the SADM is made to improve the performance.

This thesis uses the powerful mathematics of wavelet packet signal processing to efficiently extract features from sampled acoustic spectra for the purpose of discriminating between different classes of sounds. An algorithm called dictionary projection pursuit (DPP) is developed which is a fast approximate version of the projection pursuit (PP) algorithm [P.J. Huber Projection Pursuit, Annals of Statistics, 13 ( 2) 435–525, 1985]. When used with a wavelet packet or cosine packet dictionary, this algorithm is significantly faster than the PP algorithm with relatively little degradation in performance provided that the multivariate vectors are samples of an underlying continuous waveform or image. The DPP algorithm is applied to the problem of approximating the Karhunen-Loève transform (KLT) in high dimensional spaces and simulations are performed to compare this algorithm to Wickerhauser's approximate KLT algorithm [M.V. Wickerhauser. Adapted Wavelet Analysis from Theory to Software, A.K. Peters Ltd, 1994]. Both algorithms perform very well relative to the eigenanalysis form of the KLT algorithm at a small fraction of the computational cost. The DPP algorithm is then applied to the problem of finding discriminant features in acoustic spectra for sound recognition tasks; extensive simulations are performed to compare this algorithm to previously developed dictionary methods for discrimination such as Saito and Coifman's local discriminant bases [N. Saito and R. Coifman. Local Discriminant Bases and their Applications. Journal of Mathematical Imaging and Vision, 5 (4) 337–358, 1995] and Buckheit and Donoho's discriminant pursuit [J. Buckheit and D. Donoho. Improved Linear Discrimination Using Time-Frequency Dictionaries. Proceedings of SPIE Wavelet Applications in Signal and Image Processing III Vol 2569, 540–551, July, 1995]. It is found that each feature extraction algorithm performs well under different conditions, but the DPP algorithm is the most flexible and consistent performer. / Graduate

M.Sc.

No description available.

The spectral theory of the Laplace operator has long been studied in connection with physics. It appears in the wave equation, the heat equation, Schroedinger's equation and in the expression of quantum effects such as the Casimir force. The Casimir effect can be studied in terms of spectral invariants computed entirely from the spectrum of the Laplace operator. It is these spectral invariants and their computation that are the object of study in the present work. The objective of this thesis is to present a computational framework for the spectral zeta function $\zeta(s)$ and its derivative on a Euclidean domain in $\mathbb{R}^2$, with rigorous theoretical error bounds when this domain is polygonal. To obtain error bounds that remain practical in applications an improvement to existing heat trace estimates is necessary. Our main result is an original estimate and proof of a heat trace estimate for polygons that improves the one of van den Berg and Srisatkunarajah, using finite propagation speed of the corresponding wave kernel. We then use this heat trace estimate to obtain a rigorous error bound for $\zeta(s)$ computations. We will provide numerous examples of our computational framework being used to calculate $\zeta(s)$ for a variety of situations involving a polygonal domain, including examples involving cutouts and extrusions that are interesting in applications. Our second result is the development a new eigenvalue solver for a planar polygonal domain using a partition of unity decomposition technique. Its advantages include multiple precision and ease of use, as well as reduced complexity compared to Finite Elemement Method. While we hoped that it would be able to contend with existing packages in terms of speed, our implementation was many times slower than MPSPack when dealing with the same problem (obtaining the first 5 digits of the principal eigenvalue of the regular unit hexagon). Finally, we present a collection of numerical examples where we compute the spectral determinant and Casimir energy of various polygonal domains. We also use our numerical tools to investigate extremal properties of these spectral invariants. For example, we consider a square with a small square cut out of the interior, which is allowed to rotate freely about its center.