Develop, Apply and Evaluate Wavelet Technology.

On this contract, they completed work in three major areas the mathematical foundations of wavelet theory, and applications of wavelets to signal processing and partial differential equations. In the area of mathematical foundations, they have investigated both discrete and continuous aspects of wavelet theory. In their investigations of the applications of wavelets to signal processing, they have had two major foci image compression and computational algorithms. Furthermore they have investigated connections between the wavelet and Fourier transforms and described the characteristics of some fundamental signals In wavelet Phase space. They have applied wavelet based numerical methods to the solution of partial differential equations. Specifically, they compare the Wavelet-Galerkin method to standard numerical methods for the numerical solution of the Euler equations of a two-dimensional, incompressible fluid in a Periodic domain, the Biharmonic Helmholtz equation and the Reduced Wave equation in nonseparable, two-dimensional geometry and the Euler and Navier-Stokes equations in nonseparable, two dimensional geometry. The wavelet methods have significant advantages with regard to stability, accuracy, and rate of convergence.