Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate...Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate this impulse game problem with the modified objective function including interaction costs among the players in a discontinuous fashion,and subsequently,to derive a verification theorem for identifying the feedback Nash equilibrium strategy.展开更多
We construct the Riemann-Hilbert problem of the Lakshmanan-Porsezian-Daniel equation with nonzero boundary conditions,and use the Laurent expansion and Taylor series expansion to obtain the exact formulas of the solit...We construct the Riemann-Hilbert problem of the Lakshmanan-Porsezian-Daniel equation with nonzero boundary conditions,and use the Laurent expansion and Taylor series expansion to obtain the exact formulas of the soliton solutions in the case of a higher-order pole and multiple higher-order poles.The dynamic behaviors of a simple pole,a second-order pole and a simple pole plus a second-order pole are demonstrated.展开更多
The Riemann–Hilbert approach is demonstrated to investigate the defocusing Lakshmanan–Porsezian–Daniel equation under fully asymmetric nonzero boundary conditions.In contrast to the symmetry case,this paper focuses...The Riemann–Hilbert approach is demonstrated to investigate the defocusing Lakshmanan–Porsezian–Daniel equation under fully asymmetric nonzero boundary conditions.In contrast to the symmetry case,this paper focuses on the branch points related to the scattering problem rather than using the Riemann surfaces.For the direct problem,we analyze the Jost solution of lax pairs and some properties of scattering matrix,including two kinds of symmetries.The inverse problem at branch points can be presented,corresponding to the associated Riemann–Hilbert.Moreover,we investigate the time evolution problem and estimate the value of solving the solutions by Jost function.For the inverse problem,we construct it as a Riemann–Hilbert problem and formulate the reconstruction formula for the defocusing Lakshmanan–Porsezian–Daniel equation.The solutions of the Riemann–Hilbert problem can be constructed by estimating the solutions.Finally,we work out the solutions under fully asymmetric nonzero boundary conditions precisely via utilizing the Sokhotski–Plemelj formula and the square of the negative column transformation with the assistance of Riemann surfaces.These results are valuable for understanding physical phenomena and developing further applications of optical problems.展开更多
A generalized policy-iteration-based solution to a class of discrete-time multi-player nonzero-sum games concerning the control constraints was proposed.Based on initial admissible control policies,the iterative value...A generalized policy-iteration-based solution to a class of discrete-time multi-player nonzero-sum games concerning the control constraints was proposed.Based on initial admissible control policies,the iterative value function of each player converges to the optimum approximately,which is structured by the iterative control policies satisfying the Nash equilibrium.Afterwards,the stability analysis is shown to illustrate that the iterative control policies can stabilize the system and minimize the performance index function of each player.Meanwhile,neural networks are implemented to approximate the iterative control policies and value functions with the impact of control constraints.Finally,two numerical simulations of the discrete-time two-player non-zero-sum games for linear and non-linear systems are shown to illustrate the effectiveness of the proposed scheme.展开更多
The stationary response of viscoelastic dynamical system with the right unilateral nonzero offset barrier impacts subjected to stochastic excitations is investigated.First,the viscoelastic force is approximately treat...The stationary response of viscoelastic dynamical system with the right unilateral nonzero offset barrier impacts subjected to stochastic excitations is investigated.First,the viscoelastic force is approximately treated as equivalent terms associated with effects.Then,the free vibro-impact(VI)system is absorbed to describe the periodic motion without impacts and quasi-periodic motion with impacts based upon the level of system energy.The stochastic averaging of energy envelope(SAEE)is adopted to seek the stationary probability density functions(PDFs).The detailed theoretical results for Van der Pol viscoelastic VI system with the right unilateral nonzero offset barrier are solved to demonstrate the important effects of the viscoelastic damping and nonzero rigid barrier impacts condition.Monte Carlo(MC)simulation is also performed to verify the reliability of the suggested approach.The stochastic P-bifurcation caused by certain system parameters is further explored.The variation of elastic modulus from negative to zero and then to positive witnesses the evolution process of stochastic P-bifurcation.From the vicinity of the common value to a wider range,the relaxation time induces the stochastic P-bifurcation in the two interval schemes.展开更多
We exhibit some new dark soliton phenomena on the general nonzero background for a defocusing three-component nonlinear Schrodinger equation. As the plane wave background undergoes unitary transformation SU(3), we obt...We exhibit some new dark soliton phenomena on the general nonzero background for a defocusing three-component nonlinear Schrodinger equation. As the plane wave background undergoes unitary transformation SU(3), we obtain the general nonzero background and study its modulational instability by the linear stability analysis. On the basis of this background, we study the dynamics of one-dark soliton and two-dark-soliton phenomena, which are different from the dark solitons studied before. Furthermore, we use the numerical method for checking the stability of the one-dark-soliton solution. These results further enrich the content in nonlinear Schrodinger systems, and require more in-depth studies in the future.展开更多
The semi-analytical method, previously used to construct model double-null and single-null diverted tokamak equi- libria （Bingren Shi, Plasma Phys. Control Fusion 50 （2008） 085006, 51 （2009） 105008, Nucl. Fusion ...The semi-analytical method, previously used to construct model double-null and single-null diverted tokamak equi- libria （Bingren Shi, Plasma Phys. Control Fusion 50 （2008） 085006, 51 （2009） 105008, Nucl. Fusion 51 （2011） 023004）, is extended to describe diverted tokamak equilibria with nonzero edge current, including the Pfirsch Schliiter（PS） cur- rent. The PS current density is expressed in a way suitable to describe a diverted tokamak configuration in the near separatrix region. The model equilibrium is expressed by only two terms of the exact separable solutions of the Grad Shafranov equation, one of which is governed by a homogeneous ordinary differential equation, and the other by an inhomogeneous one. The particular merits of such a model configuration are that the internal region inside the separa- trix and a suitable scrape-off layer can be simultaneously described by this exact solution. To investigate the physics in the region near the X-point, the magnetic surfaces can be satisfactorily described by approximate hyperbolic curves.展开更多
The existence of nonzero solutions for a class of generalized variational inequalities is studied by ?xed point index approach for multivalued mappings in ?nite dimensional spaces and re?exive Banach spaces. Some new ...The existence of nonzero solutions for a class of generalized variational inequalities is studied by ?xed point index approach for multivalued mappings in ?nite dimensional spaces and re?exive Banach spaces. Some new existence theorems of nonzero solutions for this class of generalized variational inequalities are established.展开更多
The present work studies the inverse scattering transforms(IST)of the inhomogeneous fifth-order nonlinear Schrodinger(NLS)equation with zero boundary conditions(ZBCs)and nonzero boundary conditions(NZBCs).Firstly,the ...The present work studies the inverse scattering transforms(IST)of the inhomogeneous fifth-order nonlinear Schrodinger(NLS)equation with zero boundary conditions(ZBCs)and nonzero boundary conditions(NZBCs).Firstly,the bound-state solitons of the inhomogeneous fifth-order NLS equation with ZBCs are derived by the residue theorem and the Laurent's series for the first time.Then,by combining with the robust IST,the Riemann-Hilbert(RH)problem of the inhomogeneous fifth-order NLS equation with NZBCs is revealed.Furthermore,based on the resulting RH problem,some new rogue wave solutions of the inhomogeneous fifth-order NLS equation are found by the Darboux transformation.Finally,some corresponding graphs are given by selecting appropriate parameters to further analyze the unreported dynamic characteristics of the corresponding solutions.展开更多
In this paper we will generalize the author's two nonzero component lemma to general self-reducing functions and utilize it to find closed from answers for some resource allocation problems.
We explored the Cauchy problem for the evolution of the charge density distribution function for a spherically symmetric system with nonzero initial conditions. In our model, the evolution of the charge density distri...We explored the Cauchy problem for the evolution of the charge density distribution function for a spherically symmetric system with nonzero initial conditions. In our model, the evolution of the charge density distribution function is simulated for the case of a non-uniform charged sphere. The initial speed of the system is nonzero. The solution breaks down into two components: the first one describes the system’s motion as a whole and the second describes the process of the evolution of the charge density function under the influence of its own electric field in the center-of-mass system. In this paper we considered the characteristic features of the implementation of a difference scheme for numerical simulation. We also illustrate the process of “scattering” of a moving charged system under the influence of its own electric field on the basis of the solution of the Cauchy problem for vector functions of the electric field and vector velocity field of a charged medium.展开更多
To keep the secrecy performance from being badly influenced by untrusted relay(UR), a multi-UR network through amplify-and-forward(AF) cooperative scheme is put forward, which takes relay weight and harmful factor int...To keep the secrecy performance from being badly influenced by untrusted relay(UR), a multi-UR network through amplify-and-forward(AF) cooperative scheme is put forward, which takes relay weight and harmful factor into account. A nonzero-sum game is established to capture the interaction among URs and detection strategies. Secrecy capacity is investigated as game payoff to indicate the untrusted behaviors of the relays. The maximum probabilities of the behaviors of relay and the optimal system detection strategy can be obtained by using the proposed algorithm.展开更多
We will use the author’s Two Nonzero Component Lemma to give a new proof for the Greub-Reinboldt Inequality. This method has the advantage of showing exactly when the inequality becomes equality. It also provides inf...We will use the author’s Two Nonzero Component Lemma to give a new proof for the Greub-Reinboldt Inequality. This method has the advantage of showing exactly when the inequality becomes equality. It also provides information about vectors for which the inequality becomes equality. Furthermore, using the Two Nonzero Component Lemma, we will generalize Greub-Reinboldt Inequality to operators on infinite dimensional separable Hilbert spaces.展开更多
The outage performance of the multihop free-space optical(FSO) communication system with decode-and-forward(DF) protocol is studied by considering the joint effects of nonzero boresight pointing errors and atmospheric...The outage performance of the multihop free-space optical(FSO) communication system with decode-and-forward(DF) protocol is studied by considering the joint effects of nonzero boresight pointing errors and atmospheric turbulence modeled by exponentiated Weibull(EW) distribution. The closed-form analytical expression of outage probability is derived, and the results are validated through Monte Carlo simulation. Furthermore, the detailed analysis is provided to evaluate the impacts of turbulence strength, receiver aperture size, boresight displacement, beamwidth and number of relays on the outage performance for the studied system.展开更多
This article investigates the bipartite consensus problem for a class of multi-agent systems(MASs)with parameter uncertainty and leader of nonzero input under a signed digraph.Due to the unknown and time-varying input...This article investigates the bipartite consensus problem for a class of multi-agent systems(MASs)with parameter uncertainty and leader of nonzero input under a signed digraph.Due to the unknown and time-varying input signal of the leader,followers are unable to obtain accurate information about the leader.For this purpose,a distributed adaptive observer is designed based on parameterization theory.Then,considering the existence of parameter uncertainty in the MASs,an auxiliary function is designed to compensate the impact of uncertainty.Afterwards,an adaptive controller with dynamic coupling gain is designed based on observation errors and auxiliary function.Subsequently,it is demonstrated that the MASs with parameter uncertainty and leader of nonzero input can achieve bipartite consensus by stability analysis.Finally,the effectiveness of the proposed scheme is verified through simulation.展开更多
In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash ...In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash equilibrium point for nonzero sum differential games problem. We also discuss the solvability of the generalized Riccati equation system and give the linear feedback regulator for the optimal control problem using the solution of this kind of Riccati equation system.展开更多
A recent theoretical estimation indicated that the NM/FI/FI/NM double spin-filter junction (DSFJ, here the NM and FI represent the nonmagnetic electrode and the ferromagnetic insulator (semiconductor) spacer, respecti...A recent theoretical estimation indicated that the NM/FI/FI/NM double spin-filter junction (DSFJ, here the NM and FI represent the nonmagnetic electrode and the ferromagnetic insulator (semiconductor) spacer, respectively) could have very high tunneling magnetoresistance (TMR) at zero bias. To meet the requirement in research and application of the magnetoresistance devices, we have calculated the dependences of tunneling magnetoresistance of DSF J on the bias (volt-age), the thicknesses of ferromagnetic insulators (semiconductors) and the average barrier height. Our results show that except its very high value, the TMR of DSFJ does not decrease montonously and rapidly with rising bias, but increase slowly at first and decrease then after having reached a maximum value. This feature is in distinct contrast to the ordinary magnetic tunnel junction FM/NI/FM (FM and NI denote the ferromagnetic electrode and the nonmagnetic insulator (semiconductor) spacer, respectively), and is of benefit to the use of DSFJ as a magnetoresistance device.展开更多
基金supported in part by the National Natural Science Foundation of China(62173051)the Fundamental Research Funds for the Central Universities(2024CDJCGJ012,2023CDJXY-010)+1 种基金the Chongqing Technology Innovation and Application Development Special Key Project(CSTB2022TIADCUX0015,CSTB2022TIAD-KPX0162)the China Postdoctoral Science Foundation(2024M763865)
文摘Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate this impulse game problem with the modified objective function including interaction costs among the players in a discontinuous fashion,and subsequently,to derive a verification theorem for identifying the feedback Nash equilibrium strategy.
基金supported by the National Natural Science Foundation of China under Grant Nos.12175111,12275144 and 12235007the KC Wong Magna Fund in Ningbo University。
文摘We construct the Riemann-Hilbert problem of the Lakshmanan-Porsezian-Daniel equation with nonzero boundary conditions,and use the Laurent expansion and Taylor series expansion to obtain the exact formulas of the soliton solutions in the case of a higher-order pole and multiple higher-order poles.The dynamic behaviors of a simple pole,a second-order pole and a simple pole plus a second-order pole are demonstrated.
基金the Fundamental Research Funds for the Central Universities(Grant No.2024MS126).
文摘The Riemann–Hilbert approach is demonstrated to investigate the defocusing Lakshmanan–Porsezian–Daniel equation under fully asymmetric nonzero boundary conditions.In contrast to the symmetry case,this paper focuses on the branch points related to the scattering problem rather than using the Riemann surfaces.For the direct problem,we analyze the Jost solution of lax pairs and some properties of scattering matrix,including two kinds of symmetries.The inverse problem at branch points can be presented,corresponding to the associated Riemann–Hilbert.Moreover,we investigate the time evolution problem and estimate the value of solving the solutions by Jost function.For the inverse problem,we construct it as a Riemann–Hilbert problem and formulate the reconstruction formula for the defocusing Lakshmanan–Porsezian–Daniel equation.The solutions of the Riemann–Hilbert problem can be constructed by estimating the solutions.Finally,we work out the solutions under fully asymmetric nonzero boundary conditions precisely via utilizing the Sokhotski–Plemelj formula and the square of the negative column transformation with the assistance of Riemann surfaces.These results are valuable for understanding physical phenomena and developing further applications of optical problems.
基金National Natural Science Foundation of China,Grant/Award Number:62022061,61773284。
文摘A generalized policy-iteration-based solution to a class of discrete-time multi-player nonzero-sum games concerning the control constraints was proposed.Based on initial admissible control policies,the iterative value function of each player converges to the optimum approximately,which is structured by the iterative control policies satisfying the Nash equilibrium.Afterwards,the stability analysis is shown to illustrate that the iterative control policies can stabilize the system and minimize the performance index function of each player.Meanwhile,neural networks are implemented to approximate the iterative control policies and value functions with the impact of control constraints.Finally,two numerical simulations of the discrete-time two-player non-zero-sum games for linear and non-linear systems are shown to illustrate the effectiveness of the proposed scheme.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11872305 and 11872307)the Excellent Doctorate Cultivating Foundation of Northwestern Polytechnical University,China
文摘The stationary response of viscoelastic dynamical system with the right unilateral nonzero offset barrier impacts subjected to stochastic excitations is investigated.First,the viscoelastic force is approximately treated as equivalent terms associated with effects.Then,the free vibro-impact(VI)system is absorbed to describe the periodic motion without impacts and quasi-periodic motion with impacts based upon the level of system energy.The stochastic averaging of energy envelope(SAEE)is adopted to seek the stationary probability density functions(PDFs).The detailed theoretical results for Van der Pol viscoelastic VI system with the right unilateral nonzero offset barrier are solved to demonstrate the important effects of the viscoelastic damping and nonzero rigid barrier impacts condition.Monte Carlo(MC)simulation is also performed to verify the reliability of the suggested approach.The stochastic P-bifurcation caused by certain system parameters is further explored.The variation of elastic modulus from negative to zero and then to positive witnesses the evolution process of stochastic P-bifurcation.From the vicinity of the common value to a wider range,the relaxation time induces the stochastic P-bifurcation in the two interval schemes.
基金Project supported by the National Natural Science Foundation of China(Grant No.11771151)the Guangdong Natural Science Foundation of China(Grant No.2017A030313008)+1 种基金the Guangzhou Science and Technology Program of China(Grant No.201904010362)the Fundamental Research Funds for the Central Universities of China(Grant No.2019MS110)
文摘We exhibit some new dark soliton phenomena on the general nonzero background for a defocusing three-component nonlinear Schrodinger equation. As the plane wave background undergoes unitary transformation SU(3), we obtain the general nonzero background and study its modulational instability by the linear stability analysis. On the basis of this background, we study the dynamics of one-dark soliton and two-dark-soliton phenomena, which are different from the dark solitons studied before. Furthermore, we use the numerical method for checking the stability of the one-dark-soliton solution. These results further enrich the content in nonlinear Schrodinger systems, and require more in-depth studies in the future.
基金supported by the National Magnetic Confinement Fusion Science Program of China (Grant No. 2009GB101002)
文摘The semi-analytical method, previously used to construct model double-null and single-null diverted tokamak equi- libria （Bingren Shi, Plasma Phys. Control Fusion 50 （2008） 085006, 51 （2009） 105008, Nucl. Fusion 51 （2011） 023004）, is extended to describe diverted tokamak equilibria with nonzero edge current, including the Pfirsch Schliiter（PS） cur- rent. The PS current density is expressed in a way suitable to describe a diverted tokamak configuration in the near separatrix region. The model equilibrium is expressed by only two terms of the exact separable solutions of the Grad Shafranov equation, one of which is governed by a homogeneous ordinary differential equation, and the other by an inhomogeneous one. The particular merits of such a model configuration are that the internal region inside the separa- trix and a suitable scrape-off layer can be simultaneously described by this exact solution. To investigate the physics in the region near the X-point, the magnetic surfaces can be satisfactorily described by approximate hyperbolic curves.
文摘The existence of nonzero solutions for a class of generalized variational inequalities is studied by ?xed point index approach for multivalued mappings in ?nite dimensional spaces and re?exive Banach spaces. Some new existence theorems of nonzero solutions for this class of generalized variational inequalities are established.
基金supported by the National Natural Science Foundation of China under Grant No.11975306the Natural Science Foundation of Jiangsu Province under Grant No.BK20181351+1 种基金the Six Talent Peaks Project in Jiangsu Province under Grant No.JY-059the Fundamental Research Fund for the Central Universities under the Grant Nos.2019ZDPY07 and 2019QNA35。
文摘The present work studies the inverse scattering transforms(IST)of the inhomogeneous fifth-order nonlinear Schrodinger(NLS)equation with zero boundary conditions(ZBCs)and nonzero boundary conditions(NZBCs).Firstly,the bound-state solitons of the inhomogeneous fifth-order NLS equation with ZBCs are derived by the residue theorem and the Laurent's series for the first time.Then,by combining with the robust IST,the Riemann-Hilbert(RH)problem of the inhomogeneous fifth-order NLS equation with NZBCs is revealed.Furthermore,based on the resulting RH problem,some new rogue wave solutions of the inhomogeneous fifth-order NLS equation are found by the Darboux transformation.Finally,some corresponding graphs are given by selecting appropriate parameters to further analyze the unreported dynamic characteristics of the corresponding solutions.
文摘In this paper we will generalize the author's two nonzero component lemma to general self-reducing functions and utilize it to find closed from answers for some resource allocation problems.
文摘We explored the Cauchy problem for the evolution of the charge density distribution function for a spherically symmetric system with nonzero initial conditions. In our model, the evolution of the charge density distribution function is simulated for the case of a non-uniform charged sphere. The initial speed of the system is nonzero. The solution breaks down into two components: the first one describes the system’s motion as a whole and the second describes the process of the evolution of the charge density function under the influence of its own electric field in the center-of-mass system. In this paper we considered the characteristic features of the implementation of a difference scheme for numerical simulation. We also illustrate the process of “scattering” of a moving charged system under the influence of its own electric field on the basis of the solution of the Cauchy problem for vector functions of the electric field and vector velocity field of a charged medium.
基金Supported by the National Natural Science Foundation of China(No.61101223)
文摘To keep the secrecy performance from being badly influenced by untrusted relay(UR), a multi-UR network through amplify-and-forward(AF) cooperative scheme is put forward, which takes relay weight and harmful factor into account. A nonzero-sum game is established to capture the interaction among URs and detection strategies. Secrecy capacity is investigated as game payoff to indicate the untrusted behaviors of the relays. The maximum probabilities of the behaviors of relay and the optimal system detection strategy can be obtained by using the proposed algorithm.
文摘We will use the author’s Two Nonzero Component Lemma to give a new proof for the Greub-Reinboldt Inequality. This method has the advantage of showing exactly when the inequality becomes equality. It also provides information about vectors for which the inequality becomes equality. Furthermore, using the Two Nonzero Component Lemma, we will generalize Greub-Reinboldt Inequality to operators on infinite dimensional separable Hilbert spaces.
基金supported by the Fundamental Research Funds for the Central Universities(No.JB160105)the“111 Project”of China(No.B08038)
文摘The outage performance of the multihop free-space optical(FSO) communication system with decode-and-forward(DF) protocol is studied by considering the joint effects of nonzero boresight pointing errors and atmospheric turbulence modeled by exponentiated Weibull(EW) distribution. The closed-form analytical expression of outage probability is derived, and the results are validated through Monte Carlo simulation. Furthermore, the detailed analysis is provided to evaluate the impacts of turbulence strength, receiver aperture size, boresight displacement, beamwidth and number of relays on the outage performance for the studied system.
基金supported by the National Natural Science Foundation of China(Nos.61973070 and 62373089)the Natural Science Foundation of Liaoning Province,China(No.2022JH25/10100008)the Synthetical Automation for Process Industries(SAPI)Fundamental Research Funds(No.2018ZCX22).
文摘This article investigates the bipartite consensus problem for a class of multi-agent systems(MASs)with parameter uncertainty and leader of nonzero input under a signed digraph.Due to the unknown and time-varying input signal of the leader,followers are unable to obtain accurate information about the leader.For this purpose,a distributed adaptive observer is designed based on parameterization theory.Then,considering the existence of parameter uncertainty in the MASs,an auxiliary function is designed to compensate the impact of uncertainty.Afterwards,an adaptive controller with dynamic coupling gain is designed based on observation errors and auxiliary function.Subsequently,it is demonstrated that the MASs with parameter uncertainty and leader of nonzero input can achieve bipartite consensus by stability analysis.Finally,the effectiveness of the proposed scheme is verified through simulation.
基金This work is supported by the National Natural Science Foundation (Grant No.10371067)the Youth Teacher Foundation of Fok Ying Tung Education Foundation, the Excellent Young Teachers Program and the Doctoral Program Foundation of MOE and Shandong Province, China.
文摘In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash equilibrium point for nonzero sum differential games problem. We also discuss the solvability of the generalized Riccati equation system and give the linear feedback regulator for the optimal control problem using the solution of this kind of Riccati equation system.
基金the National Natural Science Foundation of China(Grant No.10074075)the Department of Science and Technology under the National Key Project of Basic Research(Grant No.G1999064509).
文摘A recent theoretical estimation indicated that the NM/FI/FI/NM double spin-filter junction (DSFJ, here the NM and FI represent the nonmagnetic electrode and the ferromagnetic insulator (semiconductor) spacer, respectively) could have very high tunneling magnetoresistance (TMR) at zero bias. To meet the requirement in research and application of the magnetoresistance devices, we have calculated the dependences of tunneling magnetoresistance of DSF J on the bias (volt-age), the thicknesses of ferromagnetic insulators (semiconductors) and the average barrier height. Our results show that except its very high value, the TMR of DSFJ does not decrease montonously and rapidly with rising bias, but increase slowly at first and decrease then after having reached a maximum value. This feature is in distinct contrast to the ordinary magnetic tunnel junction FM/NI/FM (FM and NI denote the ferromagnetic electrode and the nonmagnetic insulator (semiconductor) spacer, respectively), and is of benefit to the use of DSFJ as a magnetoresistance device.
