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引用次数: 0
摘要
在这篇文章中，我们找到了几个对称函数的最大值，这些变量是距离的平方|zi - z j|， 1 i < j d，在一些d个复点z1，…之间。，单位圆盘中的zd。我们显式地计算了m = 1,2,3,4时σm的最大值，并找到了z1，…的条件。，zd，在此条件下达到最大值。这个问题是由Cassels(1966)的一个不等式和Alexander随后的一个猜想引起的。数学学科分类(2010):52A40, 11R06。
Maximal values of symmetric functions in distances between points
In this note we find the maximal values of several symmetric functions in the variables which are the squares of distances |zi − z j| , 1 i < j d , between some d complex points z1, . . . ,zd in the unit disc. We compute the maximums of σm , for m = 1,2,3,4 , explicitly and find the conditions on z1, . . . ,zd under which those maximal values are attained. This problem is motivated by an inequality of Cassels (1966) and a subsequent conjecture of Alexander. Mathematics subject classification (2010): 52A40, 11R06.
期刊介绍：
''Mathematical Inequalities & Applications'' (''MIA'') brings together original research papers in all areas of mathematics, provided they are concerned with inequalities or their role. From time to time ''MIA'' will publish invited survey articles. Short notes with interesting results or open problems will also be accepted. ''MIA'' is published quarterly, in January, April, July, and October.
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