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

Abstract and Applied Analysis. 2007;2007 DOI 10.1155/2007/76209

 

Journal Homepage

Journal Title: Abstract and Applied Analysis

ISSN: 1085-3375 (Print); 1687-0409 (Online)

Publisher: Hindawi Publishing Corporation

LCC Subject Category: Science: Mathematics

Country of publisher: Egypt

Language of fulltext: English

Full-text formats available: PDF, HTML, ePUB, XML

 

AUTHORS

Hongyun Wang (Department of Applied Mathematics and Statistics, University of California, Santa Cruz, CA 95064, USA)
Hong Zhou (Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943, USA)

EDITORIAL INFORMATION

Blind peer review

Editorial Board

Instructions for authors

Time From Submission to Publication: 27 weeks

 

Abstract | Full Text

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.