不变性

The experiment results show that the model does not change the illumination and contrast, has commonality and noise immunity, and corresponds to the characteristics of human vision system.

实验结果表明：该算法对图像亮度和对比度具有不变性，并且具有较好的抗噪性能和通用性，符合人类视觉系统特性。

On the other hand, it is exemplified in the present paper that the principle of material frame – indifference with the admissible equivalent dynamic processes of a body by Truesdell and Noll (1965) [14] is more convenient than the form-invariance of constitutive functionals by Svendsen and Bertram (1999) [13] and Liu (2004)[4], especially for the rate-form constitutive equations.

通过例子说明了Truesdell和Noll 用等价动力过程，关于物质标架无关性原理的陈述，比Svendsen 和Bertram及Liu的本构关系在参考标架变换下的形式不变性更合理且方便，尤其是对微分方程形式的本构关系更是如此。

Both of them are faster than the standard algorithm of the circle about one order of magnitude.

第四部分叙述了在机器视觉研究中占有重要地位的所谓"不变性识别"原理。

The main contributions include:(1) Energy conservation law of Haar wavelets transform is proved to compress data streams.(2) The relation between the coincidence measure and trend of streams is revealed as along with the invariability under parallel shift and the equivalence law over coincidence measure to approximately express data-streams by the wavelet coefficient of the characteristic stream and its energy.(3) Multi-Scales energy decomposition model is proposed to improve the compression precision.(4) The multi-scales compression algorithm and the energy conservation reconstruction algorithm are designed.(5) Extended experiments show that the compression ratio of the new methods is 2~4 times as the traditional method.

主要研究成果包括：(1)证明了Haar小波变换服从能量守恒规律，并用于压缩数据流；(2)揭示了数据流的偶合度与变化趋势的相关性、偶合度的平移不变性及等价规律，采用特征流序列的小波系数和流能量近似表示流的趋势，达到压缩的目的；(3)提出了多尺度能量分解模型，提高了表示精度；(4)设计了多尺度能量分解压缩算法以及多尺度重构算法；(5)在真实数据集上的实验表明，新方法的压缩比是传统小波方法的2～4倍。

In this dissertation, we develop the research work of the following three aspects based on existed work.First, using the scale-invariant property of multiscale model, i.e. Markovian among scales, a method of qth-order tree-based for multiscale representation of a class of 1-D stochastic process is presented. The multiscale stochastic model is established. The representation forms of parameter matrices, such as, the state transition matrix, the disturbance matrix, the initial state and the corresponding covariance matrix are deduced in detail. The multiscale sample paths based on distinctive order tree are presented by computer simulation.

本文在已有工作的基础上，开展了以下几个方面的研究工作： 1、根据多尺度模型尺度不变性，即利用尺度间的Markov性，给出了一类1-D随机过程基于一般q阶树的多尺度表示方法，建立了相应的多尺度动态模型，详细推导了多尺度模型中的状态转移阵、扰动阵、初始状态和相应的协方差阵，并通过计算机仿真给出了不同阶树的多尺度采样路径。

For some parametric estimation, whether it is the best estimation or not, its consistency, unbiasedness, effectiveness, invariance, and so on are often discussed. Then, it is compared with the data we get from experiment, and the deviation with the experimental data is considered.

某一参数估计是否是"最优"估计，通常要从一致性、无偏性、有效性、不变性等方面进行讨论，进而通过实际的观察对其进行数据拟合，分析其相对于实际模型的偏差程度。

This method exhibits shift-invariance property and can effectively improve Pec (Probability of Correct Classification) and training as well as testing speed.

该方法保证了目标的平移不变性，有效地提高了识别率、训练速度和识别速度，降低了对目标方位估计精度的要求。

Mei.Application of the measured equation of invariance to solve scattering problems involving a penetrable medium.

Dai。一种提取多层介质多导体互连线电磁参数的快速算法：有限差分-不变性测试方程法。

A new kind of method for recognition of planar object is presented based on steerable filters.

本文提出一种基于可调滤波器的平面物体射影不变性识别方法。

Then, a method is proposed to maintain the necessary rotation invariance by transforming image matrix to polar coordinate form followed by the proven of the effectiveness in theory and with numeric calculation results.

最后，提出了用图像矩阵的极变换来重建奇异值的旋转不变性，并给出了理论和实例证明。

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。