Mathematics
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Research from the Department of Mathematics. The department website may be found at https://www.ndsu.edu/math/
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Local Risk Minimization Under TimeVarying Transaction Costs
(North Dakota State University, 2010)Closely following the results of Lamberton, Pham, and Schweizer [5] we construct a locally riskminimizing 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 NonLinear, TimeVarying Systems
(North Dakota State University, 2010)In this thesis, we consider the problem of absolute stability of continuous time feedback systems with a single, timevarying nonlinearity. Necessary and sufficient conditions for absolute stability of secondorder systems ... 
The First ExitTime Analysis of an Approximate BarndorffNielsen and Shephard Model, with Data ScienceBased Applications in the Commodity Market
(North Dakota State University, 2021)In this dissertation, an approximate version of the BarndorffNielsen and Shephard model, driven by a Brownian motion and a Lévy subordinator, is formulated. The firstexit time of the logreturn process for this model is ... 
New Perspectives on Promotion and Rowmotion: Generalizations and Translations
(North Dakota State University, 2022)We define Pstrict labelings for a finite poset P as a generalization of semistandard Young tableaux and show that promotion on these objects is in equivariant bijection with a toggle action on Bbounded Qpartitions of ... 
The Square of Adjacency Matrices
(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 ... 
Enumeration of Reduced Words of Length N for Coxeter Groups via BrinkHowlett Automaton
(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 BrinkHowlett automaton. [6] [7] To build our automaton, we focus on Coxeter systems ... 
The Game of Nim on Graphs
(North Dakota State University, 2011)The ordinary game of Nim has a long history and is wellknown 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
(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
(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
(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 twosensor systems. In one case, each ... 
Stochastic Processes, and Development of the BarndorffNielsen and Shephard Model for Financial Markets
(North Dakota State University, 2022)In this paper, we introduce Brownian motion, and some of its drawbacks in connection to the financial modeling. We then introduce geometric Brownian motion as the basis for European call option pricing as we navigate our ... 
Mathematical Modeling of Epidemics: Parametric Heterogeneity and Pathogen Coexistence
(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 BiOrderable HNN Extensions of Free Groups
(North Dakota State University, 2020)Suppose K is a fibered knot with biorderable knot group. We perform a topological winding operation to halftwist 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
(North Dakota State University, 2018)This dissertation studies a couple of variancedependent instruments in the financial market. Firstly, a number of aspects of the variance swap in connection to the BarndorffNielsen and Shephard model are studied. A partial ... 
Hook Formula For Skew Shapes
(North Dakota State University, 2019)The number of standard Young tableaux is given by the hooklength formula of Frame, Robinson, and Thrall. Recently, Naruse found a hooklength formula for the number of skew shaped standard Young tableaux. In a series of ... 
Atomicity in Rings with Zero Divisors
(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
(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
(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
(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 EdgeColored Directed Graph Algebras
(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 gaugeinvariant uniqueness theorem to first ...