11:30-11:50
	Strongly Regular k-friendly Graphs    Kelly Bragan, Birmingham-Southern College Graphs in which any two vertices have exactly k adjacent vertices in common are considered k-friendly.  This talk will address specific results concerning the necessary conditions for k-friendliness, particularly the question of how many k-friendly graphs are possible for any given value of k.
	An Investigation into Statistical Tests for Stochastic Dominance     David Kahle, University of Richmond   An alternative method of inference using critical values is proposed for the first, second, and third order stochastic dominance tests proposed by Barrett and Donald (Econometrica 2003). These critical values are then used to evaluate the power and probability of type one error for the test using various distributions and sample sizes.
	The Mathematics of a Tennis Serve       Jake Bennett, Roanoke College During a serve, a tennis ball is subject to several forces, which include gravity, air drag and a Magnus force.  Using the laws of physics, first-order nonlinear differential equations can be derived from these forces.  This project uses these unsolvable equations to analyze and improve a tennis serve.

11:50-12:10
	On the Action of Weight-Preserving Sets       Matthew Badger, University of Pittsburgh We introduce weight-preserving sets of binary words. Any transformation that respects the row and column weights of a 0-1 matrix can be decomposed as the composition of two types of action on the matrix. We conjecture that weight-preserving sets perform only one type of action, permutations of rows and columns.
	Discovering Human Route-Planning Knowledge from Everyday Location Traces       John Suarez, James Madison University   Trip planning applications currently use optimal route or optimal travel time to generate driving directions and neglect changing road conditions, traffic, and unexpected interference. GPS location traces, providing human generated arc weights, instead of distance, on a road network, allow human route-planning knowledge to be obtained and utilized.
	Using High Performance Computer Visualizations to Describe Complex Algorithms and Theories    John Magnotti and Karl Ridgeway, James Madison University The Immersive Visualization Center allows people of all levels of expertise to conceptually grasp complex mathematical and computational problems. Included in the demonstration will be a visualization of Newton's N-Body problem involving planetary motion, and a look at delayed chaos theory as represented by the double-pendulum. Note: The high-performance computer  room holds only 20 people, so this talk will be offered more than once.

12:10-12:30
	Resolving the 6,4 Problem    Joshua Link, The College of William and Mary For any n * n pattern with maximum triangle size k, the minimum rank of that pattern is at least k.  We know a lot about whether a minimum rank of k necessitates the existence of a k-triangle for all n and for all k except for when n = 6, and k = 4.  We resolve the problem in this paper.
	Newton's First Great Mathematical Discovery    Goldie Regina Darr, Mary Baldwin College Newton's first great mathematical discovery, the binomial theorem. Demonstration of Newton's application of this theorem for extracting roots. Explanation of how Newton computed the value of pi to sixteen decimal places.
	Using High Performance Computer Visualizations to Describe Complex Algorithms and Theories    John Magnotti and Karl Ridgeway, James Madison University The Immersive Visualization Center allows people of all levels of expertise to conceptually grasp complex mathematical and computational problems. Included in the demonstration will be a visualization of Newton's N-Body problem involving planetary motion, and a look at delayed chaos theory as represented by the double-pendulum. Note: The high-performance computer  room holds only 20 people, so this talk will be offered more than once.

2:00-2:20
	Triangle Tessellations of the Hyperbolic Plane    Anton Lukyanenko, University of Maryland, College Park   Hyperbolic geometry presents an exciting alternative to the familiar Euclidean and spherical geometries by breaking Euclid's parallel postulate. The talk will introduce hyperbolic geometry, demonstrate triangle tessellations to provide an intuitive feel of the subject, and discuss the mathematics involved in the development of the tessellation-generating program qTess.
	On the Counting of Lower Hessenberg Matrices      Hakan Seyalioglu and Katie Field, The College of William and Mary Lower Hessenberg matrices with integer entries, when restricted with the condition of having non-decreasing row and column sums, follow very interesting patterns and display stunning symmetries. We deal with proving several properties about the distributions. Topics used heavily include the partitioning of families of matrices and bijective counting.
	Building a Research Lab, An Experimental and Theoretical Study of the Aeroacoustics of External-Coanda Gas Flares    Steven Andrews, James Madison University This talk will examine the problems faced with building a research lab from the ground up and the considerations that must be made in designing an experiment on a large scale.  We will focus on the construction of the Anechoic Chamber at JMU and the current research on the aeroacoustics of external-coanda gas flares.

 

2:20-2:40
	Geometric Properties of the Cevian Box    Shamia Jones and William Rankin, Virginia State University   A Cevian box is a plane figure composed of 8 vertices and 12 line segments which form 6 Cevian quadrilateral faces. We show that the four long diagonals of a Cevian box are concurrent. We also show that a Cevian box is generated in natural way by two noncocevial points.
	Comparing Ratio Estimators Based on Systematic Samples      John Szarka, James Madison University This study evaluates two competitive ratio estimators, the mean of ratios and ratio of means, when a systematic sample with a random start is used. Variance estimators are presented and compared using simulated objects. New approaches include a bootstrap estimate, the other is based on finding the best linear unbiased estimator of the slope.
	From College to a Career: Post-JMU Life at Metron, Inc.     Christopher Carlson, Metron, Inc. Christopher Carlson graduated from JMU in May 2005 with a B.S. in Physics. He has since been working for Metron, Inc. in Reston, VA. This talk will offer his perspective on the transition from college to a career. It will also give an overview of opportunities at Metron and his work there to date.

2:40-3:00
	Automorphisms of the Cevian Line Algebra    Jesse Ozbat, (joint work with John Gichuru), Virginia State University    We define the Cevian Algebra on the interior points of a triangle. In this Algebra, Cevian lines are subalgebras. We show that a certain class of automorphisims of a Cevian line subalgebra forms an abelian subgroup of the group of all automorphisms of L.
	A Modified Lotka-Volterra Competition Model with a Non-Linear Relationship Between Species      Amy Vess Crizer, James Madison University A modified Lotka-Volterra competition model, incorporating a non-linear relationship representing the interaction between species,is studied to determine its qualitative properties. The properties are compared to those of the classical Lotka-Volterra equations and results are obtained suggesting that the modified model is a better representation of some biological situations.
	Using High Performance Computer Visualizations to Describe Complex Algorithms and Theories    John Magnotti and Karl Ridgeway, James Madison University The Immersive Visualization Center allows people of all levels of expertise to conceptually grasp complex mathematical and computational problems. Included in the demonstration will be a visualization of Newton's N-Body problem involving planetary motion, and a look at delayed chaos theory as represented by the double-pendulum. Note: The high-performance computer  room holds only 20 people, so this talk will be offered more than once.