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Neural Network for Solving Monotone LinearComplementary Problems

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Communications in Nonlinear Science and Numerical Simulation 1999年第2期4卷 128-132页

作者： xingban GAO(department of mathematics, {2. normal University, xi’an 710062. china) department of mathematics Shanxi Normal University Xi'an 710062 China

A neural network for solving monotone linear complementary problem isproposed. It has not involved any parameter and is proven to be uniformly, asymptoticallyand stably convergent to an exact solution of the linear co... 详细信息

关键词： linear complementary problems neural network asymptotical stability

Relations among the category of topological molecular lattices and certain related categories

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Chinese Science Bulletin 1997年第8期42卷 636-640页

作者： WANG Guojun and LI Yongming1. Institute of mathematics, shaanxi {2. University, xi’an 710062. china 2. department of Basic Science, Northwestern Institute of Architecture Engineering, xi’an 710061, china Institute of mathematics Shaanxi Normal University Xi’an China department of Basic Science Northwestern Institute of Architecture Engineering Xi’an China

TAKING the theory of fuzzy topology and point set topology as background,the theory of topo-logical molecular lattices was first advanced in 1979,and after several generalizationsrefs.[4,5] are its general *** topology and point set topology are both special casesof topological molecular lattices as pointed out in ref.[4],whereas it seems not clear whetherone can develop the theory of topological molecular lattices by means of methods in

关键词： category pick-up-one principle.

NOETHERIAN GT-REGULAR RINGS ARE REGULAR

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Chinese Annals of mathematics,Series B 1994年第4期15卷 463-468页

作者： LI HUISHI(department of mathematics, {2. normal Univisity xi’an 710062. china.) 陕西师范大学数学系陕西西安 710062

It is proved that for a left Nootherian z-graded ring A, if every finitely generated gradedA-module has finite projective dimension (i.e., A is gr-regular) then every finitely generatedA-module has finite projective dimension (i.e., A is regular). Some applications of this resultto filtered rings and some classical cases are also given.

关键词： Graded ring Regular ring Projective dimension.

Fuzzy controllers based on some fuzzy implication operators and their response functions

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Progress in Natural Science:Materials International 2004年第1期14卷 16-21页

作者： LI Hongxing 1*, YOU Fei 1 and PENG Jiayin 2.1. department of mathematics, Beijing {2. University, Beijing 100875, china 2. department of mathematics, Neijiang Teacher's College, Neijiang 641112. china) Beijing normal Univ Dept Math Beijing 100875 Peoples R China

The fuzzy controllers constructed by 2. fuzzy implication operators based on CRI algorithm and their response functions are discussed. The conclusions show that the fuzzy controllers constructed by 9 fuzzy implication operators are universal approximators to continuous functions and can be used in practical fuzzy control systems. And these 9 fuzzy implication operators except for Einstein operator intersection are all the adjoint pairs of some fuzzy implication operators. Besides, there are 3 other fuzzy controllers formed by fuzzy implication operators being regarded approximately as fitted functions.

关键词： fuzzy implication operators CRI algorithm fuzzy controllers response functions universal approximators

K-uniformly rotund spaces and k-uniformly smooth spaces

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Chinese Science Bulletin 1998年第2期43卷 92-95页

作者： Suyalatu 1 and WU Congxin 2.1. department of mathematics,Inner Mongolia {2. University, Huhhot 01002., china 2. department of mathematics, Harbin Institute of Technology, Harbin 150006, china department of mathematics Inner Mongolia Normal University Huhhot China department of mathematics Harbin Institute of Technology Harbin China

The conception of k_uniform smoothness (KUS) is introduced. It is the extension of the conception of uniform smoothness. It is proved that the k_uniform smoothness and Sullivan’s K_uniform rotundity (KUR) are the daul notions. X+* is a KUR space if and only if X is a KUS space, X+* is a KUS space if and only if X is a KUR space. If X is a KUS space, then X is a (K+1)US space. It is also proved that the KUS space includes the Nan’s k_strongly smooth space.

关键词： K_uniform smoothness K_uniform convexity.

Congruences on ideal nil-extension of completely regular semigroups

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Chinese Science Bulletin 1998年第5期43卷 379-381页

作者： REN Xueming 1, 2.GUO Yuqi 2.and CEN Jiaping (Shum Kar-ping) 31. department of mathematics, xi’an University of Architecture & Technology, xi’an 710055, {2. 2. department of mathematics, Yunnan University, Kunming 650091, {2. 3. department of department of mathematics Xi’an University of Architecture & Technology Xi’an China department of mathematics Yunnan University Kunming China department of mathematics Chinese University of Hong Kong Hong Kong

Let S be an ideal nil-extension of a completely regular semigroup K by a nil semigroup Q with zero. A concept of admissible congruence pairs (δ,ω) of S is introduced, where δ and ω are a congruence on Q and a congruence on K respectively. It is proved that every congruence on S can be uniquely respresented by an admissible congruence pair (δ,ω) of S. Suppose that ρ K denotes the Rees congruence induced by the ideal K of S. Then it is shown that for any congruence σ on S,a mapping Γ:σ|→(σ Q,σ K) is an order-preserving bijection from the set of all congruences on S onto the set of all admissible congruence pairs of S,where σ K is the restriction of σ to K and σ Q=(σ∨ρ K)/ρ K. Moreover,the lattice of congruences of S is also discussed. As a special case,every congruence on completely Archimedean semigroups S is described by an admissible quarterple of S. The following question is asked: Is the lattice of congruences of the completely Archimedean semigroup a semimodular lattice?

关键词： completely regular semigroups ideal nil-extension congruences.

Compactness theorems of fuzzy semantics

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Chinese Science Bulletin 2000年第2期45卷 120-125页

作者： WANG Guojun Institute of mathematics, shaanxi {2. University, xi’an/710062. china Institute of mathematics Shaanxi Nornial University Xi’an China

The relationship among diverse fuzzy semantics vs. the corresponding logic consequence operators has been analyzed systematically The results that compactness and logical compactness of fuzzy semantics are equivalent to compactness and continuity of the logic consequence operator induced by the semantics respectively have been proved under certain conditions. A general compactness theorem of fuzzy semantics have been established which says that every fuzzy semantics defined on a free algebra with members corresponding to continuous functions is compact.

关键词： fuzzy semantics compactness loglc compactness inductive set point compactness Lukasiewicz semantics.

The connectedness of H(λ) unit interval and H(λ) real line

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Chinese Science Bulletin 1997年第23期42卷 2016-2017页

作者： LI Shenggangdepartment of mathematics, {2. normal University, xi’an 710062. china department of mathematics Shaanxi Normal University Xi’an China

JUST like in classical mathematics, fuzzy unit interval I(L) and fuzzy real line R(L), thebasic and important research objects of fuzzy mathematics, also interest a good few *** 1992. Wang and Xu, by refining the topology of I(L), defined a new fuzzy unit in-terval——H(λ) unit interval I(L), and established the Stone-Cech compactification theoryfor weakly induced L-fuzzy topological spaces. In 1993, Zhang and Liu introduced the con-cept of weak inducification of L-fuzzy topological space, and in this way, I(L) is exactly

关键词： real line The connectedness of H unit interval and H line

Quasi-formal deductive system for fuzzy propositional calculus

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Chinese Science Bulletin 1997年第14期42卷 1154-1157页

作者： WANG GuojunInstitute of mathematics, shaanxi {2. University, xi’an 710062. china Institute of mathematics Shaanxi Normal University Xi’ an China

ELKAN’s report 'The paradoxical success of fuzzy logic' at the 11th IA Annual Conferenceof America in July, 1993 caused quite a great stir in the research field of IA as well as fuzzysystems, fifteen scholars published papers thereupon to refute it and finally Elkan answeredthem with his paper 'The paradoxical controversy over fuzzy logic'. An exclusive analysiscan be found in Prof. Wu Wangming’s paper. It seems from this event that fuzzy proposi-

关键词： ΣR-tautology α-mod us ponens α-hypothetical syllogism quasi-formal deductive system.