Mathematics Commons^™

2008 (Fall), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2008 Fall Colloquium.

Optimal Selling Rules In A Regime-Switching Exponential Gaussian Diffusion Model, Paul W. Eloe, R. H. Liu, Masako Yatsuki

Mathematics Faculty Publications

This paper develops optimal selling rules in asset trading using a regime-switching exponential Gaussian diffusion model. The optimization problem is solved by a combined approach of boundary value problems and probabilistic analysis. A system of linear differential equations with variable coefficients and two-point boundary conditions, satisfied by the objective function of the problem, is derived. The existence and uniqueness of the solution are proved. A closed-form solution in terms of Weber functions is obtained for one-dimensional cases. For m-dimensional cases, a stochastic recursive algorithm for numerically searching the optimal value is developed. Numerical results are reported.

Leadership Founded In Habits Of Inquiry And Reflection (Abstract), Robert C. Bolz Jr.

Kenneth C. Schraut Memorial Lectures

Leadership in the Science, Technology, Engineering, and Mathematics (STEM) disciplines has been the foundation of leadership in the world for over 600 years.

Ninth Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics

Kenneth C. Schraut Memorial Lectures

No abstract provided.

An Order Model For Infinite Classical States, Joe Mashburn

Mathematics Faculty Publications

In 2002 Coecke and Martin (Research Report PRG-RR-02-07, Oxford University Computing Laboratory,2002) created a model for the finite classical and quantum states in physics. This model is based on a type of ordered set which is standard in the study of information systems. It allows the information content of its elements to be compared and measured. Their work is extended to a model for the infinite classical states. These are the states which result when an observable is applied to a quantum system. When this extended order is restricted to a finite number of coordinates, the model of Coecke and …

Qualitative Properties Of Nonlinear Volterra Integral Equations, Muhammad Islam, Jeffrey T. Neugebauer

Mathematics Faculty Publications

In this article, the contraction mapping principle and Liapunov's method are used to study qualitative properties of nonlinear Volterra equations of the form x(t)=a(t)−∫^t₀C(t,s)g(s,x(s))ds,t≥0. In particular, the existence of bounded solutions and solutions with various L^p properties are studied under suitable conditions on the functions involved with this equation.

2008 Alumni Presenters, University Of Dayton. Department Of Mathematics

Biennial Alumni Seminar

No abstract provided.

2008 (Winter), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2008 Winter Colloquium.

2008 Vol. 3 Table Of Contents, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Past Content

No abstract provided.

Breaking The Curve, Amanda Dahlman, Jesse Depinto, Kyle Kremer, Joe Plattenburg

Undergraduate Mathematics Day: Past Content

Imagine you are up to bat in a major league baseball game. Would you rather face a pitch with smaller curvature or smaller break? Would you know the difference? In this paper we will derive a model for the path of a pitch based on actual data from MLB.com's GameDay™ feature. Then, employing our model, we shall analyze the curvature and break of the pitch.

An Application Of Analytic Geometry To Designing Machine Parts--And Dresses, Karl Hess

Undergraduate Mathematics Day: Past Content

This paper presents the solution of an engineering problem that the author was asked to solve. The problem involves creating a flat pattern that could be cut from a piece of sheet metal and rolled to form a tube whose top edge would be contained in a plane that is not perpendicular to the central axis of the tube. A piece of this nature needs to be fabricated whenever two sheet metal tubes must be joined at any angle other than a straight angle.

Rearrangement On Conditionally Convergent Integrals In Analogy To Series, Edward J. Timko

Undergraduate Mathematics Day: Past Content

Rearrangements on conditionally convergent series suggests the existence of a similar process for integrals, here also referred to as rearrangement. In this document, a general theorem concerning rearrangement for conditionally convergent integrals is presented, as well as supporting theorems and a corollary to the general theorem.

A New Spin On Baseball, Allison Horney, Taylor Lowry, Eric Schwenker, Evan Wray

Undergraduate Mathematics Day: Past Content

All baseball fans know what a curveball is physically, but what is curveball mathematically, and how does it differ from a fastball? The secret of a pitch lies in its spin. In this paper we shall define the spin of a baseball and investigate the effects of its magnitude and direction by employing data collected by MLB.com Gameday from the league's best pitchers. We shall then employ this model to differentiate between the spin of a curveball and that of a fastball.

Acknowledgements: We would like to thank our teacher Scott Mitter for all that he has done for us. …

Pricing The Asian Call Option, Vinh Xuan Dang, Scott Glasgow, Harrison Potter, Stephen Taylor

Undergraduate Mathematics Day: Past Content

Background material on measure-theoretic probability theory and stochastic calculus is provided in order to clarify notation and inform the reader unfamiliar with these concepts. These fields are then employed in exploring two distinct but related approaches to fair option pricing: developing a partial differential equation whose solution, given specified boundary conditions, is the desired fair option price and evaluating a riskneutral conditional expectation whose value is the fair option price. Both approaches are illustrated by example before being applied to the Asian call option. .

Two results are obtained by applying the latter option pricing approach to the Asian call …

Determining The Statistical Significance Of Observed Frequencies Of Short Dna Motifs In A Genome, Philip E. Pfeiffer, Peter W. Hovey, Sudhindra R. Gadagkar

Undergraduate Mathematics Day: Past Content

Until recently over 90 percent of the DNA in the human genome was considered junk DNA, with no known function. However, this non-coding DNA is now known to harbor elements that perform important functions in gene regulation. In particular, there is currently much interest in the search for short DNA motifs collectively known as cis-regulatory elements. Most studies attempt to identify these elements by means of cross-species comparisons. We have approached the problem of finding cis-regulatory elements by searching for conserved DNA motifs within genomes. This requires searching for DNA motifs that are repeated in the genomes either more …