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# Browsing by Degree "Mathematics"

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• (Wake Forest University, 2016)
We consider group-gradings of noncommutative algebras with the following question in mind: for what groups $G$ does there exist an Artin-Schelter regular algebra $A$ with $G$ grading $A$ such that $A_e$, the identity-graded ...
• (Wake Forest University, 2013)
We prove a completely explicit version of the Sato-Tate Conjecture for newforms f(z) on Gamma_0(N) with squarefree level. This result assumes that the symmetric power L-functions of f(z) are automorphic and satisfy the ...
• (Wake Forest University, 2015)
A \emph{knot} is the image of an embedding of $S^1$ into $\R^3$, and a \emph{link} is the disjoint union of multiple knots. Most of the thesis is spent studying knots and two-component links. Knot theory is concerned with ...
• (2005-04-26)
This thesis provides explicit, applicable bounds for solutions of a wide class of second-order difference equations with nonconstant coefficients. Among the applications is an affirmative answer to a question of Stevi´c. ...
• (Wake Forest University, 2011)
The construction of networks that model biological activities is an important open question. In this thesis, we explore the modeling of biological networks using Fuzzy Logic. Fuzzy Logic models allow for genes to not only ...
• (Wake Forest University, 2014)
Graph pebbling involves determining the minimum number of pebbles needed so that regardless of the initial arrangement of pebbles on a graph, a pebble can be moved to any vertex using specified pebbling moves.'' This ...
• (Wake Forest University, 2011)
This thesis explores the use of Bayesian statistical methods and hierarchical modeling in order to analyze massive data sets of Peruvian tree growth data. The study is important in finding connections between different ...
• (Wake Forest University, 2009-05-07)
Higher Dimensional Convex Brunnian Links and Other Explorations in Knots. Thesis under the direction of Hugh N. Howards, Ph.D., Associate Professor of Mathematics. This thesis will examine two areas of knot theory. The ...
• (Wake Forest University, 2013)
In this thesis, we examine a ranking method called HodgeRank. HodgeRank was introduced in 2008 by Jiang, Lim, Yao and Ye as a promising tool for the statistical analysis of ranking, especially for datasets with cardinal, ...
• (Wake Forest University, 2012)
Let <italic>k</italic> be a field of characteristic zero, and let <italic>R= k<sub>-1</sub>[x<sub>1</sub>, ..., x<sub>n</sub>]</italic>
• (Wake Forest University, 2009-05-06)
There exist polynomials Cn(q,t) known as the q,t-Catalan polynomials. We know from work in representation theory by Haglund, Haiman, and Garsia that the q,t-Catalan polynomials are symmetric; that is, that Cn(q,t) = ...
• (Wake Forest University, 2013)
In any ecological community, the probabilities for observance (capture) of individual animals often differ both within and between species. Previous research involving multiple species' abundances have largely ignored ...
• (Wake Forest University, 2016)
This thesis concerns the problem of minimizing a particular energy functional over an appropriate class of admissible functions on a bounded, convex domain in two-dimensional Euclidean space. We require admissible functions ...
• (Wake Forest University, 2010-05-07)
In this thesis we look to improve upon local Edgeworth expansions for probability distributions of sums of independent identically distributed random variables. Let X be a random variable with finite variance, and X1, ...
• (Wake Forest University, 2015)
Commutative local isolated singularities are a class of rings that have been studied extensively. Much work has been devoted in the area of noncommutative algebra in generalizing the notion of an isolated singularity for ...
• (Wake Forest University, 2016)
It is a difficult problem to prove that a polynomial only takes non-negative values. One way to certify that a polynomial is non-negative is to express it as a sum of squares, however not all non-negative polynomials can ...
• (Wake Forest University, 2012)
There has been research that has determined that the drag forces on a non-spinning volleyball's boundary layer causes the ball to swerve on its trajectory. The purpose of this paper is to develop a numerical model for ...
• (Wake Forest University, 2013)
In 1983, John H. Conway and Cameron Gordon published "Knots and Links in Spatial Graphs" in the Journal of Graph Theory. In this paper, Conway and Gordon proved that the complete graph on six vertices is intrinsically ...
• (2006)
This thesis investigates the properties of limiting crossing points of the standard normal density and the standardized mass function of the sum of $n$ independent, identically distributed, discrete random variables ...
• (Wake Forest University, 2014)
We will discuss the stability of certain solutions to a phase transition model. This model is typically expressed as a partial differential equation: <italic> u<sub>t</sub> = &epsilon;<super>2</super>u<sub>xx</sub>-F'(u), ...