In this paper, the solution of the matrix second semi-tensor product equation A∘lX∘lB=Cis studied. Firstly, the solvability of the matrix-vector second semi-tensor product equation is investigated. At the same time,...In this paper, the solution of the matrix second semi-tensor product equation A∘lX∘lB=Cis studied. Firstly, the solvability of the matrix-vector second semi-tensor product equation is investigated. At the same time, the compatibility conditions, the sufficient and necessary conditions and the specific solution methods for the matrix solution are given. Secondly, we further consider the solvability of the second semi-tensor product equation of the matrix. For each part, several examples are given to illustrate the validity of the results.展开更多
This paper investigates the networked evolutionary model based on snow-drift game with the strategy of rewards and penalty. Firstly, by using the semi-tensor product of matrices approach, the mathematical model of the...This paper investigates the networked evolutionary model based on snow-drift game with the strategy of rewards and penalty. Firstly, by using the semi-tensor product of matrices approach, the mathematical model of the networked evolutionary game is built. Secondly, combined with the matrix expression of logic, the mathematical model is expressed as a dynamic logical system and next converted into its evolutionary dynamic algebraic form. Thirdly, the dynamic evolution process is analyzed and the final level of cooperation is discussed. Finally, the effects of the changes in the rewarding and penalty factors on the level of cooperation in the model are studied separately, and the conclusions are verified by examples.展开更多
We study totally umbilical screen transversal lightlike submanifolds immersed in a semi-Riemannian product manifold and obtain necessary and sufficient conditions for induced connection ▽ on a totally umbilical radic...We study totally umbilical screen transversal lightlike submanifolds immersed in a semi-Riemannian product manifold and obtain necessary and sufficient conditions for induced connection ▽ on a totally umbilical radical screen transversal lightlike submanifold to be metric connection. We prove a theorem which classifies totally umbilical ST-anti-invariant lightlike submanifold immersed in a semi-Riemannian product manifold.展开更多
This paper proposes an inner product Laplacian embedding algorithm based on semi-definite programming, named as IPLE algorithm. The new algorithm learns a geodesic distance-based kernel matrix by using semi-definite p...This paper proposes an inner product Laplacian embedding algorithm based on semi-definite programming, named as IPLE algorithm. The new algorithm learns a geodesic distance-based kernel matrix by using semi-definite programming under the constraints of local contraction. The criterion function is to make the neighborhood points on manifold as close as possible while the geodesic distances between those distant points are preserved. The IPLE algorithm sufficiently integrates the advantages of LE, ISOMAP and MVU algorithms. The comparison experiments on two image datasets from COIL-20 images and USPS handwritten digit images are performed by applying LE, ISOMAP, MVU and the proposed IPLE. Experimental results show that the intrinsic low-dimensional coordinates obtained by our algorithm preserve more information according to the fraction of the dominant eigenvalues and can obtain the better comprehensive performance in clustering and manifold structure.展开更多
The purpose of this paper is to introduce and study the semi-groups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive m...The purpose of this paper is to introduce and study the semi-groups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive mappings in probabilistic normed spaces. As applications, these results are utilized to study the Cauchy problem for a kind of differential inclusions with accretive mappings in probabilistic normed spaces.展开更多
The definition of generalized product of fractal is first put forward for the research on the relations between original fractal and its product of fractal when the transformations of iteration function system （IFS）...The definition of generalized product of fractal is first put forward for the research on the relations between original fractal and its product of fractal when the transformations of iteration function system （IFS） are incomplete. Then the representations of generalized product of IFS are discussed based on the theory of the product of fractal. Furthermore, the dimensional relations between the product of fractal and its semi-product are obtained. The dimensional relations of self-similar set are discussed. Finally, the examples for rendering fractal graphs are given. These results posses potentials in image compression and pattern recognition.展开更多
随着工业4.0的发展,移动智能体系统(Mobile agent system,MAS)与多回路无线控制系统(Wireless control system,WCS)被部署到工厂中,构成异构工业物联网(Industrial internet of things,IIoT)系统,协作执行智能制造任务.在协作过程中,MAS...随着工业4.0的发展,移动智能体系统(Mobile agent system,MAS)与多回路无线控制系统(Wireless control system,WCS)被部署到工厂中,构成异构工业物联网(Industrial internet of things,IIoT)系统,协作执行智能制造任务.在协作过程中,MAS与WCS紧密耦合,导致状态相关衰落,两者性能相互制约.为解决这一问题,研究异构工业物联网系统的最优控制问题,满足WCS控制性能约束与MAS安全生产约束的同时,最小化系统平均通信成本.首先,利用有限域系统描述MAS在不同阴影衰落程度工作区间的转移,刻画MAS与WCS耦合下的状态相关衰落信道模型.基于此,利用矩阵半张量积理论,通过构建受限跟随者状态转移图(Follower state transition graph,FSTG),建立最优控制问题可行性图判据,给出关于受限集合镇定的充分必要条件.其次,基于加权跟随者状态转移图的最小平均环理论,建立领航-跟随MAS最优控制序列的构造算法,并证明其最优性.最后,通过仿真验证算法的有效性.展开更多
文摘In this paper, the solution of the matrix second semi-tensor product equation A∘lX∘lB=Cis studied. Firstly, the solvability of the matrix-vector second semi-tensor product equation is investigated. At the same time, the compatibility conditions, the sufficient and necessary conditions and the specific solution methods for the matrix solution are given. Secondly, we further consider the solvability of the second semi-tensor product equation of the matrix. For each part, several examples are given to illustrate the validity of the results.
文摘This paper investigates the networked evolutionary model based on snow-drift game with the strategy of rewards and penalty. Firstly, by using the semi-tensor product of matrices approach, the mathematical model of the networked evolutionary game is built. Secondly, combined with the matrix expression of logic, the mathematical model is expressed as a dynamic logical system and next converted into its evolutionary dynamic algebraic form. Thirdly, the dynamic evolution process is analyzed and the final level of cooperation is discussed. Finally, the effects of the changes in the rewarding and penalty factors on the level of cooperation in the model are studied separately, and the conclusions are verified by examples.
文摘We study totally umbilical screen transversal lightlike submanifolds immersed in a semi-Riemannian product manifold and obtain necessary and sufficient conditions for induced connection ▽ on a totally umbilical radical screen transversal lightlike submanifold to be metric connection. We prove a theorem which classifies totally umbilical ST-anti-invariant lightlike submanifold immersed in a semi-Riemannian product manifold.
文摘This paper proposes an inner product Laplacian embedding algorithm based on semi-definite programming, named as IPLE algorithm. The new algorithm learns a geodesic distance-based kernel matrix by using semi-definite programming under the constraints of local contraction. The criterion function is to make the neighborhood points on manifold as close as possible while the geodesic distances between those distant points are preserved. The IPLE algorithm sufficiently integrates the advantages of LE, ISOMAP and MVU algorithms. The comparison experiments on two image datasets from COIL-20 images and USPS handwritten digit images are performed by applying LE, ISOMAP, MVU and the proposed IPLE. Experimental results show that the intrinsic low-dimensional coordinates obtained by our algorithm preserve more information according to the fraction of the dominant eigenvalues and can obtain the better comprehensive performance in clustering and manifold structure.
文摘The purpose of this paper is to introduce and study the semi-groups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive mappings in probabilistic normed spaces. As applications, these results are utilized to study the Cauchy problem for a kind of differential inclusions with accretive mappings in probabilistic normed spaces.
基金supported by National Natural Science Foundation of China (50575026, 50275013), National High-Tech. R&D Program for CIMS (2001AA412011).
文摘The definition of generalized product of fractal is first put forward for the research on the relations between original fractal and its product of fractal when the transformations of iteration function system （IFS） are incomplete. Then the representations of generalized product of IFS are discussed based on the theory of the product of fractal. Furthermore, the dimensional relations between the product of fractal and its semi-product are obtained. The dimensional relations of self-similar set are discussed. Finally, the examples for rendering fractal graphs are given. These results posses potentials in image compression and pattern recognition.
文摘随着工业4.0的发展,移动智能体系统(Mobile agent system,MAS)与多回路无线控制系统(Wireless control system,WCS)被部署到工厂中,构成异构工业物联网(Industrial internet of things,IIoT)系统,协作执行智能制造任务.在协作过程中,MAS与WCS紧密耦合,导致状态相关衰落,两者性能相互制约.为解决这一问题,研究异构工业物联网系统的最优控制问题,满足WCS控制性能约束与MAS安全生产约束的同时,最小化系统平均通信成本.首先,利用有限域系统描述MAS在不同阴影衰落程度工作区间的转移,刻画MAS与WCS耦合下的状态相关衰落信道模型.基于此,利用矩阵半张量积理论,通过构建受限跟随者状态转移图(Follower state transition graph,FSTG),建立最优控制问题可行性图判据,给出关于受限集合镇定的充分必要条件.其次,基于加权跟随者状态转移图的最小平均环理论,建立领航-跟随MAS最优控制序列的构造算法,并证明其最优性.最后,通过仿真验证算法的有效性.
