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
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
Obstacle removal in crowd evacuation is critical to safety and the evacuation system efficiency. Recently, manyresearchers proposed game theoreticmodels to avoid and remove obstacles for crowd evacuation. Game theoret...Obstacle removal in crowd evacuation is critical to safety and the evacuation system efficiency. Recently, manyresearchers proposed game theoreticmodels to avoid and remove obstacles for crowd evacuation. Game theoreticalmodels aim to study and analyze the strategic behaviors of individuals within a crowd and their interactionsduring the evacuation. Game theoretical models have some limitations in the context of crowd evacuation. Thesemodels consider a group of individuals as homogeneous objects with the same goals, involve complex mathematicalformulation, and cannot model real-world scenarios such as panic, environmental information, crowds that movedynamically, etc. The proposed work presents a game theoretic model integrating an agent-based model to removethe obstacles from exits. The proposed model considered the parameters named: (1) obstacle size, length, andwidth, (2) removal time, (3) evacuation time, (4) crowd density, (5) obstacle identification, and (6) route selection.The proposed work conducts various experiments considering different conditions, such as obstacle types, obstacleremoval, and several obstacles. Evaluation results show the proposed model’s effectiveness compared with existingliterature in reducing the overall evacuation time, cell selection, and obstacle removal. The study is potentially usefulfor public safety situations such as emergency evacuations during disasters and calamities.展开更多
The octupole deformation and collectivity in octupole double-magic nucleus 144Ba are investigated using the Cranking covariant density functional theory in a three-dimensional lattice space.The reduced B(E3)transition...The octupole deformation and collectivity in octupole double-magic nucleus 144Ba are investigated using the Cranking covariant density functional theory in a three-dimensional lattice space.The reduced B(E3)transition probability is implemented for the first time in semiclassical approximation based on the microscopically calculated electric octupole moments.The available data,including the I-ωrelation and electric transitional probabilities B(E2)and B(E3)are well reproduced.Furthermore,it is shown that the ground state of 144Ba exhibits axial octupole and quadrupole deformations that persist up to high spins(I≈24h).展开更多
Background:Patients with type 2 diabetes are at high risk for developing multiple chronic complications.However,there is a lack of studies of the cumulative number of diabetic complications in China.Methods:A retrospe...Background:Patients with type 2 diabetes are at high risk for developing multiple chronic complications.However,there is a lack of studies of the cumulative number of diabetic complications in China.Methods:A retrospective cohort study was performed from 2009 to 2021.Type 2 diabetes patients who were first diagnosed after the age of 35 years between January 1,2009,and December 31,2017,were included.Five states were defined according to the number of chronic complications:no(S0),one(S1),two(S2),three(S3),and four or more complications(S4).A multi-state Markov model was constructed to estimate transition probability,transition intensity,mean sojourn time,and the possible factors for each state.Results:The study included 32653 type 2 diabetes patients(mean age,59.59 years;15929(48.8%)male),and mean follow-up time of 7.75 years.In all,4375 transitions were observed.The 12-year transition probability of from state S0 to S1 was the lowest at 16.4%,while that from S2 to S3 was the highest,at 45.6%.Higher fasting blood glucose,lower high-density lipoprotein cholesterol,higher total cholesterol,and an unhealthy diet were associated with higher risk of progression from S0 to S1.Being female,less than 60 years old,weekly physical activity,and vegetarian diet decreased this risk.Being female and less than 60 years old reduced the likelihood of transition from S1 to S2,whereas lower high-density lipoprotein cholesterol increased this likelihood.Conclusions:Following the occurrence of two complications in type 2 diabetes patients,the risk for accumulating a third complication within a short time is significantly increased.It is important to take advantage of the stable window period when patients have fewer than two complications,strengthen the monitoring of blood glucose and blood lipids,and encourage patients to maintain good living habits to prevent further deterioration.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
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
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
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
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
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
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
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
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 multipole mixing ratios have been calculated by a2-ratio method, from levels of 93Mo(p, nγ) reaction. The branching ratios of such γ-transitions are used to calculate the total gamma widths. Besides, the trans...The multipole mixing ratios have been calculated by a2-ratio method, from levels of 93Mo(p, nγ) reaction. The branching ratios of such γ-transitions are used to calculate the total gamma widths. Besides, the transition strengths and probabilities have been calculated for γ-transitions from excited states whose life times have been reported previously. The results are found to be in general in good agreement with the previous results populated from the previous work.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
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.
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.
文摘Obstacle removal in crowd evacuation is critical to safety and the evacuation system efficiency. Recently, manyresearchers proposed game theoreticmodels to avoid and remove obstacles for crowd evacuation. Game theoreticalmodels aim to study and analyze the strategic behaviors of individuals within a crowd and their interactionsduring the evacuation. Game theoretical models have some limitations in the context of crowd evacuation. Thesemodels consider a group of individuals as homogeneous objects with the same goals, involve complex mathematicalformulation, and cannot model real-world scenarios such as panic, environmental information, crowds that movedynamically, etc. The proposed work presents a game theoretic model integrating an agent-based model to removethe obstacles from exits. The proposed model considered the parameters named: (1) obstacle size, length, andwidth, (2) removal time, (3) evacuation time, (4) crowd density, (5) obstacle identification, and (6) route selection.The proposed work conducts various experiments considering different conditions, such as obstacle types, obstacleremoval, and several obstacles. Evaluation results show the proposed model’s effectiveness compared with existingliterature in reducing the overall evacuation time, cell selection, and obstacle removal. The study is potentially usefulfor public safety situations such as emergency evacuations during disasters and calamities.
基金supported by the National Natural Science Foundation of China(NSFC)(No.12205097)the Fundamental Research Funds for the Central Universities(No.2024MS071)。
文摘The octupole deformation and collectivity in octupole double-magic nucleus 144Ba are investigated using the Cranking covariant density functional theory in a three-dimensional lattice space.The reduced B(E3)transition probability is implemented for the first time in semiclassical approximation based on the microscopically calculated electric octupole moments.The available data,including the I-ωrelation and electric transitional probabilities B(E2)and B(E3)are well reproduced.Furthermore,it is shown that the ground state of 144Ba exhibits axial octupole and quadrupole deformations that persist up to high spins(I≈24h).
基金supported by the National Natural Science Foundation of China(grant No.72074011)the Real World Study Project of Hainan Boao Lecheng Pilot Zone(Real World Study Base of NMPA)(HNLC2022RWS012)+1 种基金the fundamental research funds for central public welfare research institutes(2023CZ-11)National Natural Science Foundation of China(No.82003536).
文摘Background:Patients with type 2 diabetes are at high risk for developing multiple chronic complications.However,there is a lack of studies of the cumulative number of diabetic complications in China.Methods:A retrospective cohort study was performed from 2009 to 2021.Type 2 diabetes patients who were first diagnosed after the age of 35 years between January 1,2009,and December 31,2017,were included.Five states were defined according to the number of chronic complications:no(S0),one(S1),two(S2),three(S3),and four or more complications(S4).A multi-state Markov model was constructed to estimate transition probability,transition intensity,mean sojourn time,and the possible factors for each state.Results:The study included 32653 type 2 diabetes patients(mean age,59.59 years;15929(48.8%)male),and mean follow-up time of 7.75 years.In all,4375 transitions were observed.The 12-year transition probability of from state S0 to S1 was the lowest at 16.4%,while that from S2 to S3 was the highest,at 45.6%.Higher fasting blood glucose,lower high-density lipoprotein cholesterol,higher total cholesterol,and an unhealthy diet were associated with higher risk of progression from S0 to S1.Being female,less than 60 years old,weekly physical activity,and vegetarian diet decreased this risk.Being female and less than 60 years old reduced the likelihood of transition from S1 to S2,whereas lower high-density lipoprotein cholesterol increased this likelihood.Conclusions:Following the occurrence of two complications in type 2 diabetes patients,the risk for accumulating a third complication within a short time is significantly increased.It is important to take advantage of the stable window period when patients have fewer than two complications,strengthen the monitoring of blood glucose and blood lipids,and encourage patients to maintain good living habits to prevent further deterioration.
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.
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.
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.
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.
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.
文摘The multipole mixing ratios have been calculated by a2-ratio method, from levels of 93Mo(p, nγ) reaction. The branching ratios of such γ-transitions are used to calculate the total gamma widths. Besides, the transition strengths and probabilities have been calculated for γ-transitions from excited states whose life times have been reported previously. The results are found to be in general in good agreement with the previous results populated from the previous work.
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.