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Kametaka, Y., Watanabe, K., Yamagishi, H., Nagai, A. and Takemura, K. (2011) The Best Constant of Discrete Sobolev Inequality on Regular Polyhedron. Trans. Japan Soc. Ind. Appl. Math., 21, 289-308. (In Japanese)

has been cited by the following article:

• TITLE: The Best Constant of Discrete Sobolev Inequality on a Weighted Truncated Tetrahedron

  AUTHORS: Yoshikatsu Sasaki

  KEYWORDS: The Best Constant, Sobolev Inequality, Discrete Laplacian, Weighted Graph, Truncated Polyhedron

  JOURNAL NAME: World Journal of Engineering and Technology, Vol.3 No.3C, October 22, 2015

  ABSTRACT: The best constant of discrete Sobolev inequality on the truncated tetrahedron with a weight which describes 2 kinds of spring constants or bond distances. Main results coincides with the ones of known results by Kametaka et al. under the assumption of uniformity of the spring constants. Since the buckyball fullerene C60 has 2 kinds of edges, destruction of uniformity makes us proceed the application to the chemistry of fullerenes.