Browsing Mathematics (Faculty of) 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 ... 
Effcient Simulation of MessagePassing in DistributedMemory Architectures
(University of Waterloo, 1996)In this thesis we propose a distributedmemory parallelcomputer simulation system called PUPPET (Performance Under a PseudoParallel EnvironmenT). It allows the evaluation of parallel programs run in a pseudoparallel ... 
Simulated Overloading using Generic Functions in Scheme
(University of Waterloo, 1997)This thesis investigates extending the dynamicallytyped, functional programming language Scheme, with simulated overloading in order to permit the binding of multiple, distributed defnitions to function names. Overloading ... 
Classification of Nilpotent Lie Algebras of Dimension 7 (over Algebraically Closed Field and R)
(University of Waterloo, 1998)This thesis is concerned with the classification of 7dimensional nilpotent Lie algebras. Skjelbred and Sund have published in 1977 their method of constructing all nilpotent Lie algebras of dimension <i>n</i> given those ... 
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 ... 
Coherent Beta Risk Measures for Capital Requirements
(University of Waterloo, 1999)This thesis compares insurance premium principles with current financial risk paradigms and uses distorted probabilities, a recent development in premium principle literature, to synthesize the current models for financial ... 
Differential Equations and Depth First Search for Enumeration of Maps in Surfaces
(University of Waterloo, 1999)A map is an embedding of the vertices and edges of a graph into a compact 2manifold such that the remainder of the surface has components homeomorphic to open disks. With the goal of proving the Four Colour Theorem, ... 
Folding Orthogonal Polyhedra
(University of Waterloo, 1999)In this thesis, we study foldings of orthogonal polygons into orthogonal polyhedra. The particular problem examined here is whether a paper cutout of an orthogonal polygon with fold lines indicated folds up into a simple ... 
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 ... 
Variational Spectral Analysis
(University of Waterloo, 2000)We present results on smooth and nonsmooth variational properties of {it symmetric} functions of the eigenvalues of a real symmetric matrix argument, as well as {it absolutely symmetric} functions of the singular values ... 
A survey on Traitor Tracing Schemes
(University of Waterloo, 2000)When intellectual properties are distributed over a broadcast network, the content is usually encrypted in a way such that only authorized users who have a certain set of keys, can decrypt the content. Some authorized ... 
A survey of the trust region subproblem within a semidefinite framework
(University of Waterloo, 2000)Trust region subproblems arise within a class of unconstrained methods called trust region methods. The subproblems consist of minimizing a quadratic function subject to a norm constraint. This thesis is a survey of ... 
A Framework for MachineAssisted Software Architecture Validation
(University of Waterloo, 2000)In this thesis we propose a formal framework for specifying and validating properties of software system architectures. The framework is founded on a model of software architecture description languages (ADLs) and uses ... 
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 ... 
Matrix Formulations of Matching Problems
(University of Waterloo, 2000)Finding the maximum size of a matching in an undirected graph and finding the maximum size of branching in a directed graph can be formulated as matrix rank problems. The Tutte matrix, introduced by Tutte as a representation ... 
The Model Theory of Algebraically Closed Fields
(University of Waterloo, 2000)Model theory can express properties of algebraic subsets of complex nspace. The constructible subsets are precisely the first order definable subsets, and varieties correspond to maximal consistent collections of ... 
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. ... 
An Approximation Algorithm for Character Compatibility and Fast Quartetbased Phylogenetic Tree Comparison
(University of Waterloo, 2000)Phylogenetic analysis, or the inference of evolutionary history is done routinely by biologists and is one of the most important problems in systematic biology. In this thesis, we study two computational problems in ... 
A Formalization of an Extended Object Model Using Views
(University of Waterloo, 2000)Reuse of software designs, experience and components is essential to making substantial improvements in software productivity, development cost, and quality. However, the many facets of reuse are still rarely used in ... 
Hadez, a Framework for the Specification and Verification of Hypermedia Applications
(University of Waterloo, 2000)In recent years, several methodologies for the development of hypermedia applications have been proposed. These methodologies are, primarily, guidelines to be followed during the design process. They also indicate what ...