### Symmetries and differential equations in physics and other
applications

**Organizers**: Weiqing Xie,
wxie@csupomona.edu,
Cal Poly Pomona

M. Nakashima

**Speaker: **Martin Nakashima**,
**Cal Poly Pomona

**Title: **Boundary Values in de Sitter Space

Abstract: 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

Title: Second order dynamical systems used for
generating "practical" test functions for filtering and sampling
procedures

Abstract: 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.

Speaker: Weiqing Xie,
wxie@csupomona.edu,
Cal Poly Pomona

Title: A mathematical model from stress driven
diffusion

Abstract: 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.