Browsing Applied Mathematics by Issue Date
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Contributions to the study of general relativistic shearfree perfect fluids: an approach involving Cartan's equivalence method, differential forms and symbolic computation
(University of Waterloo, 1993)It has been conjectured that general relativistic shearfree perfect ﬂuids with a barotropic equation of state, and such that the energy density, µ, and the pressure, p, satisfy µ + p ̸= 0, cannot simultaneously be rotating ... 
MultiResolution Approximate Inverses
(University of Waterloo, 1999)This thesis presents a new preconditioner for elliptic PDE problems on unstructured meshes. Using ideas from second generation wavelets, a multiresolution basis is constructed to effectively compress the inverse of the ... 
On the Solution of the HamiltonJacobi Equation by the Method of Separation of Variables
(University of Waterloo, 2000)The method of separation of variables facilitates the integration of the HamiltonJacobi equation by reducing its solution to a series of quadratures in the separable coordinates. The case in which the metric tensor is ... 
Contributions to the Study of the Validity of Huygens' Principle for the Nonselfadjoint Scalar Wave Equation on Petrov Type D Spacetimes
(University of Waterloo, 2000)This thesis makes contributions to the solution of Hadamard's problem through an examination of the question of the validity of Huygens'principle for the nonselfadjoint scalar wave equation on a Petrov type D spacetime. ... 
A Probabilistic Approach to Image Feature Extraction, Segmentation and Interpretation
(University of Waterloo, 2000)This thesis describes a probabilistic approach to imagesegmentation and interpretation. The focus of the investigation is the development of a systematic way of combining color, brightness, texture and geometric features ... 
Two and ThreeDimensional Coding Schemes for Wavelet and FractalWavelet Image Compression
(University of Waterloo, 2001)This thesis presents two novel coding schemes and applications to both two and threedimensional image compression. Image compression can be viewed as methods of functional approximation under a constraint on the amount ... 
Complex Bases, Number Systems and Their Application to FractalWavelet Image Coding
(University of Waterloo, 2002)This thesis explores new approaches to the analysis of functions by combining tools from the fields of complex bases, number systems, iterated function systems (IFS) and wavelet multiresolution analyses (MRA). The ... 
The de BroglieBohm Causal Interpretation of Quantum Mechanics and its Application to some Simple Systems
(University of Waterloo, 2003)The de BroglieBohm causal interpretation of quantum mechanics is discussed, and applied to the hydrogen atom in several contexts. Prominent critiques of the causal program are noted and responses are given; it is argued ... 
WellPosedness of Boundary Control Systems
(Society for Industrial and Applied Mathematics, 20030101)Continuity of the input/output map for boundary control systems is shown through the system transfer function. Our approach transforms the question of continuity of the input/output map of a boundary control system to ... 
Impulsive Control and Synchronization of ChaosGeneratingSystems with Applications to Secure Communication
(University of Waterloo, 2004)When two or more chaotic systems are coupled, they may exhibit synchronized chaotic oscillations. The synchronization of chaos is usually understood as the regime of chaotic oscillations in which the corresponding ... 
Probabilistic Properties of Delay Differential Equations
(University of Waterloo, 2004)Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, <em>i. e. </em> in terms of the evolution of probability distributions rather than individual trajectories. This ... 
The Dynamics of Inhomogeneous Cosmologies
(University of Waterloo, 2004)In this thesis we investigate cosmological models more general than the isotropic and homogeneous FriedmannLemaître models. We focus on cosmologies with one spatial degree of freedom, whose matter content ... 
The modeling of blood rheology in small vessels
(University of Waterloo, 2005)Blood is a dense suspension of flexible red blood cells. In response to a background flow, these cells distribute themselves nonuniformly throughout the vessel. As a result, material properties that are well defined ... 
Synchronization in Heterogeneous Networks of Hippocampal Interneurons
(University of Waterloo, 2005)The hippocampus is one of the most intensely studied brain structures and the oscillatory activity of the hippocampal neurons is believed to be involved in learning and memory consolidation. Therefore, studying rhythm ... 
Multiscale Methods in Image Modelling and Image Processing
(University of Waterloo, 2005)The field of modelling and processing of 'images' has fairly recently become important, even crucial, to areas of science, medicine, and engineering. The inevitable explosion of imaging modalities and approaches ... 
Mutual Information Based Methods to Localize Image Registration
(University of Waterloo, 2005)Modern medicine has become reliant on medical imaging. Multiple modalities, e. g. magnetic resonance imaging (MRI), computed tomography (CT), etc. , are used to provide as much information about the patient as ... 
Detectability of Singularly Perturbed Systems
(University of Waterloo, 2005)A form of detectability, known as the inputoutputtostate stability property, for singularly perturbed systems is examined in this work. This work extends the result of a paper by Christofides & Teel wherein they ... 
Consolidation and wave propagation in a porous medium
(University of Waterloo, 2006)Basic diffusion analytical solutions of onedimensional consolidation are presented for the case of a semiinfinite domain. Typical tractions considered include instantaneous loads of the medium with a free boundary ... 
Improving Coarsening and Interpolation for Algebraic Multigrid
(University of Waterloo, 2006)Algebraic multigrid (AMG) is one of the most efficient algorithms for solving large sparse linear systems on unstructured grids. Classical coarsening schemes such as the standard RugeStüben method [14] can lead ... 
Numerical Study of a Viscoelastic Model for Hydrocephalus
(University of Waterloo, 2006)Hydrocephalus is a clinical conditon where the brain tissue is deformed by the expanding ventricules. In this thesis, the mechanical deformation of a hydrocephalic brain is studied using a biomechanical model, where the ...