Browsing Mathematics URC Student Scholarship by Title
Now showing items 1-20 of 35
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A Study of Intrinsic Knots and Links: a Tale of Two Graphs Alex Barylskiy and Hannah Schwartz
(2011-01-01)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 3-linkless straight-edge embedding is realizable in 3-space. A ... -
An Artificial World and its Creatures.
(2001-01-01)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
(2002-01-01)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
(2002-01-01)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 community-based institutions, choral music has ... -
Calcium Waves in Pregnant Uterine Contractions
(2007-01-01)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
(2008-01-01)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 TY-Realizable Trees
(2011-01-01)This project centers around Triangle Y - moves (TY-moves). TY-moves 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.
(2000-01-01)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 k-ribbon Tableaux
(2005-01-01)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
(2008-01-01)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
(2002-01-01)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 Web-Based Technology as a Means of Interpreting Musical Scores
(2011-01-01)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 Edwards-Buckmire Model: An Examination of the Financial Performance of Movie Sequels
(2010-01-01)The Edwards-Buckmire Model (EBM) is a mathematical model which utilizes a system of three nonlinear coupled ordinary differential equations to model the box-office dynamics of films released theatrically in North America. ... -
Integer Partitions and their Applicationto Quantum Physics
(2002-01-01)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
(2003-01-01)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 Predator-Prey Models
(2009-01-01)The Gause-Lotka-Volterra (GLV) equations are an idealized model for competition between n species. The n-RPS and May Leonard competing species models are specific cases of (GLV) which define interaction between various ... -
Mathematical Modeling of Single Nucleotide Polymorphisms via Micro-Array Analysis
(2011-01-01)In this project, our goal is to create a mathematical model that can accurately simulate a sample of specific DNA when run through a micro-array slide. A micro-array slide has probes calibrated to bind onto specific target ... -
Modeling Airline Overbooking
(2004-01-01)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 perishable-assets, as they are not ... -
N-maximizability of Theta-less Graphs
(2002-01-01)A graph G is said to be n-maximizable if and only if we get the smallest number of proper colorings when using identical n-lists for all vertices. First we prove that all cycles are n-maximizable for n>=3 (the n=2 case ... -
New Nonstandard Finite Difference Methodsfor the Heat Equation
(2004-01-01)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 ...