Thesis (M.S.)--University of Missouri-Columbia, 2003. / Typescript. Includes bibliographical references (leaves 110-113). Also available on the Internet.

Thesis (Ph. D.)--School of Industrial and Systems Engineering, Georgia Institute of Technology, 2004. Directed by Ellis L. Johnson. / Vita. Includes bibliographical references (leaves 172-174).

The main goal of this project was to write a review about different quantum Hall effects. This review focuses on the integer and relativistic quantum Hall effect in graphene. The quantum Hall effect is a newly discovered phenomena that was experimentally observed in 1980 and relativistic quantum Hall effect in graphene was observed in 2005. This project takes a theoretical approach to describe the quantum Hall effects and graphene itself. Experiments has shown that for very strong magnetic fields applied to 2D systems, the Hall resistance becomes quantized, RH=h/ne2 and only depends on the charge of the electron and Planck's constant, two fundamental constants of nature. This sets a new standard on how to define resistance, and gives a good tool for precise measurements of the fine structure constant.

A nonogram is a logic puzzle where one shades certain cells of a 2D grid to reveal a hidden image. One uses the sequences of numbers on the left and the top of the grid to figure out how many and which cells to shade. We propose a new technique to solve a nonogram using compressive sensing. Our method avoids (1) partial fill-ins, (2) heuristics, and (3) over-complication, and only requires that we solve a binary integer programming problem. / text

published_or_final_version / Mathematics / Master / Master of Philosophy

The Time-Dependent Traveling Salesman Problem is a generalization of the well-known Traveling Salesman Problem, where the cost for travel between two nodes is dependent on the nodes and their position in the tour. Inequalities for the Asymmetric TSP can be easily extended to the TDTSP, but the added time information can be used to strengthen these inequalities. We look at extending the Lifted Cycle Inequalities, a large family of inequalities for the ATSP. We define a new inequality, the Extended Cycle (X-cycle) Inequality, based on cycles in the graph. We extend the results of Balas and Fischetti for Lifted Cycle Inequalities to define Lifted X-cycle Inequalities. We show that the Lifted X-cycle Inequalities include some inequalities which define facets of the submissive of the TDTS Polytope.

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