In this paper, the definition of weak dominance is proposed for a NTU game and two new solution concepts of NTU games are introduced: the refined core and weakly stable set. The relationship is explored among the core...In this paper, the definition of weak dominance is proposed for a NTU game and two new solution concepts of NTU games are introduced: the refined core and weakly stable set. The relationship is explored among the core, the weakly stable set and the refined core.展开更多
In this work,we give some criteria of the weakly compact sets and a representation theorem of Riesz's type in Musielak sequence spaces using the ideas and techniques of sequence spaces and Musielak function.Finall...In this work,we give some criteria of the weakly compact sets and a representation theorem of Riesz's type in Musielak sequence spaces using the ideas and techniques of sequence spaces and Musielak function.Finally,as an immediate consequence of the criteria considered in this paper,the criteria of the weakly compact sets of Orlicz sequence spaces are deduced.展开更多
The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear function...The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem.展开更多
In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 4...In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.展开更多
In this paper, category GIFS of generalized intuitionistic fuzzy sets(GIF) is built up. Topoi properties of category GIFS are studied. Firstly, it is proved that the category GIFS has all topoi properties except that ...In this paper, category GIFS of generalized intuitionistic fuzzy sets(GIF) is built up. Topoi properties of category GIFS are studied. Firstly, it is proved that the category GIFS has all topoi properties except that it has no subobject classifiers, Secondly, it is proved that the category GIFS has middle object and consequently GIFS is a weak topos. Thirdly, by the use of theory of weak topos GIFS, the power object of an object in GIFS is studied.展开更多
In this article, we investigate the global behavior of weak solutions of a simplified Ericksen-Leslie system for compressible flows of nematic liquid crystals in time in a bounded three-dimension domain-arbitrary forc...In this article, we investigate the global behavior of weak solutions of a simplified Ericksen-Leslie system for compressible flows of nematic liquid crystals in time in a bounded three-dimension domain-arbitrary forces. By adapting the arguments for the compressible Navier-Stokes equations, and carefully analyzing the direction field of liquid crystals in the equations of angular momentum, we show the existence of bounded absorbing sets, global bounded trajectories, and global attractors to weak solutions of compressible flows of nematic liquid crystals with the adiabatic constant γ〉5/3.展开更多
1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved....1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved. Nevertheless, this is not enough for the researches of biological species, demography, numerical simulation and attractors (see [1], [2]). It is necessary to know how the subsets of X moved. In this direction, we consider the set-valued discrete system associated to f, An+1 = (f|-)(An), n = 0,1,2,... where (f|-) is the natural extension of f to K(X) (the class of all compact subsets of X).展开更多
J. Mather and A. Fathi defined Mané set and Aubry set, which are the important invariant sets in positive definite Lagrangian system, in different ways. They use variational principle and Weak KAM theory respecti...J. Mather and A. Fathi defined Mané set and Aubry set, which are the important invariant sets in positive definite Lagrangian system, in different ways. They use variational principle and Weak KAM theory respectively. In this paper we provide a proof of the equivalence between the two kinds of definitions, and generalize A. Fathi＇s definition. In the end of the paper, we calculate the Mane set and Aubry set for a single pendulum system.展开更多
1 IntroductionIn this paper we study the existence of pullback attractors for multivalued nonautonomous and multivalued random semiflow. In [1] and [2], the authors have proved the existence of pullback attractors of ...1 IntroductionIn this paper we study the existence of pullback attractors for multivalued nonautonomous and multivalued random semiflow. In [1] and [2], the authors have proved the existence of pullback attractors of multivalued nonautonomous semiflow （random semiflow） under the assumption of the existence of compact absorbing set. In [3], the authors have proved the existence of pullback attractors of multivalued nonautonomous semiflow and random semiflow under the assumptions of uniformly pullback asymptotically upper semicompact and closed graph. In [4], the authors consider the existence of pullback attractor of singlevalued nonautonomous semiflow and random semiflow under the assumption of pullback asymptotic compactness. Instead of these assumptions, we consider multivalued nonautonomous semiflow and multivalued random semiflow with weak pullback asymptotic upper semi-compactness and prove the existence of pullback attractors.展开更多
隐私集合交集(private set intersection,PSI)是隐私计算中的热点,其允许参与两方在不泄露任何额外信息的要求下计算交集.现有的隐私集合交集计算方案对参与双方的计算能力要求高,且计算能力差的参与方无法在保证集合数据隐私的前提下...隐私集合交集(private set intersection,PSI)是隐私计算中的热点,其允许参与两方在不泄露任何额外信息的要求下计算交集.现有的隐私集合交集计算方案对参与双方的计算能力要求高,且计算能力差的参与方无法在保证集合数据隐私的前提下将计算安全外包给云服务器.设计了一种新的不经意两方分布式伪随机函数,允许半可信的云服务器参与相等性测试,又不泄露参与方任何集合信息.基于该不经意伪随机函数构建了半可信云服务器辅助的隐私集合交集计算协议,将主要计算量外包给云服务器.在半诚实模型下证明了协议的安全性.同时,该协议可保密地计算隐私集合交集的基数.通过与现有协议分析与实验性能比较,该协议效率高,计算复杂度与通信复杂度均与集合大小呈线性关系,适用于客户端设备受限的应用场景.展开更多
The paper proves the convergence theorem of set-valued Superpramart in the sense of weak convergence under the X<sup>*</sup> separable condition. Using support function and results about real-valued Superp...The paper proves the convergence theorem of set-valued Superpramart in the sense of weak convergence under the X<sup>*</sup> separable condition. Using support function and results about real-valued Superpramart, we give the Riesz decomposition of set-valued Superpramart.展开更多
In this paper, We give the simple criteria of weakly compact sets in L1 and l1, which perfects Auto's result [1]， Also as a corollary, we get Shur's theorem， In view of weak compactness, we give another pro...In this paper, We give the simple criteria of weakly compact sets in L1 and l1, which perfects Auto's result [1]， Also as a corollary, we get Shur's theorem， In view of weak compactness, we give another proof of the reflexivity of Orlicz spaces，展开更多
Based on an application of the Davis-Figiel-Johnson-Pelzyski procedure, this note shows that every weakly compact subset of a Banach space can be uniformly embedded into a reflexive Banach space. As its application, w...Based on an application of the Davis-Figiel-Johnson-Pelzyski procedure, this note shows that every weakly compact subset of a Banach space can be uniformly embedded into a reflexive Banach space. As its application, we present the recent renorming theorems for reflexive spaces of Odell- Schlumprecht and Hajek-Johanis can be extended and localized to weakly compact convex subsets of an arbitrary Banach space.展开更多
文摘In this paper, the definition of weak dominance is proposed for a NTU game and two new solution concepts of NTU games are introduced: the refined core and weakly stable set. The relationship is explored among the core, the weakly stable set and the refined core.
基金Supported by the National Natural Science Foundation of China(Grant No.11771273)。
文摘In this work,we give some criteria of the weakly compact sets and a representation theorem of Riesz's type in Musielak sequence spaces using the ideas and techniques of sequence spaces and Musielak function.Finally,as an immediate consequence of the criteria considered in this paper,the criteria of the weakly compact sets of Orlicz sequence spaces are deduced.
基金supported by the National Natural Science Foundation of China(11471043,11671271)the Beijing Natural Science Foundation(1172004)
文摘The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem.
文摘In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.
文摘In this paper, category GIFS of generalized intuitionistic fuzzy sets(GIF) is built up. Topoi properties of category GIFS are studied. Firstly, it is proved that the category GIFS has all topoi properties except that it has no subobject classifiers, Secondly, it is proved that the category GIFS has middle object and consequently GIFS is a weak topos. Thirdly, by the use of theory of weak topos GIFS, the power object of an object in GIFS is studied.
文摘In this article, we investigate the global behavior of weak solutions of a simplified Ericksen-Leslie system for compressible flows of nematic liquid crystals in time in a bounded three-dimension domain-arbitrary forces. By adapting the arguments for the compressible Navier-Stokes equations, and carefully analyzing the direction field of liquid crystals in the equations of angular momentum, we show the existence of bounded absorbing sets, global bounded trajectories, and global attractors to weak solutions of compressible flows of nematic liquid crystals with the adiabatic constant γ〉5/3.
文摘1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved. Nevertheless, this is not enough for the researches of biological species, demography, numerical simulation and attractors (see [1], [2]). It is necessary to know how the subsets of X moved. In this direction, we consider the set-valued discrete system associated to f, An+1 = (f|-)(An), n = 0,1,2,... where (f|-) is the natural extension of f to K(X) (the class of all compact subsets of X).
文摘J. Mather and A. Fathi defined Mané set and Aubry set, which are the important invariant sets in positive definite Lagrangian system, in different ways. They use variational principle and Weak KAM theory respectively. In this paper we provide a proof of the equivalence between the two kinds of definitions, and generalize A. Fathi＇s definition. In the end of the paper, we calculate the Mane set and Aubry set for a single pendulum system.
文摘1 IntroductionIn this paper we study the existence of pullback attractors for multivalued nonautonomous and multivalued random semiflow. In [1] and [2], the authors have proved the existence of pullback attractors of multivalued nonautonomous semiflow （random semiflow） under the assumption of the existence of compact absorbing set. In [3], the authors have proved the existence of pullback attractors of multivalued nonautonomous semiflow and random semiflow under the assumptions of uniformly pullback asymptotically upper semicompact and closed graph. In [4], the authors consider the existence of pullback attractor of singlevalued nonautonomous semiflow and random semiflow under the assumption of pullback asymptotic compactness. Instead of these assumptions, we consider multivalued nonautonomous semiflow and multivalued random semiflow with weak pullback asymptotic upper semi-compactness and prove the existence of pullback attractors.
文摘隐私集合交集(private set intersection,PSI)是隐私计算中的热点,其允许参与两方在不泄露任何额外信息的要求下计算交集.现有的隐私集合交集计算方案对参与双方的计算能力要求高,且计算能力差的参与方无法在保证集合数据隐私的前提下将计算安全外包给云服务器.设计了一种新的不经意两方分布式伪随机函数,允许半可信的云服务器参与相等性测试,又不泄露参与方任何集合信息.基于该不经意伪随机函数构建了半可信云服务器辅助的隐私集合交集计算协议,将主要计算量外包给云服务器.在半诚实模型下证明了协议的安全性.同时,该协议可保密地计算隐私集合交集的基数.通过与现有协议分析与实验性能比较,该协议效率高,计算复杂度与通信复杂度均与集合大小呈线性关系,适用于客户端设备受限的应用场景.
文摘The paper proves the convergence theorem of set-valued Superpramart in the sense of weak convergence under the X<sup>*</sup> separable condition. Using support function and results about real-valued Superpramart, we give the Riesz decomposition of set-valued Superpramart.
文摘In this paper, We give the simple criteria of weakly compact sets in L1 and l1, which perfects Auto's result [1]， Also as a corollary, we get Shur's theorem， In view of weak compactness, we give another proof of the reflexivity of Orlicz spaces，
文摘Based on an application of the Davis-Figiel-Johnson-Pelzyski procedure, this note shows that every weakly compact subset of a Banach space can be uniformly embedded into a reflexive Banach space. As its application, we present the recent renorming theorems for reflexive spaces of Odell- Schlumprecht and Hajek-Johanis can be extended and localized to weakly compact convex subsets of an arbitrary Banach space.
