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Mathematical Modeling of Epidemics: Parametric Heterogeneity and Pathogen Coexistence
(North Dakota State University, 2020)
No two species can indefinitely occupy the same ecological niche according to the competitive exclusion principle. When competing strains of the same pathogen invade a homogeneous population, the strain with the largest ...
Knot Groups and Bi-Orderable HNN Extensions of Free Groups
(North Dakota State University, 2020)
Suppose K is a fibered knot with bi-orderable knot group. We perform a topological winding operation to half-twist bands in a free incompressible Seifert surface Σ of K. This results in a Seifert surface Σ' with boundary ...
Codualizing Modules and Complexes
(North Dakota State University, 2013)
See dissertation for full abstract and properly formatted mathematical formulas.
Variational Methods for Polycrystal Plasticity and Related Topics in Partial Differential Equations
(North Dakota State University, 2013)
In the first part of the thesis the effective yield set of ionic polycrystals is characterized by means of variational principles in L∞ that are associated to supremal functionals acting on matrix-valued divergence-free ...
Semidualizing DG Modules over Tensor Products
(North Dakota State University, 2015)
In this dissertation, we study rings: sets with addition, subtraction, and multiplication. One way to study a ring is by studying its modules: the algebraic objects the ring acts on. Since it is impractical to study all ...
Atomicity in Rings with Zero Divisors
(North Dakota State University, 2011)
In this dissertation, we examine atomicity in rings with zero divisions. We begin by examining the relationship between a ring’s level of atomicity and the highest level of irreducibility shared by the ring’s irreducible ...
Ideal Graphs
(North Dakota State University, 2014)
In this dissertation, we explore various types of graphs that can be associated to a commutative ring with identity. In particular, if R is a commutative ring with identity, we consider a number of graphs with the vertex ...
Modeling Swap and Geophysical Analysis using Barndorff-Nielson and Shephard Model
(North Dakota State University, 2015)
Video summarizing Ph.D. dissertation for a non-specialist audience.
L1 Approximation in De Branges Spaces
(North Dakota State University, 2015)
In this thesis we study bandlimited approximations to various functions. Bandlimited functions
have compactly supported Fourier transforms, which is a desirable feature in many applications.
In particular, we address the ...
Modeling Financial Swaps and Geophysical data Using the Barndorff-Nielsen and Shephard Model
(North Dakota State University, 2015)
This dissertation uses Barndoff-Nielsen and Shephard (BN-S) models to model swap, a type of financial derivative, and analyze geophysical data for estimation of major earthquakes. From empirical observation of the stock ...