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| 1 | L^p-Boundedness of Marcinkiewicz Integrals with Hardy Space Function Kernels | Yong Ding Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China Dashan Fan Department of Mathematics, Anhui University and University of Wisconsin-Milwaukee. MW 53201 USA Yibiao Pan Department of Mathematics, University of Pittsburgh. Pittsburgh. Pennsylvania 15260. USA | 2000 | Acta Mathematica Sinica,English Series2000，16，4： | 88 |
| 2 | Weighted Boundedness for a Class of Rough Multilinear Operators | Yong DING Shan Zhen LU Department of Mathematics,Beijing Normal University,Beijing 100875,P.R.China E-mail:dingy@bnu.edu.cn lusz@bnu.edn.cn | 2001 | Acta Mathematica Sinica,English Series2001，17，3： | 24 |
| 3 | Continuity of Higher Order Commutators on Certain Hardy Spaces | DING Yong LU Shan Zhen Department of Mathematics,Beijing Normal University,Beijing 100875.P.R.China E-mail:dingy@bnu.edu.cn lusz@bnu.edu.cnZHANG Pu Department of Mathematics.Zhejiang University(at Xixi Campus).Hangzhou 310028,P.R.China,E-mail:zhpjj@263,net | 2002 | Acta Mathematica Sinica,English Series2002，18，2： | 21 |
| 4 | A broadband achromatic metalens array for integral imaging in the visible显示文摘Integral imaging is a promising three-dimensional(3D)imaging technique that captures and reconstructs light field information.Microlens arrays are usually used for the reconstruction process to display 3D scenes to the viewer.However,the inherent chromatic aberration of the microlens array reduces the viewing quality,and thus,broadband achromatic imaging remains a challenge for integral imaging.Here,we realize a silicon nitride metalens array in the visible region that can be used to reconstruct 3D optical scenes in the achromatic integral imaging for white light.The metalens array contains 60×60 polarization-insensitive metalenses with nearly diffraction-limited focusing.The nanoposts in each high-efficiency(measured as 47%on average)metalens are delicately designed with zero effective material dispersion and an effective achromatic refractive index distribution from 430 to 780 nm.In addition,such an achromatic metalens array is composed of only a single silicon nitride layer with an ultrathin thickness of 400 nm,making the array suitable for on-chip hybrid-CMOS integration and the parallel manipulation of optoelectronic information.We expect these findings to provide possibilities for full-color and aberration-free integral imaging,and we envision that the proposed approach may be potentially applicable in the fields of high-power microlithography,high-precision wavefront sensors,virtual/augmented reality and 3D imaging. | Zhi-Bin Fan Hao-Yang Qiu Han-Le Zhang Xiao-Ning Pang Li-Dan Zhou Lin Liu Hui Ren Qiong-Hua Wang Jian-Wen Dong | 2019 | Light(Science & Applications)2019，8，1： | 21 |
| 5 | On Some Nonlinear Integral and Discrete Inequalitites Related to Ou-Iang's Inequality | Yang Enhao Department of Mathematics, Jinan University, Guangzhou 510632, China | 1998 | Acta Mathematica Sinica,English Series1998，14，3： | 15 |
| 6 | Research advance in safety analysis methods for high concrete dam显示文摘High tensile stresses occurred in high concrete dams and in their foundation lead to the growing importance of their safety with the increase of concrete dam height. Without any exiting specification or successful experiences of concrete dams up to 300 m at home and abroad for reference, experts feel obliged to figure out how to perform safety analysis on high concrete dam. This paper involves the main contents and mechanical features of the safety analysis on high concrete dam and shows the current state and progress of the analysis methods. For the insufficiency and problems existing in normative methods, study on modern numerical method such as finite element method must be strengthened to find out the stress control criterion which is in accordance with the methods. Two aspects of the safety analysis of high dam—— local damage from material level and integral destruction from structure level——should be considered. For the local damage, we should consider the non-homogeneity of material and strengthen the research of meso-damage mechanics. While for integral destruction of the system of high dam and its foundation, a study on non-strength theory should receive enough concerns. Further, attention should be paid to the research on the failure modes and criterions of high concrete dam failure analysis and safety evaluation, and the effect of uncertainty and classification of safety should be considered too. | REN QingWen XU LanYu WAN YunHui | 2007 | Science China(Technological Sciences)2007，50，z1： | 12 |
| 7 | Boundary element-free method for elastodynamics显示文摘The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given. | CHENG Yumin1 & PENG Miaojuan2 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China 2. Department of Civil Engineering, Shanghai University, Shanghai 200072, China | 2005 | Science China(Physics,Mechanics & Astronomy)2005，48，6： | 12 |
| 8 | Age-dependent branching processes in random environments显示文摘We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ0,ξ1,...) of random variables. Given an environment ξ, the process is a non-homogenous Galton-Watson process, whose particles in n-th generation have a life length distribution G(ξn) on R+, and reproduce independently new particles according to a probability law p(ξn) on N. Let Z(t) be the number of particles alive at time t. We first find a characterization of the conditional probability generating function of Z(t) (given the environment ξ) via a functional equation, and obtain a criterion for almost certain extinction of the process by comparing it with an embedded Galton-Watson process. We then get expressions of the conditional mean EξZ(t) and the global mean EZ(t), and show their exponential growth rates by studying a renewal equation in random environments. | LI YingQiu LIU QuanSheng | 2008 | Science China Mathematics2008，51，10： | 12 |
| 9 | Orlicz-Hardy spaces associated with operators显示文摘Let L be a linear operator in L2(Rn) and generate an analytic semigroup {e-tL}t 0 with kernel satisfying an upper bound of Poisson type, whose decay is measured by θ(L) ∈ (0, ∞). Let ω on (0, ∞) be of upper type 1 and of critical lower type p0(ω) ∈ (n/(n + θ(L)), 1] and ρ(t) = t-1/ω-1(t-1) for t ∈ (0, ∞). We introduce the Orlicz-Hardy space Hω, L(Rn) and the BMO-type space BMOρ, L(Rn) and establish the John-Nirenberg inequality for BMOρ, L(Rn) functions and the duality relation between Hω, L(Rn) and BMOρ, L*(Rn), where L* denotes the adjoint operator of L in L2(Rn). Using this duality relation, we further obtain the ρ-Carleson measure characterization of BMOρ, L*(Rn) and the molecular characterization of Hω, L(Rn); the latter is used to establish the boundedness of the generalized fractional operator Lρ- γfrom Hω, L(Rn) to HL1(Rn) or Lq(Rn) with certain q > 1, where HL1(Rn) is the Hardy space introduced by Auscher, Duong and McIntosh. These results generalize the existing results by taking ω(t) = tp for t ∈ (0, ∞) and p ∈ (n/(n + θ(L)), 1]. | JIANG RenJin YANG DaChun ZHOU Yuan | 2009 | Science China Mathematics2009，52，5： | 10 |
| 10 | Boundedness in Lebesgue spaces for commutators of multilinear singular integrals and RBMO functions with non-doubling measures显示文摘The boundedness in Lebesgue spaces for commutators generated by multilinear singular integrals and RBMO(μ) functions of Tolsa with non-doubling measures is obtained, provided that‖μ‖=∞and multilinear singular integrals are bounded from L1(μ)×L1(μ)to L1/2,∞(μ). | Jing-shi XU Department of Mathematics, Hunan Normal University, Changsha 410081, China | 2007 | Science China Mathematics2007，50，3： | 10 |
| 11 | Adaptive Control Based on Neural Networks for an Uncertain 2-DOF Helicopter System With Input Deadzone and Output Constraints显示文摘In this paper, a study of control for an uncertain2-degree of freedom(DOF) helicopter system is given. The2-DOF helicopter is subject to input deadzone and output constraints. In order to cope with system uncertainties and input deadzone, the neural network technique is introduced because of its capability in approximation. In order to update the weights of the neural network, an adaptive control method is utilized to improve the system adaptability. Furthermore, the integral barrier Lyapunov function(IBLF) is adopt in control design to guarantee the condition of output constraints and boundedness of the corresponding tracking errors. The Lyapunov direct method is applied in the control design to analyze system stability and convergence. Finally, numerical simulations are conducted to prove the feasibility and effectiveness of the proposed control based on the model of Quanser's 2-DOF helicopter. | Yuncheng Ouyang Lu Dong Lei Xue Changyin Sun | 2019 | IEEE/CAA Journal of Automatica Sinica2019，6，3： | 9 |
| 12 | A prediction of the acoustic field of a vibrating box by FEM-BEM显示文摘A method based on Holmholtz equation is presented to predict thc acoustic radiation of a vibrating box by combining the finite clement method (FEM) with boundary element method (BEM). The prediction formulation is valid for all frequencies if an extra equation is added. The acoustic field of a vibrating box has been calculated and measured. The effectiveness of the method has been proved by test results. | YU Xingzhuo FANG Xing and ZHOU Yu (Department of Mechanical Engtheering I. Huazhong University of Science and Technology. Wuhan 430074) | 1995 | Chinese Journal of Acoustics1995，14，1： | 9 |
| 13 | SINGULAR INTEGRAL OPERATORS ANDSINGULAR QUADRATURE OPERATORSASSOCIATED WITH SINGULAR INTEGRAL EQUATIONS显示文摘In this paper, the author discusses some singular integral operators, singular quadrature operators and discretization matrices associated with singular integral equations with Cauchy kernels, and obtain some useful properties for them. These results improve both the classical theory of singular integral equation and the classical theory of singular quadrature. | 杜金元 | 1998 | Acta Mathematica Scientia1998，18，2： | 9 |
| 14 | 一种基于Integral Imaging和多基线立体匹配算法的深度测量方法显示文摘Integral Imaging(II)是一种能够记录和显示全真三维场景的图像技术.该技术采用微透镜阵列记录空间场景,空间任意一点的深度信息只需通过一次成像即可直接获得.本文研究结合多基线立体匹配算法采用II直接获取物体空间信息的方法.其结果既可为下一代基于II的三维电视图像的数据处理提供应用基础,同时也可望应用于开发新型的深度测量工具. | 伍春洪 杨扬 游福成 | 2006 | 电子学报2006，34，6： | 9 |
| 15 | Adaptive sliding-mode path following control system of the underactuated USV under the influence of ocean currents显示文摘The path-following control of the asymmetry underactuated unmanned surface vehicle(USV) under external disturbances such as unknown constant and irrational ocean currents is discussed, and an adaptive sliding-mode path-following control system is proposed, which comprises a path-variable updated law,a modified integral line-of-sight(ILOS) guidance law based on a time-varying lookahead distance and adaptive feedback linearizing controllers combined with sliding-mode technique. A more accurate USV model without the assumption of having diagonal inertia and damping matrices is first presented, aiming at improving the performance of the path-following control. Next, the coordinate transformation is adopted to decouple the sway dynamic from the rudder angle, and the path-following errors dynamics without non-singular problem are presented in the moving Frenet-Serret frame. Then, based on the cascaded theorem and the adaptive sliding-mode method, the adaptive control law of position errors and course error are designed, among which the lookahead distance and integral gain are all computed as different functions of cross-track error to estimate and compensate the sideslip angle caused by external disturbances adaptively. Finally, according to the Lyapunov and cascaded theorem, the control system proposed is proved to be uniform globally asymptotic stability(UGAS) and uniform semiglobal exponential stability(USGES) when the control objectives are all achieved. Simulation results illustrate the precision and high-quality performance of this new controller. | CHEN Xiao LIU Zhong ZHANG Jianqiang ZHOU Dechao DONG Jiao | 2018 | Journal of Systems Engineering and Electronics2018，29，6： | 8 |
| 16 | Experimental study on vibration suppression of gear shaft misalignment with ISFD显示文摘Misalignment faults in gear systems lead to violent vibration and noise, shortening the life of equipment. The aim of this work is the demonstration of vibration suppression of parallel-misaligned gear shafts using an integral squeeze film damper(ISFD). Using a first grade spur gear in engineering for reference, an open first-grade spur gear system is built and the vibration characteristics of the gear system with rigid supports and ISFD elastic damping supports are studied under different degrees of misalignment. The experimental results show that ISFD supports have excellent damping and vibration attenuation characteristics, which have improved control of the gear system vibration in horizontal, vertical and axial directions under different degrees of misalignment. This work shows that an ISFD structure can effectively suppress vibration of characteristic frequency components and resonance modulation frequency components. The test results provide evidence for the application of ISFD in vibration control of gear shaft misalignment faults in engineering. | 路凯华 He Lidong Zhang Yipeng Chen Zhao Yan Wei | 2019 | High Technology Letters2019，25，1： | 8 |
| 17 | Calculation of maximum ground movement and deformation caused by mining显示文摘In order to know the maximum mining ground deformation of arbitrary surface point, directions of the maximum surface tilt, curvature,horizontal displacement and horizontal deformation caused by multi-working faces were deduced based on probability integral method. The distribution forms of surface deformations in all direction φ∈[0, 2π] were obtained and also equations of maximum deformations were given based on calculation of mining ground deformation in direction φ. A mining subsidence analysis system was developed with VB6.0. The system implements the probability integral mining subsidence prediction with direct integration method, and it can avoid errors of arbitrary shaped working face subdivision of traditional method, and accuracy of mining subsidence prediction can be improved with the direct integral method. The system implements the contour chart and profile chart and also data analysis automation by manipulation of the SURFER kernel function and it complements the defect of existing subsidence prediction software. Calculation of maximum deformations caused by multi-working faces mining in a coal mine of Xuzhou, China was shown as application example. Engineering application indicates that maximum deformation of mining ground surface can be calculated and analyzed by the system. The research provides a theoretical basis and calculation tool for mining subsidence prediction and analysis. | LI Pei-xian1, 2, TAN Zhi-xiang1, 2, DENG Ka-zhong1, 2 1. Key Laboratory for Land Environment and Disaster Monitoring of State Bureau of Surveying and Mapping, China University of Mining and Technology, Xuzhou 221116, China 2. Jiangsu Key Laboratory of Resources and Environmental Information Engineering, China University of Mining and Technology, Xuzhou 221116, China | 2011 | 中国有色金属学会会刊:英文版2011，21，S3： | 8 |
| 18 | Weighted estimates for commutators of singular integral operators with non-doubling measures显示文摘Letμ be a nonnegative Radon measure on Rd which only satisfies μ(B(x,r)) ≤ Corn for all x ∈ Rd,r > 0,and some fixed constants Co > 0 and n ∈ (0,d].In this paper,some weighted weak type estimates with Aρp,(log L)σ (μ) weights are established for the commutators generated by Calderón-Zygmund singular integral operators with RBMO(μ) functions. | Guo-en HU~1 Da-chun YANG~(2+) Dong-yong YANG~2 1 Department of Applied Mathematics,University of Information Engineering,Zhengzhou 450002,China 2 School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China | 2007 | Science China Mathematics2007，50，11： | 7 |
| 19 | DYNAMIC FRACTURE MECHANICS ANALYSIS FOR COMPOSITE MATERIAL WITH MATERIAL NON-HOMOGENEITY IN THICKNESS DIRECTION显示文摘The problem considered here is the response of a non-homogeneous composite materialcontaining some cracks subjected to dynamic loading.It is assumed that the composite material is or-thotropic and all the material properties depend only on the coordinate y(along the thicknessdirection).In the analysis,the elastic region is divided into a number of plies of infinite length.Thematerial properties are taken to be constants for each ply.By utilizing the Laplace transform andFourier transform technique,the general solutions for plies are derived.The singular integral equa-tions of the entire elastic region are obtained and solved by the virtual displacement principle.Attentionis focused on the time-dependent full field solutions of stress intensity factor(SIF)and strain energyrelease rate.As a numerical illustration,the dynamic stress intensity factor of a substrate\functionallygraded film structure with two cracks under suddenly applied forces on cracks face are presented forvarious material non-homogeneity parameters. | Wang Baolin Han Jiecai Du Shanyi | 1998 | Acta Mechanica Solida Sinica1998，11，1： | 7 |
| 20 | Anisotropic singular integrals in product spaces显示文摘In this paper, the authors introduce a class of product anisotropic singular integral operators, whose kernels are adapted to the action of a pair A := (A1, A2) of expansive dilations on R n and R m , respectively. This class is a generalization of product singular integrals with convolution kernels introduced in the isotropic setting by Fefferman and Stein. The authors establish the boundedness of these operators in weighted Lebesgue and Hardy spaces with weights in product A∞ Muckenhoupt weights on R n × R m . These results are new even in the unweighted setting for product anisotropic Hardy spaces. | BOWNIK Marcin | 2010 | Science China Mathematics2010，53，12： | 7 |
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