查询词典 unitary invariant

In chapter 4, we study homological dimensions of H-invariant subring for Hopf astions and smash coproducts.

在第四章，我们研究了Hopf作用的不变子环与smash余积的同调维数。

Variational problems which are invariant under the actions of symmetric group often possess multiple solutions e.g.

根据Ljusternik-Schnirelman理论，在对称群作用下不变的泛函具有多解（见［1-6］等）。

This paper studies the invariant, which is the linear preserving problem based on generalized inverse of matrices. The generalized inverse of matrices and the research status of preserving problems of generalized inverse are outlined. In the basis of deeply understanding the basic knowledge of linear maps, the definition, characteristics of generalized inverse and decomposition of matrix, the author analyzes the decomposition form of preserving idempotence and preserving tripotence in the PID, then studies on the linear maps form of preserving group inverses of symmetric matrices.

本文研究的不变量是矩阵广义逆线性算子的保持问题，概述了广义逆矩阵，广义逆保持问题的研究现状，在对线性映射的基础知识，广义逆矩阵的定义、性质和矩阵的分解深入理解的基础上，深入分析了保幂等、保立方幂等矩阵在主理想整环上的分解形式，继而研究了保对称矩阵群逆的线性算子形式。

In section 2,we characterize the minimal ideals of finite dimensional symmetricself-dual Lie algebras over the complex field and gives an optimistic lower bound for thedimension of the space of invariant symmetric bilinear forms on a symmetric self-dualLie algebra by means of the number of linearly independent minimal ideals.

在第二节中，我们完全刻划了有限维对称自对偶李代数的极小理想；用线性无关极小理想的个数给出了一个对称自对偶李代数上由不变对称双线性型构成的线性空间维数的最好下界

Linear time-invariant state space symmetric system, model reduction, stability, nondegenerate matrix, gradient flow, optimization

湖南第一师范学校；香港理工大学应用数学系长沙410002；铜罗湾；香港重庆师范大学数学与计算机科学系；重庆400047线对称性时不变系统；梯度流；稳定性；优化

In this paper, we investigate the persistence of lower dimensional invariant tori of symplectic mappings.

首先，我们研究了辛映射椭圆型低维不变环面。

Secondly, we investigate the hyperbolic lower dimensional invariant tori of symplectic mappings.

其次，我们研究了辛映射双曲型低维不变环面。

In the study of the Lagrange stability of impact motion, we give some conditions of the bouncing solution of the asymptotically linear equation which is bounded or unbounded. Outside of a large disc, using the symplectic transformation of the Hamilton system to estimate the iteration of the successor map. Applying the Moser's small twist theorem, we get the invariant curves and then give the proof of the bouncing solutions which is bounded. We will estimate the successor map of the equation directly for proving the unboundedness of the bouncing solutions.

在碰撞运动的Lagrange稳定性的讨论中，给出了渐近线性方程碰撞解有界或无界的条件，在充分大的圆盘外，通过Hamilton系统的辛坐标变换的角度平均来估计后继映射的迭代，应用Moser小扭转定理得到不变曲线从而给出在一定条件下碰撞解有界的证明，碰撞解无界性的证明将采用直接估计后继映射的方法给出。

Invariant Manifold: An unstable periodic orbit in a Hamiltonian system (a general class of differential equations which includes the three body problem) have associated two families of orbits forming tubes connected to the periodic orbit.

不变流形：一个不稳定的周期轨道的哈密顿系统（一个微分方程一般类，其中包括三个体问题）有关联的两个形成连接管轨道周期轨道的家庭。

Experiment results show that the proposed algorithm is still order-invariant, and it can reduce the number of RIDGE labels by about 80% as well as segmented regions by 5%~20%.Keywords : Image segmentation watershed algorithm immersion method toboggan method.

实验结果表明，改进算法在增加有限计算复杂度的情况下，将RIDGE标记数量减少了约80%，改善了原顺序无关算法中不确定像素过多的问题，将分割结果区域的数量减少了5%~20%，并且算法保持了顺序无关的特性。

Diabetes is a social disease that affects several million people worldwide.

糖尿病是一个社会性疾病，全世界有数百万人罹患此病。

I'll call you on Friday to see if we can reschedule our luncheon meeting at your convenience.

我星期五会给您打电话在您方便的时候我们重新安排我们的午餐约会。