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Ambarzumyan's Theorem for the Dirac Operator on Equilateral Tree Graphs

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 568-576页

作者： Dong-Jie WU xin-jian xu Chuan-Fu YANG Department of Mathematics School of Mathematics and StatisticsNanjing University of Science and TechnologyNanjing 210094China

The classical Ambarzumyan’s theorem states that if the Neumann eigenvalues of the Sturm-Liouville operator-d^(2)/dx^(2)+q with an integrable real-valued potential q on[0,π] are {n^(2):n≥0},then q=0 for almost all x∈[0,π].In this work,the classical Ambarzumyan’s theorem is extended to the Dirac operator on equilateral tree *** prove that if the spectrum of the Dirac operator on graphs coincides with the unperturbed case,then the potential is identically zero.

关键词： dirac operator quantum graph Ambarzumyan’s theorem inverse spectral problem

Differential Evolution Based High-order Peak Filter Design with Application to Compensation of Contact-induced Vibration in HDD Servo Systems

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International Journal of Automation and computing 2017年第1期14卷 45-56页

作者： Deqing Huang jian-xin xu xin Deng Venkatakrishnan Venkataramanan The Cat Tuong Huynh Institute of Systems Science and Technology School of Electrical Engineering Southwest Jiaotong University Department of Electrical and Computer Engineering National University of Singapore Chongqing Key Laboratory of Computational Intelligence Chongqing University of Posts and Telecommunications Data Storage Institute Agency for Science Technology and Research

Sensitivity loop shaping using add-on peak filters is a simple and effective method to reject narrow-band disturbances in hard disk drive （HDD） servo systems. The parallel peak filter is introduced to provide high-gain magnitude in the concerned frequency range of open-loop transfer function. Different from almost all the known peak filters that possess second-order structures, we explore in this paper bow high-order peak filters can be designed to improve the loop shaping performance. The main idea is to replace some of the constant coefficients of common second-order peak filter by frequency-related transfer functions, and then differential evolution （DE） algorithm is adopted to perform optimal design. We creatively introduce chromosome coding and fitness function design, which are original and the key steps that lead to the success of DE applications in control system design. In other words, DE is modified to achieve a novel design for hard disk drive control. Owing to the remarkable searching ability of DE, the expected shape of sensitivity function can be achieved by incorporating the resultant high-order peak filter in parallel with baseline feedback controller. As a result, a seventh-order peak filter is designed to compensate for contact-induced vibration in a high-density HDD servo system, where the benefits of high-order filter are clearly demonstrated.

关键词： Differential evolution (DE) contact-induced vibration peak filter optimization sensitivity loop shaping hard disk drive(HDD).

Iterative Learning Control for Linear Systems with Markov Data Dropouts:Noise-free Case 36

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Iterative Learning Control for Linear Systems with Markov Da...

MODELING AND CONTROL DESIGN OF AN ANGUILLIFORM ROBOTIC FISH

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作者： Dong Shen jian-xin xu College of Information Science and Technology Beijing University of Chemical Technology Department of Electrical and Computer Engineering National University of Singapore

ISBN: (纸本)9781538629185

This paper contributes to the convergence analysis of iterative learning control(ILC) for a linear time-varying system with measurement data dropouts,where the data dropout problem is formulated by a Markov chain *** widely used Bernoulli model for data dropout is a special case of the Markov chain model.A regulating parameter is added to the classic P-type update *** mean square and almost sure convergence are strictly *** illustrative example is provided to verify the theoretical results.

关键词： Iterative Learning Control Data Dropouts Markov Chain

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International Journal of Modeling, Simulation, and Scientific Computing 2012年第4期3卷 91-114页

作者： jian-xin xu xuE-LEI NIU QIN-YUAN REN Department of Electrical and Computer Engineering National University of Singapore 117576Singapore

In this paper,the modeling and control design of a biomimetic robotic fish is *** Anguilliform robotic fish consists of N links and N−1 joints,and the driving forces are the torques applied to the *** kinematic constraints,Lagrangian formulation is used to obtain the dynamics of the fish *** computed torque control method is applied first,which can provide satisfactory tracking responses for fish *** this robotic fish is essentially an underactuated system,the reference trajectories for the orientation of the N links are planned in such a way that,at a neighborhood of the equilibrium point,the tracking task of N angles can be achieved by using N−1 joint *** deal with parameter uncertainties that exist in the actual environment,sliding mode control is *** feasibility and complexity issues,a simplified sliding mode control algorithm is given.A four-link robotic fish is modeled and simulated,and the results validate the effectiveness of reference planning and the proposed controllers.

关键词： Biomimetic robotic fish control algorithm design mathematical model.

Inverse problems for radial Schrodinger operators with the missing part of eigenvalues

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Science China Mathematics 2023年第8期66卷 1831-1848页

作者： xin-jian xu Chuan-Fu Yang Vjacheslav A.Yurko Ran Zhang Department of Mathematics School of Mathematics and StatisticsNanjing University of Science and TechnologyNanjing 210094China Department of Mathematics Saratov State UniversitySaratov 410012Russia Department of Mathematics School of ScienceNanjing University of Posts and TelecommunicationsNanjing 210023Chin

We study inverse spectral problems for radial Schrodinger operators in L^(2)(0,1).It is well known that for a radial Schrodinger operator,two spectra for the different boundary conditions can uniquely determine the ***,if the spectra corresponding to the radial Schrodinger operators with the two potential functions miss a finite number of eigenvalues,what is the relationship between the two potential functions?Inspired by Hochstadt(1973)'s work,which handled the Sturm-Liouville operator with the potential q∈L^(1)(0,1),we give a corresponding result for radial Schrodinger operators with a larger class of potentials than L^(1)(0,1).When q∈L^(1)(0,1),we also consider the case where the spectra corresponding to the radial Schrodinger operators with the two potential functions miss an infinite number of eigenvalues and the eigenvalues are close in some sense.

关键词： radial Schrodinger operator Bessel operator inverse spectral problem

Product Data Model for Performance-driven Design

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Chinese Journal of Mechanical Engineering 2017年第5期30卷 1112-1122页

作者： Guang-Zhong Hu xin-jian xu Shou-Ne Xiao Guang-Wu Yang Fan Pu School of Mechanical Engineering Sichuan University of Science and Engineering State Key Laboratory of Traction Power Southwest Jiaotong University

When designing large-sized complex machinery products, the design focus is always on the overall per- formance; however, there exist no design theory and method based on performance driven. In view of the defi- ciency of the existing design theory, according to the performance features of complex mechanical products, the performance indices are introduced into the traditional design theory of ＂Requirement-Function-Structure＂ to construct a new five-domain design theory of ＂Client Requirement-Function-Performance-Structure-Design Parameter＂. To support design practice based on this new theory, a product data model is established by using per- formance indices and the mapping relationship between them and the other four domains. When the product data model is applied to high-speed train design and combining the existing research result and relevant standards, the corresponding data model and its structure involving five domains of high-speed trains are established, which can provide technical support for studying the relationships between typical performance indices and design parame- ters and the fast achievement of a high-speed train scheme design. The five domains provide a reference for the design specification and evaluation criteria of high speed train and a new idea for the train＇s parameter design.

关键词： Complex product design Performance driven Data model Mapping relationship High-speed train

Vaccination of a multi-group model of zoonotic diseases with direct and indirect transmission

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International Journal of Biomathematics 2019年第6期12卷 119-146页

作者： Wei Lv xue-Ying Liu xin-jian xu Jie Lou Department of Mathematics Shanghai University Shanghai200444P.R.China Institute of Systems Science Shanghai University Shanghai 200444P.R.China

Vaccination plays an important role in preventing or reducing the spread of zoonotic *** this paper,we develop a susceptible-vaecinated-exposed-infectious-pathogen multi-group epidemic model of zoonotic diseases incorporating nonlinear direct and indi rect incidence rates,nonlinear pathogen shedding rates,and common environmental *** certain assumptions,we first obtained the basic reproduction number of the ***,we utilized the comparison principle and global Lyapunov function method to prove global stability of dynamical ***,we analyzed optimal vaccination *** the theoretical predictions were verified by numerical simulations.

关键词： Vaccination global stability optimal control zoonotic diseases.

A modified wire-loop snare technique for the retrieval of a large cardiac cement embolus caused by cement leakage after percutaneous vertebroplasty

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Journal of Interventional Medicine 2019年第1期2卷 38-41页

作者： Fei Teng xin jian xu Qiang Liu Department of Interventional Radiology Ningbo First Hospital.No 59Liu Ting StreetNingboZhejiang Province315000China Department of Radiology Shandong Medical Imaging Research Institute Affiliated to Shandong UniversityNo 324Warp 5 Weft 7 StreetHuaiyin DistrictJi'nanShandong Province250000China

Percutaneous vertebroplasty(PVP) is an interventional radiological procedure involving the injection of bone cement(polymethylmethacrylate) into a fractured vertebral body to remodel the vertebral body and relieve lum... 详细信息

关键词： technique cardiac cement

Ecological operation for Three Gorges Reservoir

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Water Science and Engineering 2011年第2期4卷 143-156页

作者： Wen-xian GUO Hong-xiang WANG jian-xin xu Zi-qiang XIA North China University of Water Conservancy and Electric Power Zhengzhou 450011 P. R. China State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering Hohai Univerxity Nanjing 210098 R R. China

The traditional operation of the Three Gorges Reservoir has mainly focused on water for flood control, power generation, navigation, water supply, and recreation, and given less attention to the negative impacts of reservoir operation on the river ecosystem. In order to reduce the negative influence of reservoir operation, ecological operation of the reservoir should be studied with a focus on maintaining a healthy river ecosystem. This study considered ecological operation targets, including maintaining the river environmental flow and protecting the spawning and reproduction of the Chinese sturgeon and four major Chinese carps. Using flow data from 1900 to 2006 at the Yichang gauging station as the control station data for the Yangtze River, the minimal and optimal river environmental flows were analyzed, and eco-hydrological targets for the Chinese sturgeon and four major Chinese carps in the Yangtze River were calculated. This paper proposes a reservoir ecological operation model, which comprehensively considers flood control, power generation, navigation, and the ecological environment. Three typical periods, wet, normal, and dry years, were selected, and the particle swarm optimization algorithm was used to analyze the model. The results show that ecological operation modes have different effects on the economic benefit of the hydropower station, and the reservoir ecological operation model can simulate the flood pulse for the requirements of spawning of the Chinese sturgeon and four major Chinese carps. According to the results, by adopting a suitable re-operation scheme, the hydropower benefit of the reservoir will not decrease dramatically while the ecological demand is met. The results provide a reference for designing reasonable operation schemes for the Three Gorges Reservoir.

关键词： ecological operation environmental flow Three Gorges Reservoir particle swarm optimization algorithm