不变性

The kernel requarment for the rotating invariant property of a TFD based on fractional Fourier transform is proposed and proved in chapter 5. A close formula of Radon-Wigner transform of LFM signalis given. Based on the formula, the distribution of RWT is discussed.

第五章在首先简单介绍分数阶付立叶变换的基础上，提出并证明时—频分布具有旋转不变性对核函数的要求，给出了Radon-Wigner变换在直角坐标系下分布的一个显式公式，据此讨论了RWT分布特点。

In order to overcome the handicap to extract line-segments from natural hand-printed Chinese characters, the extension is made to other structural features, and the generalized connected background region is defined, and its extraction and recognition algorithm are developed. This recognition algorithm is based on matrix singular decomposition and invariant transformation theory.

针对从自然手写体汉字中难以提取到笔段特征的难题，对汉字的其它结构类特征进行了扩充，提出了汉字的广义背景连通域的概念，并给出了提取广义背景连通域特征的算法以及基于矩阵奇异值分解与不变性变换的广义背景连通域特征的匹配算法。

This is a new dual invariant.

这是一个新的对偶不变性。

However, it is desirable for objects to be translationally invariant.

然而，能保证被画目标的坐标值的不变性是再好不过的。

The graphic recognition based on invariant moment and implementation of the method in the system is studied.

研究特征矩不变性的图形识别方法，探讨该法在系统中的应用，并提出不断修正标准模板中标准图形来提高识别精度的方法。

In every period, do the following operations:# For each 8*8 block, do the discrete cosine transform, then take out direct current coefficient in each block, using the transformation above for each DC coefficient, the gold stands for the code of the spread-spectrum we use when embedding the different watermark bit in different frames, after all of the watermark information which we want to embed is embedded, then do the inverse discrete cosine transformation, and store the current frame in a new file.

于是利用DCT变换域的这点重要的几何不变性，我们可以推导出一种能够抵抗几何攻击的视频水印算法，即将所需要嵌入的水印信息以127位扩频序列作为辅助，以求和值形式嵌入到DCT变换后的每个宏块的每个DC系数当中，具体嵌入和提取算法如下：根据使用的扩频序列的长度N，基于相关的嵌入器需要选取包含N帧的视频子序列，令这N帧视频子序列作为一个嵌入周期，对于每N帧视频子序列做如下的操作，#即对于每个8×8的像素块进行DCT变换，然后取出每个DCT变换后的直流分量，对于每个DC系数，做如上所述的变换，其中gold为在第k帧中嵌入第i位水印信息时使用的扩频码字值，待将所有需要嵌入的水印信息全部嵌入后，再做反DCT变换，保存当前帧。

In the ***, all types and fundamental principles of Radon transform are summarized systematacially. This *** starts from the general linear Radon transform, and then researches how to use the damped least square method to find the solution of the forward transform. However, the least squares smoothing effect will lead to a certain degree of trails in the data of Radon domain, which led to the application\'s limitations. After that the implementation in Radon domain and relative merits of linear Radon transform, parabolic Radon transform and polynomial Radon transform which have time invariance are introduced, the conjugate gradient method that can solve numerical solution is also given. And then the high resolution Randon transform is discussed, it introduces the regularization theory and Bayes principle into inversion, which successfully remove the negative affect caused by discrete Radon transform. Finally, we introduce the optimal weighting similar coefficient Radon transform, which adapt to the time variant quality of hyperbolic Radon transform.

本文系统总结了Radon变换的各种类型及其基本原理，从τ- p变换(即一般线性Radon变换)出发，研究利用阻尼最小二乘平方法求解其正变换，但是最小平方法的平滑作用会导致Radon域数据存在一定程度的拖尾效应，给这种方法的应用带来了很大的局限性；然后先容了具有时不变性的线性、抛物和多项式Radon变换在频率域的实现及其优缺点，给出了求解其数值解的共轭梯度算法；接着讨论了高分辨率Radon变换，它把正则化思想和贝叶斯原理引进到了反演中，很好的克服了离散Radon变换产生的截断效应对结果的不利影响；最后先容了适应双曲Radon变换时变性质的高分辨率最优相似系数加权Radon变换。

By this algorithm the search was performed from a certain initial point by use of iterated function system and attractor of inner interval.

接着利用分形的自相似性与标度不变性将内区间的分形特性进行延拓，并由此构造了具有外推功能的分形插值算法，实现交通事故预测。

Then we obtained the data of the lower limb motion of the volunteer in gait by motion capture system. Analyzing the results, we found that the relative positions of the landmarks which were used to construct JCS did not change much during the movement. That means the method on definitions of JCS in this article was reasonable at a certain range.

通过利用运动捕捉系统对自愿者步态过程中的下肢运动轨迹进行采集，分析构建坐标系的特征点在运动过程中空间相对位置的不变性，说明了文章提出的下肢关节坐标系定义方法在一定范围内是合理的。

First, the principle of Jourdain for the nonholonomic systems of variable mass in event space is presented.

1918年，Noether从研究Hamilton作用量在无限小变换下的不变性出发，找到了力学系统存在守恒量的条件和形式。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。