Browsing Mathematics by Title

Now showing items 1-20 of 42

    • Absolute Stability of a Class of Second Order Feedback Non-Linear, Time-Varying Systems 

      Omotoyinbo, Tayo (North Dakota State University, 2010)
      In this thesis, we consider the problem of absolute stability of continuous time feedback systems with a single, time-varying nonlinearity. Necessary and sufficient conditions for absolute stability of second-order systems ...

    • Almost Dedekind Domains and Atomicity 

      Hasenauer, Richard Erwin (North Dakota State University, 2012)
      The objective of this dissertation was to determine the class of domains that are both almost Dedekind and atomic. To investigate this question we constructed a global object called the norm, and used it to determine ...

    • 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 ...

    • 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 ...

    • 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 ...

    • Bifurcation Portrait of a Hybrid Spiking Neuron Model 

      Goodell, Brandon Grae (North Dakota State University, 2012)
      A bifurcation portrait classifies the behavior of a dynamical system and how it transitions between different behaviors. A hybrid dynamical system displays both continuous and discrete dynamics and may display nonsmooth ...

    • Codualizing Modules and Complexes 

      Wicklein, Richard Kenneth (North Dakota State University, 2013)
      See dissertation for full abstract and properly formatted mathematical formulas.

    • Colorings of Zero-Divisor Graphs of Commutative Rings 

      Ramos, Rebecca Elizabeth (North Dakota State University, 2015)
      We will focus on Beck’s conjecture that the chromatic number of a zero-divisor graph of a ring R is equal to the clique number of the ring R. We begin by calculating the chromatic number of the zero-divisor graphs for some ...

    • DG Homological Algebra, Properties of Ring Homomorphisms, and the Generalized Auslander-Reiten Conjecture 

      Nasseh, Saeed (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 ...

    • Enumeration of Reduced Words of Length N for Coxeter Groups via BrinkHowlett Automaton 

      Allen, Brandon James (North Dakota State University, 2022)
      The overall goal of this paper is to give a method of computing out how many words of length n there are for any Coxeter group via its Brink-Howlett automaton. [6] [7] To build our automaton, we focus on Coxeter systems ...

    • 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)

    • Hook Formula For Skew Shapes 

      Jensen, Megan Lisa (North Dakota State University, 2019)
      The number of standard Young tableaux is given by the hook-length formula of Frame, Robinson, and Thrall. Recently, Naruse found a hook-length formula for the number of skew shaped standard Young tableaux. In a series of ...

    • 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 ...