A theorem on planar continua and an application to automorphisms of the field of complex numbers

Let K be a continuum in the plane which does not lie on a line. Then the set of differences, K - K, contains an open set. Let ψ be an automorphism of the field of complex numbers which is bounded on an F_σ set of positive inductive dimension. Then ψ is continuous.     

Automorphisms of Constant Weight Codes and of Divisible Designs

We show that the automorphism group of a divisible design is isomorphic to a subgroup H of index 1 or 2 in the automorphism group of the associated constant weight code. Only in very special cases H is not the full automorphism group.     

The Bergman Kernel on Cartan-egg Domains of the First Type

Ｉｎ 1 92 1 ,Ｂｅｒｇｍａｎｉｎｔｒｏｄｕｃｅｄａｋｅｒｎｅｌｆｕｎｃｔｉｏｎ ,ｗｈｉｃｈｉｓｎｏｗｋｎｏｗｎａｓｔｈｅＢｅｒｇｍａｎｋｅｒｎｅｌｆｕｎｃｔｉｏｎ .ＩｔｉｓｗｅｌｌｋｎｏｗｎｔｈａｔｔｈｅｒｅｅｘｉｓｔｓａｕｎｉｑｕｅＢｅｒｇｍａｎｋｅｒｎｅｌｆｕｎｃｔｉｏｎｆｏｒｅａｃｈｂｏｕｎｄｅｄｄｏｍａｉｎｉｎＣｎ.ＦｏｒｗｈｉｃｈｄｏｍａｉｎｓｃａｎｔｈｅＢｅｒｇｍａｎｋｅｒｎｅｌｆｕｎｃｔｉｏｎｂｅｃｏｍｐｕｔｅｄｂｙｅｘｐｌｉｃｉｔｆｏｒｍｕｌａｓ?Ｔｈｉｓｉｓａｎｉｍｐｏｒｔａｎｔ…     

On distance nonregularity of Preparata codes

It is shown that among all Preparata codes only the code of length 16 is distance regular. An analogous result takes place for Preparata codes after puncturing any coordinate (only the code of length 15 is distance regular).     

K-POTENT PRESERVING LINEAR MAPS

Let B(X) be the Banach algebra of all bounded linear operators on a complex Banach space X. Let k ≥ 2 be an integer and φ a weakly continuous linear surjective map from B(X) into itself. It is shown that φ is k-potent preserving if and only if it is k-th-power preserving, and in turn, if and only if it is either an automorphism or an antiautomorphism on B(X) multiplied by a complex number λ satisfying λk-1= 1. Let A be a von Neumann algebra and B be a Banach algebra, it is also shown that a bounded surjective linear map from A onto B is k-potent preserving if and only if it is a Jordan homomorphism multiplied by an invertible element with (k - l)-th power I.     

交换子空间格代数的自同构与插值性质

本文第一部分用ＣＳＬ序区间投影集上的偏序给出ＣＳＬ代数自同构为拟空间实现的一个充分条件,作为推论,证明了代数自同构是拟空间实现的．第二部分,给出ＣＳＬ的序积与序和格代数的紧及有限插值性质,由此可得出一些非完全分配ＣＳＬ代数的插值性质。