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A NOTE ON THE DIPERNA-LIONS FLOWS

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Acta Mathematica Scientia 2011年第5期31卷 1719-1724页

作者：刘昕黄文亮 school of computer science and technology Huazhong University of Science and Technology Department of Mathematics East China University of Science and Technology

In this note, we give a short proof for the DiPerna-Lions flows associated to ODEs following the method of Crippa and De Lellis [3]. More precisely, assume that [divb] ∈ Ll∞oc（Rd）, ｜b｜/（1 ＋｜x｜ log ｜x｜） ∈ L∞（Rd） and ｜ b｜ φ（｜ b｜） ∈ Ll1oc（Rd）, where φ（r） = log log（r ＋ c）, c 0. Then, there exists a unique regular Lagrangian flow associated with the ODE X˙（t, x） = b（X（t, x））, X（0, x） = x.

关键词： DiPerna-Lions flow Hardy-Littlewood maximal function

JACOBI SPECTRAL APPROXIMATIONS TO DIFFERENTIALEQUATIONS ON THE HALF LINE

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Journal of Computational Mathematics 2000年第1期18卷 95-112页

作者： Ben-yu Guo(Department of Mathematics, Shanghai normal university, Shanghai 200234, china)(COM2MAC, Pohang university of science and technology, Pohang, Korea) 上海师范大学上海 200234

Presents a study which investigated some Jacobi approximations which are used for numerical solutions of differential equations on the half line. Application of the approximations to problems on unbounded domains; Alg... 详细信息

关键词： Jacobi spectral approximations differential equations on the half line stability and convergence

Image space analysis for variational inequalities with cone constraints and applications to traffic equilibria

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science china Mathematics 2012年第4期55卷 851-868页

作者： LI Jun 1,& HUANG nanjing 2 1 College of Mathematics and Information,china West normal university,Nanchong 637009,china 2 Department of Mathematics,Sichuan university,Chengdu 610064,china College of Mathematics and Information China West Normal University Nanchong China Department of Mathematics Sichuan University Chengdu China

In this paper,the image space analysis (for short,ISA) is employed to investigate variational in- equalities (for short,VI) with cone *** separation for VI with cone constraints is characterized by using the normal cone to a regularization of the image,and saddle points of the generalized Lagrangian func- ***-type necessary and sufficient optimality conditions for VI with cone constraints are presented by using a separation *** functions and weak sharpness for VI with cone constraints are also investi- ***,the obtained results are applied to standard and time-dependent traffic equilibria introduced by Daniele,Maugeri and Oettli.

关键词：变分不等式空间分析交通应用拉格朗日函数图片分离定理时间依赖

The Young's moduli prediction of random distributed short-fiber-reinforced polypropylene foams using finite element method

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science china(Technological sciences) 2009年第1期52卷 72-78页

作者： WANG Bo1, WANG RongXiu2 & WU Yong1 1 school of Mathematic science, Chongqing Institute of technology, Chongqing 400050, china 2 Department of computer science and Information Engineering, Chongqing technology and Business university, Chongqing 400067, china school of Mathematic science Chongqing Institute of Technology Chongqing China Department of computer science and Information Engineering Chongqing Technology and Business University Chongqing China

The elastic moduli of short-fiber-reinforced foams depend critically on the fiber content and fiber length, as well as on the fiber orientation distribution. Based on periodic tetrakaidecahedrons, the finite element models with short-fiber reinforcement were proposed in this paper to examine the effects of the fiber content and fiber length on Young's modulus. The fiber length distribution and fiber orientation distribution were also considered. The proposed models featured in a three-dimensional diorama with random short-fiber distribution within or on the surfaces of the walls and edges of the closed-cells of polypropylene (PP) foams. The fiber length/orientation distributions were modeled by Gaussian prob-ability density functions. Different fiber volume fractions, different lengths, and different distributions were investigated. The predicted Young's moduli of the PP foams with short-glass-fiber or short-carbon-fiber reinforcement were compared with other theoretic and experimental results, and the agreement was found to be satisfactory. The proposed finite element models were proved to be acceptable to predict the Young's moduli of the grafted closed-cell PP foams with short-fiber reinforcement.

关键词： short-fiber reinforcement Young’s modulus finite element Gaussian distribution

A new calculation method for the number of radial slots of a Terfenol rod

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science china(Technological sciences) 2009年第2期52卷 336-338页

作者： HE XiPing1 & ZHANG Pin2 1 Applied Acoustics Institute, Shaanxi normal university, Xi’an 710062, china 2 school of science, Xi’an university of Architecture and technology, Xi’an 710055, china Applied Acoustics Institute Shaanxi Normal University Xi’an China school of science Xi’an University of Architecture and Technology Xi’an China

Terfenol is an ideal choice for medium to high power low frequency sonar. It can offer the transducer designer higher strain, higher power density, but the designer must be aware of the eddy current. To enhance efficiency of the barrel-stave transducer powered by a Terfenol rod, radial slots rather than laminations were used to control eddy currents in the Terfenol drive rod, and the effectiveness and the number of these slots were studied experimentally and calculated by finite element modeling. Based on the characteristic of vortex path, a new simple geometrical method to calculate the number of the radial slots of a Terfenol rod at the operating frequency is put forward in this paper. Moreover, the calculated results are in good agreement with those of using the finite element method (FEM) for the slotted Terfenol rod given by the literature. The method will save much cost to design Terfenol rod transducers.

关键词： Terfenol-D rod eddy current losses limit operating frequency

IR STUDY ON MONOMOLECULAR PARTICLE AGGLOMERATES OF POLYSTYRENE OBTAINED BY FREEZE-DRYING OF ITS DILUTE SOLUTION

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Chinese Journal of Polymer science 2002年第4期20卷 381-383页

作者： Song Wang Qing-hua Wang Rong-shi Cheng Research Center of Materials Beijing Institute of technology Beijing 100081, china Department of Chemistry nanjing university nanjing 210093, china Research Center of Materials Beijing Institute of Technology 北京 100081 Department of Chemistry Nanjing University Nanjing 210093

The monomolecular particle agglomerates of polystyrenes were obtained by freeze-drying of its very dilute solutions of 1.3 x 10(-5)-2.0 x 10(-5) g/mL in benzene:cylcohexane (100:1) solvents, and they were annealed at room temperature for hundred days before use. According to C-13-NMR measurement the polystyrenes should be practically atactic. The number average molecular weights of the samples are 2.80 x 10(3), 2.00 x 10(4), and 1.55 x 10(6), respectively. The freeze-dried aPS with a molecular weight higher than 10(4) show two new IR absorption bands at 1098 and 1261 cm(-1), which are absent in the normal aPS and freeze-dried styrene oligomer. It was also found that the low molecular weight samples can only form powders, whereas the freeze-dried aPS with higher molecular weight form a mixture of powders and fibrils, of which the longer fibrils show a much stronger 1261 cm(-1) band than the shorter fibrils and the powder. It seems that the 1261 cm(-1) band corresponds to the stacking behavior of monomolecular particles.

关键词： monomolecular particles atactic polystyrene FTIR spectroscopy

A centrality measure based on spectral optimization of modularity density

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science china(Information sciences) 2010年第9期53卷 1727-1737页

作者： FU LiDong1,2*,GAO Lin1 & MA XiaoKe1 1school of computer science and Engineering,Xidian university,Xi'an 710071,china 2College of computer,Xi'an university of science and technology,Xi'an 710054,china school of computer science and Engineering Xidian University Xi’an China College of computer Xi’an University of Science and Technology Xi’an China

Centrality analysis has been shown to be a valuable method for the structural analysis of complex *** is used to identify key elements within networks and to rank network elements such that experiments can be tailored to interesting *** this paper,we show that the optimization process of modularity density can be written in terms of the eigenspectrum of kernel *** on the eigenvectors belonging to the largest eigenvalue of kernel matrix,we present a new centrality measure that characterizes the contribution of each node to its assigned community in a network,called modularity density *** measure is illustrated and compared with the standard centrality measures by using respectively an artificial example and a classic network data *** statistical distribution of modularity density centrality is investigated by considering large computer generated graphs and two large networks from the real *** results show the significance of the proposed approach.

关键词： centrality modularity density centrality kernel matrix eigenspectrum

A priori error analysis of a discontinuous Galerkin approximation for a kind of compressible miscible displacement problems

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science china Mathematics 2010年第10期53卷 2679-2696页

作者： YANG JiMing1,& CHEN YanPing2 1College of science,Hunan Institute of Engineering,Xiangtan 411104,china 2school of Mathematical sciences,South china normal university,Guangzhou 510631,china College of science Hunan Institute of Engineering Xiangtan China school of Mathematical sciences South China Normal University Guangzhou China

A kind of compressible miscible displacement problems which include molecular diffusion and dispersion in porous media are investigated.A symmetric interior penalty discontinuous Galerkin (SIPG) method is applied to the coupled system of flow and *** the induction hypotheses instead of the cut-off operator and the interpolation projection properties,a priori hp error estimates are *** error bounds in L2(H1) norm for concentration and in L∞(L2) norm for velocity are optimal in h and suboptimal in p with a loss of power 1/2.

关键词： a priori error discontinuous Galerkin compressible miscible displacement coupled system

Global view of Hopf bifurcations of a van der Pol oscillator with delayed state feedback

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science china(Technological sciences) 2010年第3期53卷 595-607页

作者： ZHANG Li1,WANG HuaiLei1 & HU HaiYan1,2 1 MOE Key Lab of Mechanics and Control of Aerospace Structures,nanjing university of Aeronautics and Astronautics,nanjing 210016,china 2 school of Aerospace Engineering,Beijing Institute of technology,Beijing 100081,china MOE Key Lab of Mechanics and Control of Aerospace Structures Nanjing University of Aeronautics and Astronautics Nanjing China school of Aerospace Engineering Beijing Institute of Technology Beijing China

This paper presents both analytical and numerical studies on the global view of Hopf bifurcations of a van der Pol oscillator with delayed state *** on a detailed analysis of the stability switches of the trivial equilibrium of the system,the stability charts are given in a parameter space consisting of the time delay and the feedback *** center manifold reduc-tion and the normal form method are used to study Hopf bifurcations with respect to the time *** gain an insight into the persistence of a Hopf bifurcation as the time delay varies farther away from its critical value,the method of multiple scales is used to obtain the global view of Hopf bifurcations with respect to the time *** the analytical results of Hopf bifurca-tions and global view of those bifurcations are validated via a collocation scheme implemented on *** most important discovery in this paper is the well-structured global view of Hopf bifurcations for the system of concern,showing the generality of the persistence of Hopf bifurcations.

关键词： Hopf bifurcation global view center manifold reduction method of multiple scales collocation scheme