Let (E,γ) be a locally convex space and E′ its conjugate space. AE′ be an equicontinuous set on (E,γ). In this paper,we show that for each sequence {f i}A and {x j}E, if {x j} converges to 0 in (E,γ), then we can...Let (E,γ) be a locally convex space and E′ its conjugate space. AE′ be an equicontinuous set on (E,γ). In this paper,we show that for each sequence {f i}A and {x j}E, if {x j} converges to 0 in (E,γ), then we can find a f 0∈E′ and extract subsequences {f n i } and {x n j } such that {f n i } converges to f 0 on {x n j } uniformly. If (E,γ) is metrizable,then we can show that the converse is also valid.展开更多
This paper is concerned with a modified transitional Korteweg-de Vries equation ut+f(t)u2ux+uxxx=0, (x,t)∈R+×R+with initial value u(x,0)=g(x)∈H4(R+)and inhomogeneous boundary value u(0,t)=Q(t)∈C2([ 0,∞ )). Un...This paper is concerned with a modified transitional Korteweg-de Vries equation ut+f(t)u2ux+uxxx=0, (x,t)∈R+×R+with initial value u(x,0)=g(x)∈H4(R+)and inhomogeneous boundary value u(0,t)=Q(t)∈C2([ 0,∞ )). Under the conditions either 1) f(t)≤0, f′(t)≥0or 2) f(t)≤−αwhere α>0, we prove the existence of a unique global classical solution.展开更多
In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transf...In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous.展开更多
Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the co...Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the corresponding results of ShiojiTakahashi, Suzuki, Xu and Aleyner-Reich, but also give a partially affirmative answer to the open questions raised by Suzuki and Xu.展开更多
The purpose of this article is first to introduce the concept of multi-valued to- tally Quasi-φ-asymptotically nonexpansive semi-groups, which contains many kinds of semi- groups as its special cases, and then to mod...The purpose of this article is first to introduce the concept of multi-valued to- tally Quasi-φ-asymptotically nonexpansive semi-groups, which contains many kinds of semi- groups as its special cases, and then to modify the Halpern-Mann-type iteration algorithm for multi-valued totally Quasi-cS-asymptotically nonexpansive semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in this article improve and extend the corresponding results announced by many authors recently.展开更多
Given a topological dynamical system(X,T)and a T-invariant measureμ,let B denote the Borel σ-algebra on X.This paper proves that(X,B,μ,T)is rigid if and only if(X,T)isμ-A-equicontinuous in the mean for some subseq...Given a topological dynamical system(X,T)and a T-invariant measureμ,let B denote the Borel σ-algebra on X.This paper proves that(X,B,μ,T)is rigid if and only if(X,T)isμ-A-equicontinuous in the mean for some subsequence A of N,and a function f∈L^(2)(μ)is rigid if and only if f is μ-A-equicontinuous in the mean for some subsequence A of N.In particular,this gives a positive answer to Question 4.11 in[1].展开更多
In this paper,we present the concept of Banach-mean equicontinuity and prove that the Banach-,Weyl-and Besicovitch-mean equicontinuities of a dynamic system of Abelian group action are equivalent.Furthermore,we obtain...In this paper,we present the concept of Banach-mean equicontinuity and prove that the Banach-,Weyl-and Besicovitch-mean equicontinuities of a dynamic system of Abelian group action are equivalent.Furthermore,we obtain that the topological entropy of a transitive,almost Banach-mean equicontinuous dynamical system of Abelian group action is zero.As an application of our main result,we show that the topological entropy of the Banach-mean equicontinuous system under the action of an Abelian groups is zero.展开更多
The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper e...The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.展开更多
Large deviations estimates for Poisson processes estimate the logarithm of rare events associated to a Poisson process which has more and more jump which are smaller and smaller. In stochastic analysis, they are valid...Large deviations estimates for Poisson processes estimate the logarithm of rare events associated to a Poisson process which has more and more jump which are smaller and smaller. In stochastic analysis, they are valid on the whole path space. Asoociated to this jump process is a Markov semi-group. We translate in semi group theory the proof of Wentzel-Freidlin for these estimates by translating in semi-group theory some basical tools of stochastic analysis as the exponential martingales of stochastic analysis. These Wentzel-Freidlin estimates （upper-bound） are only true for the semi-group.展开更多
文摘Let (E,γ) be a locally convex space and E′ its conjugate space. AE′ be an equicontinuous set on (E,γ). In this paper,we show that for each sequence {f i}A and {x j}E, if {x j} converges to 0 in (E,γ), then we can find a f 0∈E′ and extract subsequences {f n i } and {x n j } such that {f n i } converges to f 0 on {x n j } uniformly. If (E,γ) is metrizable,then we can show that the converse is also valid.
文摘This paper is concerned with a modified transitional Korteweg-de Vries equation ut+f(t)u2ux+uxxx=0, (x,t)∈R+×R+with initial value u(x,0)=g(x)∈H4(R+)and inhomogeneous boundary value u(0,t)=Q(t)∈C2([ 0,∞ )). Under the conditions either 1) f(t)≤0, f′(t)≥0or 2) f(t)≤−αwhere α>0, we prove the existence of a unique global classical solution.
文摘In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous.
基金Project supported by the Natural Science Foundation of Sichuan Province of China(No.2005A132)
文摘Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the corresponding results of ShiojiTakahashi, Suzuki, Xu and Aleyner-Reich, but also give a partially affirmative answer to the open questions raised by Suzuki and Xu.
基金supported by the Natural Science Foundation of Yunnan Province (2011FB074)
文摘The purpose of this article is first to introduce the concept of multi-valued to- tally Quasi-φ-asymptotically nonexpansive semi-groups, which contains many kinds of semi- groups as its special cases, and then to modify the Halpern-Mann-type iteration algorithm for multi-valued totally Quasi-cS-asymptotically nonexpansive semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in this article improve and extend the corresponding results announced by many authors recently.
基金Supported by the National Natural Science Founda-tion of China(11790274 and 11871361)partially supported by Qinglan project of Jiangsu Province。
文摘Given a topological dynamical system(X,T)and a T-invariant measureμ,let B denote the Borel σ-algebra on X.This paper proves that(X,B,μ,T)is rigid if and only if(X,T)isμ-A-equicontinuous in the mean for some subsequence A of N,and a function f∈L^(2)(μ)is rigid if and only if f is μ-A-equicontinuous in the mean for some subsequence A of N.In particular,this gives a positive answer to Question 4.11 in[1].
基金supported by NSF of China(11671057)NSF of Chongqing(cstc2020jcyj-msxmX0694)the Fundamental Research Funds for the Central Universities(2018CDQYST0023).
文摘In this paper,we present the concept of Banach-mean equicontinuity and prove that the Banach-,Weyl-and Besicovitch-mean equicontinuities of a dynamic system of Abelian group action are equivalent.Furthermore,we obtain that the topological entropy of a transitive,almost Banach-mean equicontinuous dynamical system of Abelian group action is zero.As an application of our main result,we show that the topological entropy of the Banach-mean equicontinuous system under the action of an Abelian groups is zero.
基金supported by the Natural Science Foundation of Yibin University (No. 2007Z3)
文摘The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.
文摘Large deviations estimates for Poisson processes estimate the logarithm of rare events associated to a Poisson process which has more and more jump which are smaller and smaller. In stochastic analysis, they are valid on the whole path space. Asoociated to this jump process is a Markov semi-group. We translate in semi group theory the proof of Wentzel-Freidlin for these estimates by translating in semi-group theory some basical tools of stochastic analysis as the exponential martingales of stochastic analysis. These Wentzel-Freidlin estimates （upper-bound） are only true for the semi-group.
