CSpace中国科学院数学与系统科学研究院http://ir.amss.ac.cn:802020-11-25T11:52:58Z2020-11-25T11:52:58ZOn the cycles of components of disconnected Julia setsCui, GuizhenPeng, Wenjuanhttp://ir.amss.ac.cn:80/handle/2S8OKBNM/521092020-11-18T05:04:06Z2020-11-18T05:04:06ZTitle: On the cycles of components of disconnected Julia sets
Authors: Cui, Guizhen; Peng, Wenjuan
Description: For any integers d >= 3 and n >= 1, we construct a hyperbolic rational map of degree d such that it has n cycles of the connected components of its Julia set except single points and Jordan curves.2020-11-18T05:04:06ZPositive and sign-changing least energy solutions for a fractional Schrodinger-Poisson system with critical exponentYu, YuanyangZhao, FukunZhao, Leigahttp://ir.amss.ac.cn:80/handle/2S8OKBNM/521032020-11-18T05:04:05Z2020-11-18T05:04:05ZTitle: Positive and sign-changing least energy solutions for a fractional Schrodinger-Poisson system with critical exponent
Authors: Yu, Yuanyang; Zhao, Fukun; Zhao, Leiga
Description: In this paper, we study the following fractional Schrodinger-Poisson system
(-Delta)(s)u+u+K(x)phi u = h(x)|u|(p-2)u+|u|(2s*-2)u,in R-3,
(-Delta)(t)phi=K(x)u(2),in R3,
where s is an element of(3/4,1),t is an element of(0,1)are two fixed constants, 2(s)*:=6/(3-2s)is the fractional critical exponent in dimension 3. Under some certain assumptions on non-negative functions K(x) and h(x), we obtain the existence of a positive and a sign-changing least energy solution for (FSP)via variational methods. Moreover, we show that the energy of the sign-changing least solution is strictly larger than twice of the least energy.2020-11-18T05:04:05Z3D tamed Navier-Stokes equations driven by multiplicative Levy noise: Existence, uniqueness and large deviationsDong, ZhaoZhang, Rangranghttp://ir.amss.ac.cn:80/handle/2S8OKBNM/521062020-11-18T05:04:05Z2020-11-18T05:04:05ZTitle: 3D tamed Navier-Stokes equations driven by multiplicative Levy noise: Existence, uniqueness and large deviations
Authors: Dong, Zhao; Zhang, Rangrang
Description: In this paper, we show the existence and uniqueness of a strong solution to stochastic 3D tamed Navier-Stokes equations driven by multiplicative Levy noise with periodic boundary conditions. Then we establish the large deviation principles of the strong solution on the state space D([0, T]; H-1), where the weak convergence approach plays a key role. (C) 2020 Elsevier Inc. All rights reserved.2020-11-18T05:04:05ZA new 6th-order WENO scheme with modified stencilsWang, YahuiDu, YulongZhao, KunleiYuan, Lihttp://ir.amss.ac.cn:80/handle/2S8OKBNM/520972020-11-18T05:04:04Z2020-11-18T05:04:04ZTitle: A new 6th-order WENO scheme with modified stencils
Authors: Wang, Yahui; Du, Yulong; Zhao, Kunlei; Yuan, Li
Description: In this article, a new 6th order weighted essentially non-oscillatory (WENO) scheme is developed. As with previous 6th-order central-upwind WENO schemes, the present scheme is a convex combination of four candidate linear reconstructions. The difference is that the most upwind and downwind stencils use four cell values, while the inner two stencils nominally use three cell values but the original quadratic reconstructions are modified to be 4th-order approximations by adding cubic correction terms involving the five cell values of the classical 5th-order WENO scheme. Sixth-order accuracy of the new scheme in smooth regions including critical points is achieved by using a reference smoothness indicator. Several numerical examples show that the new scheme has higher resolution compared with the recently developed 6th-order WENO schemes. (C) 2020 Elsevier Ltd. All rights reserved.2020-11-18T05:04:04ZOPTIMAL CONTROL OF NONLINEAR STOCHASTIC DIFFERENTIAL EQUATIONS ON HILBERT SPACESBarbu, ViorelRockner, MichaelZhang, Denghttp://ir.amss.ac.cn:80/handle/2S8OKBNM/521002020-11-18T05:04:04Z2020-11-18T05:04:04ZTitle: OPTIMAL CONTROL OF NONLINEAR STOCHASTIC DIFFERENTIAL EQUATIONS ON HILBERT SPACES
Authors: Barbu, Viorel; Rockner, Michael; Zhang, Deng
Description: We here consider optimal control problems governed by nonlinear stochastic equations on a Hilbert space H with nonconvex payoff, which is rewritten as a deterministic optimal control problem governed by a Kolmogorov equation in H. We prove the existence and first-order necessary condition of closed-loop optimal controls for the above control problem. The strategy is based on solving a deterministic bilinear optimal control problem for the corresponding Kolmogorov equation on the space L-2 (H, nu), where nu is the related infinitesimally invariant measure for the Kolmogorov operator.2020-11-18T05:04:04ZGlobal well-posedness of 3-D anisotropic Navier-Stokes system with large vertical viscous coefficientLiu, YanlinZhang, Pinghttp://ir.amss.ac.cn:80/handle/2S8OKBNM/520942020-11-18T05:04:04Z2020-11-18T05:04:04ZTitle: Global well-posedness of 3-D anisotropic Navier-Stokes system with large vertical viscous coefficient
Authors: Liu, Yanlin; Zhang, Ping
Description: In this paper, we first prove the global well-posedness of 3-D anisotropic Navier-Stokes system provided that the vertical viscous coefficient of the system is sufficiently large compared to some critical norm of the initial data. Then we shall construct a family of initial data, u(0,nu) which vary fast enough in the vertical variable and which can be arbitrarily large in the space BMO-1. Yet u(0,nu) still generates a unique global solution to the classical 3-D Navier-Stokes system provided that nu is sufficiently large. (C) 2020 Elsevier Inc. All rights reserved.2020-11-18T05:04:04ZNetwork flows that solve least squares for linear equationsLiu, YangLou, YouchengAnderson, Brian D. O.Shi, Guodonghttp://ir.amss.ac.cn:80/handle/2S8OKBNM/520882020-11-18T05:04:03Z2020-11-18T05:04:03ZTitle: Network flows that solve least squares for linear equations
Authors: Liu, Yang; Lou, Youcheng; Anderson, Brian D. O.; Shi, Guodong
Description: This paper presents a first-order distributed continuous-time algorithm for computing the least-squares solution to a linear equation over networks. Given the uniqueness of the solution, with nonintegrable and diminishing step size, convergence results are provided for fixed graphs. The exact rate of convergence is also established for various types of step size choices falling into that category. For the case where non-unique solutions exist, convergence to one such solution is proved for constantly connected switching graphs with square integrable step size. Validation of the results and illustration of the impact of step size on the convergence speed are made using a few numerical examples. (C) 2020 Elsevier Ltd. All rights reserved.2020-11-18T05:04:03ZPeriodic Points and Normality Concerning Meromorphic Functions with MultiplicityDeng, BingmaoFang, MingliangWang, Yuefeihttp://ir.amss.ac.cn:80/handle/2S8OKBNM/520912020-11-18T05:04:03Z2020-11-18T05:04:03ZTitle: Periodic Points and Normality Concerning Meromorphic Functions with Multiplicity
Authors: Deng, Bingmao; Fang, Mingliang; Wang, Yuefei
Description: In this article, two results concerning the periodic points and normality of meromorphic functions are obtained: (i) the exact lower bound for the numbers of periodic points of rational functions with multiple fixed points and zeros is proven by lettingR(z) be a non-polynomial rational function, and if all zeros and poles ofR(z) -zare multiple, thenR(k)(z) has at leastk+ 1 fixed points in the complex plane for each integerk >= 2; (ii) a complete solution to the problem of normality of meromorphic functions with periodic points is given by letting F be a family of meromorphic functions in a domainD, and lettingk >= 2 be a positive integer. If, for eachf is an element of F, all zeros and poles off(z) -zare multiple, and its iterationf(k)has at mostkdistinct fixed points inD, then F is normal inD. Examples show that all of the conditions are the best possible.2020-11-18T05:04:03ZExtended State Filter Based Disturbance and Uncertainty Mitigation for Nonlinear Uncertain Systems With Application to Fuel Cell Temperature ControlXue, WenchaoZhang, XiaochengSun, LiFang, Haitaohttp://ir.amss.ac.cn:80/handle/2S8OKBNM/520792020-11-18T05:04:02Z2020-11-18T05:04:02ZTitle: Extended State Filter Based Disturbance and Uncertainty Mitigation for Nonlinear Uncertain Systems With Application to Fuel Cell Temperature Control
Authors: Xue, Wenchao; Zhang, Xiaocheng; Sun, Li; Fang, Haitao
Description: The filter design for nonlinear uncertain systems is quite challenging since efficient estimation is required against stochastic noises, nonlinear uncertain dynamics as well as their concurrent effects. To this end, this article develops a novel filter algorithm by augmenting the disturbance as well as unknown nonlinear dynamics as an extended state and constructing consistent Kalman-Bucy algorithm. The proposed extended state based Kalman-Bucy filter (KBF) is shown to be of bounded estimation error, and the estimation accuracy can be online evaluated. More importantly, the estimation of asymptotic minimum variance is realized in condition that the changing rate of uncertainty approaches to zero. Therefore, the proposed extended state filter enables effective mitigation of disturbance and unknown nonlinear dynamics in real time by feedback control. The proposed algorithm is experimentally verified via a temperature control application in proton exchange membrane fuel cell, in which the thermocouple noise and the electrochemical uncertainty are seriously presented. The temperature variation of the extended state based KBF-based control is greatly reduced, in comparison with the conventional control. The results in this article depict a promising prospect of the proposed method for industrial control applications to handle both noises and nonlinear uncertain dynamics.2020-11-18T05:04:02ZA Laguerre spectral method for quadratic optimal control of nonlinear systems in a semi-infinite intervalMasoumnezhad, MojtabaSaeedi, MohammadhosseinYu, HaijunNik, Hassan Saberihttp://ir.amss.ac.cn:80/handle/2S8OKBNM/520852020-11-18T05:04:02Z2020-11-18T05:04:02ZTitle: A Laguerre spectral method for quadratic optimal control of nonlinear systems in a semi-infinite interval
Authors: Masoumnezhad, Mojtaba; Saeedi, Mohammadhossein; Yu, Haijun; Nik, Hassan Saberi
Description: This paper presents a Laguerre homotopy method for quadratic optimal control problems in semi-infinite intervals (LaHOC), with particular interests given to nonlinear interconnected largescale dynamic systems. In LaHOC, the spectral homotopy analysis method is used to derive an iterative solver for the nonlinear two-point boundary value problem derived from Pontryagin's maximum principle. A proof of local convergence of the LaHOC is provided. Numerical comparisons are made between the LaHOC, Matlab BVP5C generated results and results from the literature for two nonlinear optimal control problems. The results show that LaHOC is superior in both accuracy and efficiency.2020-11-18T05:04:02Z