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
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 time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems...In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.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
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 paper, we derive the exact analytical expressions of the transition probabilities among the Fock states of an ion in a harmonic trap due to the presence of an alternating electric field.
On the basis of the unified calculation of the thermal shifts of R1 line, R2 line and ground-state-splitting transition probabilities of direct and Raman processes have theoretically been calculated. The thermal broad...On the basis of the unified calculation of the thermal shifts of R1 line, R2 line and ground-state-splitting transition probabilities of direct and Raman processes have theoretically been calculated. The thermal broadenings of R,The theoretically predicted transition probabilities are in good agreement with the experimental ones.PACS numbers: 71.70.Ch, 78.20.Nv, 63.20.Mt, 63.20.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
Energy levels, oscillator strengths, and transition probabilities, for the 1s2 2s2 2p6, 2p53l (l = 0, 1, 2), 2p54l (l = 0, 1, 2, 3) states in Ni XIX and Cu XX are calculated using COWAN code. The Correlation and relat...Energy levels, oscillator strengths, and transition probabilities, for the 1s2 2s2 2p6, 2p53l (l = 0, 1, 2), 2p54l (l = 0, 1, 2, 3) states in Ni XIX and Cu XX are calculated using COWAN code. The Correlation and relativistic effects are considered. The calculations are compared with other results in the literature. A good agreement is found. We also report on some unpublished energy values.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
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
The method of Zeng et al. (1991) employed diameter growth to estimate the transition probability of the matrix model in uneven-aged forest stands. In this paper the Weibull distribution for even-aged forest stands ins...The method of Zeng et al. (1991) employed diameter growth to estimate the transition probability of the matrix model in uneven-aged forest stands. In this paper the Weibull distribution for even-aged forest stands instead of uniform distribution chosen by Zeng is used. By comparing the results of the improved method with those of the original method of Zeng, it turns out that the improved method of Zeng given in this paper is more efficient.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
Recent developments in the measurement of radioactive gases in passive diffusion motivate the analysis of Brownian motion of decaying particles, a subject that has received little previous attention. This paper report...Recent developments in the measurement of radioactive gases in passive diffusion motivate the analysis of Brownian motion of decaying particles, a subject that has received little previous attention. This paper reports the derivation and solution of equations comparable to the Fokker-Planck and Langevin equations for one-dimensional diffusion and decay of unstable particles. In marked contrast to the case of stable particles, the two equations are not equivalent, but provide different information regarding the same stochastic process. The differences arise because Brownian motion with particle decay is not a continuous process. The discontinuity is readily apparent in the computer-simulated trajectories of the Langevin equation that incorporate both a Wiener process for displacement fluctuations and a Bernoulli process for random decay. This paper also reports the derivation of the mean time of first passage of the decaying particle to absorbing boundaries. Here, too, particle decay can lead to an outcome markedly different from that for stable particles. In particular, the first-passage time of the decaying particle is always finite, whereas the time for a stable particle to reach a single absorbing boundary is theoretically infinite due to the heavy tail of the inverse Gaussian density. The methodology developed in this paper should prove useful in the investigation of radioactive gases, aerosols of radioactive atoms, dust particles to which adhere radioactive ions, as well as diffusing gases and liquids of unstable molecules.展开更多
In this contribution results from different disciplines of science were compared to show their intimate interweaving with each other having in common the golden ratio <i><span style="font-family:Verdana;...In this contribution results from different disciplines of science were compared to show their intimate interweaving with each other having in common the golden ratio <i><span style="font-family:Verdana;">φ</span></i><span style="font-family:Verdana;"> respectively its fifth power </span><i><span style="font-family:Verdana;">φ</span></i><sup><span style="font-family:Verdana;">5</span></sup><span style="font-family:Verdana;">. The research fields cover model calculations of statistical physics associated with phase transitions, the quantum probability of two particles, new physics of everything suggested by the information relativity theory (</span><i><span style="font-family:Verdana;">IRT</span></i><span style="font-family:Verdana;">) including explanations of cosmological relevance, the </span><i><span style="font-family:Verdana;">ε</span></i><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;">infinity theory, superconductivity, and the </span><i><span style="font-family:Verdana;">Tammes</span></i><span style="font-family:Verdana;"> problem of the largest diameter of </span><i><span style="font-family:Verdana;">N</span></i><span style="font-family:Verdana;"> non-overlapping circles on the surface of a sphere with its connection to viral morphology and crystallography. Finally, </span><i><span style="font-family:Verdana;">Fibo</span><span style="font-family:Verdana;">nacci</span></i><span style="font-family:Verdana;"> anyons proposed for topological quantum</span><span style="font-family:Verdana;"> computation (</span><i><span style="font-family:Verdana;">TQC</span></i><span style="font-family:Verdana;">) were briefly described in comparison to the recently formulated reverse </span><i><span style="font-family:Verdana;">Fibonacci</span></i><span style="font-family:Verdana;"> approach using the </span><span style="font-family:Verdana;"><em>Jani</em></span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="white-space:nowrap;"><em>č</em></span><em>ko</em></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> number sequence. An architecture applicable for a quantum computer is proposed consisting of 13-step twisted microtubules similar to tubulin microtubules of living matter. Most topics point to the omnipresence of the golden mean as the numerical dominator of our world.</span></span></span>展开更多
In real systems,the unpredictable jump changes of the random environment can induce the critical transitions(CTs)between two non-adjacent states,which are more catastrophic.Taking an asymmetric Lévy-noise-induced...In real systems,the unpredictable jump changes of the random environment can induce the critical transitions(CTs)between two non-adjacent states,which are more catastrophic.Taking an asymmetric Lévy-noise-induced tri-stable model with desirable,sub-desirable,and undesirable states as a prototype class of real systems,a prediction of the noise-induced CTs from the desirable state directly to the undesirable one is carried out.We first calculate the region that the current state of the given model is absorbed into the undesirable state based on the escape probability,which is named as the absorbed region.Then,a new concept of the parameter dependent basin of the unsafe regime(PDBUR)under the asymmetric Lévy noise is introduced.It is an efficient tool for approximately quantifying the ranges of the parameters,where the noise-induced CTs from the desirable state directly to the undesirable one may occur.More importantly,it may provide theoretical guidance for us to adopt some measures to avert a noise-induced catastrophic CT.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
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.
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partially supported by the National Natural Science Foundation of China(52375238)Science and Technology Program of Guangzhou(202201020213,202201020193,202201010399)GZHU-HKUST Joint Research Fund(YH202109).
文摘In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.
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 paper, we derive the exact analytical expressions of the transition probabilities among the Fock states of an ion in a harmonic trap due to the presence of an alternating electric field.
文摘On the basis of the unified calculation of the thermal shifts of R1 line, R2 line and ground-state-splitting transition probabilities of direct and Raman processes have theoretically been calculated. The thermal broadenings of R,The theoretically predicted transition probabilities are in good agreement with the experimental ones.PACS numbers: 71.70.Ch, 78.20.Nv, 63.20.Mt, 63.20.
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.
文摘Energy levels, oscillator strengths, and transition probabilities, for the 1s2 2s2 2p6, 2p53l (l = 0, 1, 2), 2p54l (l = 0, 1, 2, 3) states in Ni XIX and Cu XX are calculated using COWAN code. The Correlation and relativistic effects are considered. The calculations are compared with other results in the literature. A good agreement is found. We also report on some unpublished energy values.
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This paper was supported by the National Natural Science Foundation of China
文摘The method of Zeng et al. (1991) employed diameter growth to estimate the transition probability of the matrix model in uneven-aged forest stands. In this paper the Weibull distribution for even-aged forest stands instead of uniform distribution chosen by Zeng is used. By comparing the results of the improved method with those of the original method of Zeng, it turns out that the improved method of Zeng given in this paper is more efficient.
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Recent developments in the measurement of radioactive gases in passive diffusion motivate the analysis of Brownian motion of decaying particles, a subject that has received little previous attention. This paper reports the derivation and solution of equations comparable to the Fokker-Planck and Langevin equations for one-dimensional diffusion and decay of unstable particles. In marked contrast to the case of stable particles, the two equations are not equivalent, but provide different information regarding the same stochastic process. The differences arise because Brownian motion with particle decay is not a continuous process. The discontinuity is readily apparent in the computer-simulated trajectories of the Langevin equation that incorporate both a Wiener process for displacement fluctuations and a Bernoulli process for random decay. This paper also reports the derivation of the mean time of first passage of the decaying particle to absorbing boundaries. Here, too, particle decay can lead to an outcome markedly different from that for stable particles. In particular, the first-passage time of the decaying particle is always finite, whereas the time for a stable particle to reach a single absorbing boundary is theoretically infinite due to the heavy tail of the inverse Gaussian density. The methodology developed in this paper should prove useful in the investigation of radioactive gases, aerosols of radioactive atoms, dust particles to which adhere radioactive ions, as well as diffusing gases and liquids of unstable molecules.
文摘In this contribution results from different disciplines of science were compared to show their intimate interweaving with each other having in common the golden ratio <i><span style="font-family:Verdana;">φ</span></i><span style="font-family:Verdana;"> respectively its fifth power </span><i><span style="font-family:Verdana;">φ</span></i><sup><span style="font-family:Verdana;">5</span></sup><span style="font-family:Verdana;">. The research fields cover model calculations of statistical physics associated with phase transitions, the quantum probability of two particles, new physics of everything suggested by the information relativity theory (</span><i><span style="font-family:Verdana;">IRT</span></i><span style="font-family:Verdana;">) including explanations of cosmological relevance, the </span><i><span style="font-family:Verdana;">ε</span></i><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span><span><span style="font-family:;" "=""><span style="font-family:Verdana;">infinity theory, superconductivity, and the </span><i><span style="font-family:Verdana;">Tammes</span></i><span style="font-family:Verdana;"> problem of the largest diameter of </span><i><span style="font-family:Verdana;">N</span></i><span style="font-family:Verdana;"> non-overlapping circles on the surface of a sphere with its connection to viral morphology and crystallography. Finally, </span><i><span style="font-family:Verdana;">Fibo</span><span style="font-family:Verdana;">nacci</span></i><span style="font-family:Verdana;"> anyons proposed for topological quantum</span><span style="font-family:Verdana;"> computation (</span><i><span style="font-family:Verdana;">TQC</span></i><span style="font-family:Verdana;">) were briefly described in comparison to the recently formulated reverse </span><i><span style="font-family:Verdana;">Fibonacci</span></i><span style="font-family:Verdana;"> approach using the </span><span style="font-family:Verdana;"><em>Jani</em></span></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="white-space:nowrap;"><em>č</em></span><em>ko</em></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> number sequence. An architecture applicable for a quantum computer is proposed consisting of 13-step twisted microtubules similar to tubulin microtubules of living matter. Most topics point to the omnipresence of the golden mean as the numerical dominator of our world.</span></span></span>
基金Project supported by the National Natural Science Foundation of China(No.12072264)the Fundamental Research Funds for the Central Universities+3 种基金the Research Funds for Interdisciplinary Subject of Northwestern Polytechnical Universitythe Shaanxi Project for Distinguished Young Scholarsthe National Key Research and Development Program of China(No.2018AAA0102201)the Shaanxi Provincial Key R&D Program(Nos.2020KW-013 and 2019TD-010)。
文摘In real systems,the unpredictable jump changes of the random environment can induce the critical transitions(CTs)between two non-adjacent states,which are more catastrophic.Taking an asymmetric Lévy-noise-induced tri-stable model with desirable,sub-desirable,and undesirable states as a prototype class of real systems,a prediction of the noise-induced CTs from the desirable state directly to the undesirable one is carried out.We first calculate the region that the current state of the given model is absorbed into the undesirable state based on the escape probability,which is named as the absorbed region.Then,a new concept of the parameter dependent basin of the unsafe regime(PDBUR)under the asymmetric Lévy noise is introduced.It is an efficient tool for approximately quantifying the ranges of the parameters,where the noise-induced CTs from the desirable state directly to the undesirable one may occur.More importantly,it may provide theoretical guidance for us to adopt some measures to avert a noise-induced catastrophic CT.
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.