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
Dear Editor,This letter proposes a reinforcement learning-based predictive learning algorithm for unknown continuous-time nonlinear systems with observation loss.Firstly,we construct a temporal nonzero-sum game over p...Dear Editor,This letter proposes a reinforcement learning-based predictive learning algorithm for unknown continuous-time nonlinear systems with observation loss.Firstly,we construct a temporal nonzero-sum game over predictive control input sequences,deriving multiple optimal predictive control input sequences from its solution.展开更多
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
This paper presents an adaptive multi-agent coordination(AMAC)strategy suitable for complex scenarios,which only requires information exchange between neighbouring robots.Unlike traditional multi-agent coordination me...This paper presents an adaptive multi-agent coordination(AMAC)strategy suitable for complex scenarios,which only requires information exchange between neighbouring robots.Unlike traditional multi-agent coordination methods that are solved by neural dynamics,the proposed strategy displays greater flexibility,adaptability and scalability.Furthermore,the proposed AMAC strategy is reconstructed as a time-varying complex-valued matrix equation.By introducing a dynamic error function,a fixed-time convergent zeroing neural network(FTCZNN)model is designed for the online solution of the AMAC strategy,with its convergence time upper bound derived theoretically.Finally,the effectiveness and applicability of the coordination control method are demonstrated by numerical simulations and physical experiments.Numerical results indicate that this method can reduce the formation error to the order of 10^(-6)within 1.8 s.展开更多
While desalination is a key solution for global freshwater scarcity,its implementation faces environmental challenges due to concentrated brine byproducts mainly disposed of via coastal discharge systems.Solar interfa...While desalination is a key solution for global freshwater scarcity,its implementation faces environmental challenges due to concentrated brine byproducts mainly disposed of via coastal discharge systems.Solar interfacial evaporation offers sustainable management potential,yet inevitable salt nucleation at evaporation interfaces degrades photothermal conversion and operational stability via light scattering and pathway blockage.Inspired by the mangrove leaf,we propose a photothermal 3D polydopamine and polypyrrole polymerized spacer fabric(PPSF)-based upward hanging model evaporation configuration with a reverse water feeding mechanism.This design enables zero-liquiddischarge(ZLD)desalination through phase-separation crystallization.The interconnected porous architecture and the rough surface of the PPSF enable superior water transport,achieving excellent solar-absorbing efficiency of 97.8%.By adjusting the tilt angle(θ),the evaporator separates the evaporation and salt crystallization zones via controlled capillary-driven brine transport,minimizing heat dissipation from brine discharge.At an optimal tilt angle of 52°,the evaporator reaches an evaporation rate of 2.81 kg m^(−2) h^(−1) with minimal heat loss(0.366 W)under 1-sun illumination while treating a 7 wt%waste brine solution.Furthermore,it sustains an evaporation rate of 2.71 kg m^(−2) h^(−1) over 72 h while ensuring efficient salt recovery.These results highlight a scalable,energy-efficient approach for sustainable ZLD desalination.展开更多
Recently,the zeroing neural network(ZNN)has demonstrated remarkable effectiveness in tackling time-varying problems,delivering robust performance across both noise-free and noisy environments.However,existing ZNN mode...Recently,the zeroing neural network(ZNN)has demonstrated remarkable effectiveness in tackling time-varying problems,delivering robust performance across both noise-free and noisy environments.However,existing ZNN models are limited in their ability to actively suppress noise,which constrains their robustness and precision in solving time-varying problems.This paper introduces a novel active noise rejection ZNN(ANR-ZNN)design that enhances noise suppression by integrating computational error dynamics and harmonic behaviour.Through rigorous theoretical analysis,we demonstrate that the proposed ANR-ZNN maintains robust convergence in computational error performance under environmental noise.As a case study,the ANR-ZNN model is specifically applied to time-varying matrix inversion.Comprehensive computer simulations and robotic experiments further validate the ANR-ZNN's effectiveness,emphasising the proposed design's superiority and potential for solving time-varying problems.展开更多
With more and more IoT terminals being deployed in various power grid business scenarios,terminal reliability has become a practical challenge that threatens the current security protection architecture.Most IoT termi...With more and more IoT terminals being deployed in various power grid business scenarios,terminal reliability has become a practical challenge that threatens the current security protection architecture.Most IoT terminals have security risks and vulnerabilities,and limited resources make it impossible to deploy costly security protection methods on the terminal.In order to cope with these problems,this paper proposes a lightweight trust evaluation model TCL,which combines three network models,TCN,CNN,and LSTM,with stronger feature extraction capability and can score the reliability of the device by periodically analyzing the traffic behavior and activity logs generated by the terminal device,and the trust evaluation of the terminal’s continuous behavior can be achieved by combining the scores of different periods.After experiments,it is proved that TCL can effectively use the traffic behaviors and activity logs of terminal devices for trust evaluation and achieves F1-score of 95.763,94.456,99.923,and 99.195 on HDFS,BGL,N-BaIoT,and KDD99 datasets,respectively,and the size of TCL is only 91KB,which can achieve similar or better performance than CNN-LSTM,RobustLog and other methods with less computational resources and storage space.展开更多
Long associated with industrial smoke and heavy pollution,the chemical industry is undergoing a rapid transition to cleaner production.In the Jintang Economic Development Zone in Chengdu,Sichuan Province,B&M Tech...Long associated with industrial smoke and heavy pollution,the chemical industry is undergoing a rapid transition to cleaner production.In the Jintang Economic Development Zone in Chengdu,Sichuan Province,B&M Tech’s lithium-ion battery materials factory exemplifies this change.展开更多
African exporters and the business community have welcomed the elimination of customs duties on exports to China,and companies are already preparing to access this vast market of more than 1.4 billion consumers.China...African exporters and the business community have welcomed the elimination of customs duties on exports to China,and companies are already preparing to access this vast market of more than 1.4 billion consumers.China’s new tariff policy is intended to boost trade flows in favour of African economies.“This zero-tariff policy towards Africa aims to open a new chapter in the annals of Sino-African solidarity,”said Wang Yi,China’s minister of foreign affairs,during a press conference held on the sidelines of the Two Sessions held in March.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
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 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
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
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
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
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
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.
基金supported by the National Natural Science Foundation of China(62433014,62373287,62573324,62333005,62273255)in part by the International Exchange Program for Graduate Students of Tongji University(4360143306)+3 种基金in part by the Fundamental Research Funds for Central Universities(22120230311)supported by DeutscheForschungsgemeinschaft(DFG,German Research Foundation)under Germany’s Excellence Strategy(EXC 2075390740016,468094890)support by the Stuttgart Center for Simulation Science(SimTech)the International Max Planck Research School for Intelligent Systems(IMPRS-IS)for supporting Y.Xie。
文摘Dear Editor,This letter proposes a reinforcement learning-based predictive learning algorithm for unknown continuous-time nonlinear systems with observation loss.Firstly,we construct a temporal nonzero-sum game over predictive control input sequences,deriving multiple optimal predictive control input sequences from its solution.
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 Grants 61962023,61562029 and 62466019.
文摘This paper presents an adaptive multi-agent coordination(AMAC)strategy suitable for complex scenarios,which only requires information exchange between neighbouring robots.Unlike traditional multi-agent coordination methods that are solved by neural dynamics,the proposed strategy displays greater flexibility,adaptability and scalability.Furthermore,the proposed AMAC strategy is reconstructed as a time-varying complex-valued matrix equation.By introducing a dynamic error function,a fixed-time convergent zeroing neural network(FTCZNN)model is designed for the online solution of the AMAC strategy,with its convergence time upper bound derived theoretically.Finally,the effectiveness and applicability of the coordination control method are demonstrated by numerical simulations and physical experiments.Numerical results indicate that this method can reduce the formation error to the order of 10^(-6)within 1.8 s.
基金supported by National Key Research and Development Program of China(2022YFB3804902,2022YFB3804900)the National Natural Science Foundation of China(52203226,52161145406,42376045)the Fundamental Research Funds for the Central Universities(2232024Y-01,2232025D-02).
文摘While desalination is a key solution for global freshwater scarcity,its implementation faces environmental challenges due to concentrated brine byproducts mainly disposed of via coastal discharge systems.Solar interfacial evaporation offers sustainable management potential,yet inevitable salt nucleation at evaporation interfaces degrades photothermal conversion and operational stability via light scattering and pathway blockage.Inspired by the mangrove leaf,we propose a photothermal 3D polydopamine and polypyrrole polymerized spacer fabric(PPSF)-based upward hanging model evaporation configuration with a reverse water feeding mechanism.This design enables zero-liquiddischarge(ZLD)desalination through phase-separation crystallization.The interconnected porous architecture and the rough surface of the PPSF enable superior water transport,achieving excellent solar-absorbing efficiency of 97.8%.By adjusting the tilt angle(θ),the evaporator separates the evaporation and salt crystallization zones via controlled capillary-driven brine transport,minimizing heat dissipation from brine discharge.At an optimal tilt angle of 52°,the evaporator reaches an evaporation rate of 2.81 kg m^(−2) h^(−1) with minimal heat loss(0.366 W)under 1-sun illumination while treating a 7 wt%waste brine solution.Furthermore,it sustains an evaporation rate of 2.71 kg m^(−2) h^(−1) over 72 h while ensuring efficient salt recovery.These results highlight a scalable,energy-efficient approach for sustainable ZLD desalination.
基金supported by the National Science and Technology Major Project(2022ZD0119901)the National Natural Science Foundation of China under Grant(U2141234,62463004 and U24A20260)+1 种基金the Hainan Province Science and Technology Special Fund(ZDYF2024GXJS003)the Scientific Research Fund of Hainan University(KYQD(ZR)23025).
文摘Recently,the zeroing neural network(ZNN)has demonstrated remarkable effectiveness in tackling time-varying problems,delivering robust performance across both noise-free and noisy environments.However,existing ZNN models are limited in their ability to actively suppress noise,which constrains their robustness and precision in solving time-varying problems.This paper introduces a novel active noise rejection ZNN(ANR-ZNN)design that enhances noise suppression by integrating computational error dynamics and harmonic behaviour.Through rigorous theoretical analysis,we demonstrate that the proposed ANR-ZNN maintains robust convergence in computational error performance under environmental noise.As a case study,the ANR-ZNN model is specifically applied to time-varying matrix inversion.Comprehensive computer simulations and robotic experiments further validate the ANR-ZNN's effectiveness,emphasising the proposed design's superiority and potential for solving time-varying problems.
基金supported by National Key R&D Program of China(No.2022YFB3105101).
文摘With more and more IoT terminals being deployed in various power grid business scenarios,terminal reliability has become a practical challenge that threatens the current security protection architecture.Most IoT terminals have security risks and vulnerabilities,and limited resources make it impossible to deploy costly security protection methods on the terminal.In order to cope with these problems,this paper proposes a lightweight trust evaluation model TCL,which combines three network models,TCN,CNN,and LSTM,with stronger feature extraction capability and can score the reliability of the device by periodically analyzing the traffic behavior and activity logs generated by the terminal device,and the trust evaluation of the terminal’s continuous behavior can be achieved by combining the scores of different periods.After experiments,it is proved that TCL can effectively use the traffic behaviors and activity logs of terminal devices for trust evaluation and achieves F1-score of 95.763,94.456,99.923,and 99.195 on HDFS,BGL,N-BaIoT,and KDD99 datasets,respectively,and the size of TCL is only 91KB,which can achieve similar or better performance than CNN-LSTM,RobustLog and other methods with less computational resources and storage space.
文摘Long associated with industrial smoke and heavy pollution,the chemical industry is undergoing a rapid transition to cleaner production.In the Jintang Economic Development Zone in Chengdu,Sichuan Province,B&M Tech’s lithium-ion battery materials factory exemplifies this change.
文摘African exporters and the business community have welcomed the elimination of customs duties on exports to China,and companies are already preparing to access this vast market of more than 1.4 billion consumers.China’s new tariff policy is intended to boost trade flows in favour of African economies.“This zero-tariff policy towards Africa aims to open a new chapter in the annals of Sino-African solidarity,”said Wang Yi,China’s minister of foreign affairs,during a press conference held on the sidelines of the Two Sessions held in March.
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 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.
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.
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 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.
