Fuzzy线性映射

在基本Fuzzy点空间上提出了Fuzzy线性映射的概念,证明了Fuzzy线性映射的表示定理,讨论了Fuzzy线性映射的合成、可逆及保持Fuzzy集合的线性运算等相关性质。     

Fuzzy映射和乘积Fuzzy测度

从研究Ｆｕｚｚｙ集合的直积和Ｆｕｚｚｙ关系出发,讨论了Ｆｕｚｚｙ关系和Ｆｕｚｚｙ映射的一些性质,最后利用Ｆｕｚｚｙ关系的截影性质给出了乘积Ｈ型Ｆｕｚｚｙ测度的存在性定理。     

一类模糊逻辑系统幺半群与同态映射

首先利用代数中幺半群的概念给出了模糊逻辑系统专业领域的概念, 建立专业领域概念的目的是为了规范模糊逻辑系统中语言变量的取值范围, 从而将模糊逻辑系统看作是某个笛卡儿乘积幺半群的有限子集. 然后利用这个笛卡儿乘积幺半群的乘积运算构造了模糊逻辑系统幺半群. 最后, 在一定的约定条件下证明了通常使用的一类Mamdani形模糊逻辑系统的输出可以看作是从模糊逻辑系统幺半群到连续函数域的同态映射.     

L-fuzzy向量空间的L-fuzzy线性映射

给出L-fuzzy向量空间的L-fuzzy线性映射等概念,并给出了它的一些等价刻画。     

笛卡儿闭Domain范畴的两个重要性质

对于CONT的任意一个笛卡儿闭的满子范畴C,构造CONT的两个新的满子范畴R-C(以C对象的收缩为对象的范畴)和B-C(以C扩张序列的双极限为对象的范畴),并证明了它们都是笛卡儿闭范畴。由于R-C和B-C都包含C为其满子范畴,利用上述结果可得CONT的极大笛卡儿闭子范畴必对收缩和双极限封闭。本文还从范畴笛卡儿闭性的角度给出了Domain理论中一个公开问题的等价描述。     

单值映射对与集值映射对的公共不动点

在度量空间中,引进了单值映射对与集值映射对的调和概念,对调和单值映射对与集值映射对建立了公共不动点定理及相应的随机公共不动点定理。     

A hybrid-Trefftz element containing an elliptic hole

Much work on special elements that simplify geometrical modelling of structures containing holes, cracks and/ or inclusions has been reported extensively in the literature. This paper presents a hybrid-Trefftz element containing elliptic hole formulated using Hellinger–Reissner principle by employing trial functions based on the mapping technique and the Cauchy integral method. The element presented in this paper could be regarded as an improved formulation over Piltner [Special finite elements with holes and internal cracks, Int. J. Numer. Methods Eng. 21 (1985) 1471–1485] element because the chosen trail functions in this paper have provided relatively more stable solutions. The use of the element with other ordinary displacement-based finite elements has also yielded very accurate solutions even when very coarse meshes relative to the size of the elliptic hole have been used.     

Bordism invariants of the mapping class group

We define new bordism and spin bordism invariants of certain subgroups of the mapping class group of a surface. In particular, they are invariants of the Johnson filtration of the mapping class group. The second and third terms of this filtration are the well-known Torelli group and Johnson subgroup, respectively. We introduce a new representation in terms of spin bordism, and we prove that this single representation contains all of the information given by the Johnson homomorphism, the Birman-Craggs homomorphism, and the Morita homomorphism.     

A Note on Cyclic Vectors for the Shift

We strengthen a result in the literature that gives a necessary condition for the shift on the Hardy space H 2 ( G ) of some bounded, simply connected region G to be cyclic. Part of this involves a characterization, in terms of ‘ G , of what it means for G to be the image of under a conformal map whose boundary values are univalent a.e. m (normalized Lebesgue measure on ).