点变换

Photopic map is used to obtain local patterns, and a three-grade representation structure (dot pattern, line pattern and surface pattern) is proposed to memorize and match local patterns.

文中提出通过明视变换来得到局部模式，并提出了局部模式的三级表象结构（点模式、线模式和面模式）以及它们的记忆、匹配方法。

Based on the analysis of similarities and differences between core data, well log and seismic prospecting, the thesis makes a primary match between them;(2) Through layer boundary dividing by Walsh transformation, lithology determination by gray system and stratigraphy correlation by dynamic waveform match, an application to the aimed area was done;(3) This paper also gives the research on the character of well logs and reservoir parameters. According to the FBM protype, the profile of density and acoustic value between two wells was built. And the result showed good accordance with real logs.(4) By means of fractal reconstruction, it rebuilt the three dimensional shapes of the main stratigraphy boundaries in the studied area.

在详细分析总结岩心、测井和地震数据异同点的基础上，对三种数据进行了初步的匹配；②通过对测井曲线的沃尔什变换分层、灰色关联法岩性判别，综合多种动态层序对比技术，增改对比过程所需要的参数，进行了井间地层对比方法的探讨与应用研究；③详细研究了测井曲线以及储层参数分布的分形特征，以分数布朗运动为原型模拟出两口井中间对应地层的密度和时差参数剖面，结果与验证井数据表现出了良好的一致性；④采用分维重建方法再现了研究区块泉头组顶底面以及登二段底面的空间形态。

The interfacial stability of the model was studied by Chebyshev pseudospectral method for different basic velocity profiles.

并用Chebyshev配点法研究了不同速度剖面自由射流的界面稳定性问题。利用非线性的坐标变换。

The traditional skeletonization algorithms based on distance transform can not guarantee the connectivity property, so saddle points should be added to solve the connectivity problem.

传统的基于距离变换的骨架算法不能保证骨架的连通性，需要引入鞍点解决连通问题。

The connectivity property is not guaranteed by the traditional skeletonization algorithm based on the distance transform, saddle points should be added to solve the connectivity problem.

传统的基于距离变换的骨架算法不能保证骨架的连通性，需要引入鞍点解决连通问题。

In this paper Ⅰ successfully applied these methods to fault diagnosis, and presenting some new innovative machinery fault diagnosis method; First Ⅰ present a new gear wornout fault diagnosis method, this method use the vibration signal's time-frequency attribute and instantaneous phase undulation to accurately detect gear's fault, and by comparing with the traditional frequency domain analysis method, this method reveals that many nonlinear and nonstationary characteristic exist in gear's vibration, this tell us that if we use frequency domain analysis method without pay attention to the signal's characteristic, we could get wrong diagnostic result; Then Ⅰ present a new bearing fault diagnosis method, this method use ATVFD and Hilbert transform to do envelop demodulation,Ⅰ analyze the envelop with time-frequency method and find out that this method is more accurate then traditional method.Ⅰ also explain that the modulation of the fault to the carrier wave may also be non-stationary and nonlinear; Finally Ⅰ present a cylinder pressure measurement method of diesel engine by means of vibration, cylinder pressure is an important parameter of diesel engine fault diagnosis, the pressure measuring is simplified a lot by this method,Ⅰ also use the ATVFD and time-frequency analysis to realize it.

本文中将上述理论方法成功地应用到故障诊断中去，提出了几点创新性的诊断方法；提出了一种齿轮磨损故障诊断的新方法，该方法利用振动信号能量的时频域分布特征与瞬时相位波动特征可以进行精确的齿轮故障诊断，并通过与传统的频域诊断方法的比较，揭示出齿轮振动中存在的明显的非线性与非平稳特征，说明了不加选择地利用频域分析方法进行齿轮故障诊断很可能会得到错误的诊断结果；提出了一种轴承故障诊断的新方法，该方法利用ATVFD分解与Hilbert变换进行包络解调，并对解调得到的包络信号进行时频域分析，可以实现更加准确轴承故障诊断，说明了故障对载波信号的调制往往也是非平稳与非线性的；提出了一种利用振动信号进行柴油机汽缸内压力检测的新方法，柴油机汽缸压力的变化是柴油机故障诊断的重要参数，利用振动方法可大大简化汽缸压力的检测过程，该方法也是综合利用ATVFD分解与时频域分析方法实现的。

Then,introducing stretching transform and using the Bessel functions of 1/4 and-1/4 order,the interior layer solution is constructed.

然后引入伸展变量变换，并利用1/4和-1/4阶Bessel函数，构造在转向点附近的内层解。

Taking triangular-windows of car seal for an example in the article,in combination with the feature of car seal of reverse engineering and the theory of change of coordinate,the software of reverse engineering was adopted to realize alignment between the cloud data and section data of car seal.

以汽车密封条三角窗产品为例，结合汽车密封条产品逆向工程的特点和坐标变换的理论，利用逆向软件，实现了汽车密封条点云数据与截面数据的对齐。

Source images with wavelet are decomposed, and corner information can be detected in the two approximate sub-images on the wavelet coarsest level. The initial registration parameters are achieved through affine transform model. The optical flow is iteratively refined to get the coarse registration parameters. The process will continue until the final and accurate matching parameters are obtained.

首先对源图像进行小波分解，在小波金字塔最顶层的低频近似子图像上进行角点检测，通过仿射变换模型得到初始配准参数；然后将这一参数逐层进行迭代精炼，直至达到金宇塔最底层，得到最终精确的配准参数。

With only mild constraints placed on sampling locations, the inverse transform can be realized without matrix inverse in case of nonuniform frequency sampling, which is very useful in devising fast-running FIR filters.

在不一致频率采样时，只要对采样点略加一些约束条件，就可以不经矩阵求逆实现反变换，这对设计快速连续的FIR滤波器非常有用。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。