Correction to the Paper - Determination of a Domain in Complex Space by its Automorphism Group

The author offers some corrections to his article which appeared in Vol. 47, No. 3 of this journal.     

Generalized Digroups

The concept of digroup has been proposed as a generalization of continuous groups whose tangent space is a Leibniz algebra. We study a further generalization of the digroup structure in which we do not demand that the inverses are necessarily bilateral. We characterize a generalized digroup as a set and as a product. We show an analogous to the first isomorphism theorem. Additionally, we explore the concept of dialgebra digroup.     

基于合意空间的模糊子群

利用合意空间(ConsensusSpace)理论给出了一个群的C模糊子群的定义.指出这种模糊子群实际上是基于t范(Tm范)的模糊子群.证明了Rosenfeld的模糊子群是C模糊子群,且每一个C模糊子群都与一类特殊的C模糊子群同构.从而为模糊子群提供了新的理论基础.     

The Isometric Isomorphism of Toeplitz Operators on

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The Measure-Preserving Shift on the Cantor Set

ＴｈｅＭｅａｓｕｒｅ┐ＰｒｅｓｅｒｖｉｎｇＳｈｉｆｔｏｎｔｈｅＣａｎｔｏｒＳｅｔ＊）ＺｅｎｇＦａｎＰｉｎｇ＊＊）（曾凡平）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｎｊｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｎａｎｊｉｎｇ，２１００９３）Ａｂｓｔｒａ...     

2IV^m-p设计的弱最小低阶混杂与纯净效应准则等价的条件

该文给出了2IVm-p设计包含最多纯净两因子交互效应与该设计具有弱最小低阶混杂等价的几个条件．并在文章的末尾给出了一组既具有弱最小低阶混杂又包含最多纯净两因子交互效应的2IVm-p设计．     

Isomorphism in ternary complex: Poly(ethylene oxide), urea and thiourea

Herein,we demonstrated that poly(ethylene oxide)(PEO),urea and thiourea can crystallize into novel ternary complex with the molar ratio of guest polymer and host small molecule as 3:2,and proved that the ternary complex behaves isomorphism phenomenon by varying the ratio between urea and thiourea for the first time.This observation gives a boost to prepare co-crystals of different small molecules that cannot be obtained by direct mixing without the aid of polymer chains.     

La relation différence et l'anti-isomorphie

This paper deals with pairs of binary relations defined on the same finite basis and which the 3-element restrictions are isomorphic and those of 5-element restrictions are isomorphic or anti-isomorphic. To each of these pairs, we associate an equivalence relation which yields a decomposition of these relations into classes that we will characterize. As application, we get the treshold of half-reconstruction for tournaments.     

Effect of conformational adaptation of 4,4′-(hexafluoro-isopropylidene) diphthalic anhydride (6FDA) on the structural features of a perylene-containing copolyimide

A series of perylene-containing random copolyimides with different ratios of diaminododecyl perylene tetracarboxylic dianhydride (PPI-12) and 4,4′-(hexafluoro-isopropylidene) diphthalic anhydride (6FDA) have been studied. Copolymerization improves the solubility and the copolyimide with a low percentage (less than 20% of total dianhydrides) of perylene becomes highly soluble in conventional solvents, such as, CHCl₃, CH₂Cl₂, or THF etc. The positions of the absorption maxima in the UV-visible spectra do not change with 6FDA concentration, but the relative intensities do. Although the homopolymer PPI-12 does not show a distinct glass transition, its T_g was derived by extrapolation of the DSC results with the copolymers. The copolymers are semi-crystalline up to a concentration of 60% (mol) 6FDA. It is of interest that the spacings of X-ray reflections also do not change with the addition of 6FDA. This is rationalized on the basis that the conformation of the 6FDA segment does not cause any significant difference in the preferred conformational shapes of the homopolymer of PPI-12. Due to this “conformational isomorphism” 6FDA is not a significant chain “kinker” in this case.     

Fuzzy同余和正规Fuzzy子群(英文)

自从A. Rosenfeld在1971年提出Fuzzy子群的概念以来,在Fuzzy群的研究方面已有不少进展,例如见[1,2,5,6,10,11,14]。另一方面,L.A.Zadeh首创的Fuzzy关系理论的研究也是硕果累累,例如见[3,4,8,12,13,15]。本文通过Fuzzy同余关系和正规Fuzzy子群的相互联系,将这两个方向的研究成果进行“嫁接”和“杂交”,得到许多有趣的结果。主要结果是定理2.7,定理3.1和3.6。本文另一主题是引入T-Fuzzy群的正规T-Fuzzy子群的新概念,当T是正则t-范算子时,得到了T-Fuzzy群的三个同构定理,作者认为它比现有的相应同构定理更为简洁、广泛和自然。