Browsing Mathematics Doctoral Work by Title

Now showing items 7-26 of 30

    • The First Exit-Time Analysis of an Approximate Barndorff-Nielsen and Shephard Model, with Data Science-Based Applications in the Commodity Market 

      Awasthi, Shantanu (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 

      Erickson, Lindsay Anne (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 

      Aung, Pye Phyo (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 

      Batell, Mark Thomas (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 

      Totushek, Jonathan (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 

      Roberts, Michael (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 

      Al-Kaseasbeh, Saba Zakariya (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 

      Dunn, Thomas Boyd (North Dakota State University, 2015)
      See Dissertation Document for Full Abstract (Mathematical Symbols Included)

    • Knot Groups and Bi-Orderable HNN Extensions of Free Groups 

      Martin, Cody Michael (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 

      Spanier, Mark Andrew (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 

      Sarfo Amponsah, Eric (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 

      Brownlee, Erin Ann (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 

      Habtemicael, Semere Kidane (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 

      Habtemicael, Semere Kidane (North Dakota State University, 2015)
      Video summarizing Ph.D. dissertation for a non-specialist audience.

    • Multidimensional Toggle Dynamics 

      Vorland, Corey (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 

      Anderson, Benjamin John (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], ...

    • On Partial Permutations and Alternating Sign Matrices: Bijections and Polytopes 

      Heuer, Dylan (North Dakota State University, 2021)
      Motivated by the study of chained permutations and alternating sign matrices, we investigate partial permutations and alternating sign matrices. We give a length generating function for partial permutations and show ...

    • Optimization Problems Arising in Stability Analysis of Discrete Time Recurrent Neural Networks 

      Singh, Jayant (North Dakota State University, 2016)
      We consider the method of Reduction of Dissipativity Domain to prove global Lyapunov stability of Discrete Time Recurrent Neural Networks. The standard and advanced criteria for Absolute Stability of these essentially ...

    • Ramification and Infinite Extensions of Dedekind Domains 

      Hashbarger, Carl Stanley (North Dakota State University, 2010)
      This dissertation presents methods for determining the behavior of prime ideals m an integral extension of a Dedekind domain. One tool used to determine this behavior is an algorithm that computes which prime ideals ...

    • Semidualizing DG Modules over Tensor Products 

      Altmann, Hannah Lee (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 ...