  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 Rm. When we choose the Riesz kernel or the Poisson kernel
as the kernel, such centers are called a radial center or an illuminating
center, respectively. The existence of a center is easily shown but the
uniqueness does not always hold. Sufficient conditions of the uniqueness of a
center have been studied by some researchers. The main results in this paper
are some new sufficient conditions for the uniqueness of a center of a body.
