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We explain the basic conception of the Lie group, Lie algebra and Riemannian manifolds in detail, deeply analyze and research the Special Euclidean Group SE(3) and se(3) in the Lie group, Lie algebra. Establish the relation between the adjoint transformation Adg and the operatorφ(k + 1,k) under a particular condition , substitute the operatorφ(k + 1,k)with spatial adjoint operator Ad kk ?

在多体系统动力学理论体系中，详细阐述了Lie群、Lie代数和Riemannian几何的基本概念，对Lie群、Lie代数中的特殊Euclidean群SE(3)和se(3)作深入分析与研究，建立Lie括号下的伴随变换Adg在特定条件下与空间算子代数理论中的空间变换算子φ(k + 1，k)之间的相互关系，并将空间伴随算子Ad kk ？

Specify what status the spatial operator algebra locates at in many methods of multibody systems dynamics formulations and what the relations are between the spatial operator algebra and other dynamics formulations.We explain the basic conception of the Lie group, Lie algebra and Riemannian manifolds in detail, deeply analyze and research the Special Euclidean Group SE(3) and se(3) in the Lie group, Lie algebra. Establish the relation between the adjoint transformation Adg and the operatorφ(k + 1,k) under a particular condition, substitute the operatorφ(k + 1,k)with spatial adjoint operator Ad kk ?

在多体系统动力学理论体系中，详细阐述了Lie群、Lie代数和Riemannian几何的基本概念，对Lie群、Lie代数中的特殊Euclidean群SE(3)和se(3)作深入分析与研究，建立Lie括号下的伴随变换Adg在特定条件下与空间算子代数理论中的空间变换算子φ(k + 1，k)之间的相互关系，并将空间伴随算子Ad kk ？

In Chapter 2, we will use one-parameter subgroups of the Lie group to develop a version ofNewton\'s method on an arbitrary Lie group for maps from a Lie group to its correspondingLie algebra which is independent of affine connections on the Lie group and differs fromNewton\'s method for sections on Riemannian manifolds.

在第2章中，我们主要研究关于从李群到其李代数的映射f的Newton法的收敛性。利用李群的单参数子群来给出关于映射f的Newton迭代点列，此Newton迭代与李群上的联络无关，也与第1章中研究的Newton迭代不同。

The Todd polynomials were first studied in algebraic geometry and it is surprising that they play this fundamental role in classification of manifolds .

托德 多项式第一次被学习在代数几何并且它惊奇他们充当在多头管的分类的这个根本角色。

Manifolds occur in algebraic geometry, differential equations, and classical dynamics..

流形出现于代数几何、微分方程式和经典动力学中。

In this paper, we mainly study the alternating group A_4 actions on spin 4-manifolds. First we discuss the special action of A_4 on K3 surfaces of Fermat type, we compute the fixed points set of this action and some invariants of the group action, also we get some topological properties. Then we study the A_4 actions on general K3 surfaces and obtain some similar results.

本文主要是以交错群A_4在K3曲面上的作用为研究对象，从Fermat型K3曲面上的特殊的A_4作用出发，得到了Fermat型K3曲面上A_4作用的不动点，利用不动点集计算了群作用的一些不变量并得到了相关的拓扑性质，在此基础上进一步把其中的一些结果推广到一般情形下的同伦K3曲面上。

The whole vacuum manifolds filtration system includes: stainless steel manifolds, three or six filter holders, a joint flask and a vacuum source.

整套真空多联过滤系统包括：不锈钢多联支架、三或六套换膜过滤器、集液瓶和真空气源。

Disposable Luer-lock Stopcock 3-way, four wey, 3-gang manifolds, 5-gang manifolds: It has CE mark. The product can be utilized as a switch or shift of channels or connection sits when infusing.

一次性使用旋塞（三通道、四通道、三排通、五排通）：该产品通过了欧共体CE认证，主要用来在输液时作为通路的开关和选择不同通路的转换器。

Other Northstar firsts on the XLR include four-cam continuously variable valve timing; electronically controlled, hydraulically actuated intake and exhaust cam phasers on all four camshafts for extra control; electronic throttle control; low restriction intake and exhaust manifolds and cylinder head ports; close coupled catalytic converters mounted directly adjacent to the exhaust manifolds; and a new air induction system, redesigned for enhanced capacity and noise attenuation.

Other北极星上首创的XLR包括四凸轮连续可变气门正时，电子控制，液压驱动进排气上的额外控制所有四个凸轮轴凸轮相位调节；电子节气门控制；低，限制进气和排气管和缸盖港口；紧密耦合催化转化器直接安装毗邻的排气管，以及一个新的空气感应系统，增强能力和噪声衰减重新设计。

That's right--the intake manifolds are located where the exhaust manifolds usually live, and the turbos nestle in the vee formed by the two cylinder banks.

这是权利-进气歧管的位置在排气管通常生活，以及涡轮增压引擎，雀巢在V型所形成的两缸银行。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。