Colloquia — Fall 1998
Friday, November 13, 1998
| Title: |
Domination Numbers of Small Graphs |
| Speaker: |
Edwin Clark |
| Time: |
3:00-4:00 |
| Place: |
PHY 118 |
Abstract
This will be a self-contained talk on the tightest upper bound for the
domination number of graphs with n vertices and minimum degree delta.
In this talk I will concentrate on graphs with a small number of vertices. The
smallest unknown value is for n = 15 and d = 6. This work
apparently requires neither Banach spaces nor the Axiom of Determinancy. I will
define all the necessary graph theoretic terms.
Friday, November 20, 1998
| Title: |
The Wigner-Ville Distribution and Time-Frequency Signal Analysis |
| Speaker: |
Lokenath Debnath
University of Central Florida |
| Time: |
3:00-4:00 |
| Place: |
PHY 118 |
Abstract
Although the Fourier transform analysis is one of the great achievements in mathematics
and has widespread applications in science and engineering, it cannot be used effectively
to analyze non-stationary signals. In order to overcome the inherent difficulty of the
Fourier transform, three or four different methods including the Gabor transform, the Zak
transform, wavelet transform and the Wigner distribution have been developed for
time-frequency signal analysis. In this talk, recent developments of the Wigner-Ville
distribution, and M-band wavelet analysis will be discussed. Special attention will be
given to applications to a wide variety of signals encountered in physical, engineering
and biomedical sciences.
Friday, December 4, 1998
| Title: |
N Charges on the Sphere |
| Speaker: |
A. Toomre |
| Time: |
3:00-4:00 |
| Place: |
PHY 118 |
Monday, December 7, 1998
| Topic: |
New observations on the Gollnitz-Gordon and Rogers-Ramanujan identities |
| Speaker: |
Krishnaswami Alladi
University of Florida |
| Time: |
3:00-4:00 |
| Place: |
PHY 108 |
Abstract
In the entire theory of partitions and q-series, the Rogers-Ramanujan
identities are unmatched in simplicity, elegance, and depth. The Gollnitz-Gordon
identities are the perfect analogues to the modulus 8 for what the Rogers-Ramanujan
identities are to the modulus 5. In this talk two new and simple proofs of the
Gollnitz-Gordon identities will be given by bisection of well known and fundamental theta
function identities. Similar methods applied to the Rogers-Ramanujan identities lead to
new product representations modulo 80. Other implications of this method of bisection
include new shifted partition identities, a new proof of the quituple product identity,
and modular relations for various theta series arising as generating functions of
partition functions. The talk will be accessible to non-experts and graduate students.
Tuesday, December 8, 1998
| Title: |
The WZ Algorithms and Some Applications to Problems in Analysis and
Combinatorics |
| Speaker: |
Jet Wimp
Drexel University |
| Time: |
3:00-4:00 p.m. |
| Place: |
PHY 109 |
Abstract
Most mathematicians have heard about the large body of algorithms known
collectively as the WZ algorithms, which recently earned for their creators the
Steele prize. However for many of us, the processes of accessing and using these
algorithms remain mysterious.
In this lecture, I will explain how two of the most powerful algorithms in
these packages, zeil and hyper, can be accessed from the internet and I illustrate
their use in three typical problems in applied mathematics: finding explicit
formulas for the associated Legendre polynomials, calculating Hankel determinants
of combinatorial polynomials, and determining connecting coefficients that arise
in certain quantum chemistry problems.