Presentations

Stephen Rowe, Wilkes Honors College, FAU, Orbits of Operators

Abstract:  We discuss orbits of operators and their connection to invariant subspaces. Starting with a point x in a normed space and repeatedly applying an operator T on x, the sequence {x,Tx,T^2x,...} is an orbit. We will analyze the existence of certain types of orbits and solutions to the invariant subspace problem.

Isaac DeFrain, Justin Owen, Wilkes Honor College, FAU, The Leap from Classical Physics to Quantum Mechanics

Abstract:  In this talk we look at the development of ideas and concepts (such as position and momentum) from classical physics to quantum mechanics and show that many classical equations have direct analogy in quantum mechanics. We discuss the use of Hilbert space techniques and the role of unbounded linear operators.

Cathleen Horne, Broward College & John Adam, Old Dominion University, Student Projects: Quadratics and Birds’ Eggs for the Pre-Calculus and Calculus Student

Abstract:  Connections between topics and more in-depth study are the goals of our student projects. For the Precalculus students, a project on Quadratic Equations, and for the Calculus students, several mathematical models of the shape, surface area and volume of birds’ eggs are presented.

Cori Ouellette, William Severa, Wilkes Honors College, FAU, From Textbook to Reality: Was Torricelli Right?

Abstract:  Torricelli’s law relates the rate at which a tank drains through a small aperture to the water level in the tank. In reality, the ideal rate is adjusted by an experimental "fudge factor." We fit data from draining various bottles to estimate this factor and verify Torricelli’s model.

David Holz, Wilkes Honors College, FAU, Where is the Light? Connecting Shadows and Lights with Dandelin Spheres

Abstract:  The position of a light source can be inferred from the shadow cast by a sphere on a plane. According to Dandelin’s Theorem, the sphere touches its elliptical shadow on its focus. We discuss the numerical stability of this construction and several alternatives, with applications to computer vision.

Alex Kane, University of North Florida, Closure Properties of Involution Codes

Abstract:  Involution codes were inspired by difficulties with DNA strand design associated with undesirable hybridization. This talk presents examples of morphic and antimorphic involutions and discusses coding properties of languages that are preserved under certain language operations such as union and concatenation.

Michael Jones, Stetson University, Modeling a potential spread of the Avian Flu Influenza (H5N1) for the United States

Abstract:  Identified by health organizations across the world as the next potential epidemic, the H5N1 flu virus has received extensive attention in the past 5-7 years. While not transmittable between humans, many governments are attempting to develop models to represent a worse case scenario of an avian flu influenza outbreak.

While there are several epidemic models to choose from, we choose to look into a Susceptible, Exposed, Infected, and Recovered (SEIR) compartmental model. A time dependent SEIR model in terms of a system of ordinary differential equations (ODE) is implemented and solved. In addition, a new time and spatial model is developed in terms of a system of partial different equations (PDE). A constant population model with a nonzero and zero birth and death zero is considered. Using the basic SEIR model, we can look into developing future models incorporating vaccine strategies that may be utilized for any location in the United States, while also looking into the potential behavior of the disease.

Ryan Rogers, Stetson University, Using Hamilton’s Principle to Approximate Soliton Solutions for Nonlinear Partial Differential Equations

Abstract:  This project will involve the analysis of nonlinear PDE’s and ODE’s using Hamilton’s Principle. Pre-existing models will be utilized, such as the KdV and the NLS equations, to find soliton (localized structure) solutions. The use of Hamilton’s Principle will be used to justify the existence of solitons in particular systems.