Share This Article:

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

Abstract Full-Text HTML XML Download Download as PDF (Size:318KB) PP. 149-154
DOI: 10.4236/wjet.2015.33C022    3,744 Downloads   4,101 Views  

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Sasaki, Y. (2015) The Best Constant of Discrete Sobolev Inequality on a Weighted Truncated Tetrahedron. World Journal of Engineering and Technology, 3, 149-154. doi: 10.4236/wjet.2015.33C022.

References

[1] Brezis, H. (1983) Analyse fonctionnelle: Théorie et applications. Masson, Paris.
[2] Talenti, G. (1976) The Best Constant of Sobolev Inequality. Annali di Matematica Pura ed Applicata, 110, 353-372. http://dx.doi.org/10.1007/BF02418013
[3] Marti, J.T. (1983) Evaluation of the Least Constant in Sobolev’s In-equality for . SIAM J. Numer. Anal., 20, 1239-1242. http://dx.doi.org/10.1137/0720094
[4] Kametaka, Y., Yamagishi, H., Watanabe, K., Nagai, A. and Takemura, K. (2007) Riemann Zeta Function, Bernoulli Polynomials and the Best Constant of Sobolev Inequality. Sci. Math. Japan, 65, 333-359.
[5] Kametaka, Y., Watanabe, K. and Nagai, A. (2005) The Best Constant of Sobolev Inequality in an n Dimensional Euclidean Space. Proc. Japan Acad., Ser. A, 81, 57-60. http://dx.doi.org/10.3792/pjaa.81.57
[6] Kametaka, Y., Watanabe, K., Nagai, A. and Pyatkov, S. (2005) The Best Constant of Sobolev Inequality in an n Dimensional Euclidean Space. Sci. Math. Japan, 61, 15-23.
[7] Yamagishi, H., Kametaka, Y., Nagai, A., Watanabe, K. and Takemura, K. (2009) Riemann Zeta Function and the Best Constants of Five Series of Sobolev Inequalities. RIMS K?ky?roku Bessatsu, B13, 125-139.
[8] Yamagishi, H., Kametaka, Y., Takemura, K., Watanabe, K. and Nagai, A. (2009) The Best Constant of Discrete Sobolev Inequality Corresponding to a Bending Problem of a Beam under Tension on an Elastic Foundation. Trans. Japan Soc. Ind. Appl. Math., 19, 489-518. (In Japanese)
[9] Kametaka, Y., Nagai, A., Yamagishi, H., Takemura, K. and Watanabe, K. (2014) The best constant of Dicrete Sobolev Inequality on the C60 Fullerene Buckyball. arXiv.org e-Print Archive. http://arxiv.org/abs/1412.1236
[10] 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)
[11] Nagai, A., Kametaka, Y., Yamagishi, H., Takemura, K. and Watanabe, K. (2008) Discrete Bernoulli polynomials and the Best Constant of Dicrete Sobolev Inequality. Funkcial. Ekvac., 51, 307-327. http://dx.doi.org/10.1619/fesi.51.307
[12] Yamagishi, H., Kametaka, Y., Nagai, A., Watanabe, K. and Takemura, K. (2014) The Best Constant of Dicrete Sobolev Inequality on Truncated Polyhedra. Abstract of the 10th Meeting of the Union of Research Activity Groups, Japan SIAM, Kyoto Univ., Kyoto, 9-10 March 2014. (In Japanese) http://chaosken.amp.i.kyoto-u.ac.jp/_src/sc2490/jsiam_s2_no4_yamagisi_abst.pdf
[13] Yamagishi, H., Kametaka, Y., Nagai, A., Watanabe, K. and Takemura, K. (2013) The Best Constant of Three Kinds of Dicrete Sobolev Inequalities on Regular Polyhedron. Tokyo J. Math., 36, 253-268. http://dx.doi.org/10.3836/tjm/1374497523
[14] Kroto, H.W., Heath, J.R., O’Brien, S.C., Curl, R.F. and Smalley, R.E. (1985) C60: Buckminsterfullerene. Nature, 318, 162-163. http://dx.doi.org/10.1038/318162a0
[15] Shinohara, H. and Saito, Y. (2011) Science of fullerenes and CNTs. Nagoya University Press, Nagoya.
[16] Hawkins, J.M., Meyer, A.L., Timothy, A., Loren, S. and Hollander, F.J. (1991) Scinence 252, 312. http://dx.doi.org/10.1126/science.252.5003.312
[17] Hedberg, K., et al. (1991) Bond Lengths in Free Molecules of Buckminsterfullerene, C60, from Gas-Phase Electron Diffraction. Science, 254, 410. http://dx.doi.org/10.1126/science.254.5030.410
[18] Yannoni, C.S., Bernier, P.P., Bethune, D.S., Meijer, G. and Sa-lem, J.R. (1991) NMR determination of the bond lengths in C60. J. Am. Chem. Soc., 113, 3190-3192. http://dx.doi.org/10.1021/ja00008a068

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.