- 更多网络例句与变换群相关的网络例句 [注：此内容来源于网络，仅供参考]
-
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。
-
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。
-
We obtain that if any 〓 is discrete or elementaryand 〓 satisfies Condition A,then the algebraic limit G of group sequence 〓is discrete or elementary.
首先，我们不再仅仅考虑离散非初等群集〓的代数极限G，而是离散群或初等群群集〓的代数极限G，我们对〓上〓变换群中斜驶元及其不动点进行了细致研究，注意到任意一个斜驶元存在一个仅仅含有斜驶元的领域，从而证明了初等群群集〓的代数极限G仍然是初等群，进而我们得到了一个代数收敛定理：如果任一〓是离散群或者初等群并且〓满足条件A，那么，群列〓的代数极限G一定是离散群或者初等群。
-
Chapter 1 briefs the relation between invariance and computer vision and summarizes the research and application of invariance in computer vision. Chapter 2 first derives the transformations of three camera models, then makes the correpondences between the models and three typical geometrical transformation groups by analysing the transformations respectively. The correspondences supply the theoretical basis for applying geometrical invariants to resolve the problems of computer vision. In Chapter 3, we describe the geometrical invariant theory and prove some geometrical invariants of coplanar points, lines or conics by algebraic method. In order to use the invariants of conic pairs to describe general 2D shapes, we discuss the perspectively invariant representation of planar curves using conies in detail. A system consisted of two TMS320C25 and based on moment invariants is introduced in Chapter 5. The system can recognize more than 30 different shapes of object model or more than 10 plane models with similar shape in real time.
第一章简述了不变性与计算机视觉的关系，以及计算机视觉中的不变性研究和应用概况；第二章推导了计算机视觉中常用三种投影模型的变换关系，通过对这三种变换关系的分析，分别建立了这三种投影模型和几何学中的三种变换群之间的一一对应关系，为几何不变性在计算机视觉中的应用提供了理论基础；在第三章中，我们介绍了几何不变性的理论，并且用代数方法证明了共面点、直线、二次曲线的几何不变量和射影不变量；为了把二次曲线的不变量用于一般二维形状描述，在第四章中我们详细地讨论了用二次曲线实现一般平面曲线的透视不变性表示的方法；第五章介绍了用两片TMS320C25构成的、基于不变矩形特征的运动目标实时识别系统。
-
Chapter two proposes the unified form of Hojman"s conservation law and Lutzky"s conservation law. Firstly, the author introduces the general Lie group of transformations that the variations of both the time and the generalized coordinates are considered, derives the determining equation of Lie symmetry for the system, presents a new conservation law, which contains the Hojman"s and the Lutzky"s conservation law as two special cases, and obtains a condition to exclude trivial Hojmans conserved quantities.
第二章，Hojman定理和Lutzky定理的统一形式：首先，引入一般意义下的Lie变换群(即位型变量q_s和时间变量t同时变换)，给出系统的Lie对称性确定方程，提出一个新的守恒律，Hojman定理与Lutzky定理则分别是这个新守恒律在两个特殊情况下的推论，导出一个可排除平凡Hojman守恒量的定理，并分别讨论了Birkhoff系统和非完整系统的Lie对称性和Hojman守恒量，最后，讨论了Hamilton系统的梅对称性与Lie对称性的关系，给出了由梅对称性求Hojman守恒量的方法。
-
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。
-
Consider symmetry of periodic area we get the symmetry transform group, act the eigenvector of self-cognation operator on the node bases element function, a series of orthogonal function is constructed.
找出一般周期空间的对称变换群，并将已知的有限元的单元基函数转化为节点基函数，将变换群的特征子空间作用有限元的节点基函数得出一系列的正交有限元函数。
-
We note that any pure elliptic subgroup ofI somis discrete if and only if G is finite group.
最后，我们引入了一种广义非初等群，发现〓变换群经典的离散准则对我们研究的非初等群只是有条件成立，我们找到了充要条件对其建立了离散准则。
-
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。
- 更多网络解释与变换群相关的网络解释 [注：此内容来源于网络，仅供参考]
-
affine transformation group：仿射变换群
仿射变换|affine transformation | 仿射变换群|affine transformation group | 仿射超平面|affine hyperplane
-
collineation group：直射变换群
直射变换|collineation, collineatory | 直射变换群|collineation group | 直谓[的]|predicative
-
congruent transformation group：全等变换群, 合同变换群
locking indication 锁闭表示 | congruent transformation group 全等变换群, 合同变换群 | dragon tree 龙血树
-
congruent transformation group：全等变换群
全等变换|congruent transformation | 全等变换群|congruent transformation group | 全等公理|axiom of congruence
-
group of linear transformations：线性变换群
group of isotropy 迷向群 | group of linear transformations 线性变换群 | group of motions 运动群
-
group of similarity transformations：相似变换群
group of quotients 商群 | group of similarity transformations 相似变换群 | group operation 群运算
-
orthogonal transformation group：正交变换群
orthogonal transformation 正交变换 | orthogonal transformation group 正交变换群 | orthogonal translation 正交位移
-
projective transformation group：射影变换群
射影变换|projective transformation | 射影变换群|projective transformation group | 射影标架|projective frame
-
topological transformation group：拓扑变换群
拓扑阿贝尔群|topological Abelian group | 拓扑变换群|topological transformation group | 拓扑不变量|topological invariant
-
unitary transformation group：酉变换群
unitary transform of image matrix 影像矩阵酉变换 | unitary transformation group 酉变换群 | unitary vector space 酉空间