Mathematics
Recent Submissions

First Order Definition of Rings Using Group of Units
(East Carolina University, 20230503)We discuss the technical background and relevant research regarding the undecidability of $O_{\mathbb{Q}^{\text{ab}}}$. Given an algebraic extension $K/\mathbb{Q}$, we consider the subring defined by $$R_K=\{x\in O_K\,\,\forall ... 
Inferences Over Fields: A Preliminary Investigation into the Deductive Capabilities of FieldTheoretically Defined Logical Connectives
(East Carolina University, 20230503)In this paper, we will be concerned with developing an inferential structure over the field with four elements in characteristic $2$. We begin by discussing the historical context in which this research occurs. In subsequent ... 
Solutions of a Class of Multiplicatively Advanced Differential Equations II: Fourier Transforms
(20220707)For a wide class of solutions to multiplicatively advanced differential equations (MADEs), a comprehensive set of relations is established between their Fourier transforms and Jacobi theta functions. In demonstrating this ... 
Theorems in Visual Art: Art and Math Teacher Collaboration toward Creative Leadership
(2018)An artist and a mathematician meet. The authors of this article, one an art education professor and the other a mathematics professor, collaborated to conduct research as a team, examining perceptions of K12 art ... 
IDENTIFYING SUBJECTIVE VALUE IN WOMEN’S COLLEGE GOLF RECRUITING REGARDLESS OF SOCIOECONOMIC CLASS
(East Carolina University, 20180503)College athletics have grown into a major industry and athletic departments are pushing coaches to recruit the top talent. To recruit golfers, college coaches depend on multiple ranking systems. These systems are bias ... 
Theoretical aspects and modelling of cellular decision making, cell killing and informationprocessing in photodynamic therapy of cancer
(2013)BACKGROUND: The aim of this report is to provide a mathematical model of the mechanism for making binary fate decisions about cell death or survival, during and after Photodynamic Therapy (PDT) treatment, and to supply ... 
The Spectral Theorem for SelfAdjoint Operators
(East Carolina University, 20160425)The Spectral Theorem for SelfAdjoint Operators allows one to define what it means to evaluate a function on the operator for a large class of functions defined on the spectrum of the operator. This is done by developing ... 
Modeling Tsunami Waves Using QAdvanced Waves in 2D
(East Carolina University, 20151215)A twodimensional numerical approximation for modeling tsunamis is developed. New qadvanced functions are used to model the forcing due to an earthquake. These results are used to model the Japanese tsunami of 2011, and ... 
Eigenvalues for Sums of Hermitian Matrices
(East Carolina University, 2015)In this thesis we explore how the eigenvalues of nxn Hermitian matrices A,B relate to the eigenvalues of their sum C=A+B. We mainly focus on inequalities bounding sums of r eigenvalues for C by sums of r eigenvalues for A ... 
Markov Chains, Random Walks, and Card Shuffling
(East Carolina University, 2016)A common question in the study of random processes pertains to card shuffling. Whether or not a deck of cards is random can have huge implications on any game being played with those particular cards. This thesis explores ... 
COLLEGE ALGEBRA REDESIGN: IMPROVE STUDENT LEARNING AND SUCCESS USING A HYBRID EMPORIUM MODEL
(2015)The purpose of this project is to describe a learningbased college algebra (Math 1065) course redesign at East Carolina University. Historically, East Carolina University’s College Algebra program maintained a high ...