Projective synchronization problems of a drive system and a particular response network were investigated,where the drive system is an arbitrary system with n+1 dimensions;it may be a linear or nonlinear system,and ev...Projective synchronization problems of a drive system and a particular response network were investigated,where the drive system is an arbitrary system with n+1 dimensions;it may be a linear or nonlinear system,and even a chaotic or hyperchaotic system,the response network is complex system coupled by N nodes,and every node is showed by the approximately linear part of the drive system.Only controlling any one node of the response network by designed controller can achieve the projective synchronization.Some numerical examples were employed to verify the effectiveness and correctness of the designed controller.展开更多
The estimation of quantum phase differences plays an important role in quantum simulation and quantum computation,yet existing quantum phase estimation algorithms face critical limitations in noisy intermediate-scale ...The estimation of quantum phase differences plays an important role in quantum simulation and quantum computation,yet existing quantum phase estimation algorithms face critical limitations in noisy intermediate-scale quantum(NISQ)devices due to their excessive depth and circuit complexity.We demonstrate a high-precision phase difference estimation protocol based on the Bayesian phase difference estimation algorithm and single-photon projective measurement.The iterative framework of the algorithm,combined with the independence from controlled unitary operations,inherently mitigates circuit depth and complexity limitations.Through an experimental realization on the photonic system,we demonstrate high-precision estimation of diverse phase differences,showing root-mean-square errors(RMSE)below the standard quantum limit𝒪(1/√N)and reaching the Heisenberg scaling𝒪(1/N)after a certain number of iterations.Our scheme provides a critical advantage in quantum resource-constrained scenarios,and advances practical implementations of quantum information tasks under realistic hardware constraints.展开更多
Let T be a formal triangular matrix ring.We prove that,if for each 1≤j<i≤n,U_(ij) is flat on both sides,then a left T-module■is Ding projective if and only if M1 is a Ding projective left A1-module and for each ...Let T be a formal triangular matrix ring.We prove that,if for each 1≤j<i≤n,U_(ij) is flat on both sides,then a left T-module■is Ding projective if and only if M1 is a Ding projective left A1-module and for each 1≤k≤n-1 the mappingФk+1,k:U_(k+1),k■AkM_(k)→M_(k)+1 is injective with cokernel Ding projective over Ak+1.As a consequence,we describe Ding projective dimension of a left T-module.展开更多
Quantum coherence serves as a defining characteristic of quantum mechanics,finding extensive applications in quantum computing and quantum communication processing.This study explores quantum block coherence in the co...Quantum coherence serves as a defining characteristic of quantum mechanics,finding extensive applications in quantum computing and quantum communication processing.This study explores quantum block coherence in the context of projective measurements,focusing on the quantification of such coherence.Firstly,we define the correlation function between the two general projective measurements P and Q,and analyze the connection between sets of block incoherent states related to two compatible projective measurements P and Q.Secondly,we discuss the measure of quantum block coherence with respect to projective measurements.Based on a given measure of quantum block coherence,we characterize the existence of maximal block coherent states through projective measurements.This research integrates the compatibility of projective measurements with the framework of quantum block coherence,contributing to the advancement of block coherence measurement theory.展开更多
We study different types of projective synchronization （projective-anticipating, projective, and projectivelag synchronization） in a class of time-delayed chaotic systems related to optical bistable or hybrid optica...We study different types of projective synchronization （projective-anticipating, projective, and projectivelag synchronization） in a class of time-delayed chaotic systems related to optical bistable or hybrid optical bistable devices. We relax some limitations of previous work, where the scaling factor a can not be any desired value. In this paper, we achieve projective-anticipating, projective, and projective-lag synchronization without the limitation of a. A suitable controller is chosen using active control approach. Based on the Lyapunov stability theory, we derive the sufficient stability condition through theoretical analysis. The analytical results are validated by the numerical simulations using Ikeda model and Mackey-Glass model.展开更多
In order to solve the electromagnetic problems on the large multi branch domains, the decomposition projective method(DPM) is generalized for multi subspaces in this paper. Furthermore multi parameters are designed fo...In order to solve the electromagnetic problems on the large multi branch domains, the decomposition projective method(DPM) is generalized for multi subspaces in this paper. Furthermore multi parameters are designed for DPM, which is called the fast DPM(FDPM), and the convergence ratio of the above algorithm is greatly increased. The examples show that the iterative number of the FDPM with optimal parameters decreases much more, which is less than one third of the DPM iteration number. After studying the ...展开更多
As we know,a complex P is projective if and only if P is exact with Z_n(P)projective in R-Mod for each n∈Z and any morphism f:P→C is null homotopic for any complex C.In this article,we study the notion of DG-Gorenst...As we know,a complex P is projective if and only if P is exact with Z_n(P)projective in R-Mod for each n∈Z and any morphism f:P→C is null homotopic for any complex C.In this article,we study the notion of DG-Gorenstein projective complexes.We show that a complex G is DG-Gorenstein projective if and only if G is exact with Z_n(G)Gorenstein projective in R-Mod for each n∈Z and any morphism f:G→Q is null homotopic whenever Q is a DG-projective complex.展开更多
Projective synchronization and generalized projective synchronization have recently been observed in the coupled chaotic systems. In this paper, a new synchronization, called ＂generalized projective synchronization＂...Projective synchronization and generalized projective synchronization have recently been observed in the coupled chaotic systems. In this paper, a new synchronization, called ＂generalized projective synchronization＂, is reported in the chaotic Lorenz system and the chaotic Chen one.展开更多
In this paper, we study n-Gorenstein projective modules over Frobenius extensions and n-Gorenstein projective dimensions over separable Frobenius extensions. Let R ■ A be a Frobenius extension of rings and M any left...In this paper, we study n-Gorenstein projective modules over Frobenius extensions and n-Gorenstein projective dimensions over separable Frobenius extensions. Let R ■ A be a Frobenius extension of rings and M any left A-module. It is proved that M is an n-Gorenstein projective left A-module if and only if A ■_(R)M and Hom_(R)(A, M) are n-Gorenstein projective left A-modules if and only if M is an n-Gorenstein projective left R-module. Furthermore, when R ■ A is a separable Frobenius extension, n-Gorenstein projective dimensions are considered.展开更多
Let R be an associated ring with identity. A new equivalent characterization of pure projective left R-modules is given by applying homological methods. It is proved that a left R-module P is pure projective if and on...Let R be an associated ring with identity. A new equivalent characterization of pure projective left R-modules is given by applying homological methods. It is proved that a left R-module P is pure projective if and only if for any pure epimorphism E→M→0, where E is pure injective, HomR（P, E）→HomR（P, M）→0 is exact. Also, we obtain a dual result of pure injective left R-modules. Furthermore, it is shown that every pure projective left R-module is closed under pure submodule if and only if every pure injective left R-module is closed under pure epimorphic image.展开更多
In this paper the projective semi symmetric connection D is studied, which is projectively equivalent to the Levi_Civita connection . An intrinsic projective invariant is found out and a necessary and suffici...In this paper the projective semi symmetric connection D is studied, which is projectively equivalent to the Levi_Civita connection . An intrinsic projective invariant is found out and a necessary and sufficient condition is given. Furthermore, another condition is obtained when the convariant derivative of the projective invariant is kept.展开更多
This paper gives the definition of function projective synchronization with less conservative demand for a scaling function, and investigates the function projective synchronization in partially linear drive-response ...This paper gives the definition of function projective synchronization with less conservative demand for a scaling function, and investigates the function projective synchronization in partially linear drive-response chaotic systems. Based on the Lyapunov stability theory, it has been shown that the function projective synchronization with desired scaling function can be realized by simple control law. Moreover it does not need scaling function to be differentiable, bounded and non-vanished. The numerical simulations are provided to verify the theoretical result.展开更多
This paper investigates the modified function projective synchronization,which means that the drive system and the response system are synchronized up to a desired scale matrix of function. By the active control schem...This paper investigates the modified function projective synchronization,which means that the drive system and the response system are synchronized up to a desired scale matrix of function. By the active control scheme,a general method for modified function projective synchronization is proposed. Numerical simulations on chaotic Rssler system and hyper-chaotic Chen system are presented to verify the effectiveness of the proposed scheme.展开更多
Projective change between two Finsler metrics arises from Information Geom-etry. Such metrics have special geometric properties and will play an important role in Finsler geometry. The purpose of the present paper is ...Projective change between two Finsler metrics arises from Information Geom-etry. Such metrics have special geometric properties and will play an important role in Finsler geometry. The purpose of the present paper is to find a relation to characterize the projective change between generalized (α, β) - metric ( μ1, μ2 and μ3 ≠ 0 are constants) and Randers metric , where α and are two Riemannian metrics, β and are 1-forms. Further, we study such projective change when generalized (α, β) -metric F has some curvature property.展开更多
This paper is a study of strongly Ding projective modules with respect to a semidualizing module. The class of strongly Ding flat modules with respect to a semidualizing module is also investigated, and the relationsh...This paper is a study of strongly Ding projective modules with respect to a semidualizing module. The class of strongly Ding flat modules with respect to a semidualizing module is also investigated, and the relationship between strongly Ding projective modules and strongly Ding flat modules with respect to a semidualizing module is characterized.Some well-known results on strongly Ding projective modules, n-strongly Ding projective modules and strongly D_C-projective modules are generalized and unified.展开更多
Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using t...Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using the left global relative Ding projective dimensions of A and B, we estimate the relative Ding projective dimension of a left T-module.展开更多
In this paper, a learning control approach is applied to the generalized projective synchronisation （GPS） of different chaotic systems with unknown periodically time-varying parameters. Using the Lyapunov--Krasovski...In this paper, a learning control approach is applied to the generalized projective synchronisation （GPS） of different chaotic systems with unknown periodically time-varying parameters. Using the Lyapunov--Krasovskii functional stability theory, a differential-difference mixed parametric learning law and an adaptive learning control law are constructed to make the states of two different chaotic systems asymptotically synchronised. The scheme is successfully applied to the generalized projective synchronisation between the Lorenz system and Chen system. Moreover, numerical simulations results are used to verify the effectiveness of the proposed scheme.展开更多
Applying the generalized method, which is a direct and unified algebraic method for constructing multipletravelling wave solutions of nonlinear partial differential equations (PDEs), and implementing in a computer alg...Applying the generalized method, which is a direct and unified algebraic method for constructing multipletravelling wave solutions of nonlinear partial differential equations (PDEs), and implementing in a computer algebraicsystem, we consider the generalized Zakharov-Kuzentsov equation with nonlinear terms of any order. As a result, wecan not only successfully recover the previously known travelling wave solutions found by existing various tanh methodsand other sophisticated methods, but also obtain some new formal solutions. The solutions obtained include kink-shapedsolitons, bell-shaped solitons, singular solitons, and periodic solutions.展开更多
In this paper is investigated the generalized projective synchronization of a class of chaotic （or hyperchaotic） systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive...In this paper is investigated the generalized projective synchronization of a class of chaotic （or hyperchaotic） systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive technique, the globally generalized projective synchronization of two identical chaotic （hyperchaotic） systems is achieved by designing a novel nonlinear controller. Furthermore, the parameter identification is realized simultaneously. A sufficient condition for the globally projective synchronization is obtained. Finally, by taking the hyperchaotic L system as example, some numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed technique.展开更多
This study addresses the adaptive control and function projective synchronization problems between 2D Rulkov discrete-time system and Network discrete-time system. Based on backstepping design with three controllers, ...This study addresses the adaptive control and function projective synchronization problems between 2D Rulkov discrete-time system and Network discrete-time system. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of discretetime chaotic systems. In addition, the adaptive control function is applied to achieve the state synchronization of two discrete-time systems. Numerical results demonstrate the effectiveness of the proposed control scheme.展开更多
基金Supported by the National Natural Science Foundation of China (11161027)。
文摘Projective synchronization problems of a drive system and a particular response network were investigated,where the drive system is an arbitrary system with n+1 dimensions;it may be a linear or nonlinear system,and even a chaotic or hyperchaotic system,the response network is complex system coupled by N nodes,and every node is showed by the approximately linear part of the drive system.Only controlling any one node of the response network by designed controller can achieve the projective synchronization.Some numerical examples were employed to verify the effectiveness and correctness of the designed controller.
基金Project supported by the Natural Science Foundation of Jiangsu Province(Grant Nos.BK20233001 and BK20243060)the National Natural Science Foundation of China(Grant No.62288101)。
文摘The estimation of quantum phase differences plays an important role in quantum simulation and quantum computation,yet existing quantum phase estimation algorithms face critical limitations in noisy intermediate-scale quantum(NISQ)devices due to their excessive depth and circuit complexity.We demonstrate a high-precision phase difference estimation protocol based on the Bayesian phase difference estimation algorithm and single-photon projective measurement.The iterative framework of the algorithm,combined with the independence from controlled unitary operations,inherently mitigates circuit depth and complexity limitations.Through an experimental realization on the photonic system,we demonstrate high-precision estimation of diverse phase differences,showing root-mean-square errors(RMSE)below the standard quantum limit𝒪(1/√N)and reaching the Heisenberg scaling𝒪(1/N)after a certain number of iterations.Our scheme provides a critical advantage in quantum resource-constrained scenarios,and advances practical implementations of quantum information tasks under realistic hardware constraints.
基金Supported by the National Natural Science Foundation of China(Grant No.11861055)。
文摘Let T be a formal triangular matrix ring.We prove that,if for each 1≤j<i≤n,U_(ij) is flat on both sides,then a left T-module■is Ding projective if and only if M1 is a Ding projective left A1-module and for each 1≤k≤n-1 the mappingФk+1,k:U_(k+1),k■AkM_(k)→M_(k)+1 is injective with cokernel Ding projective over Ak+1.As a consequence,we describe Ding projective dimension of a left T-module.
基金partially supported by the National Natural Science Foundations of China (Grant No.11901317)the China Postdoctoral Science Foundation (Grant No.2020M680480)+1 种基金the Fundamental Research Funds for the Central Universities (Grant No.2023MS078)the Beijing Natural Science Foundation (Grant No.1232021)。
文摘Quantum coherence serves as a defining characteristic of quantum mechanics,finding extensive applications in quantum computing and quantum communication processing.This study explores quantum block coherence in the context of projective measurements,focusing on the quantification of such coherence.Firstly,we define the correlation function between the two general projective measurements P and Q,and analyze the connection between sets of block incoherent states related to two compatible projective measurements P and Q.Secondly,we discuss the measure of quantum block coherence with respect to projective measurements.Based on a given measure of quantum block coherence,we characterize the existence of maximal block coherent states through projective measurements.This research integrates the compatibility of projective measurements with the framework of quantum block coherence,contributing to the advancement of block coherence measurement theory.
基金Supported by Research Project of Hubei Provincial Department of Education under Grant No.Q20101609Foundation of Wuhan Textile University under Grant No.105040
文摘We study different types of projective synchronization （projective-anticipating, projective, and projectivelag synchronization） in a class of time-delayed chaotic systems related to optical bistable or hybrid optical bistable devices. We relax some limitations of previous work, where the scaling factor a can not be any desired value. In this paper, we achieve projective-anticipating, projective, and projective-lag synchronization without the limitation of a. A suitable controller is chosen using active control approach. Based on the Lyapunov stability theory, we derive the sufficient stability condition through theoretical analysis. The analytical results are validated by the numerical simulations using Ikeda model and Mackey-Glass model.
文摘In order to solve the electromagnetic problems on the large multi branch domains, the decomposition projective method(DPM) is generalized for multi subspaces in this paper. Furthermore multi parameters are designed for DPM, which is called the fast DPM(FDPM), and the convergence ratio of the above algorithm is greatly increased. The examples show that the iterative number of the FDPM with optimal parameters decreases much more, which is less than one third of the DPM iteration number. After studying the ...
基金Supported by the National Natural Science Foundation of China(2061061)Fundamental Research Funds for the Central Universities(31920190054)+1 种基金Funds for Talent Introduction of Northwest Minzu University(XBMUYJRC201406)First-Rate Discipline of Northwest Minzu University。
文摘As we know,a complex P is projective if and only if P is exact with Z_n(P)projective in R-Mod for each n∈Z and any morphism f:P→C is null homotopic for any complex C.In this article,we study the notion of DG-Gorenstein projective complexes.We show that a complex G is DG-Gorenstein projective if and only if G is exact with Z_n(G)Gorenstein projective in R-Mod for each n∈Z and any morphism f:G→Q is null homotopic whenever Q is a DG-projective complex.
基金Project supported by Tianyuan Foundation of China （ Grant No. A0324651）, and Natural Science Foundation of Hunaa Province of China （Grant No. 03JJY3014）
文摘Projective synchronization and generalized projective synchronization have recently been observed in the coupled chaotic systems. In this paper, a new synchronization, called ＂generalized projective synchronization＂, is reported in the chaotic Lorenz system and the chaotic Chen one.
基金Supported by the National Natural Science Foundation of China (Grant No. 11561061)。
文摘In this paper, we study n-Gorenstein projective modules over Frobenius extensions and n-Gorenstein projective dimensions over separable Frobenius extensions. Let R ■ A be a Frobenius extension of rings and M any left A-module. It is proved that M is an n-Gorenstein projective left A-module if and only if A ■_(R)M and Hom_(R)(A, M) are n-Gorenstein projective left A-modules if and only if M is an n-Gorenstein projective left R-module. Furthermore, when R ■ A is a separable Frobenius extension, n-Gorenstein projective dimensions are considered.
文摘Let R be an associated ring with identity. A new equivalent characterization of pure projective left R-modules is given by applying homological methods. It is proved that a left R-module P is pure projective if and only if for any pure epimorphism E→M→0, where E is pure injective, HomR（P, E）→HomR（P, M）→0 is exact. Also, we obtain a dual result of pure injective left R-modules. Furthermore, it is shown that every pure projective left R-module is closed under pure submodule if and only if every pure injective left R-module is closed under pure epimorphic image.
文摘In this paper the projective semi symmetric connection D is studied, which is projectively equivalent to the Levi_Civita connection . An intrinsic projective invariant is found out and a necessary and sufficient condition is given. Furthermore, another condition is obtained when the convariant derivative of the projective invariant is kept.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60875036)the Program for Innovative Research Team of Jiangnan University
文摘This paper gives the definition of function projective synchronization with less conservative demand for a scaling function, and investigates the function projective synchronization in partially linear drive-response chaotic systems. Based on the Lyapunov stability theory, it has been shown that the function projective synchronization with desired scaling function can be realized by simple control law. Moreover it does not need scaling function to be differentiable, bounded and non-vanished. The numerical simulations are provided to verify the theoretical result.
基金Sponsored by the Scientific Research Fund of Heilongjiang Provincial Education Department of China(Grant No. 11551088)Youth Foundation ofHarbin University of Science and Technology(Grant No. 2009YF018)
文摘This paper investigates the modified function projective synchronization,which means that the drive system and the response system are synchronized up to a desired scale matrix of function. By the active control scheme,a general method for modified function projective synchronization is proposed. Numerical simulations on chaotic Rssler system and hyper-chaotic Chen system are presented to verify the effectiveness of the proposed scheme.
文摘Projective change between two Finsler metrics arises from Information Geom-etry. Such metrics have special geometric properties and will play an important role in Finsler geometry. The purpose of the present paper is to find a relation to characterize the projective change between generalized (α, β) - metric ( μ1, μ2 and μ3 ≠ 0 are constants) and Randers metric , where α and are two Riemannian metrics, β and are 1-forms. Further, we study such projective change when generalized (α, β) -metric F has some curvature property.
基金Supported by the Postdoctoral Science Foundation of China（2017M611851）, the Jiangsu Planned Projects for Postdoctoral Research Funds（1601151C） and the Provincial Natural Science Foundation of Anhui Province（KJ2017A040）
文摘This paper is a study of strongly Ding projective modules with respect to a semidualizing module. The class of strongly Ding flat modules with respect to a semidualizing module is also investigated, and the relationship between strongly Ding projective modules and strongly Ding flat modules with respect to a semidualizing module is characterized.Some well-known results on strongly Ding projective modules, n-strongly Ding projective modules and strongly D_C-projective modules are generalized and unified.
文摘Let U be a (B, A)-bimodule, A and B be rings, and be a formal triangular matrix ring. In this paper, we characterize the structure of relative Ding projective modules over T under some conditions. Furthermore, using the left global relative Ding projective dimensions of A and B, we estimate the relative Ding projective dimension of a left T-module.
基金supported by the National Natural Science Foundation of China (Grant No. 60374015)
文摘In this paper, a learning control approach is applied to the generalized projective synchronisation （GPS） of different chaotic systems with unknown periodically time-varying parameters. Using the Lyapunov--Krasovskii functional stability theory, a differential-difference mixed parametric learning law and an adaptive learning control law are constructed to make the states of two different chaotic systems asymptotically synchronised. The scheme is successfully applied to the generalized projective synchronisation between the Lorenz system and Chen system. Moreover, numerical simulations results are used to verify the effectiveness of the proposed scheme.
基金The project supported by National Natural Science Foundation of China under Grant No.10072013the National Key Basic Research Development Program under Grant No.G1998030600
文摘Applying the generalized method, which is a direct and unified algebraic method for constructing multipletravelling wave solutions of nonlinear partial differential equations (PDEs), and implementing in a computer algebraicsystem, we consider the generalized Zakharov-Kuzentsov equation with nonlinear terms of any order. As a result, wecan not only successfully recover the previously known travelling wave solutions found by existing various tanh methodsand other sophisticated methods, but also obtain some new formal solutions. The solutions obtained include kink-shapedsolitons, bell-shaped solitons, singular solitons, and periodic solutions.
基金Project supported by the National Natural Science Foundation of China （Grant No 60574045） and partly by Foundation of Guangxi Department of Education, China （Grant No （2006）26-118）.
文摘In this paper is investigated the generalized projective synchronization of a class of chaotic （or hyperchaotic） systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive technique, the globally generalized projective synchronization of two identical chaotic （hyperchaotic） systems is achieved by designing a novel nonlinear controller. Furthermore, the parameter identification is realized simultaneously. A sufficient condition for the globally projective synchronization is obtained. Finally, by taking the hyperchaotic L system as example, some numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed technique.
基金supported by the Natural Science Foundation of China under Grant Nos.10747141 and 10735030Zhejiang Provincial Natural Science Foundation under Grant No.605408+3 种基金Ningbo Natural Science Foundation under Grant Nos.2007A610049 and 2008A61001National Basic Research Program of China (973 Program 2007CB814800)Programme for Changjiang Scholars and Innovative Research Team in University (IRT0734)K.C.Wong Magna Fund in Ningbo University
文摘This study addresses the adaptive control and function projective synchronization problems between 2D Rulkov discrete-time system and Network discrete-time system. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of discretetime chaotic systems. In addition, the adaptive control function is applied to achieve the state synchronization of two discrete-time systems. Numerical results demonstrate the effectiveness of the proposed control scheme.
