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
China’s booming economy and the growing demand of urban middle class are creating a favorable situation for the development of domestic cultural and creative industry.The consumption pattern has changed and families ...China’s booming economy and the growing demand of urban middle class are creating a favorable situation for the development of domestic cultural and creative industry.The consumption pattern has changed and families spend more outlay on cultural products and services.Within this flourishing industry,many museums caught development opportunities and began to get profit through successfully promoting their own cultural and creative products.However,it is unusual that Emperor Qinshihuang’s Mausoleum Site Museum,enjoying high social status and a reputation for world cultural heritage as well as a national 5A level tourist attraction,regretfully,did not achieve noticeable achievements in this area.Therefore,based on STP theory,the purpose of this paper is to study the reasons why this museum fails to fulfill its potential in promising cultural and creative industry and give some suggestions to the development and promotion of its cultural and creative goods.展开更多
This paper uses the semi-tensor product(STP)of matrices and adopts algebraic methods to study the controllability,reachability,and stabilizability of extended finite state machines(EFSMs).First,we construct the biline...This paper uses the semi-tensor product(STP)of matrices and adopts algebraic methods to study the controllability,reachability,and stabilizability of extended finite state machines(EFSMs).First,we construct the bilinear dynamic system model of the EFSM,laying the foundation for further research.Second,combined with this bilinear dynamic system model,we propose theorems for the controllability,reachability,and stabilizability of the bilinear dynamic system model of the EFSM.Finally,we design an algorithm to determine the controllability and stabilizability of the EFSM.The correctness of the main results is verified through examples.展开更多
Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control s...Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control systems with limited communication resources. In this study, the set stabilization problem and STC design of Boolean control networks are investigated via the semi-tensor product technique. On the one hand, the largest control invariant subset is calculated in terms of the strongly connected components of the state transition graph, by which a graph-theoretical condition for set stabilization is derived. On the other hand, a characteristic function is exploited to determine the triggering mechanism and feasible controls. Based on this, the minimum-time and minimum-triggering open-loop, state-feedback and output-feedback STCs for set stabilization are designed,respectively. As classic applications of self-triggered set stabilization, self-triggered synchronization, self-triggered output tracking and self-triggered output regulation are discussed as well. Additionally, several practical examples are given to illustrate the effectiveness of theoretical results.展开更多
In this paper,a criterion for the partially symmetric game(PSG)is derived by using the semitensor product approach.The dimension and the basis of the linear subspace composed of all the PSGs with respect to a given se...In this paper,a criterion for the partially symmetric game(PSG)is derived by using the semitensor product approach.The dimension and the basis of the linear subspace composed of all the PSGs with respect to a given set of partial players are calculated.The testing equations with the minimum number are concretely determined,and the computational complexity is analysed.Finally,two examples are displayed to show the theoretical results.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.
基金This paper is funded by the Innovation and Entrepreneurship Training Program for college students in Guangdong Province(No.2019126220004).
文摘China’s booming economy and the growing demand of urban middle class are creating a favorable situation for the development of domestic cultural and creative industry.The consumption pattern has changed and families spend more outlay on cultural products and services.Within this flourishing industry,many museums caught development opportunities and began to get profit through successfully promoting their own cultural and creative products.However,it is unusual that Emperor Qinshihuang’s Mausoleum Site Museum,enjoying high social status and a reputation for world cultural heritage as well as a national 5A level tourist attraction,regretfully,did not achieve noticeable achievements in this area.Therefore,based on STP theory,the purpose of this paper is to study the reasons why this museum fails to fulfill its potential in promising cultural and creative industry and give some suggestions to the development and promotion of its cultural and creative goods.
基金Project supported by the National Natural Science Foundation of China(Nos.U1804150 and 62073124)。
文摘This paper uses the semi-tensor product(STP)of matrices and adopts algebraic methods to study the controllability,reachability,and stabilizability of extended finite state machines(EFSMs).First,we construct the bilinear dynamic system model of the EFSM,laying the foundation for further research.Second,combined with this bilinear dynamic system model,we propose theorems for the controllability,reachability,and stabilizability of the bilinear dynamic system model of the EFSM.Finally,we design an algorithm to determine the controllability and stabilizability of the EFSM.The correctness of the main results is verified through examples.
基金supported by the National Natural Science Foundation of China (62273201,62173209,72134004,62303170)the Research Fund for the Taishan Scholar Project of Shandong Province of China (TSTP20221103)。
文摘Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control systems with limited communication resources. In this study, the set stabilization problem and STC design of Boolean control networks are investigated via the semi-tensor product technique. On the one hand, the largest control invariant subset is calculated in terms of the strongly connected components of the state transition graph, by which a graph-theoretical condition for set stabilization is derived. On the other hand, a characteristic function is exploited to determine the triggering mechanism and feasible controls. Based on this, the minimum-time and minimum-triggering open-loop, state-feedback and output-feedback STCs for set stabilization are designed,respectively. As classic applications of self-triggered set stabilization, self-triggered synchronization, self-triggered output tracking and self-triggered output regulation are discussed as well. Additionally, several practical examples are given to illustrate the effectiveness of theoretical results.
基金the National Natural Science Foundation of China under Grants 61673012 and 11971240,respectively。
文摘In this paper,a criterion for the partially symmetric game(PSG)is derived by using the semitensor product approach.The dimension and the basis of the linear subspace composed of all the PSGs with respect to a given set of partial players are calculated.The testing equations with the minimum number are concretely determined,and the computational complexity is analysed.Finally,two examples are displayed to show the theoretical results.
