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Brake Orbits of a Reversible Even Hamiltonian System Near an Equilibrium

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Acta Mathematica Sinica,English Series 2022年第1期38卷 263-280页

作者： Zhong Jie LIU Fan Jing WANG duan zhi zhang School of Science Tianjin Chengjian UniversityTianjin 300384P.R.China School of Mathematics and Statistics Shanghai Lixin University of Accounting and FinanceShanghai 201209P.R.China School of Mathematical Sciences and LPMC Nankai UniversityTianjin 300071P.R.China

In this paper,we consider the brake orbits of a reversible even Hamiltonian system near an *** the Hamiltonian system(H S)x=J H(x)satisfies H(0)=0,H(0)=0,reversible and even conditions H(Nx)=H(x)and H(-x)=H(x)for all x∈R^(2n).Suppose the quadratic form Q(x)=1/2 is ***τ_(0)>0 and assume that R^(2n)=E⊕F decomposes into linear subspaces E and F which are invariant under the flow associated to the linear system x=J H''(0)x and such that each solution of the above linear system in E isτ_(0)-periodic whereas no solution in F{0}isτ_(0)-***σ(τ_(0))=σ_Q(τ_(0))for the signature of Q|***σ(τ_(0))≠=0,we prove that either there exists a sequence of brake orbits x_k→0 withτk-periodic on the hypersurface H^(-1)(0)whereτ_k→τ_(0);or for eachλclose to 0 withλ_(σ)(τ_(0))>0 the hypersurface H-1(λ)contains at least 1/2|σ(τ_(0))|distinct brake orbits of the Hamiltonian system(HS)near 0 with periods nearτ_(0).Such result for periodic solutions was proved by Bartsch in 1997.

关键词： Brake orbits reversible Hamiltonian systems equilibrium even length and Conley index

Remote-controlled module-assisted synthesis of O-(2-[^(18)F]fluoroethyl)-L-tyrosine as tumor PET tracer using two different radiochemical routes

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Nuclear Science and Techniques 2006年第3期17卷 148-153页

作者： WANG Ming-Wei YIN duan-zhi zhang Lan ZHOU Wei WANG Yong-Xian Radiopharmaceutical Centre Shanghai Institute of Applied Physics the Chinese Academy of Sciences Shanghai 201800 China

The positron-emitter fluorine-18 labeled amino acid O-(2-[18F]fluoroethyl)-L-tyrosine ([18F]FET) has shown very promising perspectives for brain tumor diagnosis with positron emission tomography (PET). There have been two existing preparation routes of [18F]FET named direct nucleophilic radiofluorination of protected L-tyrosine and radiofluoroalkylation of unprotected L-tyrosine, respectively. A general module was designed specifically for the routine synthesis of [18F]FET, which could be suitable for the present two chemical methods with simple modifica- tions. The fluorinated intermediates and the final product were separated and purified using solid phase extraction (SPE) on the Sep-Pak silica plus cartridge instead of the time-consuming high performance liquid chromatography (HPLC) procedures. The total synthesis time was about 50—60 min with good radiochemical yield (about 20—40%, no-decay-corrected) and good radiochemical purity (more than 97%) for both the synthetic methods.

关键词： PET 氟化作用合成模块正电子发射亲质子

Maslov-type index and brake orbits in nonlinear Hamiltonian systems

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Science China Mathematics 2007年第6期50卷 761-772页

作者： duan-zhi zhang School of Mathematical Sciences, Peking University, Beijing 100871, China School of Mathematical Sciences Peking University Beijing China

In this paper, we study the Maslov-type index theory for linear Hamiltonian systems with brake orbits boundary value conditions and its applications to the existence of multiple brake orbits of nonlinear Hamiltonian s... 详细信息

关键词： brake orbit Maslov-type index relative Morse index dual variational method 58E05 70H05 34C25

Stabilization Controller of An Extended Chained Nonholonomic System With Disturbance:An FAS Approach

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IEEE/CAA Journal of Automatica Sinica 2024年第5期11卷 1262-1273页

作者： Zhongcai zhang Guangren duan School of Engineering Qufu Normal UniversityRizhao 276826China Center for Control Science and Technology Southern University of Science and TechnologyShenzhen 518055 Center for Control Theory and Guidance Technology Harbin Institute of TechnologyHarbin 150001China

This study examines the stabilization issue of extended chained nonholonomic systems(ECNSs)with external *** the existing approaches,we transform the considered system into a fully actuated system(FAS)model,simplifying the stabilizing controller *** implement a separate controller design and propose exponential stabilization controller and finite-time stabilization controller under finite-time disturbance observer(FTDO)for the two system *** addition,we discuss the specifics of global stabilization control *** approach demonstrates that two system states exponentially or asymptotically converge to zero under the provided switching stabilization control strategy,while all other system states converge to zero within a finite time.

关键词： design stabilization system

Distributed velocity-free formation tracking control for clustered UAVs under virtual leader-follower framework

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Science China(Technological Sciences) 2024年第5期67卷 1538-1552页

作者： zhang ZhaoYu duan HaiBin School of Automation Science and Electrical Engineering Beihang UniversityBeijing100083China

The collective formation control problem of a cluster of rotorcraft unmanned aerial vehicles(UAVs)is investigated in this *** consensus tracking towards formation centroid with following UAVs forming a predefined configuration around the leader is considered as the *** prior studies,the information of the central reference trajectory,which is deemed as a virtual leader in the leader-follower topology,is not directly accessible for partial nodes through the communication ***,a novel distributed formation tracking control scheme is ***,a decentralized saturation observer is employed to estimate the reference acceleration signal of the virtual *** the absence of linear velocity measurement,two sliding manifolds are proposed by introducing the relative discrepancy terms of position and *** a smooth saturation operator in the form of a sigmoid function is applied to generate the command force ***,under the dilemma of constrained capabilities of the airborne sensors equipped on the rotorcrafts,the angular velocity is difficult to *** cascaded auxiliary attitude error systems are established on each rotorcraft system to synthesize the rotating torque with no need to require the angular velocity *** to the strong coupling and nonlinearity of the rotorcraft UAV system,the command angular velocity and the derivatives of command input are hard to *** a continuous nonlinear differentiator is proposed to work with the difficulties in deriving the explicit expression of system ***,a detailed stability analysis is conducted progressively on the angular control loop,reference trajectory observer loop,and the position control loop.A simulation scheme for a cluster of four rotorcraft UAVs tracking sinusoidal trajectory are presented and the formation control results are proven advantageous in comparison with the control protocol in previous literature.

关键词： distributed formation control unmanned rotorcraft clusters velocity-free tracking nonlinear differentiator

Super-resolution diffractive neural network for alloptical direction of arrival estimation beyond diffraction limits

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Light(Science & Applications) 2024年第8期13卷 1602-1614页

作者： Sheng Gao Hang Chen Yichen Wang Zhengyang duan Haiou zhang zhi Sun Yuan Shen Xing Lin Department of Electronic Engineering Tsinghua UniversityBeijing 100084China Beijing National Research Center for Information Science and Technology Tsinghua UniversityBeijing 100084China

Wireless sensing of the wave propagation direction from radio sources lays the foundation for communication,radar,navigation,***,the existing signal processing paradigm for the direction of arrival estimation requires the radio frequency electronic circuit to demodulate and sample the multichannel baseband signals followed by a complicated computing process,which places the fundamental limit on its sensing speed and energy ***,we propose the super-resolution diffractive neural networks(S-DNN)to process electromagnetic(EM)waves directly for the DOA estimation at the speed of *** multilayer meta-structures of S-DNN generate super-oscillatory angular responses in local angular regions that can perform the all-optical DOA estimation with angular resolutions beyond the diffraction *** spatial-temporal multiplexing of passive and reconfigurable S-DNNs is utilized to achieve high-resolution DOA estimation over a wide field of *** S-DNN is validated for the DOA estimation of multiple radio sources over 5 GHz frequency bandwidth with estimation latency over two to four orders of magnitude lower than the state-of-the-art commercial devices in *** results achieve the angular resolution over an order of magnitude,experimentally demonstrated with four times,higher than diffraction-limited *** also apply S-DNN’s edge computing capability,assisted by reconfigurable intelligent surfaces,for extremely low-latency integrated sensing and communication with low power *** work is a significant step towards utilizing photonic computing processors to facilitate various wireless sensing and communication tasks with advantages in both computing paradigms and performance over electronic computing.

关键词： beyond optical network

Effect of dielectric material on the uniformity of nanosecond pulsed dielectric barrier discharge

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Plasma Science and Technology 2024年第9期26卷 79-87页

作者： Wenhao ZHOU Dongxuan zhang Xiaohui duan Xi ZHU Feng LIU zhi FANG College of Electrical Engineering and Control Science Nanjing Tech UniversityNanjing 211816People’s Republic of China

Dielectric barrier discharge(DBD)is considered as a promising technique to produce large volume uniform plasma at atmospheric pressure,and the dielectric barrier layer between the electrodes plays a key role in the DBD processes and enhancing discharge *** this work,the uniformity and discharge characteristics of the nanosecond(ns)pulsed DBD with dielectric barrier layers made of alumina,quartz glass,polycarbonate(PC),and polypropylene(PP)are investigated via discharge image observation,voltage-current waveform measurement and optical emission spectral *** analyzing discharge image by gray value standard deviation method,the discharge uniformity is quantitatively *** effects of the space electric field intensity,the electron density(Ne),and the space reactive species on the uniformity are studied with quantifying the gap voltage Ug and the discharge current Ig,analyzing the recorded optical emission spectra,and simulating the temporal distribution of Ne with a one-dimensional fluid *** is found that as the relative permittivity of the dielectric materials increases,the space electric field intensity is enhanced,which results in a higher Ne and electron temperature(Te).Therefore,an appropriate value of space electric field intensity can promote electron avalanches,resulting in uniform and stable plasma by the merging of electron ***,an excessive value of space electric field intensity leads to the aggregation of space charges and the distortion of the space electric field,which reduce the discharge *** surface roughness and the surface charge decay are measured to explain the influences of the surface properties and the second electron emission on the discharge *** results in this work give a comprehensive understanding of the effect of the dielectric materials on the DBD uniformity,and contribute to the selection of dielectric materials for DBD reactor and the realization of atmospheric pre

关键词： dielectric barrier discharge dielectric material uniformity discharge characteristics

A comprehensive research on wear resistance of GH4169 superalloy in longitudinal-torsional ultrasonic vibration side milling with tool wear and surface quality

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Chinese Journal of Aeronautics 2024年第4期37卷 556-573页

作者： Baoqi CHANG Zhaoxi YI Fen zhang Lian duan Ji-an duan School of Mechanical and Electrical Engineering Central South UniversityChangsha 410083China State Key Laboratory of High Performance and Complex Manufacturing Central South UniversityChangsha 410083China School of Physics and Electronics Central South UniversityChangsha 410083China

To improve the service and machining performance of the workpiece, the tool wear mechanisms, surface machining quality, and wear resistance in conventional side milling(CSM)and longitudinal-torsional ultrasonic vibration side milling(LTUVSM) of GH4169 superalloy at different cutting lengths are investigated systematically. Tool wear mechanisms are revealed and the correlation between machined surface quality with tool wear is analyzed correspondingly. Tool wear patterns mainly include adhesive wear, diffusion wear, abrasive wear, and chipping *** surface quality is achieved in LTUVSM due to a maximum reduction of flank wear bandwidth and wear rate by 71.9% and 71.5%, respectively, compared to CSM. The friction coefficient,initial wear stage time, and wear volume of dry sliding wear were measured to evaluate the workpiece wear resistance. The maximum reductions in friction coefficient and wear volume in LTUVSM are 18.2% and 15.8% compared to CSM. The regular ultrasonic vibration textures suppress the friction and the growth of contact nodes in the contact area, decreasing the degree of surface wear, which is demonstrated by a 38.8% increase in initial wear stage time compared to *** conclusion, the workpiece in LTUVSM exhibits higher wear resistance because of the improvement of tool wear and the guarantee of surface quality.

关键词： Dry sliding wear Surface quality Tool wear Ultrasonic vibration Wear resistance

Accurate Distinction of Weak and Strong AC Grids for Emerging Hierarchical-Infeed LCC-UHVDC Systems

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CSEE Journal of Power and Energy Systems 2024年第2期10卷 772-777页

作者： Hao Xiao Xianzhong duan Yi zhang Department of Electrical and Computer Engineering University of ManitobaWinnipeg R3T 2N2ManitobaCanada State Key Laboratory of Advanced Electromagnetic Engineering and Technology Hubei Electric Power Security and High Efficiency Key LaboratorySchool of Electrical and Electronic EngineeringHuazhong University of Science and TechnologyWuhan 430074HubeiChina RTDS Technologies Inc. Winnipeg R3T 2E1ManitobaCanada

Distinction of weak and strong AC grids for emerging hierarchical-infeed LCC-UHVDC systems is important for planning and operation departments. However, accuracy of earlier distinction methods is limited as they were developed by empirical reasoning without rigorous theoretical analysis. Hence in this letter, hierarchical-infeed interactive effective short-circuit ratio (HIESCR) index is first used for strength evaluation of HIDC systems with complex inter-inverter interactions considered. Boundary HIESCR (BHIESCR) is also introduced in the proposed distinction method of weak and strong AC grids. That is, weak (or strong) AC grids are, respectively, identified when HIESCR is less (or greater) than BHIESCR. Second, it is shown BHIESCR remains almost unchanged as 3.0 versus various system parameters and rated operation variables based on rigorous theoretical analysis. This salient feature makes the proposed method more accurate than earlier methods. Finally, the proposed method is validated by simulations based on the PSCAD/EMTDC program.

关键词： Hierarchical-Infeedinteractive effective short-circuit ratio hierarchical-infeed LCC-UHVDC systems inter-inverter interactions strong AC grids weak AC grids