Physical Sciences and Mathematics Commons^™

Elegance Or Alchemy? An International Cross-Case Analysis Of Faculty And Graduate Student Perceptions Of Mathematical Proofs, Brooke Nicole Denney

Masters Theses

Artist Marcel Duchamp once said, ``The painter is a medium who doesn’t realize what he is doing. No translation can express the mystery of sensibility, a word, still unreliable, which is nonetheless the basis of painting or poetry, like a kind of alchemy" (Moffitt, 2012). Just as there is a puzzling aspect of creating art or writing poetry, the aesthetic quality of mathematical proofs is a mysterious and ill-defined concept. Like many other subjective terms, it can be difficult to reach a consensus on what elegance means in a mathematical context. In this thesis, I try to better understand faculty …

Autonomous Eco-Driving With Traffic Light And Lead Vehicle Constraints: An Application Of Best Constrained Interpolation, Yara Hazem Mohamed Mahmoud

Masters Theses

Eco-Driving is a critical technology for improving automotive transportation efficiency. It is achieved by modifying the driving trajectory over a particular route to minimize required propulsion energy. Eco-Driving can be approached as an optimal control problem subject to driving constraints such as traffic lights and positions of other vehicles. Best interpolation in a strip is a problem in approximation theory and optimal control. The solution to this problem is a cubic spline. In this research we demonstrate the connection between Eco-Driving and best interpolation in the strip. By exploiting this connection, we are able to generate optimal Eco-Driving trajectories that …

Parallel Resource Defined Fitness Sharing: A Study On Parallel Optimizations For Niching Algorithms, Blayne A. Rogers

Masters Theses

The exploitation of niches by genetic algorithms (GAs) is a computationally expensive, but effective, methodology for solving complex open problems and real-world applications. Niching, differentiated on the modality of sharing, casts problems in terms of the specific resources available. These concepts arise from the broader natural algorithms that encapsulate the ideas and theories used in artificial intelligence. In remediating the computational costs, a study on exploiting niche-defined parallel structures is performed in the contest of the resourcedefined fitness sharing (RFS) algorithm.

Sharing is a natural algorithm paradigm that emulates the use of resources within an environment or population. Defining these …

Several Problems In Nonlinear Schrödinger Equations, Tim Van Hoose

Masters Theses

“We study several different problems related to nonlinear Schrödinger equations….

We prove several new results for the first equation: a modified scattering result for both an averaged version of the equation and the full equation, as well as a set of Strichartz estimates and a blowup result for the 3d cubic problem.

We also present an exposition of the classical work of Bourgain on invariant measures for the second equation in the mass-subcritical regime”--Abstract, page iv.