Geodesic
Experimental investigation on the uniqueness of a center of a body
Shigehiro Sakata1
1 Faculty of Education University of Miyazaki 1-1 Gakuen Kibanadai West Miyazaki, 889-2192, Japan
Annales Polonici Mathematici, Tome 118 (2016) no. 2-3, pp. 149-171 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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The object of our investigation is a point that gives the maximum value of a potential with a strictly decreasing radially symmetric kernel. It defines a center of a body in $\mathbb {R}^m$. When the kernel is the Riesz kernel or the Poisson kernel, such a center is called an $r^{\alpha -m}$-center or an illuminating center, respectively. The existence of a center is easily shown but uniqueness does not always hold. The main results in this paper are some new sufficient conditions for the uniqueness.
DOI : 10.4064/ap4047-12-2016
Keywords: object investigation point gives maximum value potential strictly decreasing radially symmetric kernel defines center body mathbb kernel riesz kernel poisson kernel center called alpha m center illuminating center respectively existence center easily shown uniqueness does always main results paper sufficient conditions uniqueness

Shigehiro Sakata 1

1 Faculty of Education University of Miyazaki 1-1 Gakuen Kibanadai West Miyazaki, 889-2192, Japan 
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Shigehiro Sakata. Experimental investigation on the uniqueness of a center of a body. Annales Polonici Mathematici, Tome 118 (2016) no. 2-3, pp. 149-171. doi: 10.4064/ap4047-12-2016

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