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Variational Analysis Based on Proximal Subdifferential on Smooth Banach Spaces

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Acta Mathematica Sinica,English Series 2024年第2期40卷 595-618页

作者： Xi Yin zheng Department of Mathematics Yunnan UniversityKunming 650091P.R.China

This paper first show. that for any p∈(1,2)there exists a continuously differentiable function f on l^(p)(and L^(p))such that the proximal subdifferential of f is empty everyw.ere,and hence it is not suitable to develop theory on proximal subdifferential in the classical Banach spaces l^(P)and L^(P) w.th p∈(1,2).On the other hand,this paper establishes variational analysis based on the proximal subdifferential in the framew.rk of smooth Banach spaces of pow.r type 2,w.ich conclude all Hilbert spaces and all the classical spaces l^(P)and L^(P)w.th p∈(2,+∞).In particular,in such a smooth space,w. provide the proximal subdifferential rules for sum functions,product functions,composite functions and supremum functions,w.ich extend the basic results on the proximal subdifferential established in the framew.rk of Hilbert *** of our main results are new.even in the Hilbert space *** applications,w. provide KKT-like conditions for nonsmooth optimization problems in terms of proximal subdifferential.

关键词： Smooth Banach space proximal subdifferential proximal normal cone KKT condition

Experimental and numerical simulation study on forced ventilation and dust removal of coal mine heading surface

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International Journal of Coal Science & Technology 2024年第1期11卷 204-220页

作者： Haotian zheng Bingyou Jiang Haoyu w.ng Yuannan zheng Key Laboratory of Industrial Dust Prevention and Control&Occupational Health and Safety Ministry of EducationAnhui University of Science and TechnologyHuainan232001China Joint National-Local Engineering Research Centre for Safe and Precise Coal Mining Anhui University of Science and TechnologyHuainan232001China School of Safety Science and Engineering Anhui University of Science and TechnologyHuainan232001China

In order to study the problems of unreasonable airflow.distribution and serious dust pollution in a heading surface,an experimental platform for forced ventilation and dust removal w.s built based on the similar *** the similar experiment and numerical simulation,the distribution of airflow.field in the roadw.y and the spatial and temporal evolution of dust pollution under the conditions of forced ventilation w.re *** airflow.field in the roadw.y can be divided into three zones:jet zone,vortex zone and reflux *** dust concentration gradually decreases from the head to the rear of the *** the forced ventilation conditions,there is a unilateral accumulation of dust,w.th higher dust concentrations aw.y from the *** position of the equipment has an interception effect on the *** maximum error betw.en the test value and the simulation result is 12.9%,w.ich verifies the accuracy of the experimental *** research results can provide theoretical guidance for the application of dust removal technology in coal mine.

关键词： Heading surface Forced ventilation Airflow.field Dust pollution

The rate dependence of the dielectric strength of dielectric elastomers

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International Journal of Smart and Nano Materials 2024年第1期15卷 110-126页

作者： Xianghe zheng Jianyou Zhou Pan Jia zheng Zhong School of Science Harbin Institute of TechnologyShenzhenChina

Elastomers are w.dely used in electronics and electrical devices,either as insulators or *** insulation and actuation performance of elastomers are highly suscepti-ble to their dielectric *** the factors that influ-encethedielectricstrength ofelastomers,material viscoelasticity is an important factor that needs further *** the material viscoelasticity is often character-ized by rate-dependent behaviors,w. present tw. different sample configurations to experimentally examine the electrical and mechanical rate dependence of the dielectric strength of VHB 4905 *** pre-stretch ratio of 4,the improve-ment of the dielectric strength is about 30%from voltage ramp of 50 V/s to 800 V/***,w.th an in-house biaxial test platform,the effect of the stretching rate on the dielectric strength is examined for the first *** improvement of the dielectric strength is about 35%from stretching rate of 0.1 mm/s to 5 mm/***,a dielectric strength predictor based on configurational stress is adopted to describe the experimental *** to the predictor,the loading rate affects the dielectric strength of the elastomer mainly by influencing the evolution of the inelastic deformation.

关键词： Dielectric strength dielectric elastomers material viscoelasticity rate-dependence configurational stress

On-surface synthesis and characterization of polyynic carbon chains

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National Science Review 2024年第3期11卷 192-199页

作者： w.nze Gao w.i zheng Luye Sun Faming Kang zheng Zhou w.i Xu Interdisciplinary Materials Research Center School of Materials Science and Engineering Tongji University

Carbyne, an elusive sp-hybridized linear carbon allotrope, has fascinated chemists and physicists for decades. Due to its high chemical reactivity and extreme instability, carbyne w.s much less explored in contrast to the sp2-hybridized carbon allotropes such as graphene. Herein, w. report the on-surface synthesis of polyynic carbon chains by demetallization of organometallic polyynes on the Au（111） surface;the longest one observed consists of ～60 alkyne units（120 carbon atoms）. The polyynic structure of carbon chains w.th alternating triple and single bonds w.s unambiguously revealed by bond-resolved atomic force microscopy. Moreover, an atomically precise polyyne, C14, w.s successfully produced via tip-induced dehalogenation and ring-opening of the decachloroanthracene molecule(C14Cl10) on a bilayer NaCl/Au（111） surface at 4.7 K, and a band gap of 5.8 eV w.s measured by scanning tunnelling spectroscopy,in a good agreement w.th the theoretical HOMO–LUMO gap（5.48 eV）.

关键词： polyyne scanning probe microscopy carbon allotrope on-surface synthesis organometallic polyyne

Adaptive Trajectory Tracking Control for Nonholonomic w.eeled Mobile Robots:A Barrier Function Sliding Mode Approach

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IEEE/CAA Journal of Automatica Sinica 2024年第4期11卷 1007-1021页

作者： Yunjun zheng Jinchuan zheng Ke Shao Han Zhao Hao Xie Hai w.ng the School of Mechanical Engineering Hefei University of TechnologyHefei 230009China the School of Science Computing and Engineering TechnologiesSwinburne University of TechnologyHawthorn VIC 3122Australia the School of Civil Aviation Northwestern Polytechnical UniversityXi’an 710072China the Shanghai Aerospace Control Technology Institute Shanghai 201109 the School of Automation Science and Electrical Engineering Beihang UniversityBeijing 100191China the College of Science HealthEngineering and EducationMurdoch UniversityPerth WA6150Australia

The trajectory tracking control performance of nonholonomic w.eeled mobile robots(Nw.Rs)is subject to nonholonomic constraints,system uncertainties,and external *** paper proposes a barrier function-based adaptive sliding mode control(BFASMC)method to provide high-precision,fast-response performance and robustness for *** w.th the conventional adaptive sliding mode control,the proposed control strategy can guarantee that the sliding mode variables converge to a predefined neighborhood of origin w.th a predefined reaching time independent of the prior know.edge of the uncertainties and disturbances *** advantage of the proposed algorithm is that the control gains can be adaptively adjusted to follow.the disturbances amplitudes thanks to the barrier *** benefit is that the overestimation of control gain can be eliminated,resulting in chattering ***,a modified barrier function-like control gain is employed to prevent the input saturation problem due to the physical limit of the *** stability analysis and comparative experiments demonstrate that the proposed BFASMC can ensure the prespecified convergence performance of the Nw.R system output variables and strong robustness against uncertainties/disturbances.

关键词： Adaptive sliding mode barrier function nonholonomic w.eeled mobile robot(Nw.R) trajectory tracking control

Stability and accuracy of central difference method for real-time dynamic substructure testing considering mass participation coefficient

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Earthquake Engineering and Engineering Vibration 2024年第3期23卷 625-636页

作者： zheng Lichang Xu Guoshan Yang Ge w.ng Zhen Yang Kaibo zheng Zhenyun School of Civil Engineering Harbin Institute of TechnologyHarbin 150090China Key Lab of Structures Dynamic Behavior and Control Ministry of EducationHarbin Institute of TechnologyHarbin 150090China Key Lab of Intelligent Disaster Mitigation Ministry of Industry and Information TechnologyHarbin 150090China School of Civil Engineering and Architecture Wuhan University of TechnologyWuhan 430070China

For real-time dynamic substructure testing(RTDST),the influence of the inertia force of fluid specimens on the stability and accuracy of the integration algorithms has never been ***,this study proposes to investigate the stability and accuracy of the central difference method(CDM)for RTDST considering the specimen mass participation ***,the theory of the CDM for RTDST is ***,the stability and accuracy of the CDM for RTDST considering the specimen mass participation coefficient are ***,numerical simulations and experimental tests are conducted for verifying the effectiveness of the *** study indicates that the stability of the algorithm is affected by the mass participation coefficient of the specimen,and the stability limit first increases and then decreases as the mass participation coefficient *** most cases,the mass participation coefficient w.ll increase the stability limit of the algorithm,but in specific circumstances,the algorithm may lose its *** stability and accuracy of the CDM considering the mass participation coefficient are verified by numerical simulations and experimental tests on a three-story frame structure w.th a tuned liquid damper.

关键词： real-time dynamic substructure testing central difference method stability mass participation coefficient tuned liquid damper

Robust Distributed Model Predictive Control for Formation Tracking of Nonholonomic Vehicles

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IEEE/CAA Journal of Automatica Sinica 2024年第2期11卷 560-562页

作者： Zhigang Luo Bing Zhu Jianying zheng Zew.i zheng School of Automation Science and Electrical Engineering Beihang UniversityBeijing 100191China

Dear Editor,This letter proposes a robust distributed model predictive control(MPC) strategy for formation tracking of a group of w.eeled vehicles subject to constraints and disturbances. Formation control has attract... 详细信息

关键词： letter constraints searching

Disturbance Observer-based Pointing Control of Leighton Chajnantor Telescope

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Research in Astronomy and Astrophysics 2024年第1期24卷 135-150页

作者： w.irui Chen zheng w.ng School of Automation Southeast UniversityNanjing 210096China Key Laboratory of Measurement and Control of Complex Systems of Engineering Ministry of EducationSoutheast UniversityNanjing 210096China

Leighton Chajnantor Telescope(LCT), i.e., the former Caltech Submillimeter Observatory telescope, w.ll be refurbished at the new.site in Chajnantor Plateau, Chile in 2023. The environment of LCT w.ll change significantly after its relocation, and the telescope w.ll be exposed to large w.nd disturbances directly because its enclosure w.ll be completely open during observation. The w.nd disturbance is expected to be a challenge for LCT's pointing control since the existing control method cannot reject this disturbance very w.ll. Therefore, it is very necessary to develop a new.pointing control method w.th good capability of disturbance rejection. In this research, a disturbance observer—based composite position controller(DOB-CPC) is designed, in w.ich an H∞feedback controller is employed to compress the disturbance, and a feedforw.rd linear quadratic regulator is employed to compensate the disturbance precisely based on the estimated disturbance signal. Moreover, a controller sw.tching policy is adopted, w.ich applies the proportional controller to the transient process to achieve a quick response and applies the DOB-CPC to the steady state to achieve a small position error. Numerical experiments are conducted to verify the good performance of the proposed pointing controller(i.e., DOB-CPC) for rejecting the disturbance acting on LCT.

关键词： instrumentation:miscellaneous methods:analytical methods:numerical telescopes

The Logarithmic Sobolev Inequality for a Submanifold in Manifolds w.th Nonnegative Sectional Curvature

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Chinese Annals of Mathematics,Series B 2024年第3期45卷 487-496页

作者： Chengyang YI Yu zheng School of Mathematical Sciences East China Normal UniversityShanghai 200241China

The authors prove a sharp logarithmic Sobolev inequality w.ich holds for compact submanifolds w.thout boundary in Riemannian manifolds w.th nonnegative sectional curvature of arbitrary dimension and *** the Michael-Simon Sobolev inequality,this inequality includes a term involving the mean *** extends a recent result of Brendle w.th Euclidean setting.

关键词： Logarithmic Sobolev inequality Nonnegative sectional curvature Submanifold