In this thesis, we investigate the problem of simulating Maxwell's equations in dispersive dielectric media. We begin by explaining the relevance of Maxwell's equations to 21st century problems. We also discuss the pre ...

This study deals specifically with classical cubic splines. Based on a lemma of John Rice, best approximation in the uniform norm by cubic splines is explored. The purpose of this study is to characterize the best app ...

Representations of SO(4,2;R) are constructed using 4 x 4 and 2 x 2 matrices with elements in H' ⊗ C . Using 2 x 2 matrix representations of C and H', the 4 x 4 representation is interpreted in terms of 16 x 16 real matri ...

The goal of this research project is to determine the fractal nature, if any, which certain surface water waves exhibit when viewed on a microscopic scale. We make use of the mathematical formulation of non-viscous flu ...

The purpose of this descriptive case study analysis was to provide portraits of the heuristics students used and difficulties they encountered solving conditional probability problems prior to and after two-week instruct ...

Neural networks are models which have been developed to simulate the anatomy of the nervous system. The connection between the elements of these networks, the so called artificial neurons, is similar to the connection ...

This thesis examines the mixing times for one-dimensional interacting particle systems. We use the coupling method to study the mixing rates for particle systems on the circle which move according to specific permutation ...

Water is one of the most biologically and economically important substances on Earth. A significant portion of Earth's water subsists in the subsurface. Our ability to monitor the flow and transport of water and other ...