Let f : I → I be a piecewise monotone interval map. The critical point set C(f) of f consists of all the preimages of its turning points. It is proved that the complex dynamical behaviors of f are all concentrated on...Let f : I → I be a piecewise monotone interval map. The critical point set C(f) of f consists of all the preimages of its turning points. It is proved that the complex dynamical behaviors of f are all concentrated on the derived set of C(f). f is asymptotically periodic if and only if the derived set of C(f) is countable.展开更多
We discuss formulas and techniques for finding maximum-likelihood estimators of parameters of autoregressive (with particular emphasis on Markov and Yule) models, computing their asymptotic variance-covariance matrix ...We discuss formulas and techniques for finding maximum-likelihood estimators of parameters of autoregressive (with particular emphasis on Markov and Yule) models, computing their asymptotic variance-covariance matrix and displaying the resulting confidence regions;Monte Carlo simulation is then used to establish the accuracy of the corresponding level of confidence. The results indicate that a direct application of the Central Limit Theorem yields errors too large to be acceptable;instead, we recommend using a technique based directly on the natural logarithm of the likelihood function, verifying its substantially higher accuracy. Our study is then extended to the case of estimating only a subset of a model’s parameters, when the remaining ones (called nuisance) are of no interest to us.展开更多
In this paper the existence of solutions of the singularly perturbed boundary valueproblems on infinite interval for the second order nonlinear equation containing a smallparameterε】0 :is examined,whereα_i,βare co...In this paper the existence of solutions of the singularly perturbed boundary valueproblems on infinite interval for the second order nonlinear equation containing a smallparameterε】0 :is examined,whereα_i,βare constants,and i=0,1 .Moreover,asymptoticestimates of the solutions for the above problems are given.展开更多
A neural-network-based robust control design is suggested for control of a class of nonlinear systems. The design ap- proach employs a neural network, whose activation functions satisfy the sector conditions, to appro...A neural-network-based robust control design is suggested for control of a class of nonlinear systems. The design ap- proach employs a neural network, whose activation functions satisfy the sector conditions, to approximate the nonlinear system. To improve the approximation performance and to account for the parameter perturbations during operation, a novel neural network model termed standard neural network model (SNNM) is proposed. If the uncertainty is bounded, the SNNM is called an interval SNNM (ISNNM). A state-feedback control law is designed for the nonlinear system modelled by an ISNNM such that the closed-loop system is globally, robustly, and asymptotically stable. The control design equations are shown to be a set of linear matrix inequalities (LMIs) that can be easily solved by available convex optimization algorithms. An example is given to illustrate the control design procedure, and the performance of the proposed approach is compared with that of a related method reported in literature.展开更多
For the following interval symmetric matricesG[B,C]={A│A=(a<sub>ij</sub>)<sub>n×n</sub>=A<sup>T</sup>,b<sub>ij</sub>≤a<sub>ij</sub>≤c<sub>ij<...For the following interval symmetric matricesG[B,C]={A│A=(a<sub>ij</sub>)<sub>n×n</sub>=A<sup>T</sup>,b<sub>ij</sub>≤a<sub>ij</sub>≤c<sub>ij</sub>},（1）B=(b<sub>ij</sub>)<sub>n×n</sub>=B<sup>T</sup>,C=(c<sub>ij</sub>)<sub>n×n</sub>=C<sup>T</sup>∈R<sup>n×n</sup>,Bialas has studied the necessary and sufficient condi-tion of asymptotic stabilty of G[B,C].According to refs[2-6],the following result,the asympotic stability of G[B,C],can be obtained if that of its subsetH[B,C]={A│A=(a<sub>ij</sub>)<sub>n×n</sub>∈G[B,C],a<sub>ij</sub>=b<sub>ij</sub> or c<sub>ij</sub>}. （2）展开更多
This paper concerns the asymptotic behaviors of the solutions to the initial-boundary value problem for scalar viscous conservations laws ut + f(u)x = uxx on [0, 1], with the boundary condition u(0, t) =u_,u(1,t) = u+...This paper concerns the asymptotic behaviors of the solutions to the initial-boundary value problem for scalar viscous conservations laws ut + f(u)x = uxx on [0, 1], with the boundary condition u(0, t) =u_,u(1,t) = u+ and the initial data u(x,O) = uo(x), where u-≠ u+ and f is a given function satisfying f″(u) :> 0 for u under consideration. By means of energy estimates method and under some more regular condi-tions on the initial data, both the global existence and the asymptotic behavior are obtained. When u_ < u+,which corresponds to rarefaction waves in inviscid conservation laws, no smallness conditions are needed. While for u_> u+, which corresponds to shock waves in inviscid conservation laws, it is established for weak shock waves, which means that |u_ - u+| is small. Moreover, exponential decay rates are both given.展开更多
基金This work is partially supported by the NSFC (No.60174048,70271076)
文摘Let f : I → I be a piecewise monotone interval map. The critical point set C(f) of f consists of all the preimages of its turning points. It is proved that the complex dynamical behaviors of f are all concentrated on the derived set of C(f). f is asymptotically periodic if and only if the derived set of C(f) is countable.
文摘We discuss formulas and techniques for finding maximum-likelihood estimators of parameters of autoregressive (with particular emphasis on Markov and Yule) models, computing their asymptotic variance-covariance matrix and displaying the resulting confidence regions;Monte Carlo simulation is then used to establish the accuracy of the corresponding level of confidence. The results indicate that a direct application of the Central Limit Theorem yields errors too large to be acceptable;instead, we recommend using a technique based directly on the natural logarithm of the likelihood function, verifying its substantially higher accuracy. Our study is then extended to the case of estimating only a subset of a model’s parameters, when the remaining ones (called nuisance) are of no interest to us.
文摘In this paper the existence of solutions of the singularly perturbed boundary valueproblems on infinite interval for the second order nonlinear equation containing a smallparameterε】0 :is examined,whereα_i,βare constants,and i=0,1 .Moreover,asymptoticestimates of the solutions for the above problems are given.
基金Project supported by the National Natural Science Foundation of China (No. 60504024), and Zhejiang Provincial Education Depart-ment (No. 20050905), China
文摘A neural-network-based robust control design is suggested for control of a class of nonlinear systems. The design ap- proach employs a neural network, whose activation functions satisfy the sector conditions, to approximate the nonlinear system. To improve the approximation performance and to account for the parameter perturbations during operation, a novel neural network model termed standard neural network model (SNNM) is proposed. If the uncertainty is bounded, the SNNM is called an interval SNNM (ISNNM). A state-feedback control law is designed for the nonlinear system modelled by an ISNNM such that the closed-loop system is globally, robustly, and asymptotically stable. The control design equations are shown to be a set of linear matrix inequalities (LMIs) that can be easily solved by available convex optimization algorithms. An example is given to illustrate the control design procedure, and the performance of the proposed approach is compared with that of a related method reported in literature.
文摘For the following interval symmetric matricesG[B,C]={A│A=(a<sub>ij</sub>)<sub>n×n</sub>=A<sup>T</sup>,b<sub>ij</sub>≤a<sub>ij</sub>≤c<sub>ij</sub>},（1）B=(b<sub>ij</sub>)<sub>n×n</sub>=B<sup>T</sup>,C=(c<sub>ij</sub>)<sub>n×n</sub>=C<sup>T</sup>∈R<sup>n×n</sup>,Bialas has studied the necessary and sufficient condi-tion of asymptotic stabilty of G[B,C].According to refs[2-6],the following result,the asympotic stability of G[B,C],can be obtained if that of its subsetH[B,C]={A│A=(a<sub>ij</sub>)<sub>n×n</sub>∈G[B,C],a<sub>ij</sub>=b<sub>ij</sub> or c<sub>ij</sub>}. （2）
基金Partially supported by the National Natural Sciences Foundation of China (No. 10101014), the Key Project of Natural Sciences Foundation of Beijing and Beijing Education Committee Foundation.Supported by the National Natural Science Foundation of China
文摘This paper concerns the asymptotic behaviors of the solutions to the initial-boundary value problem for scalar viscous conservations laws ut + f(u)x = uxx on [0, 1], with the boundary condition u(0, t) =u_,u(1,t) = u+ and the initial data u(x,O) = uo(x), where u-≠ u+ and f is a given function satisfying f″(u) :> 0 for u under consideration. By means of energy estimates method and under some more regular condi-tions on the initial data, both the global existence and the asymptotic behavior are obtained. When u_ < u+,which corresponds to rarefaction waves in inviscid conservation laws, no smallness conditions are needed. While for u_> u+, which corresponds to shock waves in inviscid conservation laws, it is established for weak shock waves, which means that |u_ - u+| is small. Moreover, exponential decay rates are both given.
