Mathematics (MS)
Recent Submissions

[20160825] Some Notes on Compressive Sensing
We are living in a world in which the growth rate of the data generated every year is almost exponential. A significant problem is how we can store this amount of data. Compressive sensing is giving us a clue about how we ... 
[20160825] Jost Functions for Jacobi Operators with Superexponentially Decaying Parameters
The decay of the parameters for a Jacobi operator is related to the analyticity of the Jost function associated with J, which is in turn related to the spectral measure of J. Damanik and Simon demonstrated the equivalence ... 
[20160201] Closure Operations on Subgroups
During the past five years, a number of mathematicians have conducted research involving closure operations on the ideals of commutative rings. The most accessible paper on this is written by Neil Epstein, entitled "A ... 
[20150128] Performance Analysis and Optimization of Hermite Methods on NVIDIA GPUs Using CUDA
In this thesis we present the first, to our knowledge, implementation and performance analysis of Hermite methods on GPU accelerated systems. We give analytic background for Hermite methods; give implementations of the ... 
[20150128] The Hilbert Transform as an Average of Dyadic Shift Operators
In this thesis we discuss Petermichl’s characterization of the Hilbert transform as an average of dyadic shift operators following the presentation by Thomas Hytonen [Hyt]. A linear and bounded operator T in L2(R) that ... 
[20140912] On Roots of the Macdonald Function
An overview is given for the DirichlettoNeumann map for outgoing solutions to the “radial wave equation” in the context of nonreflecting radiation boundary conditions on a spherical domain. We then consider the Macdonald ... 
[20130903] Preconditioners constructed from the interpolative decomposition for the variable coefficient Poisson problem
When trying to solve elliptical problems such as the Poisson problem on complicated domains, one procedure is to split the domain into a union of simpler subdomains. When solving these problems iteratively, it becomes ... 
[20130903] Lattice points in disks and strongly convex domains
This thesis examines the history and some major results of the Gauss Circle Problem. The goal of the Gauss Circle Problem is to determine the best bound for the error between the number of lattice points inside a disk and ... 
[20130130] Numerical simulation of traffic flow using a hydrodynamic model
We examine the solution to the system of partial differential equations for the transport and continuity equations. The model for our system of equations closely resembles the PayneWhitham model for traffic flow. The ... 
[20120316] The effects of temperature forcing on dengue dynamics via the extrinsic incubation period
Dengue fever is a mosquitotransmitted disease that is endemic in many parts of the tropical world and affects a significant proportion of the human population. Temperature is known to influence aspects of the dengue ... 
[20120201] Closure operations on the submonoids of the natural numbers
We examine the algebraic structure of closure, semiprime and prime operations on submonoids of natural numbers. We find that the closure operations under composition do not form a submonoid under composition. We also ... 
[20120201] Achievement, anxiety, selfconcept and motivation among college algebra students within a cooperative learning structure
Cooperative learning methods have been shown to increase student achievement and social skills, therefore these methods have been promoted for the intervention of falling student achievement. This study was designed to ... 
[20120201] Two cylindrical vortex sheets : evolution and singularity formation
Using Rosenhead's pointvortex approximation with correction terms, the evolution of two symmetrical, counterrotating, initially cylindrical vortex sheets in an incompressible, potential fluid flow is studied. Simulations ... 
[20110701] Optimal control problems, curves of pursuit
We study a class of problems known as pursuitevasion problems (PE). These problems can be understood as special cases of optimal control problems. After describing the two main principles to study optimal control ... 
[20110207] Orthogonality and convergence of discrete Zernike polynomials
The Zernike polynomials are an inﬁnite set of orthogonal polynomials over the unit disk, which are rotationally invariant. They are frequently utilized in optics, opthal mology, and image recognition, among many other ... 
[20100909] Quantifying uncertainty in reliability block diagrams
Reliability analysis yields statistically derived technical system performance estimates. Traditional reliability analysis employs classical statistical techniques predicated upon asymptotic properties of large data sets. ... 
[20100903] Pell's Equation and nearly equilateral triangles
In this paper, we seek a family of triangles that have integer sides and integer area. We focus mainly on scalene triangles since it is impossible to have such triangles that are equilateral and isoceles triangles with ... 
[20100625] Spatial spread of infectious diseases
In this thesis we do a comparative study of diffusive models with nondiffusive models, looking at the effect movements in the form of simple diffusion have on the spreading of infectious diseases. This study is undertaken ... 
[20100219] Maintaining pathogens with short infectivity in seasonally structured tick populations: relative importance of three transmission pathways
Infectivity periods of different tickborne pathogens in host species can vary widely, and the variation affects how the pathogens are maintained in tick populations. In addition to systemic and vertical transmission, ... 
[20090827] High performance damper optimization using computer simulation and design of experiments
Design of experiments has become an increasingly popular tool used by racing teams in professional motorsports. A race car has literally hundreds of adjustable parameters associated with it. Specialized racing engineers ...