Recent Submissions

  • 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 ...
  • 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 ...
  • Some Results on Semicrossed Products and Related Operator Algebras 

    Duchsherer, Melissa (North Dakota State University, 2021)
    We investigate various properties of two classes of operator algebras: directed graph operator algebras and semicrossed products. First we consider analytic structure in the form of derivations and point derivations on ...
  • 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 ...
  • 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 ...
  • 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 ...
  • Analysis of Variance Based Financial Instruments and Transition Probability Densities Swaps, Price Indices, and Asymptotic Expansions 

    Issaka, Aziz (North Dakota State University, 2018)
    This dissertation studies a couple of variance-dependent instruments in the financial market. Firstly, a number of aspects of the variance swap in connection to the Barndorff-Nielsen and Shephard model are studied. A partial ...
  • Atomicity in Rings with Zero Divisors 

    Trentham, Stacy Michelle (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 ...
  • Applications of Groups of Divisibility and a Generalization of Krull Dimension 

    Trentham, William Travis (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 ...
  • Sign Matrix Polytopes 

    Solhjem, Sara Louise (North Dakota State University, 2018)
    Motivated by the study of polytopes formed as the convex hull of permutation matrices and alternating sign matrices, several new families of polytopes are defined as convex hulls of sign matrices, which are certain ...
  • 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 ...
  • 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 ...
  • Integral Closure and the Generalized Multiplicity Sequence 

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

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