Mathematics
Recent Submissions

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 ... 
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 ... 
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 ... 
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 ... 
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 ... 
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 ... 
OnePalette n Color Maximizability.
(20010101)A graph is said to be OnePalette n Color Maximizable (OPNCM) if and only if, given a palette of n colors, the maximum probability of obtaining a coloring containing identicallycolored adjacent vertices occurs when ... 
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 ... 
What a Tangled Web We Weave: Epidemiological Modeling and Graph Theory
(20050101)Network theory has recently received renewed focus for its applications in modeling the spread of diseases. Drawing upon a recent sociological study on the structure of adolescent sexual networks, as well as on previous ... 
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 ... 
Some Variations on the Tennis Ball Problem
(20040101)Our study looks at Catalan, Motzkin, and Schr?der numbers. Catalan numbers are very well known mathematically and extensive research has been done highlighting their interesting properties. In contrast, Motzkin and Schroder ... 
Simulating and Evolving Bipedal Locomotion.
(20000101)I endeavored to write a computer program in C++ which implements a 2D biped (stick figure) with legs and a torso, in which the biped learns to walk and achieve other human motions. The biped simulates human actions by ... 
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 ... 
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 ... 
Polygons with Rational Sides, Diagonals and Area: Constructions and Properties
(20030101)The majority of geometric constructions do not produce rational elements. This research was on so called rational polygons, which are polygons with rational sides, diagonals and area. We found a construction method with ... 
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. ... 
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 ... 
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 ... 
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 ...