Monotonicity of a key function arised in studies of nematic liquid crystal polymers. (English) Zbl 1140.33310

Wang, Hongyun; Zhou, Hong

Abstr. Appl. Anal. 2007, Article ID 76209, 7 p. (2007).

Summary: 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.

MSC:

33E20	Other functions defined by series and integrals
82D30	Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)

References:

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