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On the periodic solutions of a type of differential-iterative equations

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Chinese Science Bulletin 1998年第3期43卷 204-206页

作者： GE Weigao 1. LIU Zhengrong 2.and YU Yuanhong 3 1. {1. of Applied {1., Beijing Institute of Technology, Beijing 1.0081. China {2., Yunnan university, Kunming 650091. China 3. Institute of Applied {1., C department of Applied {1. Beijing Institute of Technology Beijing China department of {1. Yunnan University Kunming China Institute of Applied mathematics Chinese Academy of Sciences Beijing China

Sufficient conditions for the existence of periodic solutions to a type of nonautonomous differential_iterative equations are given.

关键词： differential_iterative equation periodic solution fixed point.

The cohomology group of weak entwining structure

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Science China mathematics 2007年第5期50卷 665-674页

作者： Ling JIA & Fang LI department of {1., Ludong {2., yantai 2.402., China department of {1., Zhejiang {2., Hangzhou 31.02., China 1. department of {1. Ludong University Yantai 264025 China 2. department of mathematics Zhejiang University Hangzhou 310027 China

In this paper, we reveal that a weak entwining structure admits a rich cohomology theory. As an application we compute the cohomology of a weak entwining structure associated to a weak coalgebra-Galois extension.

关键词： weak entwining structure cohomology group 1.W80 1.W99

A complex variable meshless method for fracture problems

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Science China(Physics,Mechanics & Astronomy) 2006年第1期49卷 46-59页

作者： CHENG Yumin1.& LI Jiuhong2.1. Shanghai Institute of Applied {1. and Mechanics, Shanghai {1., Shanghai 2.0072. China 2. {2. of Building Engineering, Xi’an {1. of Technology, Xi’an 71.048, China Shanghai Institute of Applied mathematics Mechanics Shanghai University Shanghai 200072 China department of Building Engineering Xi’an University of Technology Xi’an 710048 China

Based on the moving least-square (MLS) approximation, the complex variable moving least-square approximation (CVMLS) is discussed in this paper. The complex variable moving least-square approximation cannot form ill-conditioned equations, and has greater precision and computational efficiency. Using the analytical solution near the tip of a crack, the trial functions in the complex variable moving least-square approxi- mation are extended, and the corresponding approximation function is obtained. And from the minimum potential energy principle, a complex variable meshless method for fracture problems is presented, and the formulae of the complex variable meshless method are obtained. The complex variable meshless method in this paper has greater precision and computational efficiency than the conventional meshless method. Some examples are given.

关键词： moving least-square approximation, complex variable moving least-square approximation, meshless method, complex variable meshless method, fracture.

A Fixed Point Theorem and an Equilibrium Point of an Abstract Economy in H-spaces

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Acta Mathematicae Applicatae Sinica 2003年第3期19卷 425-430页

作者： Ji-cheng Houdepartment of {1., Shantou {2., Shantou 51.063, ChinaCorrespondence address: department of {1. and Information Science, yantai university, yantai2.4005, China department of {1. Shantou University Shantou 515063 China department of {1. and Information Science Yantai University Yantai 264005 China

In this note we first prove a fixed point theorem in H-spaces which unities and extends the corresponding results in [6] and [9]. Then, by applying the fixed point theorem, we prove an existence theorem of an equilibr... 详细信息

关键词： H-space fixed points abstract economy non-compact domain Nash equilibria compactly open lower sections

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 {1. and Mechanics, Shanghai {1., Shanghai 2.0072. China 2. {2. of Civil Engineering, Shanghai {1., Shanghai 2.0072. China 1. Shanghai Institute of Applied mathematics and Mechanics Shanghai University 200072 Shanghai China 2. {1. 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.

Pole assignment in descriptor periodic systems

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Science China mathematics 2005年第10期48卷 1309-1332页

作者： FAN Hung-Yuan~1.LIN Wen-Wei~1.& XU Shufang~2.1. {1. of {1.,Tsing Hua {2.,Hsinchu 30043,China 2. LMAM,School of Mathematical Sciences,Peking {2.,Beijing 1.0871.China 1. department of {1. Tsing Hua University 30043 Hsinchu China 2. LMAM School of Mathematical Sciences Peking University 100871 Beijing China

In this paper a pole assignment problem is considered for the descriptor linear discrete-time periodic systems, which is using the periodic proportional-derivative feedback to modify a given system such that the closed loop system has a specified selfconjugate set of eigenvalues. It is shown that the complete reachability of an open loop periodic system is equivalent to the possibility of assigning an arbitrary set of the eigenvalues to the system by choosing the suitable periodic proportional-derivative feedback.A computational approach is also proposed to solve the problem, which uses the reliable numerical techniques based on the orthogonal transformations. Numerical examples are presented to illustrate the effectiveness of the proposed approach.

关键词： descriptor linear periodic system, pole assignment, proportional and derivative feedback, numerical method, periodic Schur decomposition.

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 {1., Tianjin 300072. China 2. Liu-Hui Center of Applied {2., Nankai {1. and Tianjin {1., Tianjin 300072. China 1. department of Mechanics Tianjin University 300072 Tianjin China 2. Liu-Hui Center of Applied {1. 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.

Online uniform machine covering with the known largest size

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Progress in Natural Science:Materials International 2007年第11期17卷 1271-1278页

作者： Cao Shunjuan1.2.and Tan Zhiyi1.3(1. {1. of {1., Zhejiang {2., Hangzhou 31.02., China 2. department of mathematics, Zhejiang Forestry {2., Hangzhou 31.300, China 3. State Key Laboratory of CAD & CG, Zhejiang {2., Hangzhou 31.02., China) department of {1. Zhejiang University Hangzhou 310027 China department of {1. Zhejiang Forestry University Hangzhou 311300 China State Key Laboratory of CAD & CG Zhejiang University Hangzhou 310027 China

This paper investigates the semi-online scheduling problem with the known largest size on two uniform machines. The objective is to maximize the minimum machine completion time. Both lower bounds and algorithms are given. Algorithms are optimal for the majority values of s≥1. where s is the speed ratio of the two machines. The largest gap between the competitive ratio and the lower bound is about 0.064. Moreover, the overall competitive ratio 2.matches the overall lower bound.

关键词： scheduling and covering uniform machine design and analysis of algorithm online competitive ratio

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 {1., Chinese Academy of Sciences, Beijing 1.0080, China {1., Nanjing {2., Nanjing 2.0093, China Institute of Applied mathematics Chinese Academy of Sciences Beijing China department of {1. 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.