Browsing Mathematics Doctoral Work by Title
Now showing items 3-22 of 30
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Applications of Groups of Divisibility and a Generalization of Krull Dimension
(North Dakota State University, 2011)Groups of divisibility have played an important role in commutative algebra for many years. In 1932 Wolfgang Krull showed in [12] that every linearly ordered Abelian group can be realized as the group of divisibility of a ... -
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 ... -
Codualizing Modules and Complexes
(North Dakota State University, 2013)See dissertation for full abstract and properly formatted mathematical formulas. -
DG Homological Algebra, Properties of Ring Homomorphisms, and the Generalized Auslander-Reiten Conjecture
(North Dakota State University, 2013)This dissertation contains three aspects of my research that are listed as three joint papers with my advisor and a solo paper in the bibliography [56]--[59]. Each paper will be discussed in a different chapter. Chapter 1 ... -
The First Exit-Time Analysis of an Approximate Barndorff-Nielsen and Shephard Model, with Data Science-Based Applications in the Commodity Market
(North Dakota State University, 2021)In this dissertation, an approximate version of the Barndorff-Nielsen and Shephard model, driven by a Brownian motion and a Lévy subordinator, is formulated. The first-exit time of the log-return process for this model is ... -
The Game of Nim on Graphs
(North Dakota State University, 2011)The ordinary game of Nim has a long history and is well-known in the area of combinatorial game theory. The solution to the ordinary game of Nim has been known for many years and lends itself to numerous other solutions ... -
Gorenstein Dimension over Some Rings of the Form R [0 plus]C
(North Dakota State University, 2015)Commutative algebra is the study of commutative rings and other abstract structures based on commutative rings. Modules can be viewed as a common generalization of several of those structures, and some invariants, e.g. ... -
The Half-Factorial Property in Polynomial Rings
(North Dakota State University, 2014)This dissertation investigates the following question: If R is a half-factorial domain (HFD) and x is an indeterminate, under what conditions is the polynomial ring R[x] an HFD? The question has been answered in a few ... -
Homological Dimensions with Respect to a Semidualizing Complex
(North Dakota State University, 2015)See Dissertation Document for Full Abstract (Mathematical Symbols Included) -
Hypothesis Testing on Time Series Driven by Underlying Lévy Processes, with Machine Learning Applications
(North Dakota State University, 2021)In this dissertation, we study the testing of hypotheses on streams of observations that are driven by Lévy processes. This is applicable for sequential decision making on the state of two-sensor systems. In one case, each ... -
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 ... -
Integral Closure and the Generalized Multiplicity Sequence
(North Dakota State University, 2015)See Dissertation Document for Full Abstract (Mathematical Symbols Included) -
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 ... -
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 ... -
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 ... -
Maximally Edge-Colored Directed Graph Algebras
(North Dakota State University, 2017)Graph C*-algebras are constructed using projections corresponding to the vertices of the graph, and partial isometries corresponding to the edges of the graph. Here, we use the gauge-invariant uniqueness theorem to first ... -
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 ... -
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. -
Multidimensional Toggle Dynamics
(North Dakota State University, 2018)J. Propp and T. Roby isolated a phenomenon in which a statistic on a set has the same average value over any orbit as its global average, naming it homomesy. One set they investigated was order ideals of partially ordered ... -
NAK for Ext, Ascent of Module Structures, and the Blindness of Extended Modules
(North Dakota State University, 2012)This dissertation investigates the interplay between properties of Ext modules and ascent of module structures along ring homomorphisms. First, we consider a flat local ring homomorphism ϕ: (R, [special characters omitted], ...