D. P. Dwiggins, PhD
Department of Mathematical Sciences
Bachelor of Science,
Physics, Southwestern at
Master of Science,
Doctor of Philosophy,
Dissertation: Fixed Point Theory and Periodic Solutions for Differential Equations
Major Professor: T. A. Burton
without Continuous Dependence," Equadiff 6 (
Lecture Notes in Mathematics 1192, pages 115-121 (with T. A. Burton)
Ø "An Asymptotic Fixed Point Theorem for a Locally Convex Space" (1988)
Proceedings of the American Mathematical Society 103 (1), pages 247-251
(with T. A. Burton)
Ø "Periodic Solutions of Functional Differential Equations with Infinite Delay"
(1989) Journal of the
(with T. A. Burton and Y. Feng)
reliable, and simple-to-use method for the anlaysis of a population of values
of a random variable using the Weibull probability distribution: Application to
acrylic bone cement fatigue results” (2005), Bio-Medical Materials and
Engineering 15 (5), pages 349-355 (with
Other Contributions to the University
Summary of Research Interests
During my time spent working with T. A. Burton, we were trying to find ways to extend results from Fixed Point Theory which were known to work in a Banach space to a space without the structure of the norm. As I neared completion of my dissertation, I discovered that many of the results which had been used for years (such as Schauder’s Theorem, published in 1935) did not actually require a normed space, and that a weaker structure, namely a Frechet space, would suffice. I have since then worked off and on trying to find other theorems which could be extended from a Banach space to a Frechet space, such as Nussbaum’s Asymptotic Fixed Point Theory from the 1970’s.
In trying to
sort out the technicalities, I have needed to use techniques from not only
functional analysis but also topology and a bit of degree theory. When trying to collate ideas from different
areas of mathematics, it became apparent there was not always an agreed-upon
consensus of certain ideas. For
example, I found six totally different definitions of what a Frechet space
should be, and I attempted to unify most of these in a talk I gave at a
During the past twelve years the most call I have had for my mathematical expertise has been in the area of statistics, and in particular regression analysis. While at the Center for Earthquake Research and Information, I developed a new method of linear regression (Orthogonal L1 Regression) in order to better define the equations used to calculate earthquake magnitudes based on the lengths of seismic signatures. To my knowledge this is still original research needing to be published. My most recent publication was another application of regression analysis, this time to a bio-medical engineering problem, part of the doctoral dissertation for one of my former calculus students.
Other than this statistical aside, my main interests lie in applied analysis, and I recently returned as a contributing member of the Analysis Seminar in the Department of Mathematical Sciences at The University of Memphis. In Spring 2009 Dr. Burton will be on campus as a visiting professor, and I will be studying the topic of Integral Equations with him, in particular the application of Fixed Point Theory to the existence and stability of solutions of integral equations, as well as the existence of periodic or asymptotically periodic solutions.