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Fractional Derivatives, John M. Beach

Theses and Dissertations

In this thesis, the reader will not find a study of any kind; there is no methodology, questionnaire, interview, test, or data analysis. This thesis is simply a research paper on fractional derivatives, a topic that I have found to be fascinating. The reader should be delighted by a short history of the topic in Chapter 1, where he/she will read about the contributions made by some of the great mathematicians from the last three centuries.

In Chapter 2 the reader will find an intuitive approach for finding the general fractional derivative for functions such as e^ax, x …

A Group Theoretic Tabu Search Approach To The Traveling Salesman Problem, Shane N. Hall

Theses and Dissertations

The traveling salesman problem (TSP) is a combinatorial optimization problem that is mathematically modeled as a binary integer program. The TSP is a very important problem for the operations research academician and practitioner. This research demonstrates a Group Theoretic Tabu Search (GTTS) Java algorithm for the TSP. The tabu search metaheuristic continuously finds near-optimal solutions to the TSP under various different implementations. Algebraic group theory offers a more formal mathematical setting to study the TSP providing a theoretical foundation for describing tabu search. Specifically, this thesis uses the Symmetric Group on n letters, S(n), which is the set of all …