When the escape velocity at a certain distance from the center reaches the speed of light , an event horizon is formed within which matter must inevitably collapse onto a single point , forming a singularity 当离中心某个距离的逃逸速度达到光速，形成一个活动视界，在里面的物质一定不可避免在单一点之上坍塌,形成一个奇异点。
Surveying power harmonic using the special effect on detecting singularity point and high resolving degree in time domain of wavelet , combined with the exact frequency resolving ability of fast fourier transform 利用小波变换突出的奇异点监测效果和较高的时域分辨率，结合快速傅立叶变换准确的频域分辨能力进行电力系统谐波分析。
At the center of the black hole , well inside the event horizon , general relativity predicts a singularity , a place where the curvature of spacetime becomes infinite and gravitational forces become infinitely strong 在黑洞中心，活动视界很里面的地方，广义相对论预言了时空弯曲变成了一个奇异点，一个时空弯曲无穷大和引力变得无穷大的地方。
Based on the singular stress field with multiple singularities , numerical methods to determine the orders of the multiple stress singularities are proposed from the numerical solutions obtained by common numerical procedures 其次，基于横观各向同性压电材料空间轴对称变形问题的通解，利用特征展开法，给出了奇异点附近的位移场和奇异应力场。
The most important problem in the multi - resolution method is how to reduce the effect of outliers while the estimation of the motion parameters are translating from the coarse resolution to the fine resolution 多分辨率分割过程中的一大问题是：当把低分辨率图像上的运动参数估计结果传递到高分辨率的图像上去时，要尽量降低奇异点对分析结果的影响。
Taking account of the corresponding characteristic of the signal singularity and wavelet transform module maximum in multi - scale changing , the discrete wavelet transform is applied to get the featured inflection point of negative pressure wave 利用信号奇异点与小波变换模极大值在多尺度上变化对应的性质，将离散小波变换应用到获取压力波信号序列特征奇异点中，可以对泄漏点进行定位。
Chapter 1 deals with the numerical simulation method . chapter 2 deals with the monte carlo methods . the monte carlo integration that the domain of integration is curved or complex connected curved polyhedron and the integrand has singular points is discussed in this chapter 第二章讨论了用montecarlo数值模拟方法求积分区域为曲面体和积分区域为复连通曲面体的情形，且被积函数有奇异点。
The least - squares fitting for regular surfaces , such as planes , spheres , cones , tori to 3d data points is researched . the efficiency of computing is improved greatly and the effect of singularities on fitting is avoided 研究了规则曲面的拟合算法，给出最小二乘法拟合平面、球面、圆柱面、圆锥面、圆环面等规则曲面的方法，这些方法的显著优点是提高了计算效率，避免了拟合过程中奇异点的影响。
Appropriate threshold and threshold function should be selected to fit the signal process goal when the method is applied . 3 ) developed a de - noise method based on translation invariance wavelet transform . the method performed the cycle - spinning for the signal to be de - noised 3 )针对donoho阈值去噪方法对小波基的平移依赖性而在信号奇异点产生的pseudo - gibbs现象，给出了一种平移不变小波变换去噪方法。
The relation between wavelet transform and signal singularity and the method of testing signal singularity employing wavelet transform are discussed in the paper , and gets different wavelet transform trends of signals with different characters 本文分析了小波变换与信号奇异性之间的关系，对使用小波变换检测信号奇异点的方法进行了讨论。得出了对于不同性质的信号，其小波变换的模极大值随尺度增加而变化的趋势。
