查询词典 transformation group

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。

Thismethod adopted affine transformation model and a Lie derivative-based analytical algorithm.We introduced the process and characters in extracting information of biological visionsystem, studied the feasibility of the generalized Gabor function used as receptive fieldfunction in extracting information and analyzed affine transformation group and Liederivatives. Finally, we deduced the mathematical denotation for Lie derivatives, i.e. theinfinitesimal generator of the geometric distortion in affine transformation.

对生物视觉信息提取的过程及特点进行了介绍，其中主要研究了广义Gabor函数作为感受野函数提取初级视觉信息的可行性；对仿射变换作为外界图像信息在视觉成像系统上的投影模型的原理进行了初步讨论；对Lie变换群微分算子用于提取仿射变换不变量的分析方法作了剖析，并推导了该方法中关键部分——仿射变换Lie微分算子的具体表达式，也就是几何变形无限小微分算子的计算表达式，使下一步编程实现该方法成为可能。

In the geometry of matrices, the points of the associated space are a certain kind of matrices, there is an arithmetic distance of two points in this space, and there is a transformation group acting on this space. Two distinct points is said to be adjacent if their arithmetic distance is one or minimal.

在矩阵几何中，空间中的点是某一类矩阵，两点间存在一种算术距离，还有一个变换群作用在这个空间上，两个不同的点间的算术距离为1或最小时称这两点是粘切的。

ABSTRACT This dissertation describes our investigation of the geometric invariance and geometric invariant over projective transformation group, with the emphasis on the estimation of geometric constraints in image sequence and their applications in computer vision.

本论文介绍了作者对射影变换群上的几何不变性及几何不变量的研究，重点研究了序列图象间几何约束关系的估计及其在计算机视觉中的应用。

Discrete mechanics,dynamical equation,infinitesimal transformation group,symmetry,conserved quantity

中文关键词离散力学，动力学方程，无限小变换群，对称性，守恒量

In this part, we will study some basic and important concepts such as semi-group, group, isomorphism, homomorphism, subgroup, invariant subgroup, factor group, and transformation group.

本部分考虑的主要概念有半群、群、同构、同态、子群、不变子群、商群以及变换群等。

An analytic solution of kinematic model was obtained via Lie transformation group. It shows that the velocity of particles flow is maximum when x=0. Through locating the maximum particles velocity distributing line and taking the line as the origin line of x coordinates, the modified kinematic model could simulate the eccentric discharging well.

通过Lie变换群得到"运动模型"的解析解，发现x=0时颗粒的垂直速度达到最大值，由此在确定颗粒最大速度分布线的基础上移动坐标使该线上x值均为0，对"运动模型"进行了修正，可以反映壁面对颗粒运动的影响，所得计算结果与实验测定吻合得很好。

A transformation group is induced through the symmetric group Sn.

通过对称群Sn，推导出一变换群。

Such a group of formation is briefly referred to as a transformation group.

这样一个变换的群，称为变换群。

In Chapter 2,we first generalize a waterman inequality by usering Clliffordmatrix represenation of n-dimensional 〓 transformation group 〓.

在第二章中，我们研究了关于离散群的一些不等式。首先，我们利用CHifford矩阵研究了〓上的〓变换群不等式，给以一定的限制条件，通过大量复杂的、技巧性计算，改进了Wateman不等式。

I am accused of being overreligious," she said in her quiet, frank manner,"but that does not prevent me thinking the children very cruel who obstinately commit such suicide.""

客人们在卡罗利娜·埃凯家里，举止就文雅一些，因为卡罗利娜的母亲治家很严厉。

Designed by French fashion house Herm è s, this elegant uniform was manufactured in our home, Hong Kong, and was the first without a hat.

由著名品牌 Herm è s 设计，这件高贵的制服是香港本土制造，是我们第一套不配帽子的制服。