Mathematics Commons^™

2007 Undergraduate Mathematics Day Poster, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

No abstract provided.

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

Kenneth C. Schraut Memorial Lectures

No abstract provided.

A Comparison Of Three Topologies On Ordered Sets, Joe Mashburn

Mathematics Faculty Publications

We introduce two new topologies on ordered sets: the way below topology and weakly way below topology. These are similar in definition to the Scott topology, but are very different if the set is not continuous. The basic properties of these three topologies are compared. We will show that while domain representable spaces must be Baire, this is not the case with the new topologies.

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

Colloquia

Abstracts of the talks given at the 2007 Winter Colloquium.

A Transform Method In Discrete Fractional Calculus, Ferhan M. Atici, Paul W. Eloe

Mathematics Faculty Publications

We begin with an introduction to a calculus of fractional finite differences. We extend the discrete Laplace transform to develop a discrete transform method. We define a family of finite fractional difference equations and employ the transform method to obtain solutions.

An Euler Trifecta (Abstract), William Dunham

Kenneth C. Schraut Memorial Lectures

To recognize Leonhard Euler’s 300th birthday, we sketch his life and give a brief survey of some of his mathematical achievements.

Garden-Variety Symmetry (Abstract), Colleen Hoover

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

After a gentle introduction to the topic of symmetry, we will explore the symmetry groups of bounded plane figures, pulling examples from the garden.

2007 Program And Abstracts, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

No abstract provided.

2006 (Fall), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks givn at the 2006 Fall Colloquium.

Bisections And Reflections: A Geometric Investigation, Carrie Carden, Jessie Penley

Undergraduate Mathematics Day: Past Content

This problem was first introduced as a challenge problem to high school geometry students. After receiving no responses from students, it was then taken to the collegial level. We were given this problem to investigate with the intent of generalizing the results to a broader question. This question being, what happens when we have a polygon with n sides? Before introducing the problem itself, we will recall some basic geometry definitions which will be used throughout this paper.

2006 Vol. 2 Table Of Contents, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Past Content

No abstract provided.

Mathematical And Numerical Modeling Of Inflammation, Joshua Sullivan, Ivan Yotov

Undergraduate Mathematics Day: Past Content

When the body is attacked by a bacterial infection, it initiates a series of events designed to eradicate the infection while causing minimal damage to the body. Our goal is to investigate the defenses of the organ walls to the spread of infection. To do this we have chosen to model a volume of the body that includes the organ wall, the lumen outside of it and the blood and tissue within it. We have also taken into account the varied responses of the body, and our model includes many interacting agents that are part of the infection and defense …

Adventures With Rubik's Ufo, Bill Higgins

Undergraduate Mathematics Day: Past Content

Enro Rubik invented the puzzle which is now known as Rubik’s Cube in the 1970’s. More than 100 million cubes have been sold worldwide. The mathematics behind solutions to the cube have been extensively studied by mathematicians and puzzle enthusiasts alike. In this article the mathematics behind a solution of the related puzzle known as Rubik’s UFO is analyzed.

An Investigation Of Continued Fractions, Kristi Patton, Sandra Schroeder, Richard Daquila

Undergraduate Mathematics Day: Past Content

The study of continued fractions has produced many interesting and exciting results in number theory and other related fields of mathematics. Continued fractions have been studied for centuries by many famous mathematicians such as Wallis, Euler, Gauss, Lagrange, Ramanujan, Cauchy, and Khinchin. A connection between continued fractions and the Fibonacci sequence can be revealed by examining functional parameters of various rational functions. This work makes use of existing results concerning continued fractions and Mathematica to explore the relationship between continued fractions and rational functions.

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

Kenneth C. Schraut Memorial Lectures

No abstract provided.

Brownian Motion And Its Applications In The Stock Market, Angeliki Ermogenous

Undergraduate Mathematics Day: Past Content

Wilfrid Kendall notes on the complexity of the paths of Brownian motion: If you run Brownian motion in two dimensions for a positive amount of time, it will write your name. The oddness and complexity of Brownian motion reveal a really deep subject in the field of mathematics that cannot be fully understood and explained even until now. The purpose of this paper is to introduce the Brownian motion with its properties and to explain how it is applied in an everyday but totally unpredictable environment like the stock market.

Methods Of Solution Of Second Order Linear Equations On Time Scales, Ashley Askew

Undergraduate Mathematics Day: Past Content

A time scale, T, is a nonempty, closed subset of the real numbers, R. Several methods of solution exist for second order linear equations on a time scale. An advantage of these methods is that we can obtain solutions on a system comprising of continuous and/or discrete elements. After restricting the time scale to be R, these solutions are equivalent to those obtained using differential equations methods.

A time scale, T, is a nonempty, closed subset of the real numbers, R. Several methods of solution exist for second order linear equations on a time scale. An advantage of these methods …

Shuffle Up And Deal: Should We Have Jokers Wild?, Kristen Lampe

Undergraduate Mathematics Day: Past Content

In the neighborhood poker games, one often hears of adding the Jokers as wild cards, or declaring deuces wild. In this talk, we’ll explore what happens mathematically when two Jokers are added to the deck. The probabilities for different hands change, in ways that might surprise you. Further, we will explore the mathematical consequences of playing poker with more or fewer than five cards. Finally, we will look at the historical beginnings of poker, and a mathematical anomaly that occurred along the way.

2006 Alumni Presenters, University Of Dayton. Department Of Mathematics

Biennial Alumni Seminar

No abstract provided.

2006 (Winter), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2006 Winter Colloquium.

A Qualitative Analysis On Nonconstant Graininess Of The Adaptive Grids Via Time Scales, Paul W. Eloe, Stefan Hilger, Qin Sheng

Mathematics Faculty Publications

Calculus on time scales plays a crucial role in unifying the continuous and discrete calculus. In this paper, we apply the time scales calculus methods to study qualitatively properties of the numerical solution of second order ordinary differential equations via different finite difference schemes. The properties become particularly interesting in the case when the computational grids are nonuniform, on which the finite difference operators do not commute. To investigate the solution properties, we introduce the graininess function, and express the numerical solution as functions of the variable grid steps, that is, functions of the graininess and its dynamic derivatives implemented …

The Role Of Biostatistics In Medical Devices: Making A Difference In People’S Lives Every Day (Abstract), Gregory Campbell

Kenneth C. Schraut Memorial Lectures

Statistics plays a key role in society in general and, in particular, in the fields of biology and medicine.

2005 (Fall), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2005 Fall Colloquium

2005 (Winter), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2005 Winter Colloquium

Positive Operators And Maximum Principles For Ordinary Differential Equations, Paul W. Eloe

Mathematics Faculty Publications

We show an equivalence between a classical maximum principle in differential equations and positive operators on Banach Spaces. Then we shall exhibit many types of boundary value problems for which the maximum principle is valid. Finally, we shall present extended applications of the maximum principle that have arisen with the continued study of the qualitative properties of Green’s functions.

Gröbner Bases: A Natural Extension Of Gaussian Reduction And The Euclidean Algorithm (Abstract), Patrick Flinn

Kenneth C. Schraut Memorial Lectures

Gröbner bases can be used to answer fundamental questions concerning certain sets of polynomials. For example, when are two such sets equal? Given such a set and another polynomial, is this polynomial a member of that set? In this introduction to Gröbner bases, we motivate their salient features by considering the Euclidean algorithm and Gaussian row reduction of matrices from a slightly different point of view.

Existence, Uniqueness And Constructive Results For Delay Differential Equations, Paul W. Eloe, Youssef N. Raffoul, Christopher C. Tisdell

Mathematics Faculty Publications

Here, we investigate boundary-value problems (BVPs) for systems of second-order, ordinary, delay-differential equations. We introduce some differential inequalities such that all solutions (and their derivatives) to a certain family of BVPs satisfy some a priori bounds. The results are then applied, in conjunction with topological arguments, to prove the existence of solutions. We then apply earlier abstract theory of Petryshyn to formulate some constructive results under which solutions to BVPs for systems of second-order, ordinary, delay-differential equations are A-solvable and may be approximated via a Galerkin method. Finally, we provide some differential inequalities such that solutions to our equations are …

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

Kenneth C. Schraut Memorial Lectures

No abstract provided.

Stability Properties Of Linear Volterra Integrodifferential Equations With Nonlinear Perturbation, Muhammad Islam, Youssef Raffoul

Mathematics Faculty Publications

A Lyapunov functional is employed to obtain conditions that guarantee stability, uniform stability and uniform asymptotic stability of the zero solution of a scalar linear Volterra integrodifferential equation with nonlinear perturbation.

Boundedness And Stability In Nonlinear Delay Difference Equations Employing Fixed Point Theory, Muhammad Islam, Ernest Yankson

Mathematics Faculty Publications

In this paper we study stability and boundedness of the nonlinear difference equation

x(t+1)=a(t)x(t)+c(t)Δx(t−g(t))+q(x(t),x(t−g(t))).

In particular we study equi-boundedness of solutions and the stability of the zero solution of this equation. Fixed point theorems are used in the analysis.