Lie groups are used to study space, structure, and change.
李群用于研究空间，结构和变化。
FOR more than a century mathematicians have known about Lie groups.
数学家对李群的认识已经有一个多世纪了。
Chevalley, Claude. Theory of Lie groups, I. Princeton, Princeton University Press, 1946.
《李群理论(一)》。普林斯顿：普林斯顿大学出版社，1946年。
The fundamental theory of Lie groups and Lie algebras on robotics is expatiated in brief.
对李群李代数方法在机器人中的应用做了基本的阐述，澄清了一些基本概念。
Lie Groups, Physics, and Geometry: an Introduction for Physicists, Engineers, and Chemists.
李群，物理和几何：为物理学家，工程师和化学家写的引论。
Techniques and concepts related to homology theory, K-theory, and Lie groups have been widely used.
与同调论、K -理论和李群有关的技巧和概念被广泛运用。
In this paper, we will investigate relations between complete Lie groups and complete Lie algebras.
本文给出完备李群与完备李代数的某些关系。
Algebraic Techniques; Lie Groups and Lie Algebras; Discrete Mathematics; Quantum Groups; Stochastic Methods.
代数技巧；李群和李代数；离散数学；量子群；随机方法。
There are four “simple” families of Lie groups and five others—this beingmathematics—that are notquite so simple.
李群有多个族组成，四族“简单”的和其他五族在数学上而言不那么简单的。
The Lie groups and Lie algebras is successfully extended to study the mechanical system with spatial compliant links.
将李群李代数理论成功地拓展应用于空间柔性机构系统的分析，验证了该方法的有效性。
Lie groups and Lie algebras were used to study the dynamics and control of robot system with active and passive joints.
采用李群李代数符号描述了含主被动关节机器人的动力学分析和控制问题。
The representation theory of simple Lie groups has now been established as one of the most useful tools in modern physics.
单纯李群的表示论已经成为研究现代物理学最有用的数学工具之一。
A systematic introduction to the theory of configuration space of multi-features is given, appealing to Lie groups and algebras.
结合李群李代数方法，系统地研究了多特征的位形空间理论，给出了定向公差约束子流形的局部参数显式表达。
They want to create anatlas of maps of the Lie groups. This involves making a description in the formof a matrix for each structure.
他们希望创建出李群的结构图，要做的就是以矩阵表达其中的每一个结构。
In the study of SCARA's kinematics, POE is used to obtain positive, inverse and jacobian solution, based of screw, Lie groups and Lie algebra.
SCARA运动学的研究中，以旋量，李群李代数为基础的POE指数积法求解运动学正解，逆解以及速度雅可比。
In this paper, the orientability of foliations was investigated, and an application to the free action of Lie groups on manifolds was given as well.
本文引入并研究了叶层结构的定向性，作为应用，讨论了李群在流形上的自由作用，给出了存在李群自由作用的一个必要条件。
Written by an engineer and sharply focused on practical matters, this text explores the application of Lie groups to solving ordinary differential equations (ODEs).
由一位工程师写和明显地集中于实际的事情，这份正文为了解决普通的微分方程(颂歌)探索谎话组的应用。
Upon this frame, use matrix Lie group to express the rotation space, then base on Bayesian estimation framework, calculate the minimum mean squared error bounds which use the matrix Lie groups.
在这种框架中，利用李群来表示旋转空间，然后基于贝叶斯估计结构，计算了利用李群的表示的最小均方误差估计性能界限。
They were chained together in groups of about fifty, crammed close together, forced to lie on their sides and often in their own waste.
他们约50人为一组被锁在一起，由于非常拥挤，不得不侧躺在甲板上，有时候甚至躺在自己的排泄物中。
In the answer to this seemingly mundane question may lie an important truth about our behaviour in groups.
对这些看似平淡无奇的问题的回答，可能揭示一个人们在团队中行为的重要真理。
Hunter-gatherer groups classified as pygmies live in various regions, including Africa, Indonesia, the Philippines and the Andaman Islands, which lie southeast of Burma.
被认为是矮人族的以狩猎采集为生的部落分布在非洲，印度尼西亚，菲律宾和缅甸东南的安达曼群岛等广大地区。
In this paper, the symmetries and Lie algebra of a coupled nonlinear wave equation were discussed. One-parameter transformation groups of this equation were obtained by using the symmetries.
主要考虑非线性波方程组的一些简单对称及其构成的李代数，并利用所得对称给出该方程组的一些单参数变换群。
The following is a list of the muscle groups in order and how to tense them. Remember to lie down when you do this.
下面是按顺序进行的肌肉群列表及对它们的“紧张”的方法。记住，进行的时候要躺着。
The rural vulnerable groups refer to the people who are at a lower economic level and lie to relatively weaker river position because of both inner and outer factors in rural area.
农村弱势群体是指在农村社会生活中，由于各种内在或外在原因造成经济水平低下，竞争处于弱势地位的农村居民的集合体。
Many of important concepts in the theory of abstract Lie algebras come from classical theory of groups, for example, complete Lie algebras is a generalization of complete groups.
李代数的抽象理论中很多重要的概念都来源于经典群论，完备李代数便是一个例子。
There are many transnational ethnic groups in China, and most of them lie inthe west of China.
中国是一个跨国民族众多的国家，绝大多数跨国民族分布在西部地区。
There are particular relations between the closed connected normal subgroups of algebraic groups and the ideals of Lie Algebras.
代数群的连通正规闭子群与李代数的理想之间有很特殊的关系。
The rare earth ions lie between the disilicate groups and the sheets of octahedra to form (8+3)-coordinated A(1)-polyhedra and 10-coordinated A(2)-polyhedra.
稀土离子位于双硅酸根和八面体层之间，形成（8+3 ）配位的A（1）多面体和10配位的A（2 ）多面体。
Since a Lie superalgebra can be associa ted with a Z2-graded group, properties of Z2-groups are discussed and Z2-graded structures of some special class es of groups are determined.
因为一个Z2-阶化群可以对应一个李超代数，所以对Z2-阶化群的性质进行了讨论。并对一些特殊类型的群确定了它们的Z2-阶化结构。
Since a Lie superalgebra can be associa ted with a Z2-graded group, properties of Z2-groups are discussed and Z2-graded structures of some special class es of groups are determined.
因为一个Z2-阶化群可以对应一个李超代数，所以对Z2-阶化群的性质进行了讨论。并对一些特殊类型的群确定了它们的Z2-阶化结构。
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