In this paper, we derive the stochastic maximum principle for optimal control problems of the forward-backward Markovian regime-switching system. The control system is described by an anticipated forward-backward stoc...In this paper, we derive the stochastic maximum principle for optimal control problems of the forward-backward Markovian regime-switching system. The control system is described by an anticipated forward-backward stochastic pantograph equation and modulated by a continuous-time finite-state Markov chain. By virtue of classical variational approach, duality method, and convex analysis, we obtain a stochastic maximum principle for the optimal control.展开更多
This paper proposes the SISRS epidemic model to represent alcohol addiction among people.The spreading of alcohol addiction is controlled by creating awareness among the people and also by treating them to overcome it...This paper proposes the SISRS epidemic model to represent alcohol addiction among people.The spreading of alcohol addiction is controlled by creating awareness among the people and also by treating them to overcome it.Multiplex network is used to study the dynamics of addiction.Alcoholism spreads over the physical contact layer and follows the SISRS process whereas human awareness spreads over the virtual contact layer and follows the UAU process.Based on the Microscopic Markov Chain Approach competing dynamics of spreading of alcohol addiction and human awareness diffusion are studied.Necessary conditions for the existence of an alcohol-free population are found.An optimal control problem using a suitable cost index is formulated to reduce the alcohol addicts and the optimal control strategy using Pontryagin’s Minimum Principle is determined.Numerical results are developed to find the effect of various parameters and to analyze the effects of different control strategies.The results obtained from this model are closer to the data collected in the National Survey of Drug Use and Health(NSDUH)from 2002 to 2018.展开更多
Two mean-field potentials, Woods-Saxon and Skyrme based potentials, are used to calculate the energies of low-lying one-quasiparticle states. The spectra of the low-lying states and the α-decay spectra of nuclei belo...Two mean-field potentials, Woods-Saxon and Skyrme based potentials, are used to calculate the energies of low-lying one-quasiparticle states. The spectra of the low-lying states and the α-decay spectra of nuclei belonging to the α-decay chains of ^285Fl and ^291,293Lv are calculated and compared with the available experimental data. Dependence of the splitting of the pseudospin doublets and of the energies of the unique parity neutron one-quasiparticle states on the mean field potential are discussed. As shown, the α-decay spectra could be different in the α-decay chain and at the direct production of the nucleus in a fusion reaction.展开更多
文摘In this paper, we derive the stochastic maximum principle for optimal control problems of the forward-backward Markovian regime-switching system. The control system is described by an anticipated forward-backward stochastic pantograph equation and modulated by a continuous-time finite-state Markov chain. By virtue of classical variational approach, duality method, and convex analysis, we obtain a stochastic maximum principle for the optimal control.
文摘This paper proposes the SISRS epidemic model to represent alcohol addiction among people.The spreading of alcohol addiction is controlled by creating awareness among the people and also by treating them to overcome it.Multiplex network is used to study the dynamics of addiction.Alcoholism spreads over the physical contact layer and follows the SISRS process whereas human awareness spreads over the virtual contact layer and follows the UAU process.Based on the Microscopic Markov Chain Approach competing dynamics of spreading of alcohol addiction and human awareness diffusion are studied.Necessary conditions for the existence of an alcohol-free population are found.An optimal control problem using a suitable cost index is formulated to reduce the alcohol addicts and the optimal control strategy using Pontryagin’s Minimum Principle is determined.Numerical results are developed to find the effect of various parameters and to analyze the effects of different control strategies.The results obtained from this model are closer to the data collected in the National Survey of Drug Use and Health(NSDUH)from 2002 to 2018.
基金supported by the RFBR (Moscow)DFG (Bonn)The Polish-JINR (Dubna) Cooperation Programm
文摘Two mean-field potentials, Woods-Saxon and Skyrme based potentials, are used to calculate the energies of low-lying one-quasiparticle states. The spectra of the low-lying states and the α-decay spectra of nuclei belonging to the α-decay chains of ^285Fl and ^291,293Lv are calculated and compared with the available experimental data. Dependence of the splitting of the pseudospin doublets and of the energies of the unique parity neutron one-quasiparticle states on the mean field potential are discussed. As shown, the α-decay spectra could be different in the α-decay chain and at the direct production of the nucleus in a fusion reaction.
