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Convergence of Fuzzy set Sequences

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Journal of Donghua University(English Edition) 2002年第4期19卷 29-32页

作者：冯玉瑚 Department of Applied Mathematics Dong Hua UniversityShanghai200051

There are more than one mode of convergence with respect to the fuzzy set sequences. In this paper,common six modes of convergence and their relationships are discussed. These six modes are convergence in uniform metric D, convergence in separable metric Dp or D*p, 1 ≤ p ＜∞, convergence in level set, strong convergence in level set and weak convergence. Suitable counterexamples are given. The necessary and sufficient conditions of convergence in uniform metric D are described. Some comme nts on the convergence of LRfuzzy number sequences are represented.

关键词： Fuzzy set, Hausdorff metric, convergence relationship, LR-fuzzy number

THE STRUCTURE OF LASALLE’S INVARIANT set FOR LOTKA-VOLTERRA SYSTEMS

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Science China Mathematics 1991年第7期34卷 783-790页

作者：刘立陆征一王东明 Department of Mathematics Sichuan Normal University Chengdu 610066 PRC Department of Mathematics Sichuan University Chengdu 610064 PRC Research Institute for Sumbolic Computation Johannes Kepler University Austria and Institute of Systems Science Academia Sinica Beijing 100080 PRC

By developing the mechanical proving method, we determine the structure of LaSalle’sinvariant set for 7-dimensional Lotka-Volterra food chain systems, based on Ritt-Wu’s prin-ciple. We then further show that the locally asymptotical stable equilibrium point of Lotka-Volterra food chain systems for 7 dimension must be globally stable.

关键词： Lotka-Volterra systems LaSalle’s invariant set, well-ordering principle global stability.

Quasi-cardinality of a Fuzzy set on a Measurable Universe of Discourse

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Journal of Donghua University(English Edition) 2002年第2期19卷 81-83页

作者：耿辉陆余楚 Department of Mathematics Shanghai University 200436

The concepts of quasi-cardinality, possibility and expectation of a fuzzy set on a measurable set, as a generalization of the quasi-cardinality of a fuzzy set on a finite universe of discourse is proposed. Also some p... 详细信息

关键词： Quasi-cardinality of the fuzzy set, fuzzy nature number, the measure of a set

Involutive characteristic sets of algebraic partial differential equation systems

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Science China Mathematics 2003年第4期46卷 469-487页

作者：陈玉福高小山 Graduate School Chinese Academy of SciencesBeijing 100039China Institute of Systems Science AMSSChinese Academy of SciencesBeijing 100080China

This paper presents an algorithm to reduce a nonlinear algebraic partial differential equation system into the involutive characteristic set with respect to an abstract involutive prolongation direction, which covers the existing algorithms based on Riquier method, Thomas method, and Pommaret method. It also provides new algorithms for computing involutive characteristic sets due to the existence of new involutive directions. Experiments show that these new algorithms may be used to significantly reduce the computational steps in Wu-Ritt's characteristic set method for algebraic partial differential equations.

关键词： involutive characteristic set, integrability conditions, algebraic partial differential equation system, Wu-Ritt's characteristic set method.

Julia sets of permutable Holomorphic maps Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

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Science China Mathematics 2006年第11期49卷 1715-1721页

作者： SINGH Anand P Department of Mathematics University of Jammu Jammu-180006India

Let f and g be two permutable transcendental holomorphic maps in the *** shall discuss the dynamical properties of f, g and f o g and prove, among other things, that if either f has no wandering domains or f is of bou...

关键词： Julia set, Fatou set, permutable maps.

The necessary and sufficient conditions for returns to scale properties in generalized data envelopment analysis model

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Science China(Technological Sciences) 2002年第5期45卷 503-517页

作者：魏权龄于刚陆剑受 Institute of Operations Research and Mathematical Economics People's University of China Beijing 100872 China Department of MSIS Graduate School of Business and Center for Management of Operations and LogisticsUniversity of Texas at Austin Austin TX 78712 U.S.A. Department of Economics Guangxi University Nanning 530004 China

We give definitions on increasing, constant and decreasing returns to scale under the generalized data envelopment analysis (GDEA) model. The GDEA model prossesses cone structures for describing evaluators’ preferences toward different decision making units (DMU) and toward different input / output categories. The GDEA model contains many important DEA models as its subclasses. Based upon the definition, we discuss and rigorously prove the necessary and sufficient conditions for a DMU to have increasing, constant and decreasing returns to scale under a GDEA model, and discuss and clarify the differences and relationships of these conditions under different subclasses of the GDEA model. Furthermore, we describe a method based on a two-stage linear program to test returns to scale properties.

关键词： data envelopment analysis, efficient frontier, multiple input/output decision making,production possibility set, returns to scale.

On Fatou sets concerning Yang-Lee theory

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Science China Mathematics 2005年第4期48卷 433-447页

作者： QIAO Jianyong Center of Mathematics China University of Mining and Technology Beijing100083 China

The sets of the points corresponding to the complexphases of the Potts model on the diamond hierarchcal lattice arestudied. These sets are the Fatou sets of a family of rationalmappings. The topological structures of ... 详细信息

关键词： Fatou set, phase transition, iteration, rational mapping.

Stability of Julia sets for a quadratic random dynamical system

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Science China Mathematics 2002年第11期45卷 1381-1389页

作者：龚志民邱维元王键 1. Lab of Mathematics for Nonlinear Science Fudan University 200433 Shanghai China 2. Department of Mathematics Xiangtan University 411105 Xiangtan China 3. Business School Xiangtan University 411105 Xiangtan China

For a sequence (cn) of complex numbers, the quadratic polynomials fcn:= z2 + Cn and the sequence (Fn) of iterates Fn: = fcn ο ? ο fc1 are considered. The Fatou set F(Cn) is defined as the set of all $z \in \hat {\mathbb{C}}: = {\mathbb{C}} \cup \left\{ \infty \right\}$ such that (Fn) is normal in some neighbourhood of z, while the complement J(Cn) of F(cn) (in $\hat {\mathbb{C}}$ ) is called the Julia set. The aim of this paper is to study the stability of the Julia set J(Cn) in the case where (cn) is bounded. A problem put forward by Brück is solved.

关键词： Fatou set, Julia set, random iterates, stability.

On conformal measures for infinitely renormalizable quadratic polynomials

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Science China Mathematics 2005年第10期48卷 1411-1420页

作者： HUANG Zhiyong~1 JIANG Yunping~(2,3) & WANG Yuefei~3 1. School of Information,Renmin University of China,Beijing 100872,China 2. Department of Mathematics,Queens College,City University of New York,NY 11367,USA Department of Mathematics,Graduate School,City University of New York,New York,NY 10016,USA 3. Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,China 1. School of Information Renmin University of China 100872 Beijing China 2. Department of Mathematics Queens College City University of New York 11367 NY USA 3. Department of Mathematics Graduate School City University of New York 10016 New York NY USA 4. Academy of Mathematics and Systems Science Chinese Academy of Sciences 100080 Beijing China

We study a conformal measure for an infinitely renormalizable quadratic polynomial. We prove that the conformal measure is ergodic if the polynomial is unbranched and has complex bounds. The main technique we use in t...

关键词： Julia set, conformal measure, three-dimensional puzzle, infinitely renormalizable quadratic polynomial.