李群

由于李群H上的G-仿射群是一个李群，所以它具有李群的性质。

The G-Affine group on the Lie group H is a Lie group , so it has the characteristics of the Lie group .

到无穷维Hilbert李群的映射

The Maps into Infinite Dimensional Hilbert Lie Group

设F4~2为实一阶李群&F4的一个实型式。

Let F_4 ~ 2 be a real form of F_4 with real rank one .

秩2紧致单纯李群的不可约表示（II）

On the irreducible representations of the compact simple Lie groups of rank 2 ( ii )

Poisson流形上李代数与Poisson辛李群的讨论

Lie Algebra on The Poisson Manifold and Poisson Symplectic Lie Group

用n-1个单参数李群求n阶自治系统的首次积分

Searching for First Integrals of the n-th Order Autonomous System Based on n-1 Single-Parameter Lie Groups

结合微分几何和李群方法的优点，设计了一种非解耦的新型三维（3D）制导律。

This article proposes a non-decoupling three dimensional ( 3D ) robust guidance law by combining the advantages of the differential geometry control and Lie-group control methods .

任务空间是机械系统的一种典型位形空间，在几何上对应了李群SE（3）。

Task-space is a typical configuration space of mechanical systems , whose geometrical correspondence is the Lie-group SE ( 3 ) .

整个设计过程构建于李群，综合了横截函数方法、积分器backstepping和Lyapunov重设计技术。

The design procedure was based on the transverse function method , integrator backstepping , and Lyapunov redesign technique .

本文把李群的单个对合自同构推广为由李群G的一些自同构组成的有限可换群，从而决定了一个广义对称空间，并讨论了它的某些性质。

Generalizing a single involutive automorphism to a finite Abelian group of automorphisms of G , we obtain a homogeneous space called generalized symmetric space and some of its properties .

根据确定的路径点在李群空间SE（3）中构造出一条C2连续的三次均匀B样条插值定位路径；

According to the decided configurations , a C 2 continuous uniform interpolating B spline positioning path is constructed in Lie Group SE ( 3 );

本文讨论线性二阶（常的与偏的）微分方程（非抛物型的），按照李群定义其不变式，证明了关系式λ（x，ε）（？）

In this paper , the second linear ( partial or ordinary ) differential equation ( non-parabolic ) and its invariants defined in Lie group are discussed , the relations (?)

李群表示论和Schubert条件

Representation Theory and Schubert Condition

本文研究了SU（1,1）李群Barut&Girardell（BG）相干态的叠加态的非经典性质与叠加系数之间的关系。

The properties of superpositions of the SU ( 1,1 ) Barut - Girardell ( BG ) coherent states are discussed in this paper .

对基于李群不变性的自然梯度ICA算法进行了改进，提出了一种规范化自然梯度ICA算法。

This paper presents a standardized natural gradient ICA ( Independent Component Analysis ) algorithm through improving the natural gradient ICA algorithm based on Lie Group Invariance .

自H.Hopf研究紧李群同调时提出了Hopf代数概念之后，人们发现它与李代数、微分几何、代数拓扑及统计物理具有广泛的联系。

When H.Hopf studied the homology of compact Lie group , he gave the concept of Hopf algebra .

本文应用李群理论，对紧单李群G，给出了旗流形G／T的上同调环自同态的完全分类，并对典型群计算了相应自同态的Lefschetz数。

In this paper , the cohomology endomorphisms of flag manifold G / T of compact simple Lie group G is completely classified , and the Lefschetz number of these endomorphisms are computed .

采用李群SE（3）的齐次空间描述少自由度并联机器人的末端执行器位姿，并研究了相应位置正反解的计算方法。

By identifying the configuration space of end-effector with the homogeneous space of SE ( 3 ), and transforming the kinematics problems into the optimization process with constraints , kinematics of these robots can be solved through iterative approach .

本文论述了据李群理论构造的Poincare方程所描述的非完整保守系统的相应结果。

This paper treats the corresponding result for a nonholonomic conservative system described by Poincare 's equations which are constructed from the standpoint of the theory of Lie groups .

对于速度平方力作用下的含时阻尼谐振子，我们依靠一特定坐标变换用Lewis与Leach所提出的直接方法求得其不变量，用扩张李群的方法获得其完全对称群。

For a time dependent damped harmonic oscillator with a force quadratic in velocity , we use the direct approach developed by Lewis and Leach to obtain the invariants by means of a specific coordinate transformation .

设计过程基于李群，融合横截函数方法和Lyapunov重设计技术，以轮式移动机器人的扰动运动学模型为对象。

The design procedure is based on Lie group , and the combination of the transverse function method with the Lyapunov redesign technique is utilized . The design is carried out on the perturbed kinematic model of the mobile robot .

Heisenberg型群是一类极为有意义的二阶幂零李群，备受众多学者的关注（[3][4][6][22]等等）。

Heisenberg type groups are significant kinds of nilpotent Lie groups of step two and attract attentions of many scholars ( [ 3 ] [ 4 ] [ 6 ] [ 22 ] etc. )

本文利用群表示论研究李群以及紧致对称空间的热核，特征值与特征函数.特别讨论了复格拉斯曼流形以及流形Sp（n）／U（n）上特征值及特征函数。

In this paper , we study the heat kernels , eigenvalues and eigenfunctions of Lie groups and compact symmetric spaces by means of the representation theory of groups . Especially , we discuss the complex Grassmannian manifolds and the manifolds Sp ( n ) / U ( n ) .

在黎曼几何中，带有左不变黎曼度量的幂零和可解李群具有重要作用。如：它们出现在非紧致黎曼对称空间的等距群的Iwasawa分解中；

Nilpotent and solvable Lie groups with left-invariant Riemannian metrics play a remarkable role in Riemannian geometry .

由于该系统具有Dn（？）Z2对称性，从而我们能够通过李群刻画它的对称性和李群的表示理论在探讨从平衡点分岔出来的周期解的时间空间模式。

Because the system has the Dn (?) Z2 symme-try , we could use Lie group to represent its symmetry and Lie group representation theory to explore the spatio-temporal pattern of the bifurcated periodic solutions from the trivial equilibrium .

采用微分方程的李群方法，研究了外噪声影响下的非平衡相变模型对应的FokkerPlanck（FP）方程，得出了含时间概率密度P（x，t）的严格表达式；

Some models describing first or second order nonequilibrium phase transition under exteral Gaussian white noise are studied . The exact time-dependent solution of the probability density of the relevant Fokker-Planck equation , P ( x , t ), is obtained by using a method of Lie group .

研究了李群胚在其内子群胚上的作用，并证明了李群胚上的Maurer-cartan形式在其任意左不变向量场上作用的结果为常数。

Studied the actions of Lie groupoids on its Inner subgroupoids , proved the result that its Maurer-Cartan forms acting on left invariant vector field is a constant .

李群机器学习（LML）既继承了流形学习的优点，又充分利用了李群的代数结构和几何结构的数学本质，自提出以来就引起了许多研究者的关注。

Lie Group Machine Learning ( LML ) inherit the advantages of manifold learning method and make full use of the Lie group 's structure of algebraic and geometry in mathematics .

给出了相空间小波分析步进算法偏移成像以及保幅保结构李群算法偏移成像的最新进展；第五章介绍距离徙动算法（RMA）的原理，着重比较PFA和RMA的成像性能。

And it gives the up-to-date progress on applying the wavelet , Lie group to migration algorithm . Chapter 5 analyzes the image formation theory of Range Migration Algorithm ( RMA ) and compares the image forming performance of PFA with that of RMA in detail .

以李群的Maurer-Cartan形式的外微分为辛结构，给出了辛李群的概念，进而讨论了辛李群的特殊性质。

We have taken exterior differential to Maurer-Cartan form of Lie Group as symplectic structure and given the definition of Symplectic Lie group , further we have discussed the special properties of Symplectic Lie group .