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Generalized Derivations with Periodic Values

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Algebra Colloquium 2015年第1期22卷 163-168页

作者： Kun-shan liu Department of Mathematics National Taiwan University Taipei 106 Taiwan

Let R be a prime ring and n 〉 1 be a fixed positive integer. If g is a nonzero generalized derivation of R such that g（x）n = g（x） for all x ∈ R, then R is commutative except when R is a subring of the 2 × 2 matrix ring over a field. Moreover, we generalize the result to the case g（f（xi））n = g（f（xi）） for all xl,x2,...,xt ∈ R, where f（Xi） is a multilinear polynomial.

关键词： prime ring PI GPI (generalized) derivation

Approximation Theorems and Fixed Point Theorems for Various Classes of 1-set-contractive Mappings in Banach Spaces

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Acta Mathematica Sinica,English Series 2001年第1期17卷 103-112页

作者： Li shan liu Department of Mathematics Qufu Normal University

In this paper, we will prove that Ky Fan’s Theorem (Math. Z. 112(1969), 234-240) is true for 1-set-contractive maps defined on a bounded closed convex subset K in a Banach space with int K≠ . This class of 1-set-contractive maps includes condensing maps, nonexpansive maps, semicontractive maps, LANE maps and others. As applications of our theorems, some fixed point theorems of non-self- maps are proved under various well-known boundary conditions. Our results are generalizations and improvements of the recent results obtained by many authors.

关键词： Approximation theorems Fixed point theorems 1-set-contractive maps Semicontractive maps LANE maps

Iterative Learning Control for Flexible Manipulator Using Fourier Basis Function

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International Journal of Automation and computing 2015年第6期12卷 639-647页

作者： Li Zhang shan liu College of Control Science and Engineering Zhejiang University

Perfect tracking of the tip position of a flexible-link manipulator(FLM) is unable to be achieved by causal control because it is a typical non-minimum phase system. Combined with non-causal stable inversion, an adaptive iterative learning control scheme based on Fourier basis function is presented for the tip trajectory tracking of FLM performing repetitive tasks. In this method,an iterative identification algorithm is used to construct the Fourier basis function space model of the manipulator, and a pseudoinverse type iterative learning law is designed to approximate the stable inversion of the non-minimum phase system, which guarantees the convergence and robustness of the control system. Simulation results show the performance and effectiveness of the proposed scheme.

关键词： Flexible-link manipulator(FLM) non-minimum phase s

A generalized trajectory tracking controller for robot manipulators with bounded inputs

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2009年第10期10卷 1500-1508页

作者： Hua-shan liu Shi-qiang ZHU State Key Lab of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

A generalized controller based on stability theory of singularly perturbed systems is proposed,to deal with the problem of bounded actuator inputs in robot trajectory tracking *** saturation function with error-gain matrix is applied in the torque control law,which ensures the upper bound of torque inputs in any given limited *** appropriately setting the entries of the error-gain matrix,the tracking performance can be ***,a pseudo signal is generated from a linear filter to substitute for the actual velocity error,eliminating the need for velocity ***,to verify the ef-fectiveness of the generalized controller,a new saturated controller with error-gain-contained arc tangent function is *** experiments show that the proposed controller can strictly guarantee the bound of the torque inputs in situations with non-zero initial tracking errors,and gives a better tracking result than other controllers.

关键词： Robot Tracking control Singular perturbation Bounded input

An R(x)-orthonormal theory for the vibration performance of a non-smooth symmetric composite beam with complex interface

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Acta Mechanica Sinica 2019年第1期35卷 228-241,I0007页

作者： Chein-shan liu Bo-Tong Li College of Mechanics and Materials Hohai UniversityNanjing 210098China Center of Excellence for Ocean Engineering Department of Mechanical and Mechatronic EngineeringTaiwan Ocean UniversityKeelung 202-24China School of Mathematics and Physics University of Science and Technology BeijingBeijing 100083China

A composite beam is symmetric if both the material property and support are symmetric with respect to the middle point. In order to study the free vibration performance of the symmetric composite beams with different complex nonsmooth/discontinuous interfaces, we develop an R(x)-orthonormal theory, where R(x) is an integrable flexural rigidity function. The R(x)-orthonormal bases in the linear space of boundary functions are constructed, of which the second-order derivatives of the boundary functions are asked to be orthonormal with respect to the weight function R(x). When the vibration modes of the symmetric composite beam are expressed in terms of the R(x)-orthonormal bases we can derive an eigenvalue problem endowed with a special structure of the coefficient matrix A :=[aij ],aij= 0 if i + j is odd. Based on the special structure we can prove two new theorems, which indicate that the characteristic equation of A can be decomposed into the product of the characteristic equations of two sub-matrices with dimensions half lower. Hence, we can sequentially solve the natural frequencies in closed-form owing to the specialty of A. We use this powerful new theory to analyze the free vibration performance and the vibration modes of symmetric composite beams with three different interfaces.

关键词： Symmetric composite beams R(x)-orthogonality of second-order derivatives of boundary functions R(x)-orthonormal theory Non-smooth/discontinuous interface Sequentially closed-from natural frequencies

Impact of the Time Scale of Model Sensitivity Response on Coupled Model Parameter Estimation

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Advances in Atmospheric Sciences 2017年第11期34卷 1346-1357页

作者： chang liu shaoqing zhang shan li zhengyu liu Center for Climate Research and Department of Atmospheric and Oceanic Sciences University of Wisconsin -- Madison Madison W153706 USA

That a model has sensitivity responses to parameter uncertainties is a key concept in implementing model parameter es- timation using filtering theory and methodology. Depending on the nature of associated physics and characteristic variability of the fluid in a coupled system, the response time scales of a model to parameters can be different, from hourly to decadal. Unlike state estimation, where the update frequency is usually linked with observational frequency, the update frequency for parameter estimation must be associated with the time scale of the model sensitivity response to the parameter being esti- mated. Here, with a simple coupled model, the impact of model sensitivity response time scales on coupled model parameter estimation is studied. The model includes characteristic synoptic to decadal scales by coupling a long-term varying deep ocean with a slow-varying upper ocean forced by a chaotic atmosphere. Results show that, using the update frequency deter- mined by the model sensitivity response time scale, both the reliability and quality of parameter estimation can be improved significantly, and thus the estimated parameters make the model more consistent with the observation. These simple model results provide a guideline for when real observations are used to optimize the parameters in a coupled general circulation model for improving climate analysis and prediction initialization.

关键词： coupled model parameter estimation time scale of model sensitivity

Lithium Isotopic Fractionation in Minerals from Pegmatites:Perspective of Crystal Chemistry

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Journal of Earth Science 2024年第6期35卷 1895-1901页

作者： shan-Ke liu Ben-Xun Su Key Laboratory of Mineral Resources Institute of Geology and GeophysicsChinese Academy of SciencesBeijing100029China

Lack of information regarding lithium(Li)crystal chemistry in numerous minerals,especially those containing trace amounts of Li(ranging from a few to tens of ppm),limits our understanding of Li isotopic fractionation in *** this study,we examined the Li isotopic composition and Li content in various Li-poor(e.g.,quartz or feldspar)together with Li-rich(sopdumene or lepidolite)mineral phases within granitic *** compiled a comprehensive dataset,encompassing a broad spectrum of Li contents(ranging from a few to tens of thousands of ppm)and Li isotopic values(-8‰to 41‰).The minerals exhibit distinct Li isotopic ***,elbaite and beryl show the highest values,while biotite displays a negative *** to individual minerals,whole rocks demonstrate lower Li isotopic values,with pegmatites exhibiting the highest and non-granitic pegmatite wall rocks showing the *** study also uncovers a clear“V”shape relationship between Li isotopic values and logarithm of Li contents,with different mineral groups occupying specific regions within this ***,a significant correlation was observed between average Li isotopic values and Li-O(OH,F)bond lengths in various *** discoveries underscore the crucial role of crystal chemistry in shaping the Li isotopic behavior in pegmatites from a statistical perspective.

关键词： Li isotopic fractionation Li content bond length pegmatite crystal chemistry minerals

Impedance Analysis Considering Unstable Subsystem Poles for MMC-HVDC-based Wind Farm Integration System

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CSEE Journal of Power and Energy Systems 2022年第2期8卷 634-639页

作者： Ke Ji Hui Pang shan liu Guangfu Tang China Electric Power Research Institute Beijing100192China Global Energy Interconnection Research Institute Beijing 102211China

Employing the AC/DC impedance analysis method,extensive research has been conducted on issues pertaining to harmonic resonance observed in wind farm-connected MMCHVDC systems over the past 5 *** general,this method divides the studied system into two subsystems at AC and DC ***,the impedance produced by these subsystems can be used to determine the system stability by implementing Nyquist criterion or generalized Nyquist stability ***,the existing impedance analysis methods usually assume the subsystems to be stable and disregard certain special cases with potentially unstable subsystems,where the unstable poles of these subsystems must be evaluated before applying Nyquist *** view of this consideration,a simplified method for identifying unstable subsystem poles is presented in this ***,the shortcoming of existing impedance analyses is rectified by considering the unstable subsystem *** proposed method and the stability analyses are validated by the electromagnetic transient simulation performed in PSCAD/EMTDC.

关键词： AC/DC side impedance method harmonic resonance MMC-HVDC small-signal stability wind farm

Impedance Analysis of Grid Forming Control Based Modular Multilevel Converters

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Journal of Modern Power Systems and Clean Energy 2023年第3期11卷 967-979页

作者： Rongcai Pan Guangfu Tang shan liu Zhiyuan He China Electric Power Research Institute Beijing 100192China State Grid Smart Grid Research Institute Beijing 102209China

Grid-forming control(GFC)is promising for power electronics based power systems with high renewable energy ***,the impedance modeling for GFC is necessary and has gained significant attention ***,most of the impedance analyses for GFC are based on a twolevel converter(TLC)rather than a modular multilevel converter(MMC).MMC differs from TLC with respect to its dominant multi-frequency *** is necessary to analyze the impedance of GFC-based MMC owing to its superiority in highvoltage direct current(HVDC)transmission to interlink two weak AC systems with high renewable energy *** the main contribution,this paper presents the AC-and DC-side impedance analyses for the GFC-based MMC with both power and DC voltage control using the harmonic transfer function(HTF),and compares the impedances of GFC-based MMC and *** is inferred that although the impedance is mainly influenced within 200 Hz,the instability still could occur owing to negative resistance triggered by relatively larger *** difference in AC-side impedance with power and DC voltage control is not apparent with proper parameters,while the DC-side impedance differs *** generalized Nyquist criterion is necessary for AC-side stability owing to the relatively large coupling terms under ***,the coupling between AC-and DC-side impedances is noneligible,especially considering the DC-side resonance around the system resonant *** effects of parameters,system strength,and virtual impedance on the impedance shaping are analyzed and verified through simulations.

关键词： Sequence impedance modular multilevel converter(MMC) grid-forming control(GFC) harmonic transfer function generalized Nyquist criterion