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OPTIMAL ERROR ESTIMATES OF THE PARTITION OF UNITY METHOD WITH LOCAL POLYNOMIAL APPROXIMATION SPACES

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Journal of Computational Mathematics 2006年第3期24卷 365-372页

作者： yun-qing huang Wei Li Fang Su Hunan Key Laboratory for Computation and Simulation in Science and Engineering Institute for Computational and Applied Mathematics Xiangtan University Xiangtan 4 11105 China Department of Computational Science Xiangtan University Xiangtan 4 11105 China

In this paper, we provide a theoretical method（PUFEM）, which belongs to the analysis of the partition of unity finite element family of meshfree methods. The usual error analysis only shows the order of error estimate to the same as the local approximations[12]. Using standard linear finite element base functions as partition of unity and polynomials as local approximation space, in l-d case, we derive optimal order error estimates for PUFEM interpolants. Our analysis show that the error estimate is of one order higher than the local approximations. The interpolation error estimates yield optimal error estimates for PUFEM solutions of elliptic boundary value problems.

关键词： Meshless methods Partition of unity finite element method(PUFEM) Error estimate.

PRECONDITIONING HIGHER ORDER FINITE ELEMENT SYSTEMS BY ALGEBRAIC MULTIGRID METHOD OF LINEAR ELEMENTS

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Journal of Computational Mathematics 2006年第5期24卷 657-664页

作者： yun-qing huang Shi Shu Xi-jun Yu Hunan Key Laboratory for Computation and Simulation in Science and Engineering Institute for Computational and Applied Mathematics Xiangtan University Xiangtan 411105 China Laboratory of Computational Physics Institute of Applied physics and Computational Mathematics Beijing 100088 China

We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen to be the preconditioner for higher order finite elements. Then an algebraic multigrid method of linear finite element is applied for solving the preconditioner. The optimal condition number which is independent of the mesh size is obtained. Numerical experiments confirm the efficiency of the algorithm.

关键词： Finite element Algebraic multigrid methods Preconditioned Conjugate Gradient Condition number.

Solid-state reaction of a CaO−V_(2)O_(5)mixture:A fundamental study for the vanadium extraction process

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International Journal of Minerals,Metallurgy and Materials 2021年第9期28卷 1462-1468页

作者： Jun-yi Xiang Xin Wang Gui-shang Pei qing-yun huang Xue-wei Lv College of Materials Science and Engineering Chongqing UniversityChongqing 400044China School of Metallurgy and Materials Engineering Chongqing University of Science and TechnologyChongqing 401331China Chongqing Key Laboratory of Vanadium-Titanium Metallurgy and Advanced Materials Chongqing UniversityChongqing 400044China

The aim of this study was to investigate the phase transformation and kinetics of the solid-state reaction of CaO−V_(2)O_(5),which is the predominant binary mixture involved in the vanadium recovery *** analysis,X-ray diffraction spectroscopy,scanning electron microscopy,and energy dispersive spectrometry were used to characterize the solid-state reaction of the *** extent of the solid reac-tion was derived using the preliminary quantitative phase analysis of the X-ray *** results indicate that the solid reaction of the CaO−V_(2)O_(5)mixture is strongly influenced by the reaction temperature and CaO/V_(2)O_(5)mole *** transformation of calcium vanadate in-volves a step-by-step reaction of CaO−V_(2)O_(5),CaO−CaV_(2)O_(6),and CaO−Ca_(2)V_(2)O7 depending on the CaO/V_(2)O_(5)mole *** kinetic data of the solid reaction of the CaO−V_(2)O_(5)(1:1)mixture followed a second-order reaction *** activation energy(Ea)and preexponential factor(A)were determined to be 145.38 kJ/mol,and 3.67×10^(8)min^(−1),respectively.

关键词： calcium vanadate vanadium extraction solid-state reaction kinetics

A New Route for Identification of Precipitates on Austenite Grain Boundary in an Nb-V-Ti Microalloyed Steel

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Journal of Iron and Steel Research International 2011年第8期18卷 53-57页

作者： SHA qing-yun huang Guo-jian GUAN Ju MA Xiao-jun LI Da-hang Technology Center Angang Steel Company Limited Anshan 114009 Liaoning China

The precipitates on austenite grain boundaries in an Nb-V-Ti microalloyed steel have been investigated by transmission electron microscope （TEM） examination of carbon extraction replica. The replica was prepared from specimen etched with saturated picric solution rather than Nital which is conventionally used. Then particles on both grain boundaries and triple point of grain [aoundaries were clearly observed and identified as （Nb,Ti）（C, N） parti- cles. In case of conventional way, it is difficult to determine the location of particles with respect to austenite grain boundaries. The number of particles observed in new way developed was greatly reduced compared with that found in replica prepared by the conventional way, which may be caused by the dissolution of partial precipitates during the etching with longer time and at higher temperature involved in new way. Despite this, the new way developed pro- vides an effective way to determine the precipitate particles on austenite urain boundaries_

关键词： precipitate austenite grain boundary replica etch

Recovery of vanadium from vanadium slag by composite additive roasting-acid leaching process

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Journal of Iron and Steel Research International 2023年第7期30卷 1426-1439页

作者： Jun-yi Xiang Ming-shuai Luo Xi Lu Lu-wei Bai Zhong-peng Zhu qing-yun huang Sheng-qin Zhang Kun-peng Guo Xue-wei Lv College of Metallurgy and Materials Engineering Chongqing University of Science and TechnologyChongqing 401331China College of Materials Science and Engineering Chongqing UniversityChongqing 400044China

To minimize the vanadium content in the vanadium extraction tailings, composite additive roasting with (CaO + MgO) and subsequent acid leaching process was carried out dealing with vanadium-bearing converter slag. The effect of additive with different MgO/(CaO + MgO) molar ratios on the roasting and leaching behaviours of vanadium slag was investigated, and the optimum process conditions were obtained. The results show that in the roasting experiment, under the conditions of roasting temperature of 850 ℃ and roasting time of 2 h, the main kinds of vanadate transformed from Ca_(2)V_(2)O_(7) to Ca_(5)Mg_(4)V_(6)O_(2)4 and then to Mg_(2)V_(2)O_(7) with the increase in the MgO/(CaO + MgO) molar ratio. In the leaching experiment, under the conditions of particle size less than 75 μm, leaching temperature of 50 ℃, pH of 2.5, liquid–solid ratio of 20:1, and MgO/(CaO + MgO) molar ratio of 1:3, the leaching efficiency of vanadium is increased by about 5%, but the substitution of MgO for most or all of CaO will significantly reduce the leaching efficiency of vanadium. Furthermore, the leaching efficiency of impurities (P and Cr) can also be decreased by a composite addictive (CaO + MgO) roasting process. The X-ray diffraction, scanning electron microscopy, energy dispersive spectrometry, and X-ray photoelectron spectroscopy of the original vanadium slag and solid products of both roasting and leaching processes were also evaluated.

关键词： Vanadium slag Roasting Leaching Vanadate Recovery

Recovery of vanadium from vanadium slag by composite roasting with CaO/MgO and leaching

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Transactions of Nonferrous Metals Society of China 2020年第11期30卷 3114-3123页

作者： Jun-yi XIANG Xin WANG Gui-shang PEI qing-yun huang Xue-wei LÜ College of Materials Science and Engineering Chongqing UniversityChongqing 400044China College of Metallurgy and Materials Engineering Chongqing University of Science and TechnologyChongqing 401331China Chongqing Key Laboratory of Vanadium−Titanium Metallurgy and Advanced Materials Chongqing UniversityChongqing 400044China

A novel process of composite roasting with CaO/MgO and subsequent acid leaching was proposed to improve the recovery rate of vanadium from Linz–Donawiz(LD)converter vanadium *** effects of the MgO/(CaO+MgO)molar ratio and the roasting and leaching parameters on the recovery of vanadium were *** results showed that the leaching efficiency of vanadium decreased from 88%to 81%when CaO was replaced completely by MgO;however,it could be improved by roasting with the composite of CaO/*** maximum vanadium leaching efficiency of 94%was achieved under the optimum MgO/(CaO+MgO)mole ratio of 0.5:*** results from X-ray diffractometry(XRD)and scanning electron microscopy with energy-dispersive X-ray spectroscopy(SEM−EDS)confirm that the formation rate of acid-soluble vanadates can be enhanced during roasting with the composite of CaO/MgO and that the leaching kinetics can be accelerated owing to the suppression of calcium sulfate precipitation.

关键词： vanadium vanadium slag roasting acid leaching recovery

Preparation of FeCoNi medium entropy alloy from Fe^(3+)-Co^(2+)-Ni^(2+)solution system

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International Journal of Minerals,Metallurgy and Materials 2025年第1期32卷 92-101页

作者： Zongyou Cheng qing Zhao Mengjie Tao Jijun Du Xingxi huang Chengjun Liu Key Laboratory for Ecological Metallurgy of Multimetallic Mineral(Ministry of Education) Northeastern UniversityShenyang 110819China School of Metallurgy Northeastern UniversityShenyang 110819China Engineering Research Center of Frontier Technologies for Low-carbon Steelmaking(Ministry of Education) Shenyang 110819China

In recent years,medium entropy alloys have become a research hotspot due to their excellent physical and chemical *** controlling reasonable elemental composition and processing parameters,the medium entropy alloys can exhibit similar properties to high entropy alloys and have lower *** this paper,a FeCoNi medium entropy alloy precursor was prepared via sol-gel and coprecipitation methods,respectively,and FeCoNi medium entropy alloys were prepared by carbothermal and hydrogen *** phases and magnetic properties of FeCoNi medium entropy alloy were *** showed that FeCoNi medium entropy alloy was produced by carbothermal and hydrogen reduction at 1500℃.Some carbon was detected in the FeCoNi medium entropy alloy prepared by carbothermal *** alloy prepared by hydrogen reduction was uniform and showed a relatively high ***,the hydrogen reduction product exhibited better saturation magnetization and lower coercivity.

关键词： medium entropy alloy sol-gel co-precipitation carbothermal hydrogen reduction

PARTITION PROPERLY OF DOMAIN DECOMPOSITION WITHOUT ELLIPTICITY

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Journal of Computational Mathematics 2001年第4期19卷 423-432页

作者： Mo Mu (Deportment of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong) yun-qing huang (Department of Mathematics, Xiangtan University, Xiangtan 411105, China) 香港科技大学香港湘潭大学湖南湘潭 411105

Partition property plays a central role in domain decomposition methods. Existing theory essentially assumes certain ellipticity. We prove the partition property for prod lems without ellipticity which are of practical importance. Example applications include implicit schemes applied to degenerate parabolic partial differential equations arising from superconductors, superfluids and liquid crystals. With this partition property, Schwarz algorithms can be applied to general non-elliptic problems with an h-independent optimal convergence rate. Application to the time-dependent Ginzburg-Landau model of superconductivity is illustrated and numerical results are presented.

关键词： Partition property Domain decomposition Non-ellipticity Degenerate parabolic problems Time-dependent Ginzburg-Landau model Superconductivity Preconditioning Schwarz algorithms.

Trinuclear gold-catalyzed site-selective alkylation of peptides

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Science China Chemistry 2025年第1期68卷 249-256页

作者： qing-yun Fang Chengyihan Gu Yinghan Chen Wencheng Yan Yong Liang Weipeng Li Chengjian Zhu Jie Han Jin Xie State Key Laboratory of Coordination Chemistry Jiangsu Key Laboratory of Advanced Organic MaterialsChemistry and Biomedicine Innovation Center(ChemBIC)School of Chemistry and Chemical EngineeringNanjing UniversityNanjing 210023China Green Catalysis Center College of ChemistryZhengzhou UniversityZhengzhou 450001China State Key Laboratory of Natural Medicines China Pharmaceutical UniversityNanjing 211198China

Selective modification of peptides has always been a challenging *** selective alkylation of peptides can alter the biological activity and physical properties of molecules,and it has gained significant research *** herein disclose an intriguing gold-catalyzed alkylation of peptides using bench-stable unactivated alkyl bromides under photoredox catalysis.A wide range of structurally diverse primary,secondary and tertiary alkyl bromides serve as effective coupling partners to precisely connect with theα-C(sp^(3))–H in glycine residue of *** protocol demonstrates an exceptionally broad scope for alkyl halides and excellent tolerance for a wide range of useful functional groups.A series of relay transformations to construct cyclic peptides,to proceed click reaction and to realize peptide fluorescence labeling further enhance its synthetic *** addition,mechanistic studies and density functional theory(DFT)calculations reveal an inner-sphere and subsequent outersphere single electron transfer(SET)mechanism.

关键词： gold catalysis peptide alkylation C-C coupling radical

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