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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
基金supported by the National Natural Science Foundation of China(11671252)supported by the National Natural Science Foundation of China(11771278)
文摘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.
基金The State Safety Production Science and Technology Plan Program (07-379)ShandongSoft Science Development Foundation (2007RKB241)
文摘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.
基金the NSFC(10271069)the Foundation of Weinan Teacher's College(08YKZ053)
文摘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.
文摘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.
基金Under the auspices of National Major Programs of Scientific and Technological Support Plan of the 11th Five-Year Plan Period of China(No.2006BAJ14B03)Knowledge Innovation Program of Chinese Academy of Sciences(No.KZCX2-YW-307-02)
文摘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.
基金supported by the Research Council of Norway through theprojects Nonlinear Problems in Mathematical Analysis Waves In Fluids and Solids+2 种基金 Outstanding Young Inves-tigators Award (KHK), the Russian Foundation for Basic Research (grant No. 09-01-00490-a) DFGproject No. 436 RUS 113/895/0-1 (EYuP)
文摘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.
基金Supported by the National Natural Science Foundation of China (10471039)the Grant of Higher Schools' Natural Science Basic Research of Jiangsu Province of China (06KJD11017507KJB110115)
文摘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.
文摘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.
文摘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.
基金financed by the National Natural Science Foundation of China(Grant nos.40635026and40901068)Special Fund from the Science and Technology Department of Beijing Municipality(Grant no.zz0922)the Postdoctoral Science Foundation of China(Grant no.200902133)
文摘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.
文摘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-
文摘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.
基金This work was supported by National Natural Science Foundation of China(11571369)。
文摘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.
文摘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.
基金supported in part by NSF of China(11801539)the Fundamental Research Funds of the Central Universities(WK3470000019)the USTC Research Funds of the Double First-Class Initiative(YD3470002002)。
文摘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.
文摘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.