查询词典 lie

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 ？

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。

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。

Develop the formulation of the the Lie group, Lie algebra and Riemannian manifolds and spatial operator algebra.

建立了Lie群和Lie代数、Riemannian流形与空间算子代数理论联系的模型。

Vi.上床,分层 apple-pie bed be brought to bed confined to one's bed die in one's bed feather bed flock bed get up on the wrong side of the bed get out of bed on the wrong side go to bed go to bed in one's boots keep one's bed keep to one's bed leave one's bed lie on the bed one has made lie in the bed one has made lie on a bed of thorns make one's make one's bed bed and lie on it make one's own bed make one's own bed and lie on it make the bed make a bed narrow bed narrow cell narrow house narrow home put to bed put to bed with a shovel stretch on the Procrustean bed

发生性关系；付印喝得大醉早睡早起因病躺在床上因病躺在床上病愈起床自作自受自作自受如坐针毡；坐立不安自作自受自作自受自作自受自作自受整理床铺整理床铺坟墓坟墓坟墓坟墓使睡；将扣紧准备印刷；准备编排直至印刷为止埋葬，下葬；扶送回家上床按照同一标准判断；强求一致 24 As you make your bed， so you must lie on it。

It is proved that every Lie derivation of nest algebra is the sum of an associative derivation and a general trace. Every Lie isomorphism between nest subalgebras of a factor von Neumann algebra is the sum of an isomorphism and a general trace or the sum of a negative anti-isomorphism and a general trace. Lie invariant subspace of linear mappings on Banach algebras is introduced, and linear maps from nest subalgebra of a factor von Neumann algebra into itself which satisfy the property that the space of derivations is their Lie invariant subspaces are characterized. Simultaneously, it is shown that such maps are Lie derivations modulo the set of scalar multiple of the identity.

得到Lie导子的特征表示，即套代数上的任何一个Lie导子都是内导子与广义迹之和；给出了Lie同构和同构及反同构之间的关系，即因子von Neumann代数中套子代数之间的任何一个Lie同构要么是同构与广义迹之和要么是负反同构与广义迹之和；引入了Banach代数上线性映射的Lie不变子空间，并给出von Neumann代数中套子代数上以导子空间为Lie不变子空间的线性映射的一个刻画，同时也表明在模去数乘恒等映射的意义下，以导子空间为Lie不变子空间的线性映射就是Lie导子。

Mathieu[17] discribe the form of Lie derivations on primitive ring whose charater is not 2 and which has no non-trivial idempotent. After that, Miers[18],Mathieu and Villena[19] also study Lie derivations on Von Neumann algebra and algebra.

Martindale[17]首先讨论了特征不等于2且含非平凡幂等元的本原环上的Lie导子的表达形式，随后Miers[18]，Mathien和Villena[19]也分别对VN代数，C~*-代数上的Lie导子进行了刻画。

Lie's theory is used to extract the analytic solutions of nonlinearsystems in this thesis for the first time.The basic form of Lie group is ex-pounded through Lie series and Lie transformation.

本文首次将Lie群理论用于求解非线性系统的解析解，通过引用Lie级数和Lie变换，阐明了Lie群的基本形式。

Some properties, such as primeness, semiprimeness and nondegeneracy are introduced. The primeness and semiprimeness are lifted from a Lie color algebra to its algebras of quotients.

在此基础上，本文提出了Lie color代数的商代数和弱商代数的概念，定义了Lie color代数的一些性质如素性、半素性和非退化性等，并将素性和半素性推广到Lie color代数的商代数中。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。