| 1. | 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。 |
| 2. | Finite subgroups of some fractional linear transformations groups
一类分式线性变换群的有限子群 |
| 3. | Congruent transformation group
全等变换群 |
| 4. | We will use this theory to classify joint invariants and joint differential invariants of some transformation groups
我们将利用该理论对一些特殊变换群的联合不变量、联合微分不变量进行分类。 |
| 5. | The first part deals with the construction of semisymmetric graphs and the second part classifies the edge - transitive regular coverings of the cube , whose covering transformation groups are iso - morphic to the elementary abelian p - groups
第一部分是关于半对称图的分类，第二部分是关于立方体边传递的正则覆盖图的分类，其覆盖变换群同构于初等交换p -群。 |
| 6. | To handle this problem , a novel adaptive filter for orientation parameter design technique is proposed in this thesis according the theory of one - parameter transformation group . an algorithm for the convolution of this filter and an image is also given
为了解决这个问题，本文基于变换群理论提出了一种方向自适应滤波器的设计方法；给出了这个滤波器与图像卷积的算法。 |
| 7. | With this method , in the present thesis , we will classify all the connected regular covering graphs of the cube satisfying the following two properties : ( 1 ) the covering transformation group is isomorphic to the elementary abelian p - group ; ( 2 ) the group of fibre - preserving automorphisms acts edge - transitively
本文中，我们用同一种方法分类立方体的正则连通覆盖图，并且满足两个条件，覆盖变换群同构于初等交换p -群且保纤维自同构群是边传递的。 |
| 8. | For a given finite connected graph f , a group h of automorphisms of f and a finite group a = z , du , kawk and xu ( see [ 6 ] ) get some new matrix - theoretical characterizations to classify all the connected regular coverings of f having a as its covering transformation group , on which each automorphism in h can be lifted
设为有限连通图， h为它的自同构群的一个子群， a为给定一个初等交换p -群。杜少飞， kawk和徐明曜用矩阵的方法将的正则连通覆盖图进行了分类，其中以a作其为覆盖变换群，并且h可提升。 |
| 9. | Hi the aspect of symmetry analyzing to the hopfield model neural network with hebbian learning , we study on the dynamical behavior of the state space under the action of isometric transformation group g = z2 ? n , and prove the invariant property of the energy orientation ? / / " ) of the state space under the action of g . we find that the symmetry relationship of the network is sx - sw = sh when the active function of the neuron is odd , where sx is the symmetry of the patterns set x under hebbian learning rule , sh is the symmetry of the network and sw is the symmetry of the weight matrix w of the network
) s _ n为手段，研究了网络状态空间在群g作用下各点的运动情况，证明了群g作用下的不变性。证明了当神经元的激活函数f为奇函数时， hebb法则下存储样本集x的对称性s _ x 、网络对称性s _ h以及连接矩阵对称性s _ w三者之间满足s _ x = s _ w = s _ h的关系；同时，我们还证明了：网络稳定态集vf同一s _ h轨道中的两个稳定态的动力学行为(能量和吸引域大小)相同；两个等距网络h和h 1 = g ? h ， ( ? ) g ( |
