同射变换

It is proved that the least squareestimators of linear estimable functions of regression coefficients areadmissible under matrix loss and minimax. The necessary and sufficientexistence conditions are derived for the uniformly minimum riskequivariant estimators of linear estimable functions ofregression coefficients under an affine group and a transitive group oftransformations respectively. It is also proved that there are no UMREestimators ofthe covariance matrix and variance under an affine groupof transformations and quadratic loss functions.

本文证明了回归系数的线性可估函数的最小二乘估计是极小极大的且在矩阵损失函数下是可容许的；还分别在仿射变换群和平移群下导出了存在回归系数的线性可估函数的一致最小风险同变估计的充要条件，并证明了在仿射变换和二次损失下不存在协方差阵和方差的 UMRE 估计。

In chapter 1,we find out a kind of two-parameter invariant cubic curve family of a certainquadratic system which is important one for studying the distribution of limit cycles.

第二章讨论一般的二次系统具有三次代数曲线同宿环的充要条件，针对问题，我们采用了具有双曲鞍点的二次系统的标准形，利用仿射坐标变换，我们把系统和曲线同时简化，使问题得到了完满解决。

The nonlinear dynamic model was expressed based on the format of SISO affine nonlinear system. Then the system was represented into the standard Byres-Isidori format base on the diffeomorphism transform.

使用SISO仿射非线性系统描述了所建立的自行车机器人非线性动力学模型，利用非线性微分同胚变换将该系统化成了Byres-Isidori非线性系统的标准型形式。

A class of affine nonlinear system of single input-single output is investigated. Firstly, the nonlinear system is transformed into an equivalent linear system through a diffeomorphism transformation. The networked control problems for the delays are constant, stochastic and shorter than a sampling period, and long and stochastic are investigated respectively.

针对一类单输入-单输出仿射非线性系统，首先通过微分同胚变换实现了仿射非线性系统的无反馈精确线性化；然后基于精确化线性模型，分别讨论网络延时为常时滞，随机时滞小于一个采样周期和随机长时滞情况的控制问题。

XRD,X-ray EDS analysis,AFM and Fourier transform infrared spectroscopy were employed to characterize PbSe thin films. The results show that all of the films were heteromorphy and the growth temperature has effect to the diffract peaks of the films. The contents of PbSe thin films by PLD consisted with the targets,and realizing thin films deposited with same constitutes; the films had rather flatness surface and compact structure; the peak-to-tail roughness of PbSe thin films surfaces was less than 200nm;they had sensitivity to light of a specified wavelength and obvious absorption edge at 5μm corresponding to band-gap width of PbSe thin films;light of wavelength less than 5μm was strongly absorbed.

通过脉冲激光沉积法在Si(111)和SiO2玻璃基片上制备了PbSe薄膜。X射线衍射、X射线能谱、原子力显微镜、傅里叶变换红外光谱仪测试结果表明：所有制备的薄膜都为多晶薄膜，发现薄膜生长温度对薄膜衍射峰有一定影响；PLD法制备的薄膜的成分与靶材的基本一致，实现了同组分沉积；所有薄膜表面比较平滑，表面不平整度小于200nm，结构比较致密；PbSe薄膜对红外光具有敏感的响应特性；在波长为5μm处存在有明显的吸收边，此吸收边对应于直接带隙PbSe材料的禁带宽度；对应于波长小于5μm的红外光，PbSe薄膜存在有明显的强吸收。

The fundamental compute region B is determined and self-similarly mapped into the upper half plane by using the homeomorphic affine transformationθ, so the fractal images of the upper half plane, square limit, and circle limit can be constructed.

周期化动力平面或参数平面，确定基本计算区域，应用同胚仿射变换将基本计算区域自相似地映射到上半平面，进而构造方极限和圆极限分形图。

Corresponding mathematics model was developed, hole-edge stress analysis on composite material plate with multiform holes was carried out, accurate boundary conditions was founded by conformal mapping method, boundary problems of the two stress functions could be treated by affine transformation in the same way synchronously.

建立了相应的数学模型，对含不同孔型复合材料板进行了孔边应力分析，通过保角映射方法建立精确的边界条件，解决了复杂孔型的边界条件问题，借助仿射变换能同时并且同方法的处理这两个应力函数在边界上的问题。

As with reflections, the orthogonal projection onto a line that does not pass through the origin is an affine, not linear, transformation.

同反射一样，正投影到一条不经过原点的直线的变换是仿射变换，而不是线性变换。

Then, according to research on nonisotropic transformation in geometric attack, this *** further spreads the application field of scale-space theory in watermark design and proposes an algorithm against geometric attack grounded on affine invariant feature point.

然后，通过对几何攻击中的非同向性变换的研讨，入一步扩铺尺度空间理论在水印设计中的应用，提出一种基于仿射不变特性点的抗几何攻击算法。

The feature point in affine scale-space has higher repeat rate under nonisotropic geometric transformation and the ellipse window of nonuniform Gaussian kernel on characteristic scale is founded on image contents.

仿射尺度空间上的特性点在非同向性几何变换中具有更高的反复率，并且其特性尺度上的非统一高斯核椭圆窗口是基于图像内容的。

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。