【Key words】 Element-free Galerkin method； Moving least square method； Element free-direct displacement method； Stress intensity factors； Singular basis；
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采用具有小支集的奇异基函数的有限元方法求解奇异两点边值问题的奇异解。
In this paper we suggesst a finite element method for singular two point boundary value problems with singular solution by introducing singular basis with local support.
小波是表示具有点奇异性函数的最优基，它由于具有时-频局部化特点和多尺度特性，在图像处理领域得到了广泛应用。
Wavelet is the best base of functions, with point singularity, and it has wide application in image processing because of its time-frequency localization and multiscale features.
在分析小波变换物理本质和奇异性检测原理的基础上，研究了小波基和白噪声对信号奇异性检测性能的影响。
Based on analyzing the physical essence and the principle of singularity detection, this paper discusses the effect of wavelet bases and white noise on signal singularity detection.
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