This paper presents a proper splitting iterative method for comparing the general restricted linear euqations Ax=b, x ∈T （where, b ∈AT, and T is an arbitrary but fixed subspace of C<sup>m</sup>） and th...This paper presents a proper splitting iterative method for comparing the general restricted linear euqations Ax=b, x ∈T （where, b ∈AT, and T is an arbitrary but fixed subspace of C<sup>m</sup>） and the generalized in A<sub>T,S</sub> For the special case when b ∈AT and dim（T）=dim（AT）, this splitting iterative methverse A<sub>T,S</sub> hod converges to A<sub>T,S</sub>b （the unique solution of the general restricted system Ax=bx ∈T）.展开更多
A three-party scheme for splitting an arbitrary unknown two-qutrit state is proposed,where two non-maximally-entangled three-qutrit states are taken as the quantum channel among three parties.With the sender'shelp...A three-party scheme for splitting an arbitrary unknown two-qutrit state is proposed,where two non-maximally-entangled three-qutrit states are taken as the quantum channel among three parties.With the sender'shelp,if and only if both receivers collaborate together,they can securely share the quantum state in a probabilisticway by introducing an ancilla qutrit and performing appropriate unitary operations.The relation between the successprobability and coefficients characterizing the quantum channel is revealed.The security of the present scheme is analyzedand confirmed.Moreover,the generalization of the three-party scheme to more-party case is also sketched.展开更多
The generalized Navier-Stokes equations with damping are considered.We will show that the generalized Navier-Stokes equations with damping |u|^β-1u have weak solutions for anyβ>1 and 0<α<5/4,and we will us...The generalized Navier-Stokes equations with damping are considered.We will show that the generalized Navier-Stokes equations with damping |u|^β-1u have weak solutions for anyβ>1 and 0<α<5/4,and we will use the Fourier splitting method to prove the L2 decay of weak solutions forβ>2 and 0<α<3/4.展开更多
Sunlight is the most abundant renewable energy resource,providing the earth with enough power that is capable of taking care of all of humanity’s desires-a hundred times over.However,as it is at times diffuse and int...Sunlight is the most abundant renewable energy resource,providing the earth with enough power that is capable of taking care of all of humanity’s desires-a hundred times over.However,as it is at times diffuse and intermittent,it raises issues concerning how best to reap this energy and store it for times when the Sun is not shining.With increasing population in the world and modern economic development,there will be an additional increase in energy demand.Devices that use daylight to separate water into individual chemical elements may well be the answer to this issue,as water splitting produces an ideal fuel.If such devices that generate fuel were to become widely adopted,they must be low in cost,both for supplying and operation.Therefore,it is essential to research for cheap technologies for water ripping.This review summarizes the progress made toward such development,the open challenges existing,and the approaches undertaken to generate carbon-free energy through water splitting.展开更多
The purpose of this article is to introduce a general split feasibility problems for two families of nonexpansive mappings in Hilbert spaces. We prove that the sequence generated by the proposed new algorithm converge...The purpose of this article is to introduce a general split feasibility problems for two families of nonexpansive mappings in Hilbert spaces. We prove that the sequence generated by the proposed new algorithm converges strongly to a solution of the general split feasibility problem. Our results extend and improve some recent known results.展开更多
Because of the tire nonlinearity and vehicle＇s parameters＇uncertainties,robust control methods based on the worst cases,such as H_∞,μsynthesis,have been widely used in active front steering control,however,in orde...Because of the tire nonlinearity and vehicle＇s parameters＇uncertainties,robust control methods based on the worst cases,such as H_∞,μsynthesis,have been widely used in active front steering control,however,in order to guarantee the stability of active front steering system（AFS）controller,the robust control is at the cost of performance so that the robust controller is a little conservative and has low performance for AFS control.In this paper,a generalized internal model robust control（GIMC）that can overcome the contradiction between performance and stability is used in the AFS control.In GIMC,the Youla parameterization is used in an improved way.And GIMC controller includes two sections：a high performance controller designed for the nominal vehicle model and a robust controller compensating the vehicle parameters＇uncertainties and some external disturbances.Simulations of double lane change（DLC）maneuver and that of braking on split-μroad are conducted to compare the performance and stability of the GIMC control,the nominal performance PID controller and the H_∞controller.Simulation results show that the high nominal performance PID controller will be unstable under some extreme situations because of large vehicle＇s parameters variations,H_∞controller is conservative so that the performance is a little low,and only the GIMC controller overcomes the contradiction between performance and robustness,which can both ensure the stability of the AFS controller and guarantee the high performance of the AFS controller.Therefore,the GIMC method proposed for AFS can overcome some disadvantages of control methods used by current AFS system,that is,can solve the instability of PID or LQP control methods and the low performance of the standard H_∞controller.展开更多
In this paper,we investigate the large time behavior of solutions to the three dimensional generalized Hall-magnetohydrodynamics(Hall-MHD)system in the spacesχ^(s)(R^(3)).We obtain that the temporal decay rate is‖(u...In this paper,we investigate the large time behavior of solutions to the three dimensional generalized Hall-magnetohydrodynamics(Hall-MHD)system in the spacesχ^(s)(R^(3)).We obtain that the temporal decay rate is‖(u,b)(t)‖χ^(1−2α)+‖(u,b)(t)‖χ^(1−2β)+‖(u,b)(t)‖χ^(2−2α)+‖(u,b)(t)‖χ^(2−2β)≤(1 t)^(-(5-4max{α,β}/4max{α,β})with 1/2≤α,β≤1 for the small global solution by using Fourier splitting method.The parametersαandβare the fractional dissipations corresponding to the velocity and magnetic field,respectively.展开更多
This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster aroun...This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster around 0 or 1 under mild conditions.The limited numerical results show that the TPTS preconditioner is more efficient than the classic block-diagonal and block-triangular preconditioners when applied to the flexible generalized minimal residual(FGMRES)method.展开更多
Fractional factorial split-plot design has been widely used in many fields due to its advantage of saving experimental cost. The general minimum lower order confounding criterion is usually used as one of the attracti...Fractional factorial split-plot design has been widely used in many fields due to its advantage of saving experimental cost. The general minimum lower order confounding criterion is usually used as one of the attractive design criterion for selecting fractional factorial split-plot design. In this paper, we are interested in the theoretical construction methods of the optimal fractional factorial split-plot designs under the general minimum lower order confounding criterion. We present the theoretical construction methods of optimal fractional factorial split-plot designs under general minimum lower order confounding criterion under several conditions.展开更多
A scheme, based on the system composed of three atoms separately trapped in three cavities coupled by optical fibres, for entangling two distant atoms via the adiabatic passage is proposed. It is found that the multi-...A scheme, based on the system composed of three atoms separately trapped in three cavities coupled by optical fibres, for entangling two distant atoms via the adiabatic passage is proposed. It is found that the multi-particle W entangled state can also be generated. Moreover, the quantum information sharing can be implemented using this system. These results may be helpful for the implementation of quantum network and useful in quantum cryptography. This scheme is also convenient for operating since only the laser fields applied to the atoms need to be adjusted to accomplish the processes.展开更多
The purpose of this paper is to present for the first time an elementary summary of a few recent results obtained through the application of the formal theory of partial differential equations and Lie pseudogroups in ...The purpose of this paper is to present for the first time an elementary summary of a few recent results obtained through the application of the formal theory of partial differential equations and Lie pseudogroups in order to revisit the mathematical foundations of general relativity. Other engineering examples (control theory, elasticity theory, electromagnetism) will also be considered in order to illustrate the three fundamental results that we shall provide successively. 1) VESSIOT VERSUS CARTAN: The quadratic terms appearing in the “Riemann tensor” according to the “Vessiot structure equations” must not be identified with the quadratic terms appearing in the well known “Cartan structure equations” for Lie groups. In particular, “curvature + torsion” (Cartan) must not be considered as a generalization of “curvature alone” (Vessiot). 2) JANET VERSUS SPENCER: The “Ricci tensor” only depends on the nonlinear transformations (called “elations” by Cartan in 1922) that describe the “difference” existing between the Weyl group (10 parameters of the Poincaré subgroup + 1 dilatation) and the conformal group of space-time (15 parameters). It can be defined without using the indices leading to the standard contraction or trace of the Riemann tensor. Meanwhile, we shall obtain the number of components of the Riemann and Weyl tensors without any combinatoric argument on the exchange of indices. Accordingly and contrary to the “Janet sequence”, the “Spencer sequence” for the conformal Killing system and its formal adjoint fully describe the Cosserat equations, Maxwell equations and Weyl equations but General Relativity is not coherent with this result. 3) ALGEBRA VERSUS GEOMETRY: Using the powerful methods of “Algebraic Analysis”, that is a mixture of homological agebra and differential geometry, we shall prove that, contrary to other equations of physics (Cauchy equations, Cosserat equations, Maxwell equations), the Einstein equations cannot be “parametrized”, that is the generic solution cannot be expressed by means of the derivatives of a certain number of arbitrary potential-like functions, solving therefore negatively a 1000 $ challenge proposed by J. Wheeler in 1970. Accordingly, the mathematical foundations of electromagnetism and gravitation must be revisited within this formal framework, though striking it may look like. We insist on the fact that the arguments presented are of a purely mathematical nature and are thus unavoidable.展开更多
The purpose of this paper is to introduce a split generalized mixed equi- librium problem （SGMEP） and consider some iterative sequences to find a solution of the generalized mixed equilibrium problem such that its i...The purpose of this paper is to introduce a split generalized mixed equi- librium problem （SGMEP） and consider some iterative sequences to find a solution of the generalized mixed equilibrium problem such that its image un- der a given bounded linear operator is a solution of another generalized mixed equilibrium problem. We obtain some weak and strong convergence theorems.展开更多
In this paper, we introduce a split generalized equilibrium problem and consider some iterative sequences to find a solution of the equilibrium problem such that its image under a given bounded linear operator is a so...In this paper, we introduce a split generalized equilibrium problem and consider some iterative sequences to find a solution of the equilibrium problem such that its image under a given bounded linear operator is a solution of another equilibrium problem. We obtain some strong and weak convergence theorems.展开更多
In this paper, strong convergence of an iterative sequence is proved, which computes an approximate solution of the set of solutions of split variational inclusion problem, the set of fixed points of a nonexpansive ma...In this paper, strong convergence of an iterative sequence is proved, which computes an approximate solution of the set of solutions of split variational inclusion problem, the set of fixed points of a nonexpansive mapping and the set of common fixed points of a family of generalized asymptotically nonexpansive semigroup. Results obtained in this paper extend and unify the previously known results in the previous literatures.展开更多
基金This project is supported by Science and Technology Foundation of Shanghai Higher Eduction,Doctoral Program Foundation of Higher Education in China.National Nature Science Foundation of China and Youth Science Foundation of Universities in Shanghai.
文摘This paper presents a proper splitting iterative method for comparing the general restricted linear euqations Ax=b, x ∈T （where, b ∈AT, and T is an arbitrary but fixed subspace of C<sup>m</sup>） and the generalized in A<sub>T,S</sub> For the special case when b ∈AT and dim（T）=dim（AT）, this splitting iterative methverse A<sub>T,S</sub> hod converges to A<sub>T,S</sub>b （the unique solution of the general restricted system Ax=bx ∈T）.
基金the Program for New Century Excellent Talents at Universities of China under Grant No.NCET-06-0554National Natural Science Foundation of China under Grant Nos.60677001 and 10747146+2 种基金the Science-Technology Fund of Anhui Province for Outstanding Youth under Grant No.06042087the Key Fund of the Ministry of Education of China under Grant No.206063the Natural Science Foundation of Guangdong Province under Grant Nos.06300345 and 7007806
文摘A three-party scheme for splitting an arbitrary unknown two-qutrit state is proposed,where two non-maximally-entangled three-qutrit states are taken as the quantum channel among three parties.With the sender'shelp,if and only if both receivers collaborate together,they can securely share the quantum state in a probabilisticway by introducing an ancilla qutrit and performing appropriate unitary operations.The relation between the successprobability and coefficients characterizing the quantum channel is revealed.The security of the present scheme is analyzedand confirmed.Moreover,the generalization of the three-party scheme to more-party case is also sketched.
文摘The generalized Navier-Stokes equations with damping are considered.We will show that the generalized Navier-Stokes equations with damping |u|^β-1u have weak solutions for anyβ>1 and 0<α<5/4,and we will use the Fourier splitting method to prove the L2 decay of weak solutions forβ>2 and 0<α<3/4.
文摘Sunlight is the most abundant renewable energy resource,providing the earth with enough power that is capable of taking care of all of humanity’s desires-a hundred times over.However,as it is at times diffuse and intermittent,it raises issues concerning how best to reap this energy and store it for times when the Sun is not shining.With increasing population in the world and modern economic development,there will be an additional increase in energy demand.Devices that use daylight to separate water into individual chemical elements may well be the answer to this issue,as water splitting produces an ideal fuel.If such devices that generate fuel were to become widely adopted,they must be low in cost,both for supplying and operation.Therefore,it is essential to research for cheap technologies for water ripping.This review summarizes the progress made toward such development,the open challenges existing,and the approaches undertaken to generate carbon-free energy through water splitting.
基金Supported by the Scientific Research Fund of Sichuan Provincial Department of Science and Technology(2015JY0165,2011JYZ011)the Scientific Research Fund of Sichuan Provincial Education Department(14ZA0271)+2 种基金the Scientific Research Project of Yibin University(2013YY06)the Natural Science Foundation of China Medical University,Taiwanthe National Natural Science Foundation of China(11361070)
文摘The purpose of this article is to introduce a general split feasibility problems for two families of nonexpansive mappings in Hilbert spaces. We prove that the sequence generated by the proposed new algorithm converges strongly to a solution of the general split feasibility problem. Our results extend and improve some recent known results.
基金Supported by National Natural Science Foundation of China(Grant Nos.11072106,51375009)
文摘Because of the tire nonlinearity and vehicle＇s parameters＇uncertainties,robust control methods based on the worst cases,such as H_∞,μsynthesis,have been widely used in active front steering control,however,in order to guarantee the stability of active front steering system（AFS）controller,the robust control is at the cost of performance so that the robust controller is a little conservative and has low performance for AFS control.In this paper,a generalized internal model robust control（GIMC）that can overcome the contradiction between performance and stability is used in the AFS control.In GIMC,the Youla parameterization is used in an improved way.And GIMC controller includes two sections：a high performance controller designed for the nominal vehicle model and a robust controller compensating the vehicle parameters＇uncertainties and some external disturbances.Simulations of double lane change（DLC）maneuver and that of braking on split-μroad are conducted to compare the performance and stability of the GIMC control,the nominal performance PID controller and the H_∞controller.Simulation results show that the high nominal performance PID controller will be unstable under some extreme situations because of large vehicle＇s parameters variations,H_∞controller is conservative so that the performance is a little low,and only the GIMC controller overcomes the contradiction between performance and robustness,which can both ensure the stability of the AFS controller and guarantee the high performance of the AFS controller.Therefore,the GIMC method proposed for AFS can overcome some disadvantages of control methods used by current AFS system,that is,can solve the instability of PID or LQP control methods and the low performance of the standard H_∞controller.
基金Supported by the National Natural Science Foundation of China(11871305)
文摘In this paper,we investigate the large time behavior of solutions to the three dimensional generalized Hall-magnetohydrodynamics(Hall-MHD)system in the spacesχ^(s)(R^(3)).We obtain that the temporal decay rate is‖(u,b)(t)‖χ^(1−2α)+‖(u,b)(t)‖χ^(1−2β)+‖(u,b)(t)‖χ^(2−2α)+‖(u,b)(t)‖χ^(2−2β)≤(1 t)^(-(5-4max{α,β}/4max{α,β})with 1/2≤α,β≤1 for the small global solution by using Fourier splitting method.The parametersαandβare the fractional dissipations corresponding to the velocity and magnetic field,respectively.
基金the National Natural Science Foundation of China under Grant Nos.61273311 and 61803247.
文摘This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster around 0 or 1 under mild conditions.The limited numerical results show that the TPTS preconditioner is more efficient than the classic block-diagonal and block-triangular preconditioners when applied to the flexible generalized minimal residual(FGMRES)method.
文摘Fractional factorial split-plot design has been widely used in many fields due to its advantage of saving experimental cost. The general minimum lower order confounding criterion is usually used as one of the attractive design criterion for selecting fractional factorial split-plot design. In this paper, we are interested in the theoretical construction methods of the optimal fractional factorial split-plot designs under the general minimum lower order confounding criterion. We present the theoretical construction methods of optimal fractional factorial split-plot designs under general minimum lower order confounding criterion under several conditions.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10374025)the Natural Science Foundation of Hunan Province of China (Grant No. 07JJ3013)
文摘A scheme, based on the system composed of three atoms separately trapped in three cavities coupled by optical fibres, for entangling two distant atoms via the adiabatic passage is proposed. It is found that the multi-particle W entangled state can also be generated. Moreover, the quantum information sharing can be implemented using this system. These results may be helpful for the implementation of quantum network and useful in quantum cryptography. This scheme is also convenient for operating since only the laser fields applied to the atoms need to be adjusted to accomplish the processes.
文摘The purpose of this paper is to present for the first time an elementary summary of a few recent results obtained through the application of the formal theory of partial differential equations and Lie pseudogroups in order to revisit the mathematical foundations of general relativity. Other engineering examples (control theory, elasticity theory, electromagnetism) will also be considered in order to illustrate the three fundamental results that we shall provide successively. 1) VESSIOT VERSUS CARTAN: The quadratic terms appearing in the “Riemann tensor” according to the “Vessiot structure equations” must not be identified with the quadratic terms appearing in the well known “Cartan structure equations” for Lie groups. In particular, “curvature + torsion” (Cartan) must not be considered as a generalization of “curvature alone” (Vessiot). 2) JANET VERSUS SPENCER: The “Ricci tensor” only depends on the nonlinear transformations (called “elations” by Cartan in 1922) that describe the “difference” existing between the Weyl group (10 parameters of the Poincaré subgroup + 1 dilatation) and the conformal group of space-time (15 parameters). It can be defined without using the indices leading to the standard contraction or trace of the Riemann tensor. Meanwhile, we shall obtain the number of components of the Riemann and Weyl tensors without any combinatoric argument on the exchange of indices. Accordingly and contrary to the “Janet sequence”, the “Spencer sequence” for the conformal Killing system and its formal adjoint fully describe the Cosserat equations, Maxwell equations and Weyl equations but General Relativity is not coherent with this result. 3) ALGEBRA VERSUS GEOMETRY: Using the powerful methods of “Algebraic Analysis”, that is a mixture of homological agebra and differential geometry, we shall prove that, contrary to other equations of physics (Cauchy equations, Cosserat equations, Maxwell equations), the Einstein equations cannot be “parametrized”, that is the generic solution cannot be expressed by means of the derivatives of a certain number of arbitrary potential-like functions, solving therefore negatively a 1000 $ challenge proposed by J. Wheeler in 1970. Accordingly, the mathematical foundations of electromagnetism and gravitation must be revisited within this formal framework, though striking it may look like. We insist on the fact that the arguments presented are of a purely mathematical nature and are thus unavoidable.
基金supported by the Science and Technology Project of Education Department of Fujian Province(Grant number:JA13363)
文摘The purpose of this paper is to introduce a split generalized mixed equi- librium problem （SGMEP） and consider some iterative sequences to find a solution of the generalized mixed equilibrium problem such that its image un- der a given bounded linear operator is a solution of another generalized mixed equilibrium problem. We obtain some weak and strong convergence theorems.
基金supported by the Natural Science Foundation of Fujian Province under grant No.2014J01008
文摘In this paper, we introduce a split generalized equilibrium problem and consider some iterative sequences to find a solution of the equilibrium problem such that its image under a given bounded linear operator is a solution of another equilibrium problem. We obtain some strong and weak convergence theorems.
基金supported by the Science and Technology Project of Education Department of Fujian Province under Grant No.JA14365Fujian Nature Science Foundation under Grant No.2014J01008
文摘In this paper, strong convergence of an iterative sequence is proved, which computes an approximate solution of the set of solutions of split variational inclusion problem, the set of fixed points of a nonexpansive mapping and the set of common fixed points of a family of generalized asymptotically nonexpansive semigroup. Results obtained in this paper extend and unify the previously known results in the previous literatures.
