Browsing Mathematics by Submit Date
Now showing items 1-20 of 36
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First Order Definition of Rings Using Group of Units
(East Carolina University, 2023-05-03)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 Field-Theoretically Defined Logical Connectives
(East Carolina University, 2023-05-03)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
(2022-07-07)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 K-12 art ... -
IDENTIFYING SUBJECTIVE VALUE IN WOMEN’S COLLEGE GOLF RECRUITING REGARDLESS OF SOCIO-ECONOMIC CLASS
(East Carolina University, 2018-05-03)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 information-processing 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 Self-Adjoint Operators
(East Carolina University, 2016-04-25)The Spectral Theorem for Self-Adjoint 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 Q-Advanced Waves in 2-D
(East Carolina University, 2015-12-15)A two-dimensional numerical approximation for modeling tsunamis is developed. New q-advanced 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 learning-based college algebra (Math 1065) course redesign at East Carolina University. Historically, East Carolina University’s College Algebra program maintained a high ...