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A DISCONTINUOUS GALERKIN METHOD BY PATCH RECONSTRUCTION FOR BIHARMONIC PROBLEM

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Journal of Computational Mathematics 2019年第4期37卷 524-540页

作者： Ruo Li Pingbing Ming Zhiyuan Sun Fanyi Yang Zhijian Yang CAPT LMAM and School of Mathematical Sciences Peking University Beijing 100871 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing 100190 China School of mathematical Sciences University of Chinese Academy of Sciences No. 19A Yu-Quan Road Beijing 100049 China School of mathematical Sciences Peking University Beijing 100871 China School of Mathematics and. Statistics Wuhan University Wuhan 430072 China

We propose a new discontinuous Galerkin method based on the least-squares patch reconstruction for the biharmonic problem. We prove the optimal error estimate of the proposed method. The two-dimensional and three-dimensional numerical examples are presented to confirm the accuracy and efficiency of the method with several boundary conditions and several types of polygon meshes and polyhedral meshes.

关键词： Least-squares problem Reconstructed basis function Discontinuous Galerkin method Biharmonic problem

Markov Processes and Related Topics(Ⅲ)

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Frontiers of Mathematics in China 2021年第2期16卷 255-256页

作者： Wenming HONG Yonghua MAO Yuhui ZHANG Research Center for Stochastics School of Mathematical SciencesBeijing Normal UniversityBeijing 100875China

It is our great pleasure to present the third special issue for the Markov Processes and Related Topics,on the occasion of the 20th anniversary of the Research Center for Stochastics of Beijing Normal University(BNU),supported by the innovative research group project of the National Natural Science Foundation of *** 2002,the Research Center for Stochastics started toorganize'Workshop on Markov Processes and Related Topics'.During the past 20 years,the workshop held almost each year except some special situations(for example,2003 SARS and 2020 COVID-19).Among the 16 workshops,11 of them were or will be co-organized with some universities out of Beijing。

关键词： China. Markov workshop

A parameter formula connecting PID and ADRC

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Science China(Information Sciences) 2020年第9期63卷 175-187页

作者： Sheng ZHONG Yi HUANG Lei GUO Key Laboratory of Systems and Control Academy of Mathematics and Systems ScienceChinese Academy of Sciences School of mathematical Sciences University of Chinese Academy of Sciences

This paper presents a parameter formula connecting the well-known proportional-integralderivative(PID) control and the active disturbance rejection control(ADRC). On the one hand, this formula gives a quantitative lower bound to the bandwidth of the extended state observer(ESO) used in ADRC,implying that the ESO is not necessarily of high gain. On the other hand, enlightened by the design of ADRC, a new PID tuning rule is provided, which can guarantee both strong robustness and nice tracking performance of the closed-loop systems under the PID control. Moreover, it is proved that the ESO can be rewritten as a suitable linear combination of the three terms in PID, which can give a better estimate for the system uncertainty than the single integral term in the PID controller. Theoretical results are verified also by simulations in the paper.

关键词： nonlinear uncertain systems proportional-integral-derivative PID active disturbance rejection control ADRC extended state observer ESO

On a Strongly Damped Wave Equation for the Flame Front

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Chinese Annals of Mathematics,Series B 2010年第6期31卷 819-840页

作者： Claude-Michel BRAUNER Luca LORENZI Gregory I. SIVASHINSKY Chuanju XU School of mathematical Sciences Xiamen University 361005 Xiamen Fujian China Dipartimento di Matematica Università degli Studi di Parma Viale Parco Area delle Scienze 53/A 43124 Parma Italy School of mathematical Sciences Tel Aviv University 69978 Tel Aviv Israel

In two-dimensional free-interface problems, the front dynamics can be modeled by single parabolic equations such as the Kuramoto-Sivashinsky equation (K-S). However, away from the stability threshold, the structure of the front equation may be more involved. In this paper, a generalized K-S equation, a nonlinear wave equation with a strong damping operator, is considered. As a consequence, the associated semigroup turns out to be analytic. Asymptotic convergence to K-S is shown, while numerical results illustrate the dynamics.

关键词：阻尼波动方程非线性波动方程火焰抛物型方程界面问题堪萨斯州 KS方程渐近收敛

Big Earth Data:a new challenge and opportunity for Digital Earth’s development

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International Journal of Digital Earth 2017年第1期10卷 1-12页

作者： Huadong Guo Zhen Liu Hao Jiang Changlin Wang Jie Liu Dong Liang Institute of Remote Sensing and Digital Earth Chinese Academy of SciencesBeijingPeople’s Republic of China International society for Digital Earth

Digital Earth has seen great progress during the last 19 *** it entered into the era of big data,Digital Earth developed into a new stage,namely one characterized by‘Big Earth Data’,confronting new challenges and *** this paper we give an overview of the development of Digital Earth by summarizing research achievements and marking the milestones of Digital Earth’s ***,the opportunities and challenges that Big Earth Data faces are *** a data-intensive scientific research approach,Big Earth Data provides a new vision and methodology to Earth sciences,and the paper identifies the advantages of Big Earth Data to scientific research,especially in knowledge discovery and global change *** believe that Big Earth Data will advance and promote the development of Digital Earth.

关键词： Digital Earth Big Earth Data data-intensive science knowledge discovery global change

Distributed Secondary Control and Optimal Power Sharing in Microgrids

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IEEE/CAA Journal of Automatica Sinica 2015年第3期2卷 304-312页

作者： Gang Chen Ening Feng the Key Laboratory of Dependable Service Computing in Cyber Physical society of Ministry of Education and the College of Automation Chongqing University

We address the control problem of microgrids and present a fully distributed control system which consists of primary controller,secondary controller,and optimal active power sharing *** from the existing control structure in microgrids,all these controllers are implemented as local controllers at each distributed ***,the requirement for a central controller is *** performance analysis of the proposed control systems is provided,and the finite-time convergence properties for distributed secondary frequency and voltage controllers are ***,the distributed control system possesses the optimal active power sharing *** the end,a microgrid test system is investigated to validate the effectiveness of the proposed control strategies.

关键词： Microgrid droop control distributed control optimal control

On Blocks in Restricted Representations of Lie Superalgebras of Cartan Type

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Acta Mathematica Sinica,English Series 2020年第9期36卷 1061-1075页

作者： Fei Fei DUAN Bin SHU Yu Feng YAO School of mathematical Sciences Hebei Normal UniversityShijiazhuang 050024P.R.China School of mathematical Sciences East China Normal UniversityShanghai 200241P.R.China Department of Mathematics Shanghai Maritime UniversityShanghai 201306P.R.China

Let g be a restricted Lie superalgebra of Cartan type W(n),S(n)or H(n)over an alge-braically closed field k of prime characteristic p>3,in the sense of modular version of Kac's definition in *** this note,we show that the restricted representation category over g has only one block(reckoning parities in).This phenomenon is very diff erent from the case of characteristic zero.

关键词： Lie superalgebra of Cartan type restricted representation block

Resonances in Electron Impact on Atomic Oxygen

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Chinese Physics Letters 2008年第6期25卷 2027-2029页

作者：王旸周雅君焦利光 Kuru Ratnavelu Institute of Atomic and Molecular Physics Jilin University Changchun 130012 Institute of mathematical Sciences University of Malaya 50603 Kuala Lumpur Malaysia

The momentum-space coupled-channels-optical （CCO） method is used to study the resonances in electron oxygen collision in the energy region of 9-12 eV, Present results have shown agreement with the available experime... 详细信息

关键词： supernova explosion proto-neutron star shock wave

Tsallis relativeαentropy of coherence dynamics in Grover′s search algorithm

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Communications in Theoretical Physics 2023年第8期75卷 87-99页

作者： Linlin Ye Zhaoqi Wu Shao-Ming Fei Department of Mathematics Nanchang UniversityNanchang 330031China School of mathematical Sciences Capital Normal UniversityBeijing 100048China

Quantum coherence plays a central role in Grover’s search *** study the Tsallis relative a entropy of coherence dynamics of the evolved state in Grover’s search *** prove that the Tsallis relative a entropy of coherence decreases with the increase of the success probability,and derive the complementarity relations between the coherence and the success *** show that the operator coherence of the first H■relies on the size of the database N,the success probability and the target ***,we illustrate the relationships between coherence and entanglement of the superposition state of targets,as well as the production and deletion of coherence in Grover iterations.

关键词： quantum coherence Grover's search algorithm Tsallis relativeαentropy of coherence