In this paper, a simplified definition of boundedness of the sets in probabilistic normed linear space was introduced. By means of the probabilistic norm of linear operators, the linear operator theory on probabilisti...In this paper, a simplified definition of boundedness of the sets in probabilistic normed linear space was introduced. By means of the probabilistic norm of linear operators, the linear operator theory on probabilistic normed linear space was further studied. On probabilistic normed linear operator space, some resonance theorems dealing with probabilistic bounded sets, probabilistic semi_bounded sets, and probabilistic non_unbounded sets are obtained.展开更多
Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this cont...Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.展开更多
A new method of constructing bornological vector topologies for vector spaces is discussed.In general,the convergent sequence and bounded set are concepts only in topological spaces.However,in this paper,it is first i...A new method of constructing bornological vector topologies for vector spaces is discussed.In general,the convergent sequence and bounded set are concepts only in topological spaces.However,in this paper,it is first introduced sequential convergence C and L * space which is a vector space giving some relation:x mCx between sequences and points in it,then the bounded set is defined in vector space.Let C be a sequential convergence,T(C) be a vector topology on X determined by C and B(C) be the collection of bounded sets determined by C.Then B(C)=B(T(C)).Furthermore,the bornological locally convex topological vector space is constructed by L * vector space.展开更多
It is shown that if a 'max-subadditive funtional' p(x) defined on some symmetric neighborhood U0 of zero vector θ in a 'b.f.-toplological group' X is 'upper semi-cotinuous' at a point x0 ∈ U0...It is shown that if a 'max-subadditive funtional' p(x) defined on some symmetric neighborhood U0 of zero vector θ in a 'b.f.-toplological group' X is 'upper semi-cotinuous' at a point x0 ∈ U0, or 'lower semi-continuous' in some neighborhood V(x0) U0 and X is of second category; then p(x) can attain its supremum in U0. And there is a similar conclusion for the γ-max-subadditive functional when its supremum is 0 and if U0 is 'pseudo-bounded' set in X.展开更多
In this paper we prove three equivalent conditions of bounded closed convexset K in Banach space to have the drop and weak drop properties. We also give fourequivalent conditions of Banach space and its dual space to ...In this paper we prove three equivalent conditions of bounded closed convexset K in Banach space to have the drop and weak drop properties. We also give fourequivalent conditions of Banach space and its dual space to have the drop and weak dropproperties.展开更多
In this paper, the existence of global attractors for the 2D autonomous g- Navier-Stokes equations on multi-connected bounded domains is investigated under the general assumptions of boundaries. The estimation of the ...In this paper, the existence of global attractors for the 2D autonomous g- Navier-Stokes equations on multi-connected bounded domains is investigated under the general assumptions of boundaries. The estimation of the Hausdorff dimensions for global attractors is given.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
文摘In this paper, a simplified definition of boundedness of the sets in probabilistic normed linear space was introduced. By means of the probabilistic norm of linear operators, the linear operator theory on probabilistic normed linear space was further studied. On probabilistic normed linear operator space, some resonance theorems dealing with probabilistic bounded sets, probabilistic semi_bounded sets, and probabilistic non_unbounded sets are obtained.
文摘Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.
文摘A new method of constructing bornological vector topologies for vector spaces is discussed.In general,the convergent sequence and bounded set are concepts only in topological spaces.However,in this paper,it is first introduced sequential convergence C and L * space which is a vector space giving some relation:x mCx between sequences and points in it,then the bounded set is defined in vector space.Let C be a sequential convergence,T(C) be a vector topology on X determined by C and B(C) be the collection of bounded sets determined by C.Then B(C)=B(T(C)).Furthermore,the bornological locally convex topological vector space is constructed by L * vector space.
文摘It is shown that if a 'max-subadditive funtional' p(x) defined on some symmetric neighborhood U0 of zero vector θ in a 'b.f.-toplological group' X is 'upper semi-cotinuous' at a point x0 ∈ U0, or 'lower semi-continuous' in some neighborhood V(x0) U0 and X is of second category; then p(x) can attain its supremum in U0. And there is a similar conclusion for the γ-max-subadditive functional when its supremum is 0 and if U0 is 'pseudo-bounded' set in X.
文摘In this paper we prove three equivalent conditions of bounded closed convexset K in Banach space to have the drop and weak drop properties. We also give fourequivalent conditions of Banach space and its dual space to have the drop and weak dropproperties.
基金Project supported by the National Natural Science Fundation of China (No. 11171269)the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2012JM1012)the Scientific Research Program Funded by Shaanxi Provincial Education Department (No. 12JK0849)
文摘In this paper, the existence of global attractors for the 2D autonomous g- Navier-Stokes equations on multi-connected bounded domains is investigated under the general assumptions of boundaries. The estimation of the Hausdorff dimensions for global attractors is given.
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.
