Abstract and Applied Analysis 
Volume 2007 (2007), Article ID 76209, 7 pages
doi:10.1155/2007/76209
Research Article

Monotonicity of a Key Function Arised in Studies of Nematic Liquid Crystal Polymers

Hongyun Wang1 and Hong Zhou2

 1Department of Applied Mathematics and Statistics, University of California, Santa Cruz 95064, CA, USA
2Department of Applied Mathematics, Naval Postgraduate School, Monterey 93943, CA, USA
Received 13 April 2007; Accepted 11 July 2007

Recommended by Nobuyuki Kenmochi

Abstract

We revisit a key function arised in studies of nematic liquid crystal polymers. Previously, it was conjectured that the function is strictly decreasing and the conjecture was numerically confirmed. Here we prove the conjecture analytically. More specifically, we write the derivative of the function into two parts and prove that each part is strictly negative.