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A quotient space Approximation Model of Multiresolution Signal Analysis

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Journal of Computer Science & Technology 2005年第1期20卷 90-94页

作者： LingZhang BoZhang ArtificialIntelligenceInstitute AnhuiUniversityHefei230039P.R.China／／StateKeyLabofIntelligentTechnologyandSystemsComputerScienceDepartmentTsinghuaUniversityBeijing100084P.R.China StateKeyLabofIntelligentTechnologyandSystems ComputerScienceDepartmentTsinghuaUniversityBeijing100084P.R.China

In this paper, we present a quotient space approximation model of multiresolution signal analysis and discuss the properties and characteristics of the model. Then the comparison between wavelet transform and the quotient space approximation is made. First, when wavelet transform is viewed from the new quotient space approximation perspective, it may help us to gain an insight into the essence of multiresolution signal analysis. Second, from the similarity between wavelet and quotient space approximations, it is possible to transfer the rich wavelet techniques into the latter so that a new way for multiresolution analysis may be found.

关键词： multi-resolution signal analysis wavelet transform quotient space the second-generation wavelets

Fuzzy tolerance quotient spaces and fuzzy subsets

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Science China(Information Sciences) 2010年第4期53卷 704-714页

The structure and characteristic of fuzzy subsets are discussed by using the concepts of granulation and hierarchy in quotient space theory. First, the equivalence relation based quotient space theory is extended to the fuzzy tolerance relation. Second, the isomorphism and its discriminant of fuzzy tolerance relations are discussed. Finally, by using the fuzzy tolerance relation to define the fuzzy subset, its properties are addressed. The main results are given below: (1) several equivalent statements of fuzzy tolerance relations; (2) the definition of isomorphism of fuzzy tolerance relations; (3) the isomorphic discriminant of fuzzy tolerance relations; (4) the definition and properties of fuzzy subsets based on the fuzzy tolerance relations; and (5) the necessary and sufficient condition of the isomorphism of fuzzy subsets. These results will help us further comprehend the concepts of fuzzy tolerance relations and fuzzy subsets.

关键词： Fuzzy tolerance relation quotient space isomorphism fuzzy subset

ON BEST SIMULTANEOUS APPROXIMATION IN quotient spaceS

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Analysis in Theory and Applications 2007年第1期23卷 35-49页

作者： M. Iranmanesh H. Mohebi University of Kerman

We assume that X is a normed linear space, W and M are subspaces of X. We develop a theory of best simultaneous approximation in quotient spaces and introduce equivalent assertions between the subspaces W and W ＋ M a... 详细信息

关键词： quotient space best simultaneous approximation simultaneous pseudo-Chebyshev simultaneous quasi-Chebyshev simultaneous weakly-Chebyshev

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Acta Mathematica Scientia 1996年第3期16卷 248-256页

作者：钟怀杰 Dept. of Math. Fujian Normal University Fuzhou 350007 China

The problem whether every infinite dimensional Banach space has an infinite dimensional separable quotient space has remained unsolved for a long time. In this paper we prove: the Banach space X has an infinite dimensional separable quotient if and only if X has an infinite dimensional separable quasicomplemented subspace, also if and only if there exists a Banach space Y and a bounded linear operator T is an element of B(Y,X such that the range of T is nonclosed and dense in X. Besides, the other relevant questions for such spaces e.g. the question on operator ideals that on H.I.(hereditarily indecomposable) spaces, that on invariant subspaces of operators, etc, are also discussed.

关键词： Banach space separable space quotient space bounded linear operator

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The structural analysis of fuzzy measures

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Science China(Information Sciences) 2011年第1期54卷 38-50页

作者： ZHANG Ling1,ZHANG Bo2 & ZHANG YanPing1 1 Computer Science College,Anhui University,Hefei 230039,China 2State Key Lab of Intelligent Technology & Systems Tsinghua National Lab for Information Science & Technology Information Science & Technology College,Computer Science & Technology,Tsinghua University,Beijing 100084,China Computer Science College Anhui University Hefei China State Key Lab of Intelligent Technology & Systems Tsinghua National Lab for Information Science & Technology Information Science & Technology College Computer Science & Technology Tsinghua University Beijing China

From quotient space based granular computing theory we explore the fuzzy measures of fuzzy sets. Based on the structural analysis of fuzzy sets,we present an"isotropism"*** this assumption we achieved the following insights:(1)the uniqueness of a fuzzy measure being isotropic on a finite complete semi-ordered set;(2)the necessary and suffcient condition of the isomorphism for fuzzy measure functions in fuzzy mathematics;(3)the necessary and suffcient condition that fuzzy measures have fuzzy and granular monotonicity;(4)under a certain assumption,the analytic expression for fuzzy *** results clarify the relationship between fuzzy measures and granular computing,reveal the essence of fuzzy measures,and provide a simple way of constructing fuzzy measures.

关键词： quotient space fuzzy set fuzzy measure rough set structural analysis

Asymptotically Isometric Copy of l~β(0

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Journal of Mathematical Research with Applications 2011年第3期 562-566页

作者： Chen ZHI,Mei Mei SONG Department of Mathematics,Tianjin University of Technology,Tianjin 300384,P.R.China

Assume X is a normed space,every x * ∈ S(X*) can reach its norm at some point in B(X),and Y is a β-normed *** there is a quotient space of Y which is asymptotically isometric to l β,then L(X,Y) contains an asymptotically isometric copy of l β.Some sufficient conditions are given under which L(X,Y) fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L(X,Y).

关键词： asymptotically isometric copy space of bounded linear operators quotient space fixed point property.

A NOTE ON COMPLEX STRICTLY CONVEXITY AND COMPLEX SMOOTHNESS

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数学研究 1994年第1期 198-199页

作者： Zeng Renying(Chongqing Teachers’ CollegeChongqing 630047)

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ＡＮＯＴＥＯＮＣＯＭＰＬＥＸＳＴＲＩＣＴＬＹＣＯＮＶＥＸＩＴＹＡＮＤＣＯＭＰＬＥＸＳＭＯＯＴＨＮＥＳＳ￥ＺｅｎｇＲｅｎｙｉｎｇ（ＣｈｏｎｇｑｉｎｇＴｅａｃｈｅｒｓ＇ＣｏｌｌｅｇｅＣｈｏｎｇｑｉｎｇ６３００４７）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ...

关键词： quotient space conjugate operator complex extreme point complex stricly convex space complex smooth space.

Knowledge Calling System Based on quotient

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Knowledge Calling System Based on Quotient