In this paper, some new unique common fixed points for four mappings satisfying Ф-contractive conditions on non-complete 2-metric spaces are obtained, in which the mappings do not satisfy continuity and commutation. ...In this paper, some new unique common fixed points for four mappings satisfying Ф-contractive conditions on non-complete 2-metric spaces are obtained, in which the mappings do not satisfy continuity and commutation. The main results generalize and improve many well-known and corresponding conclusions in the literatures.展开更多
Cognitive radio devices can utilize the licensed channels in an opportunistic manner to solve the spectrum scarcity issue occurring in the unlicensed spectrum.However,these cognitive radio devices(secondary users)are ...Cognitive radio devices can utilize the licensed channels in an opportunistic manner to solve the spectrum scarcity issue occurring in the unlicensed spectrum.However,these cognitive radio devices(secondary users)are greatly affected by the original users(primary users)of licensed channels.Cognitive users have to adjust operation parameters frequently to adapt to the dynamic network environment,which causes extra energy consumption.Energy consumption can be reduced by predicting the future activity of primary users.However,the traditional prediction-based algorithms require large historical data to achieve a satisfying precision accuracy which will consume a lot of time and memory space.Moreover,many of these schemes lack methods to deal with the very busy network environments.In this paper,one semi-supervised learning algorithm,i.e.,tri-training,has been employed to investigate the prediction of primary activity.Based on the prediction results of tri-training,a duty-cycle mechanism and an intermediate node selection approach are proposed to improve the energy efficiency.Simulation results show the effectiveness of the proposed algorithm.展开更多
We consider numerical methods to solve the Allen-Cahn equation using the second-order Crank-Nicolson scheme in time and the second-order central difference approach in space.The existence of the finite difference solu...We consider numerical methods to solve the Allen-Cahn equation using the second-order Crank-Nicolson scheme in time and the second-order central difference approach in space.The existence of the finite difference solution is proved with the help of Browder fixed point theorem.The difference scheme is showed to be unconditionally convergent in Loo norm by constructing an auxiliary Lipschitz continuous function.Based on this result,it is demonstrated that the difference scheme preserves the maximum principle without any restrictions on spatial step size and temporal step size.The numerical experiments also verify the reliability of the method.展开更多
文摘In this paper, some new unique common fixed points for four mappings satisfying Ф-contractive conditions on non-complete 2-metric spaces are obtained, in which the mappings do not satisfy continuity and commutation. The main results generalize and improve many well-known and corresponding conclusions in the literatures.
基金This work was partially supported by the National Natural Science Foundation of China(Grant Nos.11761074,61972207,61902041)the Natural Science Foundation of Jilin Province of China(Grant No.2020122336JC)Project of Jilin Science and Technology Development for Leading Talent of Science and Technology Innovation in Middle and Young and Team Project(No.20200301053RQ)and the Project through the Priority Academic Program Development(PAPD)of Jiangsu Higher Education Institution.
文摘Cognitive radio devices can utilize the licensed channels in an opportunistic manner to solve the spectrum scarcity issue occurring in the unlicensed spectrum.However,these cognitive radio devices(secondary users)are greatly affected by the original users(primary users)of licensed channels.Cognitive users have to adjust operation parameters frequently to adapt to the dynamic network environment,which causes extra energy consumption.Energy consumption can be reduced by predicting the future activity of primary users.However,the traditional prediction-based algorithms require large historical data to achieve a satisfying precision accuracy which will consume a lot of time and memory space.Moreover,many of these schemes lack methods to deal with the very busy network environments.In this paper,one semi-supervised learning algorithm,i.e.,tri-training,has been employed to investigate the prediction of primary activity.Based on the prediction results of tri-training,a duty-cycle mechanism and an intermediate node selection approach are proposed to improve the energy efficiency.Simulation results show the effectiveness of the proposed algorithm.
基金This work was supported by National Natural Science Foundation of China(No.11761074)the projection of the Department of Science and Technology of Jilin Province for Leading Talent of Science and Technology Innovation in Middle and Young and Team Project.
文摘We consider numerical methods to solve the Allen-Cahn equation using the second-order Crank-Nicolson scheme in time and the second-order central difference approach in space.The existence of the finite difference solution is proved with the help of Browder fixed point theorem.The difference scheme is showed to be unconditionally convergent in Loo norm by constructing an auxiliary Lipschitz continuous function.Based on this result,it is demonstrated that the difference scheme preserves the maximum principle without any restrictions on spatial step size and temporal step size.The numerical experiments also verify the reliability of the method.
