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Boundedness for commutators of fractional Hardy operators on Herz spaces

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Progress in Natural Science:Materials International 2007年第1期17卷 20-25页

作者： FU Zunwei, LIU Zongguang and lu Shanzhen ( School of Mathematical Sciences, beijing {2. University, beijing 100875, china department of mathematics, Linyi {2. University, Linyi 2.6005, china department of mathematics, china University of Mining and Technology, beijing 100083, china) School of Mathematical Sciences Beijing Normal University Beijing 100875 China department of mathematics Linyi Normal University Linyi 276005 China department of mathematics China University of Mining and Technology Beijing 100083 China

Some boundedness results are established for commutators generated by classical fractional Hardy operators and one-sided CMO functions on the homogeneous Herz spaces, which extends some known results.

关键词： fractional Hardy operator Hardy’s integral inequality commutator one-sided CMO function homogeneous Herz space.

Local field potentials,spiking activity,and receptive fields in human visual cortex

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Science china(Life Sciences) 2024年第3期67卷 543-554页

作者： lu luo Xiongfei Wang Junshi lu Guanpeng Chen Guoming luan Wu Li Qian Wang Fang Fang School of Psychological and Cognitive Sciences and beijing Key Laboratory of Behavior and Mental Health Peking UniversityBeijing 100871China School of Psychology Beijing Sport UniversityBeijing 100084China department of Neurosurgery Sanbo Brain HospitalCapital Medical UniversityBeijing 100093China beijing Key Laboratory of Epilepsy Epilepsy CenterSanbo Brain HospitalCapital Medical UniversityBeijing 100093China IDG/McGovern Institute for Brain Research Peking UniversityBeijing 100871China Peking-Tsinghua Center for Life Sciences Peking UniversityBeijing 100871China beijing Institute for Brain Disorders Beijing 100069China State Key Laboratory of Cognitive Neuroscience and Learning and IDG/McGovern Institute for Brain Research Beijing Normal UniversityBeijing 100875China

The concept of receptive field(RF) is central to sensory neuroscience. Neuronal RF properties have been substantially studied in animals,while those in humans remain nearly unexplored. Here, we measured neuronal RFs with intracranial local field potentials(LFPs) and spiking activity in human visual cortex(V1/V2.V3). We recorded LFPs via macro-contacts and discovered that RF sizes estimated from lowfrequency activity(LFA, 0.5–30 Hz) were larger than those estimated from low-gamma activity(LGA, 30–60 Hz) and high-gamma activity(HGA, 60–150 Hz). We then took a rare opportunity to record LFPs and spiking activity via microwires in V1 simultaneously. We found that RF sizes and temporal profiles measured from LGA and HGA closely matched those from spiking activity. In sum, this study reveals that spiking activity of neurons in human visual cortex could be well approximated by LGA and HGA in RF estimation and temporal profile measurement, implying the pivotal functions of LGA and HGA in early visual information processing.

关键词： human visual cortex receptive field intracranial EEG local field potential spiking activity

THE WEINSTEIN CONJECTURE ON C^1-SMOOTH HYPERSURFACE OF CONTACT TYPE

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Acta Mathematica Scientia 2002年第4期22卷 557-563页

作者：卢广存 department of mathematics Beijing Normal University Beijing 100875 China

In this note a symplectic capacity of Hofer-Zehnder type that is only invariant under C-1-symplectomorphisms is defined and all computation formulae for Hofer-Zehnder symplectic capacity obtained at present are proved still holding for it. As a consequence some results on Weinstein conjecture are generalized to C-1-smooth hypersurface of contact type.

关键词： Hofer-Zehnder symplectic capacity Weinstein conjecture

Wind disturbance compensated path-following control for fixed-wing UAVs in arbitrarily strong winds

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Chinese Journal of Aeronautics 2024年第2期37卷 431-445页

作者： Hao lu Lan GAO Yunda YAN Mingzhe HOU Chenliang WANG Hangzhou Innovation Institute Beihang UniversityHangzhou 310051China School of Information Science and Technology Hangzhou Normal UniversityHangzhou 311121China department of Computer Science University College LondonLondon WC1E 6BTUnited Kingdom Center for Control Theory and Guidance Technology Harbin Institute of TechnologyHarbin 150001China School of Automation Science and Electrical Engineering Beihang UniversityBeijing 100191China

Wind is the primary challenge for low-speed fixed-wing unmanned aerial vehicles to follow a predefined flight *** cope with various wind conditions,this paper proposes a wind disturbance compensated path following control strategy where the wind disturbance estimate is incorporated with the nominal guiding vector field to provide the desired airspeed direction for the *** the control input vector for the outer-loop kinematic subsystem needs to satisfy a magnitude constraint,a scaling mechanism is introduced to tune the proportions of the compensation and nominal ***,an optimization problem is formulated to pursue a maximum wind compensation in strong winds,which can be solved analytically to yield two scaling factors.A cascaded inner-loop tracking controller is also designed to fulfill the outer-loop wind disturbance compensated guiding vector ***-fidelity simulation results under sensor noises and realistic winds demonstrate that the proposed path following algorithm is less sensitive to sensor noises,achieves promising accuracy in normal winds,and mitigates the deviation from a desired path in wild winds.

关键词： Path following Guiding vector field Wind disturbance Disturbance rejection Fixed wings

A Remark on Multilinear Oscillatory Singular Integrals

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Acta Mathematica Sinica,English Series 2000年第4期16卷 655-668页

作者： Shanzhen lu Dunyan Yan department of {2., beijing normal University, beijing 100875. P. R. china department of mathematics Beijing Normal University Beijing 100875 P. R. China

In this paper we study multilinear oscillatory singular integrals with rough kernel and give a criterion of certain boundedness for this kind of operator

关键词： Multilinear oscillatory integrals Calderon-Zygmund kernel BLO space

Copper coordination-driven self-assembly and encapsulation of PCR reagents

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Chinese Chemical Letters 2024年第3期35卷 189-192页

作者： Chang lu Jinkai Zheng Juewen Liu Institute of Food Science and Technology Chinese Academy of Agricultural SciencesBeijing 100193China department of Chemistry Waterloo Institute for NanotechnologyUniversity of WaterlooWaterlooONN2L 3G1Canada

Polymerase chain reactions(PCR)are a very important tool for use in cloning,nucleic acid sequencing and diagnostic *** storage conditions of PCR reagents are limited to freezing and a lot of mixing steps are *** this paper,we report using metal ions to form coordination nanomaterials with the intrinsic components of the PCR reagents including dNTP,DNA primers and DNA polymerase as an integrated PCR reaction *** complete PCR reactions,users need only to dissolve the coordination nanomaterials with a buffer and add template DNA.A few transition metal ions were screened and Cu^(2.)was found to be the most effective metal ion for this *** the encapsulation efficiency of PCR reagents was measured,which can reach close to 100%for the primers and DNA polymerase,but only 10%for dNTP because dNTP was *** study also exhibited this integrated PCR reaction system can be used for DNA detection with a similar detection limit to the normal PCR,and showed good stability of encapsulated PCR nanomaterial after storage for a week.

关键词： Metal ions Coordination Encapsulation PCR Storage

Scaling laws governing the elastic properties of 3D graphenes

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Science china(Technological Sciences) 2024年第6期67卷 1748-1756页

作者： LI Ming lu Guo YU HaoDong LI MengLei ZHENG FaWei Centre for Quantum Physics Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement(MOE)School of PhysicsBeijing Institute of TechnologyBeijing100081China beijing Key Lab of Nanophotonics&Ultrafine Optoelectronic Systems School of PhysicsBeijing Institute of TechnologyBeijing100081China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing100088China department of Physics Capital Normal UniversityBeijing100048China

In this study,we comprehensively investigated the scaling law for elastic properties of three-dimensional honeycomb-like graphenes(3D graphenes)using hybrid neural network potential-based molecular dynamics simulations and theoretical *** elastic constants were obtained as functions of honeycomb hole size,denoted by the graphene wall length *** five independent elastic constants in the large-L limit are proportional to L^(-1).The associated coefficients are combinations of elastic constants of two-dimensional ***-order terms including L^(-2.and L^(-3)emerge for finite L *** have three origins,the distorted areas close to the joint lines of 3D graphenes,the variation in solid angles between graphene plates,and the bending distortion of graphene ***,the chirality becomes essential with decreasing L because the joint line structures are different between the armchair and zigzag-type 3D *** findings provide insights into the elastic properties of graphene-based superstructures and can be used for further studies on graphene-based materials.

关键词： scaling law neural network elastic properties 3D graphene

Weighted estimates for the multilinear singular integral operators with non-smooth kernels

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Science china mathematics 2011年第3期54卷 587-602页

作者： HU GuoEn1 & lu ShanZhen2.1department of Applied {2., Zhengzhou Information Science and Technology Institute, Zhengzhou 450002. china 2.1} of {2., beijing normal University, beijing 100875, china department of Applied mathematics Zhengzhou Information Science and Technology Institute Zhengzhou China department of mathematics Beijing Normal University Beijing China

In this paper, by sharp function estimates and certain weak type endpoint estimates, the authors establish some weighted norm inequalities with Ap weights for the multilinear singular integral operators with non-smoot... 详细信息

关键词：多线性奇异积分算子加权估计非平稳内核加权模不等式端点估计函数估计非光滑

Structure of 〔Na(DB18C6) (CH_3OH)〕_2._6O_(19)·(DB18C6)·(CH_3OH)

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Chinese Journal of Structural Chemistry 1997年第3期16卷 172-176页

作者： lu Xiao-Ming CHU Yi-Ming DI Jing LIU Shun-Cheng(department of Chemistry, {2. normal University beijing 100037, china) department of Chemistry Capital Normal University Beijing 100037 China

Complex [(DB18C6) (CH3OH)]2.6O19 · (DB18C6) · (CH3OH), Mr=2.30. 43, monoclinic, space group P2./c, a=18. 699(5), b=19. 568(4), c=2.. 785(5) Å, β=112. 91(2.°, V=7679(7) Å3, Z=4, Dc=2. 2.5 g/cm3, F(000) =4992. μ=92. 52.cm-1. The final R=0. 035 and Rw=0. 041 for 5689 observed reflections (I≥3σ(I)). The complex contains one hexatungstate anion and two sodium cations. Each Na cation is inlaid in the cavity of one dibenzo-18-crown-6(DB18C6) with six Na - O coordination bonds. In addition, it linked to O atom of CH3OH from one side of DB18C6 and bonded to one of the terminal O atoms in hexatungstate anion from the other side. The two DB18C6 connected with hexatungstate symmetrically by the long-distance interaction through the O - Na - O bonds with Na - O distances of 2. 2.(1)-2. 37(1) Å, W - O distances are 1. 68(2.-2. 34(2. Å. C - O distances in methanol coordinated with cation are 1. 38(4)-1. 41(4) Å.

关键词： dibenzo-18-crown-6 (DB18C6) polyoxotungstate anion crystal structure