The empirical Bayes test problem is considered for scale parameter of twoparameter exponential distribution under type-II censored data.By using wavelets estimation method,the EB test function is constructed,of which ...The empirical Bayes test problem is considered for scale parameter of twoparameter exponential distribution under type-II censored data.By using wavelets estimation method,the EB test function is constructed,of which the asymptotic optimality and convergence rates are obtained.Finally,an example concerning the main result is given.展开更多
This paper concernes analysis for the global exponential stability of a class of recurrent neural networks with mixed discrete and distributed delays. It first proves the existence and uniqueness of the balance point,...This paper concernes analysis for the global exponential stability of a class of recurrent neural networks with mixed discrete and distributed delays. It first proves the existence and uniqueness of the balance point, then by employing the Lyapunov-Krasovskii functional and Young inequality, it gives the sufficient condition of global exponential stability of cellular neural network with mixed discrete and distributed delays, in addition, the example is provided to illustrate the applicability of the result.展开更多
For a collective system,the connectedness of the adjacency matrix plays a key role in making the system achieve its emergent feature,such as flocking or multi-clustering.In this paper,we study a nonsymmetric multi-par...For a collective system,the connectedness of the adjacency matrix plays a key role in making the system achieve its emergent feature,such as flocking or multi-clustering.In this paper,we study a nonsymmetric multi-particle system with a constant and local cut-off weight.A distributed communication delay is also introduced into both the velocity adjoint term and the cut-off weight.As a new observation,we show that the desired multi-particle system undergoes both flocking and clustering behaviors when the eigenvalue 1 of the adjacency matrix is semi-simple.In this case,the adjacency matrix may lose the connectedness.In particular,the number of clusters is discussed by using subspace analysis.In terms of results,for both the non-critical and general neighbourhood situations,some criteria of flocking and clustering emergence with an exponential convergent rate are established by the standard matrix analysis for when the delay is free.As a distributed delay is involved,the corresponding criteria are also found,and these small time lags do not change the emergent properties qualitatively,but alter the final value in a nonlinear way.Consequently,some previous works[14]are extended.展开更多
Nuclear charge density distribution plays an important role in both nuclear and atomic physics,for which the two-parameter Fermi(2pF)model has been widely applied as one of the most frequently used models.Currently,th...Nuclear charge density distribution plays an important role in both nuclear and atomic physics,for which the two-parameter Fermi(2pF)model has been widely applied as one of the most frequently used models.Currently,the feedforward neural network has been employed to study the available 2pF model parameters for 86 nuclei,and the accuracy and precision of the parameter-learning effect are improved by introducing A^(1∕3)into the input parameter of the neural network.Furthermore,the average result of multiple predictions is more reliable than the best result of a single prediction and there is no significant difference between the average result of the density and parameter values for the average charge density distribution.In addition,the 2pF parameters of 284(near)stable nuclei are predicted in this study,which provides a reference for the experiment.展开更多
The global exponentially stability was studied for time-delay and time-varying measure large scale systems with impulsive effects. Firstly, the concepts are drawn for the functional category. Secondly, some sufficient...The global exponentially stability was studied for time-delay and time-varying measure large scale systems with impulsive effects. Firstly, the concepts are drawn for the functional category. Secondly, some sufficient conditions of the uniformly stability and the global exponentially stability are given for the above systems through defining a Lyapunov function of the weighting sum of the variable absolute by using the Lyapunov function method and the comparison principle. At the same time, the new conclusion of stability of these systems is more universal and contains the existing results. Finally, an example is given to illustrate the feasibility and validity of the obtained results.展开更多
The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim ...The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim amount distribution is a finite mixture of exponential distributions or a Gamma (2, α) distribution.展开更多
The question of the power-law exponent of exponential growth networks is studied here.In a discrete case,the degree distribution is defined as the probability distribution of the discrete variable.Based on this,the de...The question of the power-law exponent of exponential growth networks is studied here.In a discrete case,the degree distribution is defined as the probability distribution of the discrete variable.Based on this,the degree distribution of the pseudofractal scale-free web,an exponential growth network,is obtained.The power-law exponent ln3/ln2 is analyzed according to the maximum likelihood principle.It satisfies consistency and is good for small generations of the network.For many exponential growth networks,their power-law exponent needs to be tested.The work provides a new view on the power-law exponent of an exponential growth network.展开更多
This paper is on a distribution question of Ⅰ type in the combinatorics (see: 'Ke Zhao, Wei WanDi, combinatorial theory, science press, 1981. '). Suppose n distrinct balls, m distinct boxes. The capacity set...This paper is on a distribution question of Ⅰ type in the combinatorics (see: 'Ke Zhao, Wei WanDi, combinatorial theory, science press, 1981. '). Suppose n distrinct balls, m distinct boxes. The capacity set of every box is Now,place the n balls into the m boxes. Thenumber of distinct placed ways is expressed by , and simply by And it is called the distribution number.Main result is:Theorem The exponential generating function of sequence isThus .there is the recurrence relationhere (integer set).展开更多
In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction ...In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction principle are adjusted to ensure the existence as well as the uniqueness of the pseudo almost periodic solution, which is also its derivative pseudo almost periodic. This results are without resorting to the theory of exponential dichotomy. Furthermore, by employing the suitable Lyapunov function, some delayindependent sufficient conditions are derived for exponential convergence. The main originality lies in the fact that spaces considered in this paper generalize the notion of periodicity and almost periodicity. Lastly, two examples are given to demonstrate the validity of the proposed theoretical results.展开更多
The dispersion of Langmuir wave(LW)in an unmagnetized collisionless plasma with regularized Kappa distributed electrons is investigated from the kinetic theory.The frequency and damping rate of LW are analyzed for the...The dispersion of Langmuir wave(LW)in an unmagnetized collisionless plasma with regularized Kappa distributed electrons is investigated from the kinetic theory.The frequency and damping rate of LW are analyzed for the parameters relating to the source region of a typeⅢsolar radio burst.It is found that the linear behavior of LW is greatly modified by the suprathermal indexκand the exponential cutoff parameterα.In the regionκ<1.5,the damping rate of LW will be much larger than the one with Maxwellian distributed electrons.Hence,the nonlinear process of LW in lowκregion may exhibit different properties in comparison with the one in largeκregion.展开更多
基金Supported by the NNSF of China（70471057）Supported by the Natural Science Foundation of the Education Department of Shannxi Province（03JK065）
文摘The empirical Bayes test problem is considered for scale parameter of twoparameter exponential distribution under type-II censored data.By using wavelets estimation method,the EB test function is constructed,of which the asymptotic optimality and convergence rates are obtained.Finally,an example concerning the main result is given.
基金Project supported by the National Natural Science Foundations of China(Grant No.70871056)the Society Science Foundation from Ministry of Education of China(Grant No.08JA790057)the Advanced Talents'Foundation and Student's Foundation of Jiangsu University,China(Grant Nos.07JDG054 and 07A075)
文摘This paper concernes analysis for the global exponential stability of a class of recurrent neural networks with mixed discrete and distributed delays. It first proves the existence and uniqueness of the balance point, then by employing the Lyapunov-Krasovskii functional and Young inequality, it gives the sufficient condition of global exponential stability of cellular neural network with mixed discrete and distributed delays, in addition, the example is provided to illustrate the applicability of the result.
基金supported by the National Natural Science Foundation of China(11671011).
文摘For a collective system,the connectedness of the adjacency matrix plays a key role in making the system achieve its emergent feature,such as flocking or multi-clustering.In this paper,we study a nonsymmetric multi-particle system with a constant and local cut-off weight.A distributed communication delay is also introduced into both the velocity adjoint term and the cut-off weight.As a new observation,we show that the desired multi-particle system undergoes both flocking and clustering behaviors when the eigenvalue 1 of the adjacency matrix is semi-simple.In this case,the adjacency matrix may lose the connectedness.In particular,the number of clusters is discussed by using subspace analysis.In terms of results,for both the non-critical and general neighbourhood situations,some criteria of flocking and clustering emergence with an exponential convergent rate are established by the standard matrix analysis for when the delay is free.As a distributed delay is involved,the corresponding criteria are also found,and these small time lags do not change the emergent properties qualitatively,but alter the final value in a nonlinear way.Consequently,some previous works[14]are extended.
基金supported by the Natural Science Foundation of Jilin Province (No. 20220101017JC)the National Natural Science Foundation of China (Nos. 11675063, 11875070, and 11935001)+1 种基金Key Laboratory of Nuclear Data foundation (JCKY2020201C157)the Anhui Project (Z010118169)
文摘Nuclear charge density distribution plays an important role in both nuclear and atomic physics,for which the two-parameter Fermi(2pF)model has been widely applied as one of the most frequently used models.Currently,the feedforward neural network has been employed to study the available 2pF model parameters for 86 nuclei,and the accuracy and precision of the parameter-learning effect are improved by introducing A^(1∕3)into the input parameter of the neural network.Furthermore,the average result of multiple predictions is more reliable than the best result of a single prediction and there is no significant difference between the average result of the density and parameter values for the average charge density distribution.In addition,the 2pF parameters of 284(near)stable nuclei are predicted in this study,which provides a reference for the experiment.
基金Project (60674020) supported by the National Natural Science Foundation of ChinaProject (Z2006G11) supported by Specialized Natural Science Fund of Shandong Province,China
文摘The global exponentially stability was studied for time-delay and time-varying measure large scale systems with impulsive effects. Firstly, the concepts are drawn for the functional category. Secondly, some sufficient conditions of the uniformly stability and the global exponentially stability are given for the above systems through defining a Lyapunov function of the weighting sum of the variable absolute by using the Lyapunov function method and the comparison principle. At the same time, the new conclusion of stability of these systems is more universal and contains the existing results. Finally, an example is given to illustrate the feasibility and validity of the obtained results.
文摘The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim amount distribution is a finite mixture of exponential distributions or a Gamma (2, α) distribution.
基金Supported by the National Natural Science Foundation of China under Grant No 10774035the Foundation of Inner Mongolia University of Technology under Grant No X200937.
文摘The question of the power-law exponent of exponential growth networks is studied here.In a discrete case,the degree distribution is defined as the probability distribution of the discrete variable.Based on this,the degree distribution of the pseudofractal scale-free web,an exponential growth network,is obtained.The power-law exponent ln3/ln2 is analyzed according to the maximum likelihood principle.It satisfies consistency and is good for small generations of the network.For many exponential growth networks,their power-law exponent needs to be tested.The work provides a new view on the power-law exponent of an exponential growth network.
文摘This paper is on a distribution question of Ⅰ type in the combinatorics (see: 'Ke Zhao, Wei WanDi, combinatorial theory, science press, 1981. '). Suppose n distrinct balls, m distinct boxes. The capacity set of every box is Now,place the n balls into the m boxes. Thenumber of distinct placed ways is expressed by , and simply by And it is called the distribution number.Main result is:Theorem The exponential generating function of sequence isThus .there is the recurrence relationhere (integer set).
文摘In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction principle are adjusted to ensure the existence as well as the uniqueness of the pseudo almost periodic solution, which is also its derivative pseudo almost periodic. This results are without resorting to the theory of exponential dichotomy. Furthermore, by employing the suitable Lyapunov function, some delayindependent sufficient conditions are derived for exponential convergence. The main originality lies in the fact that spaces considered in this paper generalize the notion of periodicity and almost periodicity. Lastly, two examples are given to demonstrate the validity of the proposed theoretical results.
文摘The dispersion of Langmuir wave(LW)in an unmagnetized collisionless plasma with regularized Kappa distributed electrons is investigated from the kinetic theory.The frequency and damping rate of LW are analyzed for the parameters relating to the source region of a typeⅢsolar radio burst.It is found that the linear behavior of LW is greatly modified by the suprathermal indexκand the exponential cutoff parameterα.In the regionκ<1.5,the damping rate of LW will be much larger than the one with Maxwellian distributed electrons.Hence,the nonlinear process of LW in lowκregion may exhibit different properties in comparison with the one in largeκregion.
基金supported by the National Natural Science Foundation of China(Grant No.72161009)the Natural Science Foundation of Hainan Province of China(Grant Nos.122MS057,124MS055).
