In the present paper, we consider the majorization theorem (also known as Karamata's inequality) and the respective minima of the majorization (the so-called M-sets) for f-energy potentials of $m$-point configurations on the unit sphere. In particular, we show the optimality of regular simplexes, describe some M-sets of small cardinality, define and discuss spherical f-designs.

翻译：在本文件中,我们考虑了单位领域F-能源潜力(即所谓的M-set)的主要定理(又称Karamata的不平等)和各自的微小定理(即所谓的M-set),特别是,我们显示了常规简单轴的最佳性,描述了一些小基点的M-set,定义和讨论球形设计。