NCTS(South)/ NCKU Math Colloquium
DATE	2012-03-08　16:10-17:00
PLACE	R204, 2F, NCTS, NCKU
SPEAKER	Prof. Moody T. Chu (朱天照 教授)（North Carolina State University, USA）
TITLE	DNA-Like Structure of Nonlinear Functions
ABSTRACT	Nonlinear functions have been employed as the most basic tool for characterizing or exploring nonlinear phenomena in nature. Yet even this fundamental device, as will be demonstrated in this article, exhibits certain inherent dynamics never realized before. Generalizing the notion of gradient over a scalar field to vector fields, singular vectors of the Jacobian of any given function form a moving frame pointing in directions along which the norm of the function changes most critically. Trajectories of these singular vectors, referred to as singular curves, unveil some interesting, perplexing, innate dynamics per the given function. At points where two or more singular values coalesce, curious and complex behavior occurs, manifesting specific landmarks for the underlying function. This talk reports for the first time such a dynamics system. For demonstration purpose only, the current study focuses primarily on the case of two-variable functions which, commonly used to characterize parametric surfaces, already exhibits some intriguing patterns. It is shown that, analogous to the double helix structure of DNA, two strands and eight base pairings could determine the respective properties.