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Pointwise characterization for combinations of Szász-Mirakjan operators

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Applied Mathematics(A Journal of Chinese Universities) 2008年第2期23卷 202-212页

作者： xie lin-sen SHI Zhong-rui Dept. of Math. Shanghai Univ. Shanghai 200444 China Dept. of Math. Lishui Univ. Lishui 323000 China

The purpose of this paper is to characterize the pointwise rate of convergence for the combinations of Szász-Mirakjan operators using Ditzian-Totik modulus of smoothness.

关键词： Szász-Mirakjan operator combination pointwise approximation.

Pointwise Simultaneous Approximation by Combinations of Baskakov Operators

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Acta Mathematica Sinica,English Series 2007年第5期23卷 935-944页

作者： lin Sen xie Zhong Rui SHI Department of Mathematics Shanghai University Shanghai 200444 P. R. China Department of Mathematics Lishui University Lishui 323000 P. R. China

In this paper, we investigate the relation between the rate of convergence for the derivatives of the combinations of Baskakov operators and the smoothness for the derivatives of the functions approximated. We give some direct and inverse results on pointwise simultaneous approximation by the combinations of Baskakov operators. We also give a new equivalent result on pointwise approximation by these operators.

关键词： Baskakov operator combination simultaneous approximation modulus of smoothness

SUPER-GEOMETRIC CONVERGENCE OF A SPECTRAL ELEMENT METHOD FOR EIGENVALUE PROBLEMS WITH JUMP COEFFICIENTS

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Journal of Computational Mathematics 2010年第3期28卷 418-428页

作者： lin Wang Ziqing xie Zhimin Zhang College of Mathematics and Computer Science Hunan Normal University Changsha 410081 China and College of Information Technical Science Nankai University Tianjin 300071 China College of Mathematics and Computer Science Hunan Normal University Changsha 310081 China Department of Mathematics Wayne State University Detroit MI 48202 USA and College of Mathematics and Computer Science Hunan Normal University Changsha 410081 China

We propose and analyze a C^0 spectral element method for a model eigenvalue problem with discontinuous coefficients in the one dimensional setting. A super-geometric rate of convergence is proved for the piecewise constant coefficients case and verified by numerical tests. Furthermore, the asymptotical equivalence between a Gauss-Lobatto collocation method and a spectral Galerkin method is established for a simplified model.

关键词： Eigenvalue Spectral method Collocation Galerkin finite element method.

Microstructure and mechanical properties of WC-Co-based cemented carbide with bimodal WC grain size distribution

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Rare Metals 2023年第8期42卷 2809-2815页

作者： Rui-Jun Cao Chen-Guang lin Xing-Cheng xie Zhong-Kun lin Powder Metallurgy and Special Materials Department General Research Institute for Nonferrous MetalsBeijing 100088China

In order to improve the wear resistance of coarse-grained WC-Co cemented carbides,the fine WC powder were used to reinforce the metallic *** WC-Co-based cemented carbides having bimodal WC grain size distributions were synthesized by liquid phase *** comparison,the cemented carbides having unimodal WC grain size distributions were *** microstructure,hardness,fracture toughness and wear resistance of these cemented carbides were *** results show that adding fine WC powder is an effective method to improve the wear resistance of coarsegrained WC-Co cemented *** WC size,mean free path and fracture toughness decrease with the addition of fine WC powder,while the hardness exhibits an opposite *** impact-wear coefficient of bimodal distribution cemented carbides is noticeably lower than that of the unimodal one with the same hardness,which means that the cemented carbides with bimodal grain structure have better combination of hardness and impact-abrasive wear *** impact-abrasive wear mechanism of the bimodal cemented carbides is that the fine WC grains prevent abrasive wear and the coarse WC grains prevent impact wear.

关键词： WC-Co cemented carbide Impact wearing Bimodal distribution Hardness Mean free path

3D anisotropy in shear failure of a typical shale

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Petroleum Science 2023年第1期20卷 212-229页

作者： Zi-Dong Fan Li Ren He-Ping xie Ru Zhang Cun-bao Li Hui-Jun Lu An-lin Zhang Qin Zhou Wei-Qiang ling MOE Key Laboratory of Deep Earth Science and Engineering Sichuan UniversityChengduSichuan 610065China College of Architecture and Environment Sichuan UniversityChengduSichuan 610065China Institute of Deep Earth Sciences and Green Energy Shenzhen UniversityShenzhenGuangdong 518052China College of Water Resources and Hydropower Sichuan UniversityChengduSichuan 610065China

It is inadequate to study the shear failure anisotropy of shale in only 2D *** at a 3D analysis,a series of direct shear tests was conducted on Longmaxi shale with three typical bedding orientations:arrester,divider and short-transverse *** testing,acoustic emission(AE)and digital image correlation(DIC)techniques were simultaneously employed to monitor failure development,after testing,X-ray computed tomography(CT)scanning was adopted to acquire and reconstruct the fractures inside typical ruptured samples for more detailed *** results indicated that the shear strength parameters exhibited 3D anisotropies and those of the arrester sample did not have equivalent shear strength parameters to the shale *** maximum(minimum)shear strength and cohesion were obtained with the divider(short-transverse)orientation,and the internal friction angle reached its maximum(minimum)with the divider(arrester)*** the AE,DIC and CT techniques,four characteristic stress levels that can capture the progressive shear failure process of shale rocks were identified,and the onset and accelerated development of shear damage-induced dilation were observed at the crack initiation and coalesce stress thresholds,*** the crack coalescence stage,the dominated microcracking mechanism transferred from tensile-mode to *** the arrester and divider orientations,more tensile-mode AE events were generated due to the microcracking along the vertical *** with the divider samples,a more complex fracture network with a larger fracture area and volume was obtained in the arrester samples,whose strengths were smaller.

关键词： Shale Shear Acoustic emission Digital image correlation X-ray computed tomography Fracture network

Six-fold swelling expansion microscopy assisted cell painting for high-content phenotypic screening

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Optoelectronics Letters 2025年

作者： Junfang xie Yipeng DONG Jin WANG Zhichao DENG Jianguo TIAN Qing YE Key Laboratory of Weak-Light Nonlinear Photonics， Ministry of Education， School of Physics and TEDA Applied Physics， Nankai University

Imaging-based phenotypic screening uses cellular phenotypes to describe the drug performance， which generally focuses on single cellular feature， lacking of a comprehensive characterization. Here， we propose a high content phenotypic screening method based on expansion microscopy (ExM) assisted Cell Painting， which enables multi-channel imaging with approximately 50 nm resolution. As a demonstration， we applied this method to a phenotypic screening involving five drugs. The morphological attributes of three subcellular structures were summarized to consist a “fingerprint” describing the drug effect. The proposed method can provide comprehensive and detailed clues for drug evaluation， enriching the content of phenotypic screening.

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Mechanism of Spine Motion About Contact Time in Quadruped Running

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Chinese Journal of Mechanical Engineering 2019年第2期32卷 53-60页

作者： Qi Liu Yannian bao Wei Yu Jianming Zhang Chao Li Xinru xie Institute of Chemical Materials China Academy of Engineering Physics College of Automation Harbin Engineering University

The current research of quadruped robot focuses on the quadruped robot with spine motion. Contact time is a very important part of system performance. However, the mechanism of spine motion about contact time has not been clearly elucidated. In this paper, the e ect of spine motion on contact time is studied deeply from dynamic ***, a simplified model of the quadruped robot with spine joint is set up, its dynamic equations are derivated, and a method that can generate passive periodic locomotion is proposed. Secondly, according to the vertical spring oscillator model, the two-dimension planar locomotion of the simplified model is regarded as a special vibration in the vertical direction, and the approximate formula of calculating contact time is obtained. Finally, the approximate formula of calculating contact time is verified by the simulation results of passive periodic locomotion, and the e ect of spine motion on contact time is deeply discussed based on the approximate formula of calculating contact time. The discussion proves that spine motion indeed has little e ect on contact time, but spine motion can slightly reduce body pith movement and regulate the leg sti ness in leg contact phase. This research proposes an e ective research method which can be used to study the motion mechanism of the quadruped robot with spine motion,and the mechanism of spine motion about contact time is clearly elucidated which is helpful to set the parameters of mechanical structure and study control algorithm about the quadruped robot with spine motion.

关键词： Quadruped robot Spine motion Passive locomotion Contact time Leg sti ness

Flutter of Finite-Span Flexible Plates in Uniform Flow

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Chinese Physics Letters 2010年第6期27卷 126-128页

作者： bao Chun-Yu TANG Chao YIN xie-Zhen LU Xi-Yun Department of Modern Mechanics University of Science and Technology of China Hefei 230027

The flutter instability and response of finite-span flexible plates in uniform flow are investigated experimentally. The effects of the plate aspect ratio on its dynamic responses are mainly analyzed. A hysteretic phenomenon is observed and can be described such that the plate flutters spontaneously as the flow velocity is greater than a critical value UC and the plate returns to its stable state as the flow velocity is slowly decreased to another critical one UD. We find that the aspect ratio has a greater effect on UC than on UD. The flutter frequency decreases and the amplitude increases with the increase in the flow velocity. When the flutter instability of the plate occurs, three typical flutter modes are identified and are associated with the aspect ratio and the flow velocity.

关键词： Velocity Flutter Uniform Flow

The correlation between expansion speed and magnetic field in solar flare ribbons

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Science China(Physics,Mechanics & Astronomy) 2009年第11期52卷 1754-1759页

作者： xie WenBin WANG HaiMin JING Ju bao XingMing ZHANG HongQi Key Laboratory of Solar Activity National Astronomical Observatories of ChinaBeijing 100012China Physics Department New Jersey Institute of TechnologyNewarkNJ07102USA Jilin Normal University Jilin 136000China

In this paper, we study the correlation between the expansion speed of two-ribbon flares and the magnetic field measured in the ribbon location, and compare such correlation for two events with different magnetic configurations. These two events are: an M1.0 flare in the quiet sun on September 12, 2000 and an X2.3 flare in Active Region NOAA 9415 on April 10, 2001. The magnetic configuration of the M1.0 flare is simple, while that of X2.3 event is complex. We have derived a power-law correlation between the ribbon expansion speed (V r) and the longitudinal magnetic field (Bz) with an empirical relationship V r = A×Bz-δ, where A is a constant and δ is the index of the power-law correlation. We have found that δ for the M1.0 flare in the simple magnetic configuration is larger than that for the X2.3 flare in the complex magnetic configuration.

关键词： solar activity solar flares solar magnetic field