线性变换群

They include:collinearity--an invariance under the projective transformation group;Parallelisminvariance under the affine transformation group;the direction of angles--aninvariance under the rotation transformation group.

这些几何不变性质包括共线性——在射影变换群下的不变性；平行性——在仿射变换群下的不变性；角的方向——在欧氏平移变换群下的不变性。

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。

Analog circuits;Neural network;Fault diagnosis;Particle swarm optimization;Bilinear transformation;multidimensional spaces

模拟电路；神经网络；故障诊断；粒子群算法；双线性变换；多维变换

By finding a set of basis, we use matrices of transformation under a set of basis to describe the structure of the Galois group.

因此寻找一组基，我们利用线性变换在基下的矩阵来描述Galois群的结构，特别地，当正规扩张存在一组正规基时，用这种方式表示Galois群的更加简单。

By finding a set of basis, we use matrices of transformation under a set of basis to describe the structure of the Galois group. If a normal extension has a normal basis, then it is simpler to describe the structure of Galois group in this method.

因此寻找一组基，我们利用线性变换在基下的矩阵来描述Galois群的结构，特别地，当正规扩张存在一组正规基时，用这种方式表示Galois群的更加简单。

Using this method,we discussed for generalized Burger equation with variable coefficients and linear danping,obtained its symmetry group,simliar reduced equations,infinitesimal generator and Lie algebras;In chapter 6,using the Exp-function method,the generalized solutions of combined KdV-mKdV equation with variable coefficients are discussed.

首先介绍了Lie群分析法的基本思想，其次用Lie群分析法得到了带线性阻尼项的变系数广义Burgers方程的无穷小变换、无穷小算子的李代数结构，并具体求出了带线性阻尼项的变系数广义Burger方程的群不变解和约化方程。

The noise frequency modulation signal was particularly analyzed. The Fokker-Planck equation of noise frequency modulation was presented and the Motion-Group Fourier Transform was used by converting the partial differential equation into the variable coefficient homogenous linear differential equations. Then the solutions were given by using the peano-baker series. So the probability density function of noise frequency modulation in the filter was given. On the basis of the probability density function the stochastic resonance of noise frequency modulation signal is analyzed.

首先建立了噪声调频干扰信号通过脉冲压缩雷达中频滤波器后所满足的福克尔－普朗克方程，然后利用群移傅立叶变换（Motion-Group Fourier Transform，MGFT）将此偏微分方程化成了变系数齐次线性微分方程组，并利用Peano-Baker级数法给出了该方程组的解，最后得到了噪声调频干扰信号通过脉冲压缩雷达中频滤波器后的概率密度函数，在此基础上研究了噪声调频干扰信号造成的随机共振现象。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。