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Spectrum of a class of fourth order left-definite differential operators

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Applied Mathematics(A Journal of Chinese Universities) 2008年第1期23卷 51-56页

作者： gao yun-lan SUN Jiong Dept. of Math. Inner Mongolia Univ. of Tech. Hohhot 010051 China. Dept. of Math. Inner Mongolia Univ. Hohhot 010021 China.

The spectrum of a class of fourth order left-definite differential operators is studied. By using the theory of indefinite differential operators in Krein space and the relationship between left-definite and right-definite operators, the following conclusions are obtained： if a fourth order differential operator with a self-adjoint boundary condition that is left-definite and right-indefinite, then all its eigenvalues are real, and there exist countably infinitely many positive and negative eigenvalues which are unbounded from below and above, have no finite cluster point and can be indexed to satisfy the inequality …≤λ-2≤λ-1≤λ-0〈0〈λ0≤λ1≤λ2≤…

关键词： left-definite differential operator right-definite differential operator Krein space spectrum,eigenvalue.

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.

COUPLING EFFECT OF FLEXIBLE JOINT AND FLEXIBLE LINK ON DYNAMIC SINGULARITY OF FLEXIBLE MANIPULATOR

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Chinese Journal of Mechanical Engineering 2008年第1期21卷 9-12页

作者： gao Zhihui yun Chao BIAN Yushu School of Mechanical Engineering and Automation Beihang University Beijing 100083 China

The coupling effect of the flexible joint and the flexible link on the dynamic singularity of the flexible manipulator is addressed. Firstly, the dynamic equations of a flexible manipulator with a flexible joint and a flexible link are derived. Secondly, the relationship and property between the flexible joint and the flexible link are analyzed. It shows that the flexible joint＇s amplitude will increase abruptly, thereby the dynamic singularity occurs if the frequency of a flexible joint is near or equal to some natural frequency of a flexible link. Finally, some numerical simulations which will verify the correctness of the theoretical analysis, are carded out. The results are fundamental for the design of a flexible manipulator and for the avoidance of the dynamic singularity.

关键词： Dynamic singularity Resonance Natural frequency Flexible manipulator

OPTIMAL CONTROL OF THE FLEXI-BLE LINK MANIPULATOR WITH CONTROLLABLE LOCAL DEGREES OF FREEDOM

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Chinese Journal of Mechanical Engineering 2008年第4期21卷 27-30页

作者： BIAN Yushu yun Chao gao Zhihui School of Mechanical Engineering and Automation Beihang Universily Beijing 100083 China State Key Laboratory for Manufacturing Systems Engineering Xi＇an Jiaotong University Xi＇an 710049 China School of Mechanical Engineering and Automation Beihang University Beijing 100083 China

Although flexible manipulators own many potential advantages, one of their major disadvantages is the deterioration of the end-effector accuracy due to the flexibility. Therefore, how to reduce vibration is a significant problem. Inspired by the observation on the motion behaviors of animals, a new idea of decreasing motion deflection of the flexible manipulator is suggested. The concept of controllable local degrees of freedom is proposed and analyzed. By way of optimizing local motion provided by the controllable local degrees of freedom, the end-effector deflection of the flexible manipulator can be effectively decreased through dynamic coupling. The corresponding optimal method for vibration control of the flexible manipulator is put forward. The kinematic simulation is carried ant on a three-link flexible manipulator The corresponding results verify the feasibility of this method.

关键词： Flexible manipulator Vibration Flexibility Local degree of freedom

“Cutting effect” of organoclay platelets in compatibilizing immiscible polypropylene/polystyrene blends

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2008年第11期9卷 1614-1620页

作者： Yan ZHU Hai-yun MA Li-fang TONG Zheng-ping fang MOE Key Laboratory of Macromolecular Synthesis and Functionalization Institute of Polymer Composites Zhejiang University Hangzhou 310027 China Department of Blochemical and Chemical Engineermg Ningbo Institute of Technology Zhejiang University Ningbo 315100 China

In this work, polypropylene (PP)/polystyrene (PS) blends with different organoclay concentrations were prepared via melt compounding. Differing from the results of previous reports, the organoclay platelets are mostly located in the dispersed PS phase instead of the interface. The dimensions of the dispersed PS droplets are greatly reduced and apparent compatibilization effect still exists, which cannot be explained by the traditional compatibilization mechanism. A novel compatibilization mecha- nism, "cutting" to apparently compatibilize the immiscible PP/PS blends was proposed. The organoclay platelets tend to form a special "knife-like structure" in the PS domain under the shear stress of the continuous PP phase during compounding. The "clay knife" can split the dispersed PS domain apart and lead to the dramatic reduction of the dispersed domain size.

关键词： Compatibilization Organoclay Polymer blends Polypropylene (PP) Polystyrene (PS)

Scattering Versus Blowup Beyond the Mass-Energy Threshold for the Davey–Stewartson Equation in R^(3)

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Acta Mathematica Sinica,English Series 2021年第9期37卷 1415-1436页

作者： Yan fang gao Zhi Yong WANG School of Mathematics and Statistics&Fujian Key Laboratory of Mathematical Analysis and Applications Fujian Normal UniversityFuzhou 350117P.R.China

We study the Cauchy problem for the Davey–Stewartson equation i?tu+Δu+|u|^(2) u+E1(|u|^(2))u=0,(t,x)∈R×R^(3).The dichotomy between scattering and finite time blow-up shall be proved for initial data with finite va... 详细信息

关键词： Davey–Stewartson equation scattering blow-up finite variance

Effects of Prandtl number in two-dimensional turbulent convection

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Chinese Physics B 2021年第9期30卷 290-296页

作者： Jian-Chao He Ming-Wei fang Zhen-Yuan gao Shi-Di Huang yun Bao School of Aeronautics and Astronautics Sun Yat-sen UniversityGuangzhou 510275China Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering Southern University of Science and TechnologyShenzhen 518055China Guangdong Provincial Key Laboratory of Turbulence Research and Applications Southern University of Science and TechnologyShenzhen 518055China

We report a numerical study of the Prandtl-number(Pr)effects in two-dimensional turbulent Rayleigh-Bénard *** simulations were conducted in a square box over the Pr range from 0.25 to 100 and over the Rayleigh number(Ra)range from 10^(7) to 10^(10).We find that both the strength and the stability of the large-scale flow decrease with the increasing of Pr,and the flow pattern becomes plume-dominated at high *** evolution in flow pattern is quantified by the Reynolds number(Re),with the Ra and the Pr scaling exponents varying from 0.54 to 0.67 and-0.87 to-0.93,*** is further found that the non-dimensional heat flux at small Ra diverges strongly for different Pr,but their difference becomes marginal as Ra *** the thermal boundary layer,the spatially averaged thicknesses for all the Pr numbers can be described byδθ~Ra^(-0.30) approximately,but the local values vary a lot for different Pr,which become more uniform with Pr increasing.

关键词： turbulent convection Prandtl number direct numerical simulations(DNS)

The Spectrum Sequences of Periodic Frame Multiresolution Analysis

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Acta Mathematica Sinica,English Series 2009年第3期25卷 403-418页

作者： yun Zhang LI Qiao fang LIAN College of Applied Sciences Beijing University of Technology Beijing 100124 P. R. China Department of Mathematics Beijing Jiaotong University Beijing 100044 P. R. China

The periodic multiresolution analysis （PMRA） and the periodic frame multiresolution analysis （PFMRA） provide a general recipe for the construction of periodic wavelets and periodic wavelet frames, respectively. This paper addresses PFMRAs by the introduction of the notion of spectrum sequence. In terms of spectrum sequences, the scaling function sequences generating a normalized PFMRA are characterized; a characterization of the spectrum sequences of PFMRAs is obtained, which provides a method to construct PFMRAs since its proof is constructive; a necessary and sufficient condition for a PFMRA to admit a single wavelet frame sequence is obtained; a necessary and sufficient condition for a PFMRA to be contained in a given PMRA is also obtained. What is more, it is proved that an arbitrary PFMRA must be contained in some PMRA. In the meanwhile, some examples are provided to illustrate the general theory.

关键词： PFMRA periodic wavelet frame scaling function sequence spectrum spectrum sequence

A collaborative strategy for enhanced reduction of Cr(Ⅵ) by Fe(0) in the presence of oxalate under sunlight:Performance and mechanism

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Journal of Environmental Sciences 2020年第4期32卷 385-394页

作者： Qi Zhou Yang Li Heng Yang yun gao College of Chemistry and Chemical Engineering Anhui UniversityHefei 230601China Guangzhou Key Laboratory of Environmental Catalysis and Pollution Control School of Environmental Science and EngineeringInstitute of Environmental Health and Pollution ControlGuangdong University of TechnologyGuangzhou 510006China Chengdu Integrated Testing Center of Rocks and Ores Sichuan Geology and Mineral Exploration and Development BureauChengdu 610081China Anhui Electric Power Construction Second Engineering Co.Ltd. China Energy Construction GroupHefei 230000China

Nanometer-size zero-valent iron(NZVI)is an efficient reducing agent,but its surface is easily passivated with an oxide layer,leading to reaction *** our study,oxalate(OA)was introduced into this heterogeneous system of NZVI,which could form ferrioxalate complexes with the NZVI surface-bound Fe3+and dissolved Fe3+in the *** of ferrioxalate complexes can facilitate the generation of Fe2+from Fe3+and CO2·-radical,both species have strong reduction ***,a"photo-oxalate-Fe(0)"system through sunlight induction was established,which not only prohibited the formation of a surface passivation layer,but also displayed a synergetic mechanism of ferrioxalate photolysis to enhance reduction,exhibiting remarkably higher degradation activity(several times faster)toward the model pollutant Cr(Ⅵ)than the mechanism with NZVI *** tests suggested that both NZVI dosage and OA content markedly affected the reduction *** pH was beneficial to the reduction ***,recyclability experiment showed that the reduction rate decreased from 0.21706 to 0.03977 min-1 after three cycles of reuse due to the NZVI losing reaction activity generally,but the system still maintained considerable reduction ***,a mechanism was revealed whereby NZVI would transform to Fe oxides after the exhaustion of its reductive power,and the photolysis of ferrioxalate to promote the cycling of iron species played the predominant role in providing extra reduction *** features confirm that introduction of OA into Cr(Ⅵ)reduction by NZVI through sunlight induction is advantageous and promising.

关键词： Nanometer-size zero-valent iron Oxalate Sun irradiation Photolysis of ferrioxalate Cycling of surface iron Synergetic mechanism