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A NOTE IN APPROXIMATIVE COMPACTNESS AND MIDPOINT LOCALLY K-UNIFORM ROTUNDITY IN BANACH SPACES 被引量:4
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作者 刘春燕 张子厚 周宇 《Acta Mathematica Scientia》 SCIE CSCD 2018年第2期643-650,共8页
In this article, we prove the following results: (1) A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; (2) A ... In this article, we prove the following results: (1) A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; (2) A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set. 展开更多
关键词 k-Chebyshev set approximatively weak compactness approximative compactness weak midpoint locally k-uniform rotundity midpoint locally k-uniform rotundity k-strict rotundity
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Degree of Compactness in I-fuzzy Topological Spaces 被引量:1
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作者 李宏艳 《Northeastern Mathematical Journal》 CSCD 2008年第6期485-491,共7页
In this paper, the concept of degree of compactness is introduced in the general framework of I-fuzzy topological spaces, and its property is discussed. All good compactness are generalized to I-fuzzy topological spac... In this paper, the concept of degree of compactness is introduced in the general framework of I-fuzzy topological spaces, and its property is discussed. All good compactness are generalized to I-fuzzy topological spaces accordingly. 展开更多
关键词 I-fuzzy topology value set of compactness degrees of compactness
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Relative Strong F Compactness and Relative Ultra-F Compactness in L-topological Spaces
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作者 李尧龙 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第1期8-15,共8页
In this paper, two concepts of relative compactness-the relative strong fuzzy compactness and the relative ultra-fuzzy compactness are defined in L-topological spaces for an arbitrary L-set. Properties of relative str... In this paper, two concepts of relative compactness-the relative strong fuzzy compactness and the relative ultra-fuzzy compactness are defined in L-topological spaces for an arbitrary L-set. Properties of relative strong fuzzy sets and relative ultra-fuzzy compact sets are studied in detail and some characteristic theorems are given. Some examples are illustrated. 展开更多
关键词 Fuzzy topology complete latice relative strong F compactness relative ultra- F compactness coprime element remote neighborhood
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Almost Fuzzy Compactness in L-fuzzy Topological Spaces
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作者 Li Hong-yan Cui Wei Lei Feng-chun 《Communications in Mathematical Research》 CSCD 2015年第3期267-273,共7页
In this paper, the notion of almost fuzzy compactness is dened in L-fuzzy topological spaces by means of inequality, where L is a completely distributiveDeMorgan algebra. Its properties are discussed and many characte... In this paper, the notion of almost fuzzy compactness is dened in L-fuzzy topological spaces by means of inequality, where L is a completely distributiveDeMorgan algebra. Its properties are discussed and many characterizations of it arepresented. 展开更多
关键词 L-fuzzy topological space L-fuzzy almost compactness L-fuzzy compactness almost fuzzy compactness
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Measurement and Spatial Distribution of Urban Agglomeration Industrial Compactness in China 被引量:4
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作者 QI Weifeng FANG Chuanglin SONG Jitao 《Chinese Geographical Science》 SCIE CSCD 2008年第4期291-299,共9页
Urban agglomeration (UA) compactness means spatial concentration degree of physical entities, such as cities (towns), industries, resources, funds, traffic and technologies, whose concentration is formed according to ... Urban agglomeration (UA) compactness means spatial concentration degree of physical entities, such as cities (towns), industries, resources, funds, traffic and technologies, whose concentration is formed according to specified economic and technologic association in the process of UA formation and development. The UA industrial compactness means the concentration degree of industry and industry clusters with reference to the industrial, technologi- cal and economic relations among the cities in the UA in the process of rational industrial division and with the exten- sion of industrial chain. After analyzing the researches on compactness, this paper finds that the relevant measurement coefficient and methods reflecting industrial geographical concentration fail to link industries spatial concentration with urban spatial concentration. Taking 23 UAs as samples and classifying them by development degree, this paper probes into UA compactness and spatial distribution characteristics from the perspective of industry by adopting UA index systems of industry and measurement models. The research finds out: 1) there is obvious positive correlation between UA industrial compactness and UA development degree; 2) the spatial distribution difference of UA industrial compactness is relatively great; and 3) UA industrial compactness shows a gradually decreasing tendency from the eastern part, the middle part to the western part of China. From the research thoughts and approaches, this article suggests that studies on the UA integrated compactness measurement should be enhanced from a multidimensional perspective involving space, traffic, population density and so on. 展开更多
关键词 industrial compactness urban agglomeration(UA) China
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STRONG COMPACTNESS OF APPROXIMATE SOLUTIONS TO DEGENERATE ELLIPTIC-HYPERBOLIC EQUATIONS WITH DISCONTINUOUS FLUX FUNCTION 被引量:1
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作者 Helge Holden Kenneth H. Karlsen +1 位作者 Darko Mitrovic Evgueni Yu. Panov 《Acta Mathematica Scientia》 SCIE CSCD 2009年第6期1573-1612,共40页
Under a non-degeneracy condition on the nonlinearities we show that sequences of approximate entropy solutions of mixed elliptic-hyperbolic equations are strongly precompact in the general case of a Caratheodory flux ... Under a non-degeneracy condition on the nonlinearities we show that sequences of approximate entropy solutions of mixed elliptic-hyperbolic equations are strongly precompact in the general case of a Caratheodory flux vector. The proofs are based on deriving localization principles for H-measures associated to sequences of measurevalued functions. This main result implies existence of solutions to degenerate parabolic convection-diffusion equations with discontinuous flux. Moreover, it provides a framework in which one can prove convergence of various types of approximate solutions, such as those generated by the vanishing viscosity method and numerical schemes. 展开更多
关键词 degenerate hyperbolic-elliptic equation degenerate convection-diffusion equation conservation law discontinuous flux approximate solutions compactness
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ON COMPACTNESS FOR ITERATED COMMUTATORS 被引量:1
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作者 刘永民 于燕燕 《Acta Mathematica Scientia》 SCIE CSCD 2011年第2期491-500,共10页
The authors study the iterated commutators on the weighted Bergman spaces A2(φ), and prove that Cnh is compact on A2(φ) if and only if h ∈ B0.
关键词 Weighted Bergman space iterated commutator normal function littleBloch function compactness
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Application of Compactness Detection to Complicated Concrete-Filled Steel Tube by Ultrasonic Method 被引量:1
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作者 杨建江 王飞 +1 位作者 陆苏亮 王川 《Transactions of Tianjin University》 EI CAS 2014年第2期126-132,共7页
An example of using ultrasonic method to detect the compactness of complicated concrete-filled steel tube in certain high-rise building was discussed in this study.Because of the particularity of the complicated concr... An example of using ultrasonic method to detect the compactness of complicated concrete-filled steel tube in certain high-rise building was discussed in this study.Because of the particularity of the complicated concrete-filled steel tubular column,the plane detection method and embedded sounding pipe method were adopted in the process of effectively detecting the column.According to the results of the plane detection method and embedded sounding pipe method,the cementing status of steel tube and concrete can be concluded,which cannot be judged by the hammering method in the rectangular steel tube-reinforced concrete. 展开更多
关键词 ultrasonic method concrete-filled steel tube plane detection method embedded sounding pipe method compactness
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THE COMPACTNESS OF A KIND OF GENERALIZED HANKEL OPERATORS ON THE BERGMAN SPACE OF THE UNIT BALL 被引量:1
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作者 罗罗 史济怀 《Acta Mathematica Scientia》 SCIE CSCD 2000年第4期471-475,共5页
This paper gives the compactness criteria for a kind of generalized Hankel operators on Bergman spaces Lpa(B) defined by M. M. Peloso.
关键词 Hankel operator compactness Bergman spa?
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Compactness of Composition Operators from the p-Bloch Space to the q-Bloch Space on the Classical Bounded Symmetric Domains 被引量:1
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作者 Jianbing Su Huijuan Li +1 位作者 Xingxing Miao Rui Wang 《Advances in Pure Mathematics》 2014年第12期649-664,共16页
In this paper, we introduce the weighted Bloch spaces on the first type of classical bounded symmetric domains , and prove the equivalence of the norms and . Furthermore, we study the compactness of composition operat... In this paper, we introduce the weighted Bloch spaces on the first type of classical bounded symmetric domains , and prove the equivalence of the norms and . Furthermore, we study the compactness of composition operator from to , and obtain a sufficient and necessary condition for to be compact. 展开更多
关键词 BLOCH Space Classical Bounded Symmetric DOMAINS Composition Operators compactness BERGMAN Metric
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Measurement and Spatial Distribution of Urban Land Use Compactness in Chaoyang District of Beijing,China 被引量:1
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作者 Hong Min Jin Fengjun Brian D. Fath 《Chinese Journal of Population,Resources and Environment》 2010年第4期3-9,共7页
China is in the process of rapid urbanization,and wise land use is critical to the long-term sustainability of Chinese cities.Promotion of a compact city is typically believed to be helpful for sustainable land use ma... China is in the process of rapid urbanization,and wise land use is critical to the long-term sustainability of Chinese cities.Promotion of a compact city is typically believed to be helpful for sustainable land use management.However,given the fact that Chinese cities are characterized by high population densities,the applicability of a more compact solution to expand cities in China remains questionable;there is little evidence to support the many claims in its favor.In seeking to provide empirical data to explore the application of compact city theory in China,one of the key problems researchers face is the task of measuring the urban compactness,in order to objectively investigate the current characteristics of urban compactness.To meet this need,indices were developed for measuring the urban land use compactness,by which the spatial distribution characteristics of urban land use compactness were identified and applied to the Chaoyang District of Beijing.The conclusions can be made as follows:(1) comprehensive land use compactness in Chaoyang District has increased during the period of 2001-2007,especially the population density;(2) the spatial distribution of land use compactness has the characteristics of a ring structure,which shows a decreasing trend with its distance to the city center;(3) there is a strong positive correlation between urban land use compactness and location.The better the location is,the higher the land use compactness is. 展开更多
关键词 urban land use compactness measurement indices Chaoyang District
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A Short Note on Compactness in Aligned Spaces and Higgs Spaces 被引量:1
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作者 J. M. S. Sim6es-Pereira 《Journal of Mathematics and System Science》 2017年第6期151-153,共3页
We generalize to aligned spaces and to Higgs spaces the concept of compact topological spaces.
关键词 aligned spaces Higgs spaces compactness.
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EXTENDING POMPEIU OPERATOR AND THE COMPACTNESS OF SOLUTION SET FOR A CLASS OF HIGHER ORDER PARTIAL DIFFERENTIAL EQUATIONS
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作者 陈冬贵 《四川师范大学学报(自然科学版)》 CAS CSCD 1991年第1期3-4,共2页
This paper discusses chiefly the compactness of solution set of following equationswhere △ is the Laplacian in Sobolev’s sense, a;(x),i= 0,1,…n, n≥ 3, are real square matrices of dimen-sion N×V , bounded an... This paper discusses chiefly the compactness of solution set of following equationswhere △ is the Laplacian in Sobolev’s sense, a;(x),i= 0,1,…n, n≥ 3, are real square matrices of dimen-sion N×V , bounded and measurable in a bounded multiply connected domain Ω, the boundary S is as-sumed to be sufficiently smooth, u(x) is unknown vector, z = (x<sub>1</sub>,x<sub>2</sub>,…,x<sub>n</sub>) Ω R<sup>z</sup>,m≥1,|S<sub>1</sub>|issuperficial measure of the unit sphere of R<sup>Z</sup>, |i|=i<sub>1</sub>+ i<sub>2</sub> +… + i., △<sup>m</sup>=△(△<sup>m-1</sup>). ,(Ω), ,(Ω), … denote the classes of vectors or matrices whose elements belong to L,(Ω),W,(Ω),…. A vector or a matrix is said to be continuous differentiable, bounded and measurable if so are its ele- 展开更多
关键词 measurable LAPLACIAN matrices DIFFERENTIABLE CLASS connected compactness multiply sufficiently 子一
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COMPENSATED COMPACTNESS APPLIED TO PERTURBED FOURTH AND SIXTH ORDER P.D.E
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作者 殷朝阳 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1997年第9期913-919,共7页
In the paper, by using the methods of compensated compactness and energy estimate, the convergence of class of fourth and sixth orders singular perturbed, partial differential equations is obtained, and furthermore, t... In the paper, by using the methods of compensated compactness and energy estimate, the convergence of class of fourth and sixth orders singular perturbed, partial differential equations is obtained, and furthermore, the regularity of solutions are improved. 展开更多
关键词 compensated compactness energy estimate singular perturbation convergence of solution regularity of solution
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L^0-CONVEX COMPACTNESS AND RANDOM NORMAL STRUCTURE IN L^0(F,B)
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作者 Tiexin GUO Erxin ZHANG +1 位作者 Yachao WANG George YUAN 《Acta Mathematica Scientia》 SCIE CSCD 2020年第2期457-469,共13页
Let(B,||·||)be a Banach space,(?,F,P)a probability space,and L^0(F,B)the set of equivalence classes of strong random elements(or strongly measurable functions)from(?,F,P)to(B,||·||).It is well known that L^0... Let(B,||·||)be a Banach space,(?,F,P)a probability space,and L^0(F,B)the set of equivalence classes of strong random elements(or strongly measurable functions)from(?,F,P)to(B,||·||).It is well known that L^0(F,B)becomes a complete random normed module,which has played an important role in the process of applications of random normed modules to the theory of Lebesgue-Bochner function spaces and random operator theory.Let V be a closed convex subset of B and L^0(F,V)the set of equivalence classes of strong random elements from(?,F,P)to V.The central purpose of this article is to prove the following two results:(1)L^0(F,V)is L^0-convexly compact if and only if V is weakly compact;(2)L^0(F,V)has random normal structure if V is weakly compact and has normal structure.As an application,a general random fixed point theorem for a strong random nonexpansive operator is given,which generalizes and improves several well known results.We hope that our new method,namely skillfully combining measurable selection theorems,the theory of random normed modules,and Banach space techniques,can be applied in the other related aspects. 展开更多
关键词 Complete random normed modules fixed point theorem L^0-convex compactness random normal structure random nonexpansive operators
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COMPACTNESS DEGREE AND A GENERALIZATION OF THE TYCHONOFF THEOREM
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作者 李邦河 冯汉桥 《Acta Mathematica Scientia》 SCIE CSCD 1990年第4期422-426,共5页
The most interesting result of this paper is the following generalization of the Tychonoff theorem: [GRAPHICS].
关键词 TH over compactness DEGREE AND A GENERALIZATION OF THE TYCHONOFF THEOREM
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COMPENSATED COMPACTNESS AND THE STRATIFIED LIE GROUP
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作者 Yu Liu 《Analysis in Theory and Applications》 2009年第2期101-108,共8页
In this paper we prove that the Jacobian J(F) of a map F(f1,…,f1 from Ginto Rt maps the product of Lebesgue space Lp1×…× Lp1 into local Hardy space hY(G),whereQ/Q+1〈r〈1,and Q is the homogeneous dim... In this paper we prove that the Jacobian J(F) of a map F(f1,…,f1 from Ginto Rt maps the product of Lebesgue space Lp1×…× Lp1 into local Hardy space hY(G),whereQ/Q+1〈r〈1,and Q is the homogeneous dimension of the stratified Lie group G. 展开更多
关键词 compensated compactness stratified Lie group Hardy space maximal function
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A COMPACTNESS THEOREM FOR STABLE FLAT SL(2, C) CONNECTIONS ON 3-FOLDS
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作者 Teng HUANG 《Acta Mathematica Scientia》 SCIE CSCD 2022年第3期1160-1172,共13页
Let Y be a closed 3-manifold such that all flat SU(2)-connections on Y are non-degenerate.In this article,we prove a Uhlenbeck-type compactness theorem on Y for stable flat SL(2,C)connections satisfying an L^(2)-bound... Let Y be a closed 3-manifold such that all flat SU(2)-connections on Y are non-degenerate.In this article,we prove a Uhlenbeck-type compactness theorem on Y for stable flat SL(2,C)connections satisfying an L^(2)-bound for the real curvature.Combining the compactness theorem and a result from[7],we prove that the moduli space of the stable flat SL(2,C)connections is disconnected under certain technical assumptions. 展开更多
关键词 Stable flat SL(2 C)connections Vafa-Witten equations compactness theorem
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The Compactness of Composition Operator Between βμ(B)and βμ(D)
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作者 ZHAI Fan LEI Yuqiong ZHANG Jianjun 《International English Education Research》 2016年第6期77-79,共3页
Necessary and sufficient are given for a composition operator Co = foφ to be compact between βμ(B) and βμ(D) and between βμ,0(B) and βμ,0(D) .
关键词 composition operator analytic function banach space bloch space compactness
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Nonlinear Dimensionality Reduction via Homeomorphic Tangent Space and Compactness
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作者 Shaoqun Zhang Wanyun Xie 《国际计算机前沿大会会议论文集》 2017年第1期132-133,共2页
This paper establishes the geometric framework of manifold learning.After summarizing the requirements of the classical manifold learning methods,we construct the smooth homeomorphism between the manifold and its tang... This paper establishes the geometric framework of manifold learning.After summarizing the requirements of the classical manifold learning methods,we construct the smooth homeomorphism between the manifold and its tangent space.Then we propose a new algorithm via homeomorphic tangent space(LHTS).We also present another algorithm via compactness(CSLI)by analyzing the topological properties of manifolds.We illustrate our algorithm on the completed manifold and non-completed manifold.We also address several theoretical issues for further research and improvements. 展开更多
关键词 MANIFOLD learning SMOOTH HOMEOMORPHISM Homeomorphic TANGENT SPACE compactness
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