In the present paper a general formula for exact calculation of the discrepancy of an arbitrary finite point set of dimension d≥2 is explicitly given only in terms of the components of the points.
In this paper, we first give the concept of m-degree center-connecting line in n-dimensional Euclidean space Enand investigate its several properties, then we obtain the length of m-degree center-connecting line formu...In this paper, we first give the concept of m-degree center-connecting line in n-dimensional Euclidean space Enand investigate its several properties, then we obtain the length of m-degree center-connecting line formula in finite points set. As its application,we extend the Leibniz formula and length of medians formula in n-dimensional simplex to polytope.展开更多
文摘In the present paper a general formula for exact calculation of the discrepancy of an arbitrary finite point set of dimension d≥2 is explicitly given only in terms of the components of the points.
基金Supported by the Department of Education Science Research Project of Hunan Province(09C470)
文摘In this paper, we first give the concept of m-degree center-connecting line in n-dimensional Euclidean space Enand investigate its several properties, then we obtain the length of m-degree center-connecting line formula in finite points set. As its application,we extend the Leibniz formula and length of medians formula in n-dimensional simplex to polytope.
