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

Hongyun Wang | Zendy; Hong Zhou | Zendy

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

Author(s) -

Hongyun Wang,

Hong Zhou

Publication year - 2007

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2007/76209

Subject(s) - conjecture , liquid crystal , monotonic function , mathematics , function (biology) , key (lock) , derivative (finance) , polymer , pure mathematics , mathematical analysis , condensed matter physics , chemistry , physics , computer science , organic chemistry , computer security , evolutionary biology , financial economics , economics , biology

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

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