Abstract and Applied Analysis
Volume 2007 (2007), Article ID 76209, 7 pages
Monotonicity of a Key Function Arised in Studies of Nematic Liquid Crystal Polymers
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
Academic Editor: Nobuyuki Kenmochi
Copyright © 2007 Hongyun Wang and Hong Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.