Browsing Mathematics by Issue Date

Now showing items 1-20 of 45

    • Local Risk Minimization Under Time-Varying Transaction Costs 

      Nitschke, Matthew Cody (North Dakota State University, 2010)
      Closely following the results of Lamberton, Pham, and Schweizer [5] we construct a locally risk-minimizing strategy in a general incomplete market including transactiou costs. This is done in dbcrete time under the ...

    • 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 ...

    • 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 ...

    • 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 ...

    • 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 ...

    • The Square of Adjacency Matrices 

      Kranda, Daniel Joseph (North Dakota State University, 2011)
      It can be shown that any symmetric (0, 1)-matrix A with tr A = 0 can be interpreted as the adjacency matrix of a simple, finite graph. The square of an adjacency matrix A2 = (si1) has the property that Sij represents the ...

    • 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], ...

    • 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 ...

    • 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.

    • 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 ...

    • 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 ...

    • Resolutions and Semidualizing Modules 

      Feickert, Aaron James (North Dakota State University, 2014)
      Projective and injective modules are of key importance in algebra, in part because of their useful homological properties. The notion of C-projective and C-injective modules generalizes these constructions. In particular, ...

    • Integral Closure and the Generalized Multiplicity Sequence 

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

    • 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 ...

    • 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.