Physical Sciences and Mathematics Commons^™

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.

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 …

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

Undergraduate Mathematics Day

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

Undergraduate Mathematics Day

No abstract provided.

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

Undergraduate Mathematics Day

No abstract provided.

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

Kenneth C. Schraut Memorial Lectures

No abstract provided.

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.

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 …

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.