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
Semi-tensor product of matrices is a generalization of conventional matrix product for the case when the two factor matrices do not meet the dimension matching condition. It was firstly proposed about ten years ago. S...Semi-tensor product of matrices is a generalization of conventional matrix product for the case when the two factor matrices do not meet the dimension matching condition. It was firstly proposed about ten years ago. Since then it has been developed and applied to several different fields. In this paper we will first give a brief introduction. Then give a survey on its applications to dynamic systems, to logic, to differential geometry, to abstract algebra, respectively.展开更多
This paper addresses the synchronization problem of Boolean networks.Based on the matrix expression of logic,solvability conditions and design procedures of the synchronization of Boolean networks with outputs are giv...This paper addresses the synchronization problem of Boolean networks.Based on the matrix expression of logic,solvability conditions and design procedures of the synchronization of Boolean networks with outputs are given for both open-loop and feedback control.Necessary and sufficient conditions on open-loop control are proposed first with a constructive design procedure.Then sufficient condition for the feedback control case is obtained,and corresponding design procedure is proposed with the help of algorithms to solve logic matrix equations.Numerical examples are also provided to illustrate the proposed control design.展开更多
Nowadays the semi-tensor product(STP)approach to finite games has become a promising new direction.This paper provides a comprehensive survey on this prosperous field.After a brief introduction for STP and finite(netw...Nowadays the semi-tensor product(STP)approach to finite games has become a promising new direction.This paper provides a comprehensive survey on this prosperous field.After a brief introduction for STP and finite(networked)games,a description for the principle and fundamental technique of STP approach to finite games is presented.Then several problems and recent results about theory and applications of finite games via STP are presented.A brief comment about the potential use of STP to artificial intelligence is also proposed.展开更多
In this paper,we first propose a hidden rule among the secure message,the initial tensor product of two Bell states and the final tensor product when respectively applying local unitary transformations to the first pa...In this paper,we first propose a hidden rule among the secure message,the initial tensor product of two Bell states and the final tensor product when respectively applying local unitary transformations to the first particle of the two initial Bell states,and then present a high-efficiency quantum steganography protocol under the control of the hidden rule.In the proposed quantum steganography scheme,a hidden channel is established to transfer a secret message within any quantum secure direct communication(QSDC) scheme that is based on 2-level quantum states and unitary transformations.The secret message hiding/unhiding process is linked with the QSDC process only by unitary transformations.To accurately describe the capacity of a steganography scheme,a quantitative measure,named embedding efficiency,is introduced in this paper.The performance analysis shows that the proposed steganography scheme achieves a high efficiency as well as a good imperceptibility.Moreover,it is shown that this scheme can resist all serious attacks including the intercept-resend attack,measurement-resend attack,auxiliary particle attack and even the Denial of Service attack.To improve the efficiency of the proposed scheme,the hidden rule is extended based on the tensor product of multiple Bell states.展开更多
In this research, we explore the properties and applications of the mapping cone and its variant, the pinched mapping cone. The mapping cone is a construction that arises naturally in algebraic topology and is used to...In this research, we explore the properties and applications of the mapping cone and its variant, the pinched mapping cone. The mapping cone is a construction that arises naturally in algebraic topology and is used to study the homotopy type of spaces. It has several key properties, including its homotopy equivalence to the cofiber of a continuous map, and its ability to compute homotopy groups using the long exact sequence associated with the cofiber. We also provide an overview of the properties and applications of the mapping cone and the pinched mapping cone in algebraic topology. This work highlights the importance of these constructions in the study of homotopy theory and the calculation of homotopy groups. The study also points to the potential for further research in this area which includes the study of higher homotopy groups and the applications of these constructions to other areas of mathematics.展开更多
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 partly by National Natural Science Foundation of China under Grant No. 60221301 and 60334040 .Dedicated to Academician Han-Fu Chen on the occasion of his 70th birthday.
文摘Semi-tensor product of matrices is a generalization of conventional matrix product for the case when the two factor matrices do not meet the dimension matching condition. It was firstly proposed about ten years ago. Since then it has been developed and applied to several different fields. In this paper we will first give a brief introduction. Then give a survey on its applications to dynamic systems, to logic, to differential geometry, to abstract algebra, respectively.
基金supported by the National Natural Science Foundation of China under Grant No.61174071
文摘This paper addresses the synchronization problem of Boolean networks.Based on the matrix expression of logic,solvability conditions and design procedures of the synchronization of Boolean networks with outputs are given for both open-loop and feedback control.Necessary and sufficient conditions on open-loop control are proposed first with a constructive design procedure.Then sufficient condition for the feedback control case is obtained,and corresponding design procedure is proposed with the help of algorithms to solve logic matrix equations.Numerical examples are also provided to illustrate the proposed control design.
基金the National Natural Science Foundation of China(NSFC)under Grant Nos.62073315,61074114,and 61273013。
文摘Nowadays the semi-tensor product(STP)approach to finite games has become a promising new direction.This paper provides a comprehensive survey on this prosperous field.After a brief introduction for STP and finite(networked)games,a description for the principle and fundamental technique of STP approach to finite games is presented.Then several problems and recent results about theory and applications of finite games via STP are presented.A brief comment about the potential use of STP to artificial intelligence is also proposed.
基金supported by the National Natural Science Foundation of China (Grant Nos.61170272,61272514,61003287 and 61070163)the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20100005120002)+3 种基金the Fok Ying Tong Education Foundation (Grant No.131067)the Shandong Provincial Natural Science Foundation,China (Grant Nos.ZR2011FM023 and ZR2009GM036)the Shandong Province Outstanding Research Award Fund for Young Scientists of China (Grant No.BS2011DX034)the Fundamental Research Funds for the Central Universities (Grant No.BUPT2012RC0221)
文摘In this paper,we first propose a hidden rule among the secure message,the initial tensor product of two Bell states and the final tensor product when respectively applying local unitary transformations to the first particle of the two initial Bell states,and then present a high-efficiency quantum steganography protocol under the control of the hidden rule.In the proposed quantum steganography scheme,a hidden channel is established to transfer a secret message within any quantum secure direct communication(QSDC) scheme that is based on 2-level quantum states and unitary transformations.The secret message hiding/unhiding process is linked with the QSDC process only by unitary transformations.To accurately describe the capacity of a steganography scheme,a quantitative measure,named embedding efficiency,is introduced in this paper.The performance analysis shows that the proposed steganography scheme achieves a high efficiency as well as a good imperceptibility.Moreover,it is shown that this scheme can resist all serious attacks including the intercept-resend attack,measurement-resend attack,auxiliary particle attack and even the Denial of Service attack.To improve the efficiency of the proposed scheme,the hidden rule is extended based on the tensor product of multiple Bell states.
文摘In this research, we explore the properties and applications of the mapping cone and its variant, the pinched mapping cone. The mapping cone is a construction that arises naturally in algebraic topology and is used to study the homotopy type of spaces. It has several key properties, including its homotopy equivalence to the cofiber of a continuous map, and its ability to compute homotopy groups using the long exact sequence associated with the cofiber. We also provide an overview of the properties and applications of the mapping cone and the pinched mapping cone in algebraic topology. This work highlights the importance of these constructions in the study of homotopy theory and the calculation of homotopy groups. The study also points to the potential for further research in this area which includes the study of higher homotopy groups and the applications of these constructions to other areas of mathematics.
