Mathematics: Recent submissions

Now showing items 21-40 of 45

    • 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 ...

    • Understanding Students’ Perceptions of Difficulty and the Effect Difficulty Has on Mathematical Anxiety 

      Larson, Caleb Bridger (North Dakota State University, 2018)
      There exists a growing atmosphere surrounding mathematics that allows individuals to exclaim their belief they are deficient in math without any societal judgement. Compared to a state like being illiterate, we have reached ...

    • 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 ...

    • A New Generalization of Cohen-Kaplansky Domains 

      Kennedy, Diana Michelle (North Dakota State University, 2015)
      The goal of this thesis is to provide an new generalization of Cohen-Kaplansky domains, stemming from questions related to valuation domains. Recall that a Cohen-Kaplansky domain is an atomic integral domain that contains ...

    • 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 ...

    • Variational Methods for Polycrystal Plasticity and Related Topics in Partial Differential Equations 

      Abdullayev, Farhod (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 ...

    • 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 ...

    • Codualizing Modules and Complexes 

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

    • 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 ...

    • 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 ...

    • 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], ...

    • Subfractals Induced by Subshifts 

      Sattler, Elizabeth (North Dakota State University, 2016)
      In this thesis, a subfractal is the subset of points in the attractor of an iterated function system in which every point in the subfractal is associated with an allowable word from a subshift on the underlying symbolic ...