Monotonicity of a Key Function Arised in Studies of Nematic Liquid Crystal Polymers
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2007/76209 |
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| _version_ | 1832559946299867136 |
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| author | Hongyun Wang Hong Zhou |
| author_facet | Hongyun Wang Hong Zhou |
| author_sort | Hongyun Wang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0051b698a564443492a45382801d3f89 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0051b698a564443492a45382801d3f892025-02-03T01:28:44ZengWileyAbstract and Applied Analysis1085-33751687-04092007-01-01200710.1155/2007/7620976209Monotonicity of a Key Function Arised in Studies of Nematic Liquid Crystal PolymersHongyun Wang0Hong Zhou1Department of Applied Mathematics and Statistics, University of California, Santa Cruz, CA 95064, USADepartment of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943, USAWe 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.http://dx.doi.org/10.1155/2007/76209 |
| spellingShingle | Hongyun Wang Hong Zhou Monotonicity of a Key Function Arised in Studies of Nematic Liquid Crystal Polymers Abstract and Applied Analysis |
| title | Monotonicity of a Key Function Arised in Studies of Nematic Liquid Crystal Polymers |
| title_full | Monotonicity of a Key Function Arised in Studies of Nematic Liquid Crystal Polymers |
| title_fullStr | Monotonicity of a Key Function Arised in Studies of Nematic Liquid Crystal Polymers |
| title_full_unstemmed | Monotonicity of a Key Function Arised in Studies of Nematic Liquid Crystal Polymers |
| title_short | Monotonicity of a Key Function Arised in Studies of Nematic Liquid Crystal Polymers |
| title_sort | monotonicity of a key function arised in studies of nematic liquid crystal polymers |
| url | http://dx.doi.org/10.1155/2007/76209 |
| work_keys_str_mv | AT hongyunwang monotonicityofakeyfunctionarisedinstudiesofnematicliquidcrystalpolymers AT hongzhou monotonicityofakeyfunctionarisedinstudiesofnematicliquidcrystalpolymers |