Browsing Mathematics URC Student Scholarship by Title
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A Study of Intrinsic Knots and Links: a Tale of Two Graphs Alex Barylskiy and Hannah Schwartz
(20110101)Our research focused on two questions in graph and knot theory. Our first question addressed the complete graph of nine vertices (K9) and whether or not a 3linkless straightedge embedding is realizable in 3space. A ... 
An Artificial World and its Creatures.
(20010101)The project studies the evolution of some digital organisms in a simple world whose rules they learn by trial and genetic evolution. The creatures and the world are modeled to resemble a simple natural ecosystem. The world ... 
Bulgarian Choral Traditions:Music and Vocal Techniques Influenced byReligion, Education and the Singing Community
(20020101)As a living art form unique to every culture, choral music reflects strongly upon a country's history, culture, and people. It is an art form that is always evolving to depict changes within a culture. The sound of Bulgarian ... 
Bulgarian Choral Traditions:Music and Vocal Techniques Influenced byReligion, Education and the Singing Community Leanna Cooper and Akiko Minaga
(20020101)A tumultuous history is the cause of a rich cultural identity and unity that has enhanced music, particularly choral singing, in Bulgaria. Through religious, educational and communitybased institutions, choral music has ... 
Calcium Waves in Pregnant Uterine Contractions
(20070101)Uterine contractions during childbirth stem from cellular processes. This complex process occurs when pacemaker cells generate action potentials that trigger intercellular calcium waves which result in contraction of the ... 
Calculable Congestion: Modeling Effects of Traffic Light on Traffic Flow Using ODEs and PDEs
(20080101)The study analyzes the effect of traffic lights on traffic flow using ordinary differential equation (ODE) and partial differential equations (PDE) models. I consider several different cases. First, I assume constant inflow ... 
Classifying and Documenting TYRealizable Trees
(20110101)This project centers around Triangle Y  moves (TYmoves). TYmoves are an operation on graphs (collections of vertices and edges), where we remove the edges AB, AC, and BC of a triangle with vertices A, B, and C, insert ... 
Deletions and Collapsions with Partitioned Binary Matrices.
(20000101)It has been proven that, given any table of integers, one ? and only one ? of these statements is true: either some rows, excluding the first, can be deleted so that every column has an even sum, or some columns can be ... 
Differential Posets and kribbon Tableaux
(20050101)In this study we examine a class of partially ordered sets (posets). Differential posets were first introduced by R. Stanley in 1988 and are a group of posets which meet criteria set forth by Stanley. After examining Young's ... 
Discovering New Intrinsically Knotted Graphs Nancy Moore and Michael Wade
(20080101)In the field of topology, intrinsically knotted graphs are rare graphs in which all embeddings contain a nontrivial knot. There are a finite number of these graphs and only a handful of graphs have been proven to be ... 
Edge Coloring Graphs with Distance Restrictions
(20020101)Using probabilistic methods developed by Michael Molloy and Bruce Reed, we attempt to prove a conjecture that says the strong chromatic index for bipartite graphs is less than or equal to 5/4(D)^2$ where (D) is the maximum ... 
Expressive Musical Terms Index: A Case for WebBased Technology as a Means of Interpreting Musical Scores
(20110101)One of the most commonplace elements of the graphic notation of music is the most elusive element to interpret: the Italian expressive terms that populate most music scores. Nowhere is this more the case than in the music ... 
Film Franchises and the EdwardsBuckmire Model: An Examination of the Financial Performance of Movie Sequels
(20100101)The EdwardsBuckmire Model (EBM) is a mathematical model which utilizes a system of three nonlinear coupled ordinary differential equations to model the boxoffice dynamics of films released theatrically in North America. ... 
Integer Partitions and their Applicationto Quantum Physics
(20020101)Combinatorial mathematics is not frequently associated with quantum physics. However, work in one discipline can motivate investigations in the other. A recent conjecture regarding allowed multiplets in the composite fermion ... 
Integer Partitions and their Applicationto Quantum Physics
(20030101)Combinatorial mathematics is not frequently associated with quantum physics. However, work in one discipline can motivate investigations in the other. A recent conjecture regarding allowed multiplets in the composite fermion ... 
Investigations of Multidimensional PredatorPrey Models
(20090101)The GauseLotkaVolterra (GLV) equations are an idealized model for competition between n species. The nRPS and May Leonard competing species models are specific cases of (GLV) which define interaction between various ... 
Mathematical Modeling of Single Nucleotide Polymorphisms via MicroArray Analysis
(20110101)In this project, our goal is to create a mathematical model that can accurately simulate a sample of specific DNA when run through a microarray slide. A microarray slide has probes calibrated to bind onto specific target ... 
Modeling Airline Overbooking
(20040101)The airline industry uses mathematical models in order to increase its profits. Airlines face two major constraints: fixed capacity and the fact that seats on a certain flight represent perishableassets, as they are not ... 
Nmaximizability of Thetaless Graphs
(20020101)A graph G is said to be nmaximizable if and only if we get the smallest number of proper colorings when using identical nlists for all vertices. First we prove that all cycles are nmaximizable for n>=3 (the n=2 case ... 
New Nonstandard Finite Difference Methodsfor the Heat Equation
(20040101)Many physical phenomena around us can be described by mathematical models, which often take the form of a differential equation. Diffusion of heat through a homogenous bar or rod obeys a linear partial differential equations ...