This paper shows that exact calculation for transition probability can make some systems deviate fromFermi golden rule seriously. This paper also shows that the corresponding exact calculation of hopping rate inducedb...This paper shows that exact calculation for transition probability can make some systems deviate fromFermi golden rule seriously. This paper also shows that the corresponding exact calculation of hopping rate inducedby phonons for deuteron in Pd-D system with the many-body electron screening, proposed by Ichimaru, can explainthe experimental fact observed in Pd-D system, and predicts that perfection and low-dimension of Pd lattice are veryimportant for the phonon-induced hopping rate enhancement in Pd-D system.展开更多
This paper suggests a principle to find a unitary operator U which transforms non-physical quantity, zero-potential Hamiltonian H<SUB>0</SUB>, into true physical quantity UH<SUB>0</SUB>U<SUP...This paper suggests a principle to find a unitary operator U which transforms non-physical quantity, zero-potential Hamiltonian H<SUB>0</SUB>, into true physical quantity UH<SUB>0</SUB>U<SUP>?</SUP> for a charged particle in classical electromagnetic field, and puts forward a unified form of constructing gauge-independent transition probabilities in this case. Different methods correspond to different unitary operators which satisfy the above-mentioned principle.展开更多
This paper focuses on the reachable set estimation for Markovian jump neural networks with time delay.By allowing uncertainty in the transition probabilities,a framework unifies and enhances the generality and realism...This paper focuses on the reachable set estimation for Markovian jump neural networks with time delay.By allowing uncertainty in the transition probabilities,a framework unifies and enhances the generality and realism of these systems.To fully exploit the unified uncertain transition probabilities,an equivalent transformation technique is introduced as an alternative to traditional estimation methods,effectively utilizing the information of transition probabilities.Furthermore,a vector Wirtinger-based summation inequality is proposed,which captures more system information compared to existing ones.Building upon these components,a novel condition that guarantees a reachable set estimation is presented for Markovian jump neural networks with unified uncertain transition probabilities.A numerical example is illustrated to demonstrate the superiority of the approaches.展开更多
In this paper we consider a Markov chain model in an ATM network, which has been studied by Dag and Stavrakakis. On the basis of the iterative formulas obtained by Dag and Stavrakakis, we obtain the explicit analytica...In this paper we consider a Markov chain model in an ATM network, which has been studied by Dag and Stavrakakis. On the basis of the iterative formulas obtained by Dag and Stavrakakis, we obtain the explicit analytical expression of the transition probability matrix. It is very simple to calculate the transition probabilities of the Markov chain by these expressions. In addition, we obtain some results about the structure of the transition probability matrix, which are helpful in numerical calculation and theoretical analysis.展开更多
In this paper, we study the basic properties of stationary transition probability of Markov processes on a general measurable space （E, δ）, such as the continuity, maximum probability, zero point, positive probabil...In this paper, we study the basic properties of stationary transition probability of Markov processes on a general measurable space （E, δ）, such as the continuity, maximum probability, zero point, positive probability set,standardization, and obtain a series of important results such as Continuity Theorem, Representation Theorem, Levy Theorem and so on. These results are very useful for us to study stationary tri-point transition probability on a general measurable space （E, δ）. Our main tools such as Egoroff＇s Theorem, Vitali-Hahn-Saks＇s Theorem and the theory of atomic set and well- posedness of measure are also very interesting and fashionable.展开更多
The Weakest Bound Electron Potential Model theory is used to calculate transition probability-values and oscillator strength-values for individual lines of Sc（Ⅲ） and Y（Ⅲ）. In this method, by solving the SchrSdin...The Weakest Bound Electron Potential Model theory is used to calculate transition probability-values and oscillator strength-values for individual lines of Sc（Ⅲ） and Y（Ⅲ）. In this method, by solving the SchrSdinger equation of the weakest bound electron, the expressions of energy eigenvalue and the radial function can be obtained. And a coupled equation is used to determine the parameters which are needed in the calculations. The ob- tained results of Sc（III） from this work agree very well with the accepted values taken from the National Institute of Standards and Technoligy （NIST） data base, most deviations are within the accepted level. For Y（Ⅲ） there are no accepted values reported by the NIST data base. So we compared our results of Y（Ⅲ） with other theoretical results, good agreement is also obtained.展开更多
Based on NII spectra, some transition probabilities for 2p4f-2p3d and 2s2p23d-2s2p23p are obtained by a semi- classical method. The results are in good agreement with other measurements and the data reported by the Na...Based on NII spectra, some transition probabilities for 2p4f-2p3d and 2s2p23d-2s2p23p are obtained by a semi- classical method. The results are in good agreement with other measurements and the data reported by the National Institute of Standards and Technology. The transition probability for a line of 424.18nm is reported for the first time. Meanwhile, a feasible method of calculating transition parameters related to special excited configurations or highly excited states is provided.展开更多
Inadequate maintenance decisions lead to incremental overall costs. In order to minimize costs in maintenance of the multi-state repairable system, we model a preventive maintenance(PM) scheme of the multistate repair...Inadequate maintenance decisions lead to incremental overall costs. In order to minimize costs in maintenance of the multi-state repairable system, we model a preventive maintenance(PM) scheme of the multistate repairable system using non-Markov process. The periodically decreasing reliability model of the non-Markov dynamic system with dynamic transition probabilities is established to satisfy the probability change. The diesel engine system is taken as an example to illustrate the model. The reliability of the diesel engine is analyzed and its PM scheme is worked out. RENO software is used to simulate the diesel engine system. The maintenance cost of components and the optimal PM interval data of the system are obtained by using the minimal average cost as the objective function. The adaptability of PM is judged, and the optimal PM scheme is presented.展开更多
By applying systematically enlarged multi-configuration Dirac-Fock wavefunction, the transitions for electricdipole allowed （E1） and forbidden （E2, M1 and M2） lines are studied among 4f pair coupling and low-lying...By applying systematically enlarged multi-configuration Dirac-Fock wavefunction, the transitions for electricdipole allowed （E1） and forbidden （E2, M1 and M2） lines are studied among 4f pair coupling and low-lying configurations for singly ionized nitrogen. Most important effects of relativity, electron correlation, the rearrangement of electron density, Breit interaction, and quantum electrodynamic effects are included in the computation. Then, allowed （E1） and forbidden （E2, M1 and M2） transition probabilities of 4f for N＋ are obtained and compared with experimental results. Good agreement with available experimental results is found and most of the data of 4f are presented for the first time.展开更多
Energy levels, radiative rates, oscillator strengths and line strengths are reported for transitions among the lowest 97 levels of the（1s22s22p6） 3s23p2, 3s23p3 d, 3s3p3, 3p4, 3s3p23 d, and 3s23d2 configurations of ...Energy levels, radiative rates, oscillator strengths and line strengths are reported for transitions among the lowest 97 levels of the（1s22s22p6） 3s23p2, 3s23p3 d, 3s3p3, 3p4, 3s3p23 d, and 3s23d2 configurations of Rb XXIV. A multiconfiguration Dirac-Fock（MCDF） method is adopted for the calculations. Radiative rates, oscillator strengths, and line strengths are provided for all electric dipole（E1）, magnetic dipole（M1）, electric quadrupole（E2）, and magnetic quadrupole（M2）transitions from the ground level to all 97 levels, although calculations are performed for a much larger number of levels.To achieve the accuracy of the data, comparisons are provided with similar data obtained from the Flexible Atomic Code（FAC） and also with the available theoretical and experimental results. Our energy levels are found to be accurate to better than 1.2%. Wavelengths calculated are found to lie in EUV（extreme ultraviolet） and x-ray regions. Additionally, lifetimes for all 97 levels are obtained for the first time.展开更多
The multi-configuration Dirac-Fock method is employed to calculate the transition energies, probabilities, and oscillator strengths for electric dipole allowed （El） and forbidden （M1, E2, M2） lines for the 3s^23p,...The multi-configuration Dirac-Fock method is employed to calculate the transition energies, probabilities, and oscillator strengths for electric dipole allowed （El） and forbidden （M1, E2, M2） lines for the 3s^23p, 3s3p^2, 3s^23d, 3p^3, and 3s3p3d configurations of Fe XIV. The lifetimes of all 40 levels of these low-lying configurations are also derived. The valence valence and core-valence correlation effects are accounted for in a systematic way. Breit interactions and quantum electrodynamics （QED） effects are estimated in subsequent relativistic configuration interaction （CI） calculations. The present results are in good agreement with other available theoretical and experimental values, and therefore can be used for the further astrophysical investigations.展开更多
In this research work, the upward transition probabilities for the transition levels, 0<sup>+</sup> → 2<sup>+</sup>, 2<sup>+</sup> → 4<sup>+</sup>, 4<sup>+</s...In this research work, the upward transition probabilities for the transition levels, 0<sup>+</sup> → 2<sup>+</sup>, 2<sup>+</sup> → 4<sup>+</sup>, 4<sup>+</sup> → 6<sup>+</sup> and 6<sup>+</sup> → 8<sup>+</sup> levels of even-even neutron rich <sup>104-114</sup>Ru isotopes have been calculated by using the Global Best Fit (GBF) method. In addition, the associated parameters such as, Quadrupole moment and Deformation parameter of even-even <sup>104-114</sup>Ru have been calculated. The dependency of these nuclear parameters shows the nuclear magic number tendency.展开更多
Optimal policies in Markov decision problems may be quite sensitive with regard to transition probabilities.In practice,some transition probabilities may be uncertain.The goals of the present study are to find the rob...Optimal policies in Markov decision problems may be quite sensitive with regard to transition probabilities.In practice,some transition probabilities may be uncertain.The goals of the present study are to find the robust range for a certain optimal policy and to obtain value intervals of exact transition probabilities.Our research yields powerful contributions for Markov decision processes(MDPs)with uncertain transition probabilities.We first propose a method for estimating unknown transition probabilities based on maximum likelihood.Since the estimation may be far from accurate,and the highest expected total reward of the MDP may be sensitive to these transition probabilities,we analyze the robustness of an optimal policy and propose an approach for robust analysis.After giving the definition of a robust optimal policy with uncertain transition probabilities represented as sets of numbers,we formulate a model to obtain the optimal policy.Finally,we define the value intervals of the exact transition probabilities and construct models to determine the lower and upper bounds.Numerical examples are given to show the practicability of our methods.展开更多
Quantum aspects of the Joule-Lenz law for the transmission of energy allowed us to calculate the time rate of energy transitions between the quantum states of the hydrogen atom in a fully non-probabilistic way. The ca...Quantum aspects of the Joule-Lenz law for the transmission of energy allowed us to calculate the time rate of energy transitions between the quantum states of the hydrogen atom in a fully non-probabilistic way. The calculation has been extended to all transitions between p and s states having main quantum numbers not exceeding 6. An evident similarity between the intensity pattern obtained from the Joule-Lenz law and the corresponding quantum-mechanical transition pro-babilities has been shown.展开更多
Based on relativistic wave functions from multiconfiguration Dirac-Hartree-Fock and configuration interaction cal- culations, E2 and M1 transition probabilities of 2p3 4S3/2-2p3 2D3/2,5/2 are investigated in the nitro...Based on relativistic wave functions from multiconfiguration Dirac-Hartree-Fock and configuration interaction cal- culations, E2 and M1 transition probabilities of 2p3 4S3/2-2p3 2D3/2,5/2 are investigated in the nitrogen-like sequence with 7 〈 Z 〈 16. The contributions of the electron correlations, Breit interaction, and the quantum electrodynamic （QED） effects on the transition properties are analyzed. The present results can be used for diagnosing plasma. In addition, several N-like ions can also be recommended as a promising candidate for a highly charged ion （HCI） clock with a quality factor （Q） of trnnsition as hitch as 1020.展开更多
The energy levels,transition energies,transition probabilities,weighted oscillator strengths,and line strengths of Li-like ions(Z=7-11)in dense plasmas are investigated in this work.The relativistic effects and electr...The energy levels,transition energies,transition probabilities,weighted oscillator strengths,and line strengths of Li-like ions(Z=7-11)in dense plasmas are investigated in this work.The relativistic effects and electron correlation effects are described by the MCDHF method.The ion sphere model is applied to include the dense plasma screening effect.The ground configuration 1s^(2)2s and the excited 1s^(2)2p,1s^(2)3l(l=0-2)are considered.The configuration sets are enlarged until n=7 where the calculated energy levels have converged.The critical free electron densities of 1s^(2)3d states are estimated.Except for 1s^(2)3s-1s^(2)3p transitions,the transition energies for△n=0 increase,and for△n≠0 decrease with increasing free electron densities.For 1s^(2)3s-1s^(2)3p transitions,the spectra show blue-shift at lower free electron densities and red-shift at higher free electron densities,and the energy level crossing phenomens are observed at higher free electron densities.展开更多
Excitation energies, magnetic dipole, and electric quadrupole transition probabilities of the 3d ^2D3/2-3d ^2D5/2 transition in the potassium-like （K-like） sequence with 26 ≤ Z ≤ 36 are investigated by using the m...Excitation energies, magnetic dipole, and electric quadrupole transition probabilities of the 3d ^2D3/2-3d ^2D5/2 transition in the potassium-like （K-like） sequence with 26 ≤ Z ≤ 36 are investigated by using the multi-configuration Dirac-Hartree-Fock （MCDHF） method. The contributions of the electron correlations, Breit interaction, and the leading-order quantum electrodynamic （QED） effects on the transition properties are analyzed. The present results are interested in the laboratory tokamak and the astronomical observations. Furthermore, the feasibility of these ions for the highly charged ion （HCI） clocks is discussed. Considering the wavelength of lasers and manipulation process of the atomic clocks, Cu^10＋ and Zn^11＋ are recommended as promising candidates with achievable quality factors at the 10^15 level.展开更多
Interacting Boson Model-2(IBM-2)is used to determine the Hamiltonian for Er nuclei.Fit values of parameters are used to construct the Hamiltonian,energy levels and electromagnetic transitions(B(E2),B(M1))multipole mix...Interacting Boson Model-2(IBM-2)is used to determine the Hamiltonian for Er nuclei.Fit values of parameters are used to construct the Hamiltonian,energy levels and electromagnetic transitions(B(E2),B(M1))multipole mixing ratios(δ(E2/M1))for some even-even Er nuclei and monopole transition probability are estimated.New ideas are used for counting bosons number at N=64 and results are compared with previous works.展开更多
The descriptor Markovian jump systems( DMJSs)with partially unknown transition probabilities( PUTPs) are studied by means of variable structure control. First,by virtue of the strictly linear matrix inequality( LMI) t...The descriptor Markovian jump systems( DMJSs)with partially unknown transition probabilities( PUTPs) are studied by means of variable structure control. First,by virtue of the strictly linear matrix inequality( LMI) technique,a sufficient condition is presented, under which the DMJSs subject to PUTPs are stochastically admissible. Secondly,a novel sliding surface function based on the system state and input is constructed for DMJSs subject to PUTPs; and a dynamic sliding mode controller is synthesized, which guarantees that state trajectories will reach the pre-specified sliding surface in finite time despite uncertainties and disturbances. The results indicate that by checking the feasibility of a series of LMIs,the stochastic admissibility of the overall closed loop system is determined. Finally,the validity of the theoretical results is illustrated with the example of the direct-current motor. Furthermore,compared with the existing literature,the state convergence rate,buffeting reduction and overshoot reduction are obviously optimized.展开更多
The effects of stochastic perturbations and periodic excitations on the eutrophicated lake ecosystem are explored.Unlike the existing work in detecting early warning signals,this paper presents the most probable trans...The effects of stochastic perturbations and periodic excitations on the eutrophicated lake ecosystem are explored.Unlike the existing work in detecting early warning signals,this paper presents the most probable transition paths to characterize the regime shifts.The most probable transition paths are obtained by minimizing the Freidlin-Wentzell(FW)action functional and Onsager-Machlup(OM)action functional,respectively.The most probable path shows the movement trend of the lake eutrophication system under noise excitation,and describes the global transition behavior of the system.Under the excitation of Gaussian noise,the results show that the stability of the eutrophic state and the oligotrophic state has different results from two perspectives of potential well and the most probable transition paths.Under the excitation of Gaussian white noise and periodic force,we find that the transition occurs near the nearest distance between the stable periodic solution and the unstable periodic solution.展开更多
文摘This paper shows that exact calculation for transition probability can make some systems deviate fromFermi golden rule seriously. This paper also shows that the corresponding exact calculation of hopping rate inducedby phonons for deuteron in Pd-D system with the many-body electron screening, proposed by Ichimaru, can explainthe experimental fact observed in Pd-D system, and predicts that perfection and low-dimension of Pd lattice are veryimportant for the phonon-induced hopping rate enhancement in Pd-D system.
文摘This paper suggests a principle to find a unitary operator U which transforms non-physical quantity, zero-potential Hamiltonian H<SUB>0</SUB>, into true physical quantity UH<SUB>0</SUB>U<SUP>?</SUP> for a charged particle in classical electromagnetic field, and puts forward a unified form of constructing gauge-independent transition probabilities in this case. Different methods correspond to different unitary operators which satisfy the above-mentioned principle.
基金funded by National Key Research and Development Program of China under Grant 2022YFE0107300the Chongqing Technology Innovation and Application Development Special Key Project under Grant CSTB2022TIAD-KPX0162+3 种基金the National Natural Science Foundation of China under Grant U22A20101the Chongqing Technology Innovation and Application Development Special Key Project under Grant CSTB2022TIAD-CUX0015the Chongqing postdoctoral innovativetalents support program under Grant CQBX202205the China Postdoctoral Science Foundation under Grant 2023M730411.
文摘This paper focuses on the reachable set estimation for Markovian jump neural networks with time delay.By allowing uncertainty in the transition probabilities,a framework unifies and enhances the generality and realism of these systems.To fully exploit the unified uncertain transition probabilities,an equivalent transformation technique is introduced as an alternative to traditional estimation methods,effectively utilizing the information of transition probabilities.Furthermore,a vector Wirtinger-based summation inequality is proposed,which captures more system information compared to existing ones.Building upon these components,a novel condition that guarantees a reachable set estimation is presented for Markovian jump neural networks with unified uncertain transition probabilities.A numerical example is illustrated to demonstrate the superiority of the approaches.
基金This work is supported by the National Key Project of China(No 970211017,the National Natural Science Foundation of China(No,10271102)and Hebei Province Doctoral Foundation(No.2002131)
文摘In this paper we consider a Markov chain model in an ATM network, which has been studied by Dag and Stavrakakis. On the basis of the iterative formulas obtained by Dag and Stavrakakis, we obtain the explicit analytical expression of the transition probability matrix. It is very simple to calculate the transition probabilities of the Markov chain by these expressions. In addition, we obtain some results about the structure of the transition probability matrix, which are helpful in numerical calculation and theoretical analysis.
基金Hunan Provincial Natural Science Foundation of China (06JJ50004)the Construct Program of the Key Discipline in Hunan Province
文摘In this paper, we study the basic properties of stationary transition probability of Markov processes on a general measurable space （E, δ）, such as the continuity, maximum probability, zero point, positive probability set,standardization, and obtain a series of important results such as Continuity Theorem, Representation Theorem, Levy Theorem and so on. These results are very useful for us to study stationary tri-point transition probability on a general measurable space （E, δ）. Our main tools such as Egoroff＇s Theorem, Vitali-Hahn-Saks＇s Theorem and the theory of atomic set and well- posedness of measure are also very interesting and fashionable.
文摘The Weakest Bound Electron Potential Model theory is used to calculate transition probability-values and oscillator strength-values for individual lines of Sc（Ⅲ） and Y（Ⅲ）. In this method, by solving the SchrSdinger equation of the weakest bound electron, the expressions of energy eigenvalue and the radial function can be obtained. And a coupled equation is used to determine the parameters which are needed in the calculations. The ob- tained results of Sc（III） from this work agree very well with the accepted values taken from the National Institute of Standards and Technoligy （NIST） data base, most deviations are within the accepted level. For Y（Ⅲ） there are no accepted values reported by the NIST data base. So we compared our results of Y（Ⅲ） with other theoretical results, good agreement is also obtained.
基金Project supported by the National Natural Science Foundation of China （Grant No 40475007）.
文摘Based on NII spectra, some transition probabilities for 2p4f-2p3d and 2s2p23d-2s2p23p are obtained by a semi- classical method. The results are in good agreement with other measurements and the data reported by the National Institute of Standards and Technology. The transition probability for a line of 424.18nm is reported for the first time. Meanwhile, a feasible method of calculating transition parameters related to special excited configurations or highly excited states is provided.
基金the National Natural Science Foundation of China(Nos.61164009 and 61463021)the Science Foundation of Education Commission of Jiangxi Province(No.GJJ14420)+1 种基金the Young Scientists Object Program of Jiangxi Province(No.20144BCB23037)the Natural Science Foundation of Jiangxi Province(No.20132BAB206026)
文摘Inadequate maintenance decisions lead to incremental overall costs. In order to minimize costs in maintenance of the multi-state repairable system, we model a preventive maintenance(PM) scheme of the multistate repairable system using non-Markov process. The periodically decreasing reliability model of the non-Markov dynamic system with dynamic transition probabilities is established to satisfy the probability change. The diesel engine system is taken as an example to illustrate the model. The reliability of the diesel engine is analyzed and its PM scheme is worked out. RENO software is used to simulate the diesel engine system. The maintenance cost of components and the optimal PM interval data of the system are obtained by using the minimal average cost as the objective function. The adaptability of PM is judged, and the optimal PM scheme is presented.
基金Project supported by the Foundation of Handan College,China (Grant No. 09005)the National Natural Science Foundation of China (Grant No. 40475007)
文摘By applying systematically enlarged multi-configuration Dirac-Fock wavefunction, the transitions for electricdipole allowed （E1） and forbidden （E2, M1 and M2） lines are studied among 4f pair coupling and low-lying configurations for singly ionized nitrogen. Most important effects of relativity, electron correlation, the rearrangement of electron density, Breit interaction, and quantum electrodynamic effects are included in the computation. Then, allowed （E1） and forbidden （E2, M1 and M2） transition probabilities of 4f for N＋ are obtained and compared with experimental results. Good agreement with available experimental results is found and most of the data of 4f are presented for the first time.
基金supported by the U.G.C.,India for their Junior Research FellowshipMan Mohan by the U.G.C.for Basic Science Research Fellowship
文摘Energy levels, radiative rates, oscillator strengths and line strengths are reported for transitions among the lowest 97 levels of the（1s22s22p6） 3s23p2, 3s23p3 d, 3s3p3, 3p4, 3s3p23 d, and 3s23d2 configurations of Rb XXIV. A multiconfiguration Dirac-Fock（MCDF） method is adopted for the calculations. Radiative rates, oscillator strengths, and line strengths are provided for all electric dipole（E1）, magnetic dipole（M1）, electric quadrupole（E2）, and magnetic quadrupole（M2）transitions from the ground level to all 97 levels, although calculations are performed for a much larger number of levels.To achieve the accuracy of the data, comparisons are provided with similar data obtained from the Flexible Atomic Code（FAC） and also with the available theoretical and experimental results. Our energy levels are found to be accurate to better than 1.2%. Wavelengths calculated are found to lie in EUV（extreme ultraviolet） and x-ray regions. Additionally, lifetimes for all 97 levels are obtained for the first time.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10876028,10847007,and 10964010)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20070736001)
文摘The multi-configuration Dirac-Fock method is employed to calculate the transition energies, probabilities, and oscillator strengths for electric dipole allowed （El） and forbidden （M1, E2, M2） lines for the 3s^23p, 3s3p^2, 3s^23d, 3p^3, and 3s3p3d configurations of Fe XIV. The lifetimes of all 40 levels of these low-lying configurations are also derived. The valence valence and core-valence correlation effects are accounted for in a systematic way. Breit interactions and quantum electrodynamics （QED） effects are estimated in subsequent relativistic configuration interaction （CI） calculations. The present results are in good agreement with other available theoretical and experimental values, and therefore can be used for the further astrophysical investigations.
文摘In this research work, the upward transition probabilities for the transition levels, 0<sup>+</sup> → 2<sup>+</sup>, 2<sup>+</sup> → 4<sup>+</sup>, 4<sup>+</sup> → 6<sup>+</sup> and 6<sup>+</sup> → 8<sup>+</sup> levels of even-even neutron rich <sup>104-114</sup>Ru isotopes have been calculated by using the Global Best Fit (GBF) method. In addition, the associated parameters such as, Quadrupole moment and Deformation parameter of even-even <sup>104-114</sup>Ru have been calculated. The dependency of these nuclear parameters shows the nuclear magic number tendency.
基金Supported by the National Natural Science Foundation of China(71571019).
文摘Optimal policies in Markov decision problems may be quite sensitive with regard to transition probabilities.In practice,some transition probabilities may be uncertain.The goals of the present study are to find the robust range for a certain optimal policy and to obtain value intervals of exact transition probabilities.Our research yields powerful contributions for Markov decision processes(MDPs)with uncertain transition probabilities.We first propose a method for estimating unknown transition probabilities based on maximum likelihood.Since the estimation may be far from accurate,and the highest expected total reward of the MDP may be sensitive to these transition probabilities,we analyze the robustness of an optimal policy and propose an approach for robust analysis.After giving the definition of a robust optimal policy with uncertain transition probabilities represented as sets of numbers,we formulate a model to obtain the optimal policy.Finally,we define the value intervals of the exact transition probabilities and construct models to determine the lower and upper bounds.Numerical examples are given to show the practicability of our methods.
文摘Quantum aspects of the Joule-Lenz law for the transmission of energy allowed us to calculate the time rate of energy transitions between the quantum states of the hydrogen atom in a fully non-probabilistic way. The calculation has been extended to all transitions between p and s states having main quantum numbers not exceeding 6. An evident similarity between the intensity pattern obtained from the Joule-Lenz law and the corresponding quantum-mechanical transition pro-babilities has been shown.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11604385 and 91436103)
文摘Based on relativistic wave functions from multiconfiguration Dirac-Hartree-Fock and configuration interaction cal- culations, E2 and M1 transition probabilities of 2p3 4S3/2-2p3 2D3/2,5/2 are investigated in the nitrogen-like sequence with 7 〈 Z 〈 16. The contributions of the electron correlations, Breit interaction, and the quantum electrodynamic （QED） effects on the transition properties are analyzed. The present results can be used for diagnosing plasma. In addition, several N-like ions can also be recommended as a promising candidate for a highly charged ion （HCI） clock with a quality factor （Q） of trnnsition as hitch as 1020.
基金the National Natural Science Foundation of China(Grant No.11847163)the Natural Science Foundation of Gansu Province(Grant No.20JR10RA131)+2 种基金the Doctoral Science Foundation of Longdong University(Grant No.XYBY202005)the Natural Science Foundation of Shaanxi Province(Grant No.2021JQ-698)the Special Project of Department of Education of Shaanxi Province(Grant No.18JK0710).
文摘The energy levels,transition energies,transition probabilities,weighted oscillator strengths,and line strengths of Li-like ions(Z=7-11)in dense plasmas are investigated in this work.The relativistic effects and electron correlation effects are described by the MCDHF method.The ion sphere model is applied to include the dense plasma screening effect.The ground configuration 1s^(2)2s and the excited 1s^(2)2p,1s^(2)3l(l=0-2)are considered.The configuration sets are enlarged until n=7 where the calculated energy levels have converged.The critical free electron densities of 1s^(2)3d states are estimated.Except for 1s^(2)3s-1s^(2)3p transitions,the transition energies for△n=0 increase,and for△n≠0 decrease with increasing free electron densities.For 1s^(2)3s-1s^(2)3p transitions,the spectra show blue-shift at lower free electron densities and red-shift at higher free electron densities,and the energy level crossing phenomens are observed at higher free electron densities.
基金supported by the National Natural Science Foundation of China(Grant Nos.91436103,91536102,and 91336211)the Research Programme of National University of Defense Technology,China(Grant No.JC15-0203)the Strategic Priority Research Programme of the Chinese Academy of Sciences(Grant No.XDB21030300)
文摘Excitation energies, magnetic dipole, and electric quadrupole transition probabilities of the 3d ^2D3/2-3d ^2D5/2 transition in the potassium-like （K-like） sequence with 26 ≤ Z ≤ 36 are investigated by using the multi-configuration Dirac-Hartree-Fock （MCDHF） method. The contributions of the electron correlations, Breit interaction, and the leading-order quantum electrodynamic （QED） effects on the transition properties are analyzed. The present results are interested in the laboratory tokamak and the astronomical observations. Furthermore, the feasibility of these ions for the highly charged ion （HCI） clocks is discussed. Considering the wavelength of lasers and manipulation process of the atomic clocks, Cu^10＋ and Zn^11＋ are recommended as promising candidates with achievable quality factors at the 10^15 level.
文摘Interacting Boson Model-2(IBM-2)is used to determine the Hamiltonian for Er nuclei.Fit values of parameters are used to construct the Hamiltonian,energy levels and electromagnetic transitions(B(E2),B(M1))multipole mixing ratios(δ(E2/M1))for some even-even Er nuclei and monopole transition probability are estimated.New ideas are used for counting bosons number at N=64 and results are compared with previous works.
基金The National Natural Science Foundation of China(No.61573199)
文摘The descriptor Markovian jump systems( DMJSs)with partially unknown transition probabilities( PUTPs) are studied by means of variable structure control. First,by virtue of the strictly linear matrix inequality( LMI) technique,a sufficient condition is presented, under which the DMJSs subject to PUTPs are stochastically admissible. Secondly,a novel sliding surface function based on the system state and input is constructed for DMJSs subject to PUTPs; and a dynamic sliding mode controller is synthesized, which guarantees that state trajectories will reach the pre-specified sliding surface in finite time despite uncertainties and disturbances. The results indicate that by checking the feasibility of a series of LMIs,the stochastic admissibility of the overall closed loop system is determined. Finally,the validity of the theoretical results is illustrated with the example of the direct-current motor. Furthermore,compared with the existing literature,the state convergence rate,buffeting reduction and overshoot reduction are obviously optimized.
基金supported by the National Natural Science Foundation of China(Grant Nos.12072261 and 11872305)。
文摘The effects of stochastic perturbations and periodic excitations on the eutrophicated lake ecosystem are explored.Unlike the existing work in detecting early warning signals,this paper presents the most probable transition paths to characterize the regime shifts.The most probable transition paths are obtained by minimizing the Freidlin-Wentzell(FW)action functional and Onsager-Machlup(OM)action functional,respectively.The most probable path shows the movement trend of the lake eutrophication system under noise excitation,and describes the global transition behavior of the system.Under the excitation of Gaussian noise,the results show that the stability of the eutrophic state and the oligotrophic state has different results from two perspectives of potential well and the most probable transition paths.Under the excitation of Gaussian white noise and periodic force,we find that the transition occurs near the nearest distance between the stable periodic solution and the unstable periodic solution.
