Abstract and Applied Analysis

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

Hongyun Wang and Hong Zhou

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2007 (2007), Article ID 76209, 7 pages.

Dates
First available in Project Euclid: 27 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1204126595

Digital Object Identifier
doi:10.1155/2007/76209

Mathematical Reviews number (MathSciNet)
MR2345987

Zentralblatt MATH identifier
1140.33310

Citation

Wang, Hongyun; Zhou, Hong. Monotonicity of a Key Function Arised in Studies of Nematic Liqorder Crystal Polymers. Abstr. Appl. Anal. 2007 (2007), Article ID 76209, 7 pages. doi:10.1155/2007/76209. https://projecteuclid.org/euclid.aaa/1204126595


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References

  • H. Zhou and H. Wang, ``Steady states and dynamics of 2-D nematic polymers driven by an imposed weak shear,'' Communications in Mathematical Sciences, vol. 5, no. 1, pp. 113--132, 2007.
  • A. W. Bush, Perturbation Methods for Engineers and Scientists, CRC Press, Boca Raton, Fla, USA, 1992.
  • E. J. Hinch, Perturbation Methods, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, UK, 1991.
  • C. Luo, H. Zhang, and P. Zhang, ``The structure of equilibrium solutions of the one-dimensional Doi equation,'' Nonlinearity, vol. 18, no. 1, pp. 379--389, 2005.
  • P. Constantin and J. Vukadinovic, ``Note on the number of steady states for a two-dimensional Smoluchowski equation,'' Nonlinearity, vol. 18, no. 1, pp. 441--443, 2005.
  • I. Fatkullin and V. Slastikov, ``A note on the Onsager model of nematic phase transitions,'' Communications in Mathematical Sciences, vol. 3, no. 1, pp. 21--26, 2005.