8:45-9:00 Taufiquar Khan, Clemson University
On some integrals over a unit sphere
In this talk, we will discuss some new integrals over a unit sphere arising from modeling photon transport in biological tissue. We will first discuss our motivation behind evaluating these integrals. Then we will use simple undergraduate analysis including Cauchy principle value theorem to evaluate these integrals. Our talk will be very general and should be accessible to a wide audience including undergraduate students.
9:05-9:20 Bo Zhang, Fayetteville State University
Stability in a System of Linear Partial Differential Equations
In this paper, we introduce the concept of weakly similar matrices and derive formulas of Liapunov functions for showing the asymptotic stablity of a system of linear partial differential equations ∂u/∂t = AΔu(t,x), where A is an n x n matrix, u = (u1, u2, …, un)T, and Δu = (Δu1, Δu2, ... , Δun)T. These formulas are also modified and applied to a number of nonautonomous linear and nonlinear systems and models in structural stability, traveling wave, and Navier-Stoker equations.
Late change: the talk by Russell Herman on Revisiting Quasistationary Perturbation Theory for Equations in 1+1 Dimensions has been move to session MSSI1, Saturday 10:00-10:15.
9:25-9:40 Rajah P. Varatharajah, North Carolina A&T State University
Collimated Light Channel Propagation in Waveguides
The dynamics of light beams interacting at an interface separating tow nonlinear optical media and in waveguides is studied numerically and analytically. The beam dynamics is simulated by the Beam propagation method. Some new results will be presented in this talk.