平移群

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。

We prove that on the localgauge group C∞(M a compact manifold,G a matrix Lie group)there does not exist afinite translationally invariant Borel measure.

我们证明了在局域规范群C∽(M为一紧致流形，G为一矩阵李群)上不存在有限的平移不变的Borel测度。

Here the key assumption is the existence of a translationallyinvariant measure on the local gauge group.

这里一个关键的假设是局域规范群上存在一个平移不变的测度。

We investigated Gaussian model on some fractal lattices firstly with anexactly Real-Space Renormalization Group method.

由于分形结构不具备欧几里得空间晶格所具有的空间平移不变性，通常采用的基于傅立叶变换的动量空间重正化群方法已经不再适用。

The translation group symmetry of phononic crystal is changed by changing the size of adjacent rods.

通过改变两相邻的柱体底面边长之比来改变声子晶体的平移群对称性。

In Chapter 2,we introduce the definition of adding machines,and give sev-eral equivalent conditions on the existence of several kinds of conjugacy and semi-conjugacy relations between adding machines.

第二章介绍了广义符号空间上的加法机器的定义，给出了加法机器之间存在着各种共轭及半共轭关系的多个充要条件，证明了加法机器之间的拓扑半共轭一定是一个群同态与一个平移映射的复合，并研究了此同态的核的构成。

The sandstone bodies of this sedimentary system are buried in shallow position and in good quality of porosity and permeability.Shengbei structure zone and its south flank are the main position for sandstone and available for the north pinch out subtle traps development.Combined the background of upheaval in sag and cling to the strike-...

根据胜北洼中隆良好的古构造背景，结合胜北3、4号南北向平移断层沟通中、下侏罗统水西沟群煤系地层和中侏罗统七克台组湖相泥岩烃源岩系等情况，认为胜北洼陷白垩系是浅层次生岩性油气藏勘探的有利地区。

There are two actions on this topological space, one is the group G of isomorphisms between complexes, the other is the translation action T induced by contractible complexes.

在这个拓扑空间上，有两种作用，一个是复形的同构群的作用G，另一个是可缩复形引起的平移作用T。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。