2017
Том 69
№ 5

All Issues

Local Maxima of the Potential Energy on Spheres

Radchenko D. V.

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Abstract

Let S d be a unit sphere in ℝ d+1, and let α be a positive real number. For pairwise different points x 1,x 2, . . . ,x N S d , we consider a functional E α (x 1,x 2, . . . ,x N ) = Σ ij ||x i x j ||α . The following theorem is proved: for αd − 2, the functional E α (x 1,x 2, . . . ,x N ) does not have local maxima.

English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 10, pp 1585-1587.

Citation Example: Radchenko D. V. Local Maxima of the Potential Energy on Spheres // Ukr. Mat. Zh. - 2013. - 65, № 10. - pp. 1427–1429.

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