Mathematics Commons^™

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

Kenneth C. Schraut Memorial Lectures

No abstract provided.

Every Time I Turn Around There's Dr. Schraut Or You Can't Take Mathematics Out Of A U. D. Mathematics Major (Abstract), Eugene Steuerie

Kenneth C. Schraut Memorial Lectures

In this lecture, Gene Steurele, a math major from the 1968 graduating class, will discuss the many ways that mathematics & statistics crop up in almost every major public policy debate in which he has participated.

Forced Oscillations Of The Korteweg-De Vries Equation On A Bounded Domain And Their Stability, Muhammad Usman, Bingyu Zhang

Mathematics Faculty Publications

It has been observed in laboratory experiments that when nonlinear dispersive waves are forced periodically from one end of undisturbed stretch of the medium of propagation, the signal eventually becomes temporally periodic at each spatial point. The observation has been confirmed mathematically in the context of the damped Kortewg-de Vries (KdV) equation and the damped Benjamin-Bona-Mahony (BBM) equation. In this paper we intend to show the same results hold for the pure KdV equation (without the damping terms) posed on a bounded domain. Consideration is given to the initial-boundary-value problem

uu_xu_xxx 0 < x < 1, t > 0, (*)

It is shown …

2009 (Fall), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2009 Fall Colloquium.

2009 (Spring), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2009 Spring Colloquium.

2009 Undergraduate Mathematics Day Poster, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

No abstract provided.

Discrete Fractional Calculus With The Nabla Operator, Ferhan M. Atici, Paul W. Eloe

Mathematics Faculty Publications

Properties of discrete fractional calculus in the sense of a backward difference are introduced and developed. Exponential laws and a product rule are developed and relations to the forward fractional calculus are explored. Properties of the Laplace transform for the nabla derivative on the time scale of integers are developed and a fractional finite difference equation is solved with a transform method. As a corollary, two new identities for the gamma function are exhibited.

Coarser Connected Topologies And Non-Normality Points, Lynne Yengulalp

Mathematics Faculty Publications

We investigate two topics, coarser connected topologies and non-normality points. The motivating question in the first topic is:

Question 0.0.1. When does a space have a coarser connected topology with a nice topological property? We will discuss some results when the property is Hausdorff and prove that if X is a non-compact metric space that has weight at least c, then it has a coarser connected metrizable topology. The second topic is concerned with the following question:

Question 0.0.2. When is a point y ∈ β X\X a non-normality point of β X\X? We will discuss the question in the …

Preface [Honoring The Career Of John Graef On The Occasion Of His Sixty-Seventh Birthday], Paul W. Eloe, Johnny Henderson

Mathematics Faculty Publications

John R. Graef did not retire from Mississippi State University in order to retire. Rather, he was seeking ways to add to his overfilled schedule . . . which he found in Fall 1999 in the form of position of Head of the Department of Mathematics at the University of Tennessee at Chattanooga. He currently remains in that position, and during his time in that position, he has become a strong proponent in upgrading the visibility of the department, in improving the level of the department faculty, in seeking out benefactors for the department, in obtaining external funding for the …

These Aren't Your Mothers And Fathers Experiments (Abstract), Thomas J. Santner

Kenneth C. Schraut Memorial Lectures

Informal experimentation is as old as humankind. Statisticians became seriously involved in the conduct of experiments during the early 1900s when they devised methods for the design of efficient field trials to improve agricultural yields. During the 1900s statistical methodology was developed for many complicated sampling settings and a wide variety of design objectives.

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

Kenneth C. Schraut Memorial Lectures

No abstract provided.

Keeping Up-To-Date With Bayes (Abstract), Kristin Duncan

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

Bayes’ theorem, a rule for updating probabilities as new information is obtained, may be over two centuries old but it has been the driving force behind many of the most significant recent advances in statistics and other sciences.

2009 Program And Abstracts,, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

No abstract provided.

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

Colloquia

Abstracts of the talks given at the 2008 Fall Colloquium.

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 …

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.

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.

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 …

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. …

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 …

2008 Alumni Presenters, University Of Dayton. Department Of Mathematics

Biennial Alumni Seminar

No abstract provided.

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.

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

Colloquia

Abstracts of the talks given at the 2008 Winter Colloquium.

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.

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.

2007 (Fall), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2007 Fall Colloquium.

A Spectral Order For Infinite Dimensional Quantum Spaces: A Preliminary Report, Joe Mashburn

Mathematics Faculty Publications

In 2002 Coecke and Martin created a Bayesian order for the finite dimensional spaces of classical states in physics and used this to define a similar order, the spectral order on the finite dimensional quantum states. These orders gave the spaces a structure similar to that of a domain. This allows for measuring information content of states and for determining which partial states are approximations of which pure states. In a previous paper the author extended the Bayesian order to infinite dimensional spaces of classical states. The order on infinite dimensional spaces retains many of the characteristics important to physics, …