Integral transform solution of multi-material structure with finite crack perpendicular to the interface

The plane elasticity problem for layered elastic systems containing a finite crack perpendicular to the interface is considered. To derive the singular integral equations. Fourier transform in conjunction with dislocation is used. The singular integral equation is solved with the Lobatto-Chebyshev method commonly applied to such problems. In order to have an idea about the usefulness of the method described, a two-layer structure which contains a cut parallel toh is considered.     

Analysis of Digital Lateral Shearing Interferometer

A new method is proposed for reconstructing wavefront from discretely sampled interferogram data obtained by a digital lateral shearing interferometer. Assumptions applied in the conventional methods are not used and reconstruction error caused by the difference between the amount of shear and the sampling interval can be removed. System error and the influence of the discrete sampling, which limit accuracy of the tested results of the lateral shearing interferometer, are analyzed.     

基于经验模态分解滤波的低频振荡Prony分析

传统Prony法在分析低频振荡时对输入信号要求较高,存在着对噪声敏感的弱点.因此提出一种经验模态分解滤波和改进Prony法相结合的低频振荡分析方法.该方法先用经验模态分解对低频振荡信号进行自适应滤波,再用改进Prony法对滤波后的信号进行分析.其中,改进Prony法有效阶数用归一化奇异值法确定.将该方法分别用于分析试验信号和IEEE 4机系统振荡信号,并与基于低通滤波器的Prony分析进行比较.结果表明,在较大噪声环境下,该方法仍然能相对准确的辨识出低频振荡主导模式,验证了其有效性. 关键词： 低频振荡 经验模态分解 改进Prony法 归一化奇异值法     

Atomization process for convolution operators on locally compact groups

We develop for a large class of locally compact groups a method of approximation of convolution operators on by finitely supported measures with control of the support and of the operator norm of the approximating measures.

     

Nonlinear Parabolic Equations with Singularities in Colombeau Vector Spaces

We consider nonlinear parabolic equations with nonlinear non-Lipschitz＇s term and singular initial data like Dirac measure, its derivatives and powers. We prove existence-uniqueness theorems in Colombeau vector space yC^1,W^2,2（[0,T）,R^n）,n ≤ 3. Due to high singularity in a case of parabolic equation with nonlinear conservative term we employ the regularized derivative for the conservative term, in order to obtain the global existence-uniqueness result in Colombeau vector space yC^1,L^2（[0,T）,R^n）,n≤ 3.     

A transform involving Chebyshev polynomials and its inversion formula

We define a functional analytic transform involving the Chebyshev polynomials Tn(x), with an inversion formula in which the Möbius function μ(n) appears. If s∈C with Re(s)>1, then given a bounded function from [−1,1] into C, or from C into itself, the following inversion formula holds:

     

C-Series Discrete Chains

We find analogues of the generalized two-dimensional Toda chains of the C^N and series with three discrete independent variables and give Lax pairs for these chains. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 2, pp. 208–221, February, 2006.     

Zero cycles on certain surfaces in arbitrary characteristic

Letk be a field of arbitrary characteristic. LetS be a singular surface defined overk with multiple rational curve singularities and suppose that the Chow group of zero cycles of its normalisation is finite dimensional. We give numerical conditions under which the Chow group of zero cycles ofS is finite dimensional.