Symmetries and differential equations in physics and other applications

A special session in 

Fourth International Conference on Dynamical Systems and Differential Equations

Wilmington, NC, USA, May 24-27, 2002


Organizers:   Weiqing Xie,,  Cal Poly Pomona
                       M. Nakashima


Speaker:  Martin Nakashima,   Cal Poly Pomona
Title:  Boundary Values in de Sitter Space
The theory of Dirac Singletons, as developed by Flato and Fronsdal, is a massless gauge theory in de Sitter space. Although noted primarily for its physical content and connections to group theory, it may be of further interest to mathematicians as it suggests some problems in differential equations. This talk will present some of these issues.

Speaker:   Cristian I. Toma,  Physics Department, Politehnica University, Bucharest, Romania
Second order dynamical systems used for generating "practical" test functions for filtering and sampling      procedures
As it is known, in averaging procedures the user is interested in the mean value of the received signal over a certain time interval. Usually this operation is performed by an integration of the signal on this time interval (considered to be constant) the result of the integration being proportional to the mean value of the signal. However, such structures are very sensitive at random variations of the integration period (generated by the switching phenomena at the end of the integration). For this reason, a multiplication of the received signal with a test-function (a function which differs to zero only on this time interval and with continuous derivatives of any order on the whole real axis) is recommended. This paper presents some invariance properties of differential equations, which can be used for generating a "practical" test-function on this time interval, and it presents also the properties of second order oscillating systems (considered as generating "practical" test functions) in filtering and sampling procedures.

Weiqing Xie,,  Cal Poly Pomona
A mathematical model from stress driven diffusion
This talk concerns the study of a system of differential equations involving stress-driven diffusion which occurs in materials science and technology and its applications.  We will explain and analyse the mathematical model and present mathematical analysis for the problem.