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

Abstract

We revisit a key function arised in studies of nematic liqorder 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.