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# Theses and Dissertations - Department of Mathematics

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### Browsing Theses and Dissertations - Department of Mathematics by Author "Allen, Paul J."

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Item Capping the variance of cash flow of hedging strategy(University of Alabama Libraries, 2011) Ginting, Maydison; Wu, Zhijian; University of Alabama TuscaloosaShow more This dissertation consolidates previous research on an optimal strategy to reduce the running risk in hedging a long-term supply commitment with short-dated futures contracts. By introducing a cap function, this dissertation defines scenarios of running risk over the hedging horizon. We introduce a linear cap function and wish to find a hedging strategy G with the smallest constant F such that the variance of the cumulative cash flow is less than or equal the multiplication of a cap function and the constant F. The objective is to seek the best function G(s) to cap the variance of cash flow under a given non-negative cap function. We also implement the result in MATLAB by creating a Graphical User Interface application that enables the user to see the various results of the variance of cash flow of the best hedging scenario.Show more Item A graph theoretical model for the analysis of the game of football and a discussion of applications thereof(University of Alabama Libraries, 2009) Taylor, Patrick; Neggers, Joseph; University of Alabama TuscaloosaShow more In this dissertation an epidemiological approach is used to develop a graph theoretical model for the game of football. This model is a preliminary model due to the limitation of available resources. Even in its preliminary form, it is evident that significant information is obtained and easily displayed using graphs and adjacency matrices. A similar approach may be used in other game-like situations where coaches (manipulators) make decisions about strategy and tactics in order to prevail over opponents. In our case, the goal is to create a package of tools for the working professional in the field, i.e., the football coach and his assistants. As a study, this paper discusses its construction and methods, including procedures used to collect the data, analysis of the data, conclusions drawn, and commentary on future designs.Show more Item P-algebras and Q-algebras(University of Alabama Libraries, 2010) Mahawanniarachchi, Padmal Sathyajith; Neggers, Joseph; University of Alabama TuscaloosaShow more We define two classes of algebras P- and Q-, which are derived from the definitions of BCK- and BCI- algebras. The birth of P-algebras is based on the symmetric difference in set theory. We prove that the class of P-algebras is a variety, and the definition of P-algebras is an alternative definition for groups of exponent 2, which we call P-groups. The class of Q-algebras consists of a combination of three axioms of BCK- and P- algebras. We study the relationship among P-, Q- and BCI- algebras. The theory of P- and Q- algebras is developed parallel to the theory of BCK- and BCI- algebras.Show more