Colloquium: Dr. Murray Muraskin

Friday Apr 10, 4:00–5:00pm, 211 Witmer Hall. Refreshments at 3:30pm.

Mathematical Aesthetic Principles/Nonintegrable Systems

This talk presents a study of a set of mathematical principles that can be classified as "aesthetic", and shows that these principles can be cast into a set of nonlinear equations. This system of equations is nonintegrable in general. New techniques to handle the nonintegrability feature are discussed. We then show how this system of equation leads to sinusoidal solutions, sine within sine solutions, the phenomenon known as beats, random type oscillations, two and three dimensional lattices, as well as multi wavepacket systems. The sinusoidal solutions occur when the arbitrary data associated with equations causes the equations to be linearized. This sinusoidal behavior totally disappears once the integrability equations are satisfied, illustrating how important the nonintegrability concept is to the development.

Dr. Murray Muraskin obtained his Bachelor's degree from Massachusetts Institute of Technology and his Ph.D. from the University of Illinois at Urbana. He has held positions at the University of Minnesota and the University of Nebraska, and he was a professor at the University of North Dakota from 1966–1995. His research interests are in mathematical physics, and he is the author of the book "Mathematical Aesthetic Principles/Nonintegrable Systems" published by World Scientific in 1995.