Fuzzy压缩原理

本文给出以Ｆｕｚｚｙ数作为Ｌｉｐｓｃｈｉｔｚ常数的压缩映射的新概念，并成功证明了Ｆｕｚｚｙ数值函数的不动点定理。     

Locally Weak Version of the Contraction Mapping Principle

Mathematical Notes - The Banach Contraction Mapping Principle has many generalizations and extensions in different directions. Here we define $$(\varepsilon,\psi)$$ -Uniformly Local Weak...     

连续函数压缩映射问题的讨论

就连续函数应用问题的教学内容进行探讨.介绍数列和连续函数的压缩映射原理及其在方程求解,数学建模等方面的应用,并给出压缩映射的一般形式.续而通过压缩映射原理在图像处理和导航系统中的应用,阐明创新思想的重要性,以求开拓学生的思路和想象空间.     

拟对称映射的最大伸缩商与边界伸缩商

文献[1]在研究单位圆周$\pd$上的拟对称自同胚的最大伸缩商与极值最大伸缩商之间的关系时,证明了:如果拟对称自同胚h的最大伸缩商K_q(h)不能在某个以开单位圆△为域、顶点在单位圆周$\pd$上的拓扑四边形Q处达到,则一定有K_q(h)≤H(h)成立,其中H(h)为h的边界伸缩商.这一结论在文献[1]中起着重要作用,但证明比较烦琐.该文主要给出该结论一个简单的证明,并且利用这一结论研究拟对称自同胚的最大伸缩商何时可以在某个拓扑四边形上达到.     

概率度量空间中压缩映象的不动点定理

本文通过引入压缩映象集序列的概念,推广并综合了张石生以及V.M.Sehger和A.T.Bharucha-Reid中某些主要定理的结果。     

The Action of the Mapping Class Group on Maximal Representations

Let Γ _g be the fundamental group of a closed oriented Riemann surface Σ _g , g ≥ 2, and let G be a simple Lie group of Hermitian type. The Toledo invariant defines the subset of maximal representations Rep_max(Γ _g , G) in the representation variety Rep(Γ _g , G). Rep_max(Γ _g , G) is a union of connected components with similar properties as Teichmüller space . We prove that the mapping class group acts properly on Rep_max(Γ _g , G) when , SU(n,n), SO*(4n), Spin(2,n).     

极大单调映象的零点定理的推广

设Ｅ是自反Ｂａｎａｃｈ空间，极大单调满足其中Ω为Ｅ中有界开集且０∈Ω∩Ｄ（Ｔ），则Ｔ在中有零点．     

利用压缩映像原理证明连续函数的介值性定理

以压缩映像原理为工具,给出了闭区间上连续函数介值性定理的另一种证明.     

概率度量空间压缩映象的拟Picard迭代收敛性定理

In this paper the notion of quasi-Picard iteration of a contraction mapping on a probabilistic metric space is introduced, and four convergence theorems for such an iteration are proved.     

直觉Menger空间中的广义压缩映射原理及其在微分方程中的应用

利用Atanassov的思路,将直觉Menger空间定义为由Menger提出的Menger空间的自然推广.同时也得出一个新广义压缩映射,并运用该压缩映射证明了直觉Menger空间中微分方程解的存在性定理.     

Mapping a sphere into Euclidean space

Translated from Matematicheskie Zametki, Vol. 46, No. 3, pp. 3–8, September, 1989.     

Mapping Planar Graphs into Projective Cubes

Projective cubes are obtained by identifying antipodal vertices of hypercubes. We introduce a general problem of mapping planar graphs into projective cubes. This question, surprisingly, captures several well‐known theorems and conjectures in the theory of planar graphs. As a special case , we prove that the Clebsch graph, a triangle‐free graph on 16 vertices, is the smallest triangle‐free graph to which every triangle‐free planar graph admits a homomorphism.     

Multiplicative Lattice with Maximal Condition

This paper defines multiplicative lattice. The conception of multiplicative lattice is abstracted from several lattices, which may be composed of ideals of the associative ring, ideals of the non-associative ring, or ideals of the both non-assooiatiye and non-distributive ring and which may be composed of normal subgroups of the group as well. Definition 1. The multiplicative lattice L is a lattice with following conditions: 1. L is complemented and Dedekind's, the least upper bound of L equals 1 and the greatest lower bound of L equals 0. 2. The multiplication is closed and ab\leq a \cap b, where a\cap b denotes the greatest lower bound of a and b. 3.a(b+c)=ab+ac,(b+c)=ba+bc, where b+c denotes the least upper bound of b and c. Suppose L is multiplicative lattice with maximal condition, the following theorems are proved: Theorem 1. Every element a of L has normal (right) third decomposition, that means every element is the intersection of finite number of (right) third elements, whose (right) third roots are different from each other and if $a=T_1\cap \cdots \cap T_m=T_1'\cap \cdots\cap T_n'$ are two different normal (right) third decomposition of a, then m=n and their third roots are equal correspondingly by rearranging properly Theorem 2. If A is an element of L and has property that c^2\leq A \rightarrow c\leq A, then A is the intersection of finite number of prime elements. Theorem 3. Every element of L has primary decomposition if and only if L satisfies Artin-Rees condition. Definition 2. u is called a solvable radical of the multiplicative lattice with maximal condition if u is the least upper bound, of the subset of L whose every element a? satisfies that there exists a group of positive integers n_1,\cdots,n_r such that $X^n_1,\cdots,n_r=0$. Theorem 4. u is an intersection of finite number of prime elements. Theorem 5. If L is semi-simple, i. e. $O=u=\cap\limits_{i=1}^n P_i$, and if $P_i+P_j=1(i\ne j)$ and $1\cdot 1=1$ then 1 is the direct sum in R_1,\cdots,R_n, where $R_i=P_1\cap \cdots \cap P_i-1\cap P_i+1\cap \cdots \cap P_n$     

Rings with Maximal Finite Subrings

In[1 ] and[2 ] ,itwas proved thata ring with a finite maximal subring mustbe finite.Special cases of this result had been shown for commutative ring(see[3 ] ) and for PI-rings (see [4 ] ) . Lanski[5] extends the result to the ring with a finite maximal invariantsubring with respect to certain automorphism.In this paper,we shall consider ringswith maximal finite subrings. Such a ring,of course,is not necessarily finite. Becauseevery finite ring has maximal finite subrings,we shall be interest…     

The Intersection of a Maximal Intransitive Subgroup with a Maximal Imprimitive Subgroup

Ａｃｌａｓｓｉｆｉｃａｔｉｏｎｏｆｔｈｅｍａｘｉｍａｌｓｕｂｇｒｏｕｐｓｏｆａｌｔｅｒｎａｔｉｎｇａｎｄｓｙｍｍｅｔｒｉｃｇｒｏｕｐｓｈａｓｂｅｅｎｄｅｔｅｒｍｉｎｅｄｂｙ [1 ]Ｂａｓｅｄｏｎ [1 ] ,ｗｅｉｎｖｅｓｔｅｇａｔｅｔｈｅｉｎｔｅｒｓｅｃｔｉｏｎｏｆａｍａｘｉｍａｌｉｎｔｒａｎｓｉｔｉｖｅｓｕｂｇｒｏｕｐｗｉｔｈａｍａｘｉｍａｌｉｍｐｒｉｍｉｔｉｖｅｓｕｂｇｒｏｕｐ .Ｉｔｐｌａｙｓａｎｉｍｐｏｒｔａｎｔｒｏｌｅｉｎｉｎｖｅｓｔｅｇａｔｉｎｇｔｈｅｒｅｌａｔｉｏｎｓｈｉｐｂｅｔｗｅｅｎａｂ…