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Bifurcations of travelling wave solutions for two generalized Boussinesq systems

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Science China mathematics 2008年第9期51卷 1577-1592页

作者： LI JiBin1,2.1 department of mathematics, Zhejiang Normal university, Jinhua 32.004, China 2.department of mathematics, Kunming university of Science and Technology, Kunming 650093, China department of mathematics Zhejiang Normal University Jinhua 321004 China department of mathematics Kunming University of Science and Technology Kunming 650093 China

Using the methods of dynamical systems for two generalized Boussinesq systems, the existence of all possible solitary wave solutions and many uncountably infinite periodic wave solutions is obtained. Exact explicit parametric representations of the travelling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined.

关键词： nonlinear wave bifurcation solitary wave exact explicit solution generalized Boussinesq system 34C37 34C2. 74J30 58Z05

Boundary element-free method for elastodynamics

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Science China(Physics,Mechanics & Astronomy) 2005年第6期48卷 641-657页

作者： CHENG Yumin1 & PENG Miaojuan2.1. Shanghai Institute of Applied mathematics and Mechanics, Shanghai university, Shanghai 2.0072. China 2. {2. of Civil Engineering, Shanghai university, Shanghai 2.0072. China 1. Shanghai Institute of Applied mathematics and Mechanics Shanghai University 200072 Shanghai China 2. department of Civil Engineering Shanghai University 200072 Shanghai China

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.

关键词： moving least-square approximation, improved moving least-square approximation, elastodynamics, boundary integral equation, meshless method, boundary element-free method, Fourier eigen transform.

A predict-correct projection method for monotone variant variational inequalities

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Chinese Science Bulletin 1998年第15期43卷 1264-1267页

作者： HAN Qiaoming 1 and HE Bingsheng 2.1. Institute of Applied mathematics, Chinese Academy of Sciences, Beijing 100080, China 2. department of mathematics, Nanjing {2., Nanjing 2.0093, China Institute of Applied mathematics Chinese Academy of Sciences Beijing China department of mathematics Nanjing University Nanjing China

A predict_correct projection method is presented for solving monotone variant variational inequalities, which could exploit the advantages and overcome the difficulties of both explicit and implicit projection methods.

关键词： variant variational inequality explicit projection method implicit projection method predict_correct projection method.

On the Cayley-Bacharach property and the construction of vector bundles

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Science China mathematics 2011年第9期54卷 1891-1898页

作者： SUN Hao 1,2.1 department of mathematics and Statistics,Huazhong Normal university,Wuhan 430079,China 2.department of mathematics,East China Normal university,Shanghai 2.02.1,China 1. department of mathematics and Statistics Huazhong Normal University Wuhan 430079 China2. Department of Mathematics East China Normal University Shanghai 200241 China

We study the Cayley-Bacharach property on complex projective smooth varieties of dimension n≥2.for zero dimensional subscheme defined by the zero set of the wedge of r-n + 1 global sections of a rank r≥n vector bund... 详细信息

关键词： Cayley-Bacharach property vector bundle reflexive sheaf k-very ample

Mathematical stencil and its application in finite difference approximation to the Poisson equation

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Science China mathematics 2005年第10期48卷 1421-1429页

作者： FENG Hui~1 ZHANG Baolin~(1,2. & LIU Yang~1 1. department of mathematics,Wuhan university,Wuhan 430072.China 2. Laboratory of Computational Physics,Institute of Applied Physics and Computational {2.,Beijing 100088. China 1. department of mathematics Wuhan University 430072 Wuhan China 2. Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics 100088 Beijing China

The concept of mathematical stencil and the strategy of stencil elimination for solving the finite difference equation is presented, and then a new type of the iteration algorithm is established for the Poisson equation. The new algorithm has not only the obvious property of parallelism, but also faster convergence rate than that of the classical Jacobi iteration. Numerical experiments show that the time for the new algorithm is less than that of Jacobi and Gauss-Seidel methods to obtain the same precision, and the computational velocity increases obviously when the new iterative method, instead of Jacobi method, is applied to polish operation in multi-grid method, furthermore, the polynomial acceleration method is still applicable to the new iterative method.

关键词： mathematical stencil, stencil elimination, Poisson equation, finite difference, iterative algorithm,parallelism.

Flatness of CR submanifolds in a sphere

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Science China mathematics 2010年第3期53卷 701-718页

作者： JI ShanYu 1, & YUAN Yuan 2.1 department of mathematics, university of Houston, Houston, TX 772.4, USA 2.department of mathematics, Rutgers university, Piscataway, NJ 08854, USA 1. department of mathematics University of Houston Houston TX 77204 USA2. Department of Mathematics Rutgers University Piscataway NJ 08854 USA

In Euclidean geometry, for a real submanifold M in E n+a , M is a piece of E n if and only if its second fundamental form is identically zero. In projective geometry, for a complex submanifold M in CP n+a , M is a piece of CP n if and only if its projective second fundamental form is identically zero. In CR geometry, we prove the CR analogue of this fact in this paper.

关键词： CR submanifolds sphere CR second fundamental form proper holomorphic mappings between balls

Direct numerical simulation of a supersonic turbulent boundary layer on a flat plate and its analysis

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Science China(Physics,Mechanics & Astronomy) 2005年第5期48卷 626-640页

作者： HUANG Zhangfeng1, ZHOU Heng1,2.& LUO Jisheng1,2.1. department of Mechanics, Tianjin university, Tianjin 300072. China 2. Liu-Hui Center of Applied {2., Nankai university and Tianjin university, Tianjin 300072. China 1. department of Mechanics Tianjin University 300072 Tianjin China 2. Liu-Hui Center of Applied mathematics Nankai University and Tianjin University 300072 Tianjin China

Temporal mode direct numerical simulation (DNS) has been done for a supersonic turbulent boundary layer on a flat plate with Mach number 4.5. It was found that the mean flow profile, the normal-wise distribution of turbulent Mach number and the root mean square (RMS) of the fluctuations of various variables, as well as the Reynolds stresses, bore similarity in nature, when the turbulence reached a fully developed state. But the compressibility effect was strong and must be considered. The strong Reynolds analogy (SRA) and the Morkovin hypothesis were no longer valid. From the end of transition to the fully developed state of turbulence, it was in the transient period, for which the similarity did not hold.

关键词： turbulence, similarity, compressibility effect, supersonic boundary layer, direct numerical simulation.

Two applications of generalized Carleson measures to meromorphic Besov-type spaces

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Chinese Science Bulletin 1998年第15期43卷 1260-1264页

作者： TAN Haiou 1 and XIAO Jie 2.1. department of mathematics, Wuyi university, Jiangmen 52.02., China 2. School of Mathematical Sciences, Peking university, Beijing 100871, China department of mathematics Wuyi University Jiangmen China School of Mathematical Sciences Peking University Beijing China

The generalized Carleson measures are used to characterize the meromorphic Besov_type spaces and to explore some inclusions between these spaces.

关键词： generalized Carleson measures meromorphic Besov_type spaces.

DIRECT DIGITAL DESIGN AND SIMULATION OF MESHING IN WORM-GEAR DRIVE

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Chinese Journal of Mechanical Engineering 2006年第3期19卷 428-433页

作者： XU Wujiao QIN datong SHI Wankai State Key Laboratory of Mechanical Transmission Chongqing University Chongqing 400044 China

A direct digital design method （DDDM） of worm-gear drive is proposed. It is directly based on the simulation of manufacturing process and completely different from the conventional modeling method. The loaded tooth contact analysis （LTCA） method is analyzed, in which the advanced surface to surface searching technique is included. The influence of misalignment errors and contact deformations on contact zone and transmission error （TE） is discussed. Combined modification approach on worm tooth surface is presented. By means of DDDM and LTCA, it is very conven- ient to verify the effect of worm-gear drive＇s modification approach. The analysis results show that, the modification in profile direction reduces the sensitivity of worm-gear drive to misalignment errors and the modification in longitudinal direction decreases the TE. Thus the optimization design of worm-gear drive can be achieved prior to the actual manufacturing process.

关键词： Direct digital design Loaded tooth contact analysis Combined modification approach Worm-gear drive