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WAVELET-NUMERICAL METHOD IN CRACK ANALYSIS

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Applied Mathematics and Mechanics(English Edition) 2000年第10期21卷 1139-1144页

作者：沈远彤羿旭明 Department of Mathematics and Physics China University of Geosciences 430074 Wuhan P R China School of Mathematics Sciences Wuhan University 430072 Wuhan P R China

Properties of wavelet of good localization were used to approximate displacement fields near the crack tip. Wavelet-numerical algorithm and simulation singularity problem of the crack tip,cere established. As an examp... 详细信息

关键词： wavelet-numerical algorithm scaling function stress intensity factor singularity

CONSTRUCTION OF WAVELET BASES WITH VANISHING MOVEMENT

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Applied Mathematics and Mechanics(English Edition) 1999年第3期20卷 247-253页

作者：彭瑞仁陈基明彭康 Science College Shanghai University Shanghai P R China Changzhou Textile Industrial College Changzhou P R China

A kind of mother wavelet with good properties is constructed for any N greater than or equal to 2, which is differentiable for N times, converges to Zero at the order of O( I t I-N)( t --> infinity) and has N - 2 orde... 详细信息

关键词： vanishing movement scaling function orthogonal mother wavelet

A CLASS OF BIDIMENSIONAL NONSEPARABLEWAVELET PACKETS

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Acta Mathematica Scientia 2002年第1期22卷 131-137页

作者：田雄飞李云章 Beijing Polytech Univ Sch Appl Math & Phys Beijing 100022 Peoples R China

2-band wavelet packets in L-2 (R-s) were constructed in [3]. In this note, a way to construct bidimensional orthonormal wavelet packets related to the dilation matrix M = ((1)(1) (1)(-1)) is obtained. M-wavelets are used ill quincunx subsampling in two dimensions for image processing. What is more., the approach of this paper can be generalized to construct wavelet packets in L-2 (R-s) related to a general diltion matrix.

关键词： scaling function wavelet wavelet packet

Asymptotic Behavior of Gibbs functions for M-Band Wavelet Expansions

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Acta Mathematica Sinica,English Series 1999年第2期15卷 165-172页

作者： Daren Huang Zeyin Zhang, Center for Mathematical Sciences, Zhejiang University, Hangzhou 310027, P. R. China Center for Mathematical Sciences Zhejiang University Hangzhou P. R. China

In this paper the asymptotic behavior of Gibbs function for a class of M-band wavelet expansions is given. In particular, the Daubechies’ wavelets are included in this class.

关键词： Gibbs phenomenon Wavelet expansion Filter scaling function Vanishing moment

Minimum-energy wavelet frame on the interval

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Science in China(Series F) 2008年第10期51卷 1547-1562页

作者： GAO XiePing CAO ChunHong College of Information and Engineering Xiangtan University Xiangtan 411105 China

The construction and properties of interval minimum-energy wavelet frame are systematically studied in this paper. They are as follows： 1） give the definition of interval minimum-energy wavelet frame; 2） give the necessary and sufficient conditions for the minimum-energy frames for L^2[0,1]; 3） present the construction algorithm for minimum-energy wavelet frame associated with refinable functions on the interval with any support y; 4） give the decomposition and reconstruction formulas of the minimum-energy frame on the interval [0,1],

关键词： scaling function multi-resolution analysis wavelet on the interval frame minimum-energy

Distributed Average Consensus in Multi-agent Networks with Limited Bandwidth and Time-delays

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IEEE/CAA Journal of Automatica Sinica 2014年第2期1卷 193-203页

作者： Wenhui Liu Feiqi Deng Jiarong Liang Haijun Liu College of Automation Science and Engineering South China University of Technology School of Computer Electronics and InformationGuangxi University School of Mathematics and Statistics Zhengzhou University

This paper studies the distributed average consensus problem of multi-agent digital networks with time-delays. For the network, each agent can only exchange symbolic data with its neighbours. We provide a distributed average consensus protocol which uses the quantized and time-delay information. We consider two types of dynamic encoders/decoders in our *** uses inverse proportion function as scaling function, while the other uses exponential function as scaling function. All agents can reach average consensus asymptotically with our ***, we show that the average consensus protocol is robust to finite symmetric time-delays, but is sensitive to asymmetric time-delays that will destroy the average consensus of the networks. Finally, simulations are presented to illustrate validity of our theoretical results.

关键词： Algorithm design and analysis Bandwidth Communication channels Decoding Protocols Quantization (signal) Multi-agent networks average consensus communication constraints quantization time-delays NETWORKING AGENT Bandwidth Quantization time delay scaling function Algorithm design and analysis Communication channels DECODING protocols

Daubechies Wavelet Meshless Method for 2-D Elastic Problems

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Tsinghua Science and Technology 2008年第5期13卷 605-608页

作者：刘亚男刘应华岑章志 epartment of Engineering Mechanics Tsinghua University

This paper introduces a meshless method based on Daubechies （DB） wavelets for 2-D elastic problems. The scaling and wavelet functions of the DB wavelet are used as basis functions to approximate the unknown field functions, so there is no need to construct costly shape functions as in the finite element method （FEM） and other meshless methods. In addition, the properties of the DB wavelets facilitate implementation of the method. The new method is used to analyze the elastic problem of a plain plate with a circle hole, and the numerical results agree well with the FEM. This method is effective and can be extended to solve complicated two or three dimensional problems.

关键词： wavelet meshless method scaling function shape function

AN MRA YIELDS AN ORTHONORMAL WAVELET BASIS——AN OPERATOR THEORETIC PROOF

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Applied Mathematics(A Journal of Chinese Universities) 1996年第1期11卷 77-84页

作者： DAI XINGDE LU SHIJIE Department of Mathematics, UNCC, Charlotte, UN 28223, USA. Department of Applied Mathematics, Zhejiang University Hangzhou 310027 Department of Mathematics UNCC Charlotte USA Department of Applied Mathematics Zhejiang University Hangzhou

In this paper we show how to construct a scaling function and an orthonor-mal wavelet basis from a multiresolution approximation using an operator theoreticmethod.

关键词： Multiresolution approximation scaling function orthonormal wavlet conjugate linear operator.

Two—phase flow in correlated pore—throat random porous media

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Chinese Physics B 2002年第4期11卷 358-365页

作者：田巨平姚凯伦 DepartmentofPhysics WuhanInstituteofScienceandTechnologyWuhan430073China DepartmentofPhysicsHuazhongUniversityofScienceandTechnology Wuhan430074China CCAST(WorldLaboratory) Beiji

We have constructed a porous media model in which there are percolation clusters with varying percolation probability P and correlated site-bonds. Taking into account both the pore and the throat geometry, the viscous fingering (VF) in porous media has been investigated by using the standard over-relaxed Gauss-Seidel scheme. The simulation results show that the VF structure varies with the correlation parameter ε, the viscosity ratio M and the percolation probability P. The smaller the correlation parameter ε, the greater the deviation of the normalized size distribution of the invaded throat Ninv(r) from the truncated Rayleigh distribution. For a larger viscosity ratio M, the VF pattern looks like a diffusion-limited-aggregation structure in percolation clusters. The fractal dimension D increases with the increase of the percolation probability P and the correlation parameter ε. The velocity distribution f?(α) of VF in percolation clusters is of a parabola-like curve. The tail of the distribution (large α) is longer for a larger correlation parameter ε. For a smaller ε, the distribution is very sharp. The sweep efficiency E decreases along with the decrease of the correlation parameter ε and the increase of the network size Lnz. E has a minimum as Lnz increases up to the maximum no matter what the values of P, M and ε. The E?~?Lnz curve has a frozen zone and an active zone. The geometry and the topology of the porous media have strong effects on the displacement processes and the structure of VF.

关键词： correlation parameter fractal dimension sweep efficiency scaling function