This paper is a continuation of [8]. In Section 1, three kinds of communication are introdnced for two states and the relations among them are investigated. In Section 2, two kinds of period of a state are introdnced ...This paper is a continuation of [8]. In Section 1, three kinds of communication are introdnced for two states and the relations among them are investigated. In Section 2, two kinds of period of a state are introdnced and it is obtained that the period is a 'class property',i.e. two states x and y belong to same class implies the period of x is equal to the period of y.展开更多
In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the c...In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].展开更多
The structure of any a.s. self-similar set K(w) generated by a class of random elements {gn,wσ} taking values in the space of contractive operators is given and the approximation of K(w) by the fixed points {Pn,wσ} ...The structure of any a.s. self-similar set K(w) generated by a class of random elements {gn,wσ} taking values in the space of contractive operators is given and the approximation of K(w) by the fixed points {Pn,wσ} of {gn,ow} is obtained. It is useful to generate the fractal in computer.展开更多
In this article the authors introduce the minimal operator on martingale spaces, discuss some one-weight and two-weight inequalities for the minimal operator and characterize the conditions which make the inequalities...In this article the authors introduce the minimal operator on martingale spaces, discuss some one-weight and two-weight inequalities for the minimal operator and characterize the conditions which make the inequalities hold.展开更多
The concepts of Markov process in random environment and homogeneous random transition functions are introduced. The necessary and sufficient conditions for homogeneous random transition function are given. The main r...The concepts of Markov process in random environment and homogeneous random transition functions are introduced. The necessary and sufficient conditions for homogeneous random transition function are given. The main results in this article are the analytical properties, such as continuity, differentiability, random Kolmogorov backward equation and random Kolmogorov forward equation of homogeneous random transition functions.展开更多
We consider the adaptive consensus problem for leader-follower multi-agent systems with time delay coupling. Under the condition that the interconnection graph of the agents is directed and balanced, a neighbor-based ...We consider the adaptive consensus problem for leader-follower multi-agent systems with time delay coupling. Under the condition that the interconnection graph of the agents is directed and balanced, a neighbor-based consensus protocol with adaptive feedback gain is proposed for the follower agents to track the leader. The stability is performed based on the Lyapunov stability theorem. Some simulation examples are provided to show the efficiency of the control scheme.展开更多
The cooperative behaviors resulted from the interaction of coupled identical oscillators have been investigated intensively.However,the coupled oscillators in practice are nonidentical,and there exist mismatched param...The cooperative behaviors resulted from the interaction of coupled identical oscillators have been investigated intensively.However,the coupled oscillators in practice are nonidentical,and there exist mismatched parameters.It has been proved that under certain conditions,complete synchronization can take place in coupled nonidentical oscillators with the same equilibrium points,yet other cooperative behaviors are not addressed.In this paper,we further consider two coupled nonidentical oscillators with the same equilibrium points,where one oscillator is convergent while the other is chaotic,and explore their cooperative behaviors.We find that the coupling mode and the coupling strength can bring the coupled oscillators to different cooperation behaviors in unidirectional or undirected couplings.In the case of directed coupling,death islands appear in two-parameter spaces.The mechanism inducing these transitions is presented.展开更多
For convolution-type Calderon-Zygmund operators, by the boundedness on Besov spaces and Hardy spaces, applying interpolation theory and duality, it is known that H5rmander condition can ensure the boundedness on Trieb...For convolution-type Calderon-Zygmund operators, by the boundedness on Besov spaces and Hardy spaces, applying interpolation theory and duality, it is known that H5rmander condition can ensure the boundedness on Triebel-Lizorkin spaces Fp^0,q （1 〈 p,q 〈 ∞） and on a party of endpoint spaces FO,q （1 ≤ q ≤ 2）, hut this idea is invalid for endpoint Triebel-Lizorkin spaces F1^0,q （2 〈 q ≤ ∞）. In this article, the authors apply wavelets and interpolation theory to establish the boundedness on F1^0,q （2 〈 q ≤ ∞） under an integrable condition which approaches HSrmander condition infinitely.展开更多
The uniqueness of meromorphic functions that share four values is investigated. A necessary condition to the case is acquired, and some partial results for question '1CM+3IM=4CM' are obtained.
文摘This paper is a continuation of [8]. In Section 1, three kinds of communication are introdnced for two states and the relations among them are investigated. In Section 2, two kinds of period of a state are introdnced and it is obtained that the period is a 'class property',i.e. two states x and y belong to same class implies the period of x is equal to the period of y.
文摘In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].
基金Supported by NNSF of China and the Foundation of Wuhan University
文摘The structure of any a.s. self-similar set K(w) generated by a class of random elements {gn,wσ} taking values in the space of contractive operators is given and the approximation of K(w) by the fixed points {Pn,wσ} of {gn,ow} is obtained. It is useful to generate the fractal in computer.
基金supported by the National Natural Science Foundation of China (61071189)Innovation Scientists and Technicians Troop Construction of Henan Province of China (084100510012)the Natural Science Foundation for the Education Department of Henan Province of China (2008B510001)
文摘In this paper, a characterization of orthonormal wavelet families in Sobolev spaces H s （R） is established.
基金This work was supported by the NSF of China and the aid financial plan for the backbone of the young teachers of University of Henan
文摘In this article the authors introduce the minimal operator on martingale spaces, discuss some one-weight and two-weight inequalities for the minimal operator and characterize the conditions which make the inequalities hold.
基金Supported by the NNSF of China (10371092)the Foundation of Wuhan University.
文摘The concepts of Markov process in random environment and homogeneous random transition functions are introduced. The necessary and sufficient conditions for homogeneous random transition function are given. The main results in this article are the analytical properties, such as continuity, differentiability, random Kolmogorov backward equation and random Kolmogorov forward equation of homogeneous random transition functions.
基金Supported by the National Nature Science Foundation of China under Grant No 70571059.
文摘We consider the adaptive consensus problem for leader-follower multi-agent systems with time delay coupling. Under the condition that the interconnection graph of the agents is directed and balanced, a neighbor-based consensus protocol with adaptive feedback gain is proposed for the follower agents to track the leader. The stability is performed based on the Lyapunov stability theorem. Some simulation examples are provided to show the efficiency of the control scheme.
基金supported by the National Natural Science Foundation of China(Grant No.11875135)Fundamental Research Funds for National University,China University of Geosciences(Wuhan)(Grant No.CUGGC05)。
文摘The cooperative behaviors resulted from the interaction of coupled identical oscillators have been investigated intensively.However,the coupled oscillators in practice are nonidentical,and there exist mismatched parameters.It has been proved that under certain conditions,complete synchronization can take place in coupled nonidentical oscillators with the same equilibrium points,yet other cooperative behaviors are not addressed.In this paper,we further consider two coupled nonidentical oscillators with the same equilibrium points,where one oscillator is convergent while the other is chaotic,and explore their cooperative behaviors.We find that the coupling mode and the coupling strength can bring the coupled oscillators to different cooperation behaviors in unidirectional or undirected couplings.In the case of directed coupling,death islands appear in two-parameter spaces.The mechanism inducing these transitions is presented.
基金Sponsored by the NSF of South-Central University for Nationalities (YZZ08004)the Doctoral programme foundation of National Education Ministry of China
文摘For convolution-type Calderon-Zygmund operators, by the boundedness on Besov spaces and Hardy spaces, applying interpolation theory and duality, it is known that H5rmander condition can ensure the boundedness on Triebel-Lizorkin spaces Fp^0,q （1 〈 p,q 〈 ∞） and on a party of endpoint spaces FO,q （1 ≤ q ≤ 2）, hut this idea is invalid for endpoint Triebel-Lizorkin spaces F1^0,q （2 〈 q ≤ ∞）. In this article, the authors apply wavelets and interpolation theory to establish the boundedness on F1^0,q （2 〈 q ≤ ∞） under an integrable condition which approaches HSrmander condition infinitely.
基金Project supported by the National Natural Science Foundation of China(19971052) and the Programme of Hunan Education Foundation(02C095)
文摘The uniqueness of meromorphic functions that share four values is investigated. A necessary condition to the case is acquired, and some partial results for question '1CM+3IM=4CM' are obtained.
