This paper presents the method for the construction of tensor-product representation for multivariate switched linear systems, based on a suitable tensor-product representation of vectors and matrices. We obtain a rep...This paper presents the method for the construction of tensor-product representation for multivariate switched linear systems, based on a suitable tensor-product representation of vectors and matrices. We obtain a representation theorem for multivariate switched linear systems. The stability properties of the tensor-product representation are investigated in depth, achieving the important result that any stable switched systems can be constructed a stable tensor-product representation of finite dimension. It is shown that the tensor-product representation provides a high level framework for describing the dynamic behavior. The interpretation of expressions within the tensor-product representation framework leads to enhanced conceptual and physical understanding of switched linear systems dynamic behavior.展开更多
This paper finds a way to extend the well-known Fourier methods, to so-called n+1 directions partition domains in n-dimension. In particular, in 2-D and 3-D cases, we study Fourier methods over 3-direction parallel he...This paper finds a way to extend the well-known Fourier methods, to so-called n+1 directions partition domains in n-dimension. In particular, in 2-D and 3-D cases, we study Fourier methods over 3-direction parallel hexagon partitions and 4-direction parallel parallelogram dodecahedron partitions, respectively. It has pointed that, the most concepts and results of Fourier methods on tensor-product case, such as periodicity,orthogonality of Fourier basis system, partial sum of Fourier series and its approximation behavior, can be moved on the new non tensor-product partition case.展开更多
For a general second-order variable coefficient elliptic boundary value problem in three dimensions, the authors derive the weak estimate of the first type for tensor-product linear pentahedral finite elements. In add...For a general second-order variable coefficient elliptic boundary value problem in three dimensions, the authors derive the weak estimate of the first type for tensor-product linear pentahedral finite elements. In addition, the estimate for the W1,1-seminorm of the discrete derivative Green＇s function is given. Finally, the authors show that the derivatives of the finite element solution uh and the corresponding interpolant Hu are superclose in the pointwise sense of the L∞-norm.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
In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a se...In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.展开更多
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
文摘This paper presents the method for the construction of tensor-product representation for multivariate switched linear systems, based on a suitable tensor-product representation of vectors and matrices. We obtain a representation theorem for multivariate switched linear systems. The stability properties of the tensor-product representation are investigated in depth, achieving the important result that any stable switched systems can be constructed a stable tensor-product representation of finite dimension. It is shown that the tensor-product representation provides a high level framework for describing the dynamic behavior. The interpretation of expressions within the tensor-product representation framework leads to enhanced conceptual and physical understanding of switched linear systems dynamic behavior.
基金Project supported by the Major Basic Project of China (No.Gl9990328) and National Natural Science Foundation of China (No. 60173021)
文摘This paper finds a way to extend the well-known Fourier methods, to so-called n+1 directions partition domains in n-dimension. In particular, in 2-D and 3-D cases, we study Fourier methods over 3-direction parallel hexagon partitions and 4-direction parallel parallelogram dodecahedron partitions, respectively. It has pointed that, the most concepts and results of Fourier methods on tensor-product case, such as periodicity,orthogonality of Fourier basis system, partial sum of Fourier series and its approximation behavior, can be moved on the new non tensor-product partition case.
基金supported by the Natural Science Foundation of Zhejiang Province under Grant No.Y6090131the Natural Science Foundation of Ningbo City under Grant No.2010A610101
文摘For a general second-order variable coefficient elliptic boundary value problem in three dimensions, the authors derive the weak estimate of the first type for tensor-product linear pentahedral finite elements. In addition, the estimate for the W1,1-seminorm of the discrete derivative Green＇s function is given. Finally, the authors show that the derivatives of the finite element solution uh and the corresponding interpolant Hu are superclose in the pointwise sense of the L∞-norm.
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.
文摘In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.
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.
