软BCK-代数的模糊理想

将模糊集理论应用到软BCK-代数中,引入了软BCK-代数的模糊理想,并获得了它的基本性质。然后,讨论了BCK-代数的模糊理想在同态下的像和逆像的性质。最后,通过软同态概念的引入,给出了软BCK-代数的模糊同构定理。     

广义对偶犹豫模糊软集及其在决策中的应用

犹豫模糊软集作为一种处理不确定问题的工具受到了广泛关注。本文将广义模糊软集与对偶犹豫模糊集相结合,提出了广义对偶犹豫模糊软集的概念,给出了广义对偶犹豫模糊软集的交、并、补、“且”、“或”运算的概念,并基于这些概念研究其若干相关性质。此外,定义了广义对偶犹豫模糊软集的信息能量、相关性和相关系数的概念并讨论了它的性质。最后,给出了基于广义对偶犹豫模糊软集的多属性决策方法,并通过实例说明了该方法的的可行性和有效性。     

模糊软集与模糊软群

在进行了阐述模糊软集的相关概念和性质后,给出了模糊软群的定义并研究了相关性质.     

BCI代数的软关联理想和软正定关联理想

给出BCI代数的软关联理想和软正定关联理想的概念,讨论软理想、软关联理想和软正定关联理想三者之间的关系,研究了两个软关联理想(软正定关联理想)的扩展交、限制交、限制并和限制差分的性质。     

软BCI-代数的软固执理想

将Molodtsov的软集理论应用到BCI-代数的理想中,引进了软BCI-代数的软固执理想的概念,并给出具体实例证明了软BCI--代数的软固执理想的存在性.讨论了软BCI-代数的软固执理想与软理想的关系,给出了软BCI-代数的软固执理想的扩张性质,研究了两个软BCI-代数的软固执理想的扩展交、限制交、限制并和限制差分的性质.     

对偶导集及其应用

借助对偶范畴的思想和方法在点集拓扑学中引入了对偶导集概念,讨论了对偶导集和对偶导集运算的相关性质.并以此为基础引入了对偶连通空间的概念,讨论了对偶连通空间和连通空间之间的关系,借此给出了不连通空间的几个等价刻画.为拓扑空间的研究提供了新的途径.     

等差数列和等比数列性质的对偶

在等差数列和等比数列的性质中,存在着一种有趣的对偶关系.例如:等差数列{an}中等比数列{bn}中     

新型软半环

将软集的参数集赋予半环的代数结构,提出新型软半环的概念,并利用对偶软集的方法给出新型软半环的等价刻画;然后讨论了两个新型软半环在限制交和且等运算下仍然是新型软半环的性质;最后得到新型软半环的同态像和原像仍然是新型软半环的结论.     

新型软半环北大核心

将软集的参数集赋予半环的代数结构,提出新型软半环的概念,并利用对偶软集的方法给出新型软半环的等价刻画;然后讨论了两个新型软半环在限制交和且等运算下仍然是新型软半环的性质;最后得到新型软半环的同态像和原像仍然是新型软半环的结论.     

Fuchsian Groups, Quasiconformal Groups, and Conical Limit Sets

We construct examples showing that the normalized Lebesgue measure of the conical limit set of a uniformly quasiconformal group acting discontinuously on the disc may take any value between zero and one. This is in contrast to the cases of Fuchsian groups acting on the disc, conformal groups acting discontinuously on the ball in dimension three or higher, uniformly quasiconformal groups acting discontinuously on the ball in dimension three or higher, and discrete groups of biholomorphic mappings acting on the ball in several complex dimensions. In these cases the normalized Lebesgue measure is either zero or one.

     

Regular Sets and Geometric Groups

If G is a permutation group acting on a set Ω, a subset Λ of Ω is called a regular set for G if the set-stabilizer of Λ in G is the identity subgroup. We show here that the projective and affine semi-linear groups acting in the natural way as permutation groups on their respective finite geometries, have, in general, for all finite dimensions and all finite fields, regular sets of points. The exceptions to this are found, and an extension of the results to infinite fields is discussed.     

群上的Fuzzy子集的换位子

引入群上的n个Fuzzy子集的换位子的概念,讨论群上的n个Fuzzy子集的换位子的重要性质,其中一些性质推广了文[3]中相应的结论。     

Interpretable Groups, Stably Embedded Sets, and Vaughtian Pairs

The paper concerns sufficiently saturated structures M overa countable language with a unary predicate P. It is shown thatif P(M)is stably embedded and there are no Vaughtian pairs withrespect to P, then an infinite group is interpretable over M(in an infinitary sense of ‘interpretable’). Also,it is shown that if M is -categorical, f:DP is a 0-definablemap with finite fibres, and P(M) is stably embedded but D isnot, then some infinite group is first-order interpretable overM.     

Rn上的非初等变换群及其极限集

该文对高维非初等Mò'bius变换群进行了研究,得到了一些重要性质,给出了几个关于离散准则和代数收敛性的定理.     

Limit Sets of Free Convergence Groups

We study the limit sets of convergence groups and prove that the limit set of a free discontinuous cocompact convergence group with an invariant component of the discontinuity domain is a discontinuum.     

Limit Sets of Free Convergence Groups

We study the limit sets of convergence groups and prove that the limit set of a free discontinuous cocompact convergence group with an invariant component of the discontinuity domain is a discontinuum.     

The finite embeddability property for residuated lattices, pocrims and BCK-algebras

A class of algebras has the finite embeddability property (FEP) if every finite partial subalgebra of an algebra in the class can be embedded into a finite algebra in the class. We investigate the relationship of the FEP with the finite model property (FMP) and strong finite model property (SFMP).? For quasivarieties the FEP and the SFMP are equivalent, and for quasivarieties with equationally definable principal relative congruences the three notions FEP, FMP and SFMP are equivalent. The variety of intuitionistic linear algebras –which is known to have the FMP–fails to have the FEP, and hence the SFMP as well. The variety of integral intuitionistic linear algebras (also known as the variety of residuated lattices) does possess the FEP, and hence also the SFMP. Similarly contrasting statements hold for various subreduct classes. In particular, the quasivarieties of pocrims and of BCK-algebras possess the FEP. As a consequence, the universal theories of the classes of residuated lattices, pocrims and BCK-algebras are decidable. Received February 16, 2001; accepted in final form November 2, 2001. RID="h1" ID="h1"The second author was supported by a postdoctoral research fellowship of the National Research Foundation of South Africa, hosted by the University of Illinois at Chicago.