查询词典 manifold classification

One important feature ofHamiltonian systems is that it has energy(its energic function is Hamiltonian func-tion),then,its solutions on 2-dimensional plane are some contour lines,the points onstable manifold emanating from hyperbolic equilibrium point have the same energyas that on unstable manifold,then,one can guess that they form a closed curve,i.e.homoclinic orbits under certain conditions,and the contour lines in the innerpart of homoclinic orbit are periodic orbits.

哈氏系统的一个重要特征是它有能量存在(以Hamiltonian函数作为它的能量)，那么在二维平面上，它的解表现为一些等值线，从双曲平衡点发出的稳定流形和不稳定流形上的点具有相同的能量，那么可以猜测，在一定条件下它们构成一条封闭的曲线，即同宿轨，而且其内部的等值线都是周期轨道。

Another definition of linear manifold is given, some properties of linear manifold as well as its relationship with linear space and system of linear equations are obtained.

本文从线性流形另一定义出发，得到线性流形的有关性质，并指出其与线性空间以及线性方程组之间的关系。

In Chapter 2, the D-symmetric solutions of matrix equation A~TXA = B on the linear manifold S ={X ∈ D~(-2)SR~|XZ = Y, Y = Y{D~2Z+D~2Z, Z~TD~2Y = Y~TD~2Z, Y,Z∈ R~}, by applying the generalized singular value decomposition of a matrix pair, the necessary and sufficient conditions for the existence and the expressions for the D-symmetric solutions of matrix equation A~TXA — B on the linear manifold are established.

运用矩阵对的广义奇异值分解，给出了这类线性流形上矩阵方程A~TXA=B存在D对称解的充要条件及其通解的表达式。另外给出了它的D对称最小二乘解的表达式。

In Chapter 4, the centro-symmetric solutions of matrix equation A~TXA = B on the linear manifold S ={X ∈ CSR~|||XY - Z||= min, Y,Z ∈ R~|}, using the quotient singular value decomposition of matrix pairs, the necessary and sufficient conditions for the existence and the expressions for the centro-symmetric solutions of matrix equation A~TXA = B on the linear manifold are established.

利用矩阵对的商奇异值分解，给出了这类线性流形上矩阵方程A~TXA=B存在中心对称解的充要条件及其通解表达式。

F irst of all from global viewpoint we define a kind of nonlinear control systems on Riemannian manifold , and give the representation of state equation for the nonlinear systems under a local coordinate system of Riemannian manifold

首先从整体化的观点定义了一种建立在黎曼流形上的非线性控制系统，给出了系统的状态方程在黎曼流形的局部坐标系下的表达式

Riemannian normal coordinates contain information about the direction and distance from a specific point on a manifold to other points nearby. It is worth to translate this technique from its original setting in differential geometry, to the task of manifold learning.

黎曼正则坐标包含了流形中指定点到邻近点的方向和距离信息，如何将这种源于微分几何的技术应用到流形学习中也是值得研究的课题之一。

In the second part of this paper, by considering the geometric properties of some well-known classical Riemannian manifold and combining with results we had got, we give the definition of the parallel rays in a complete nocompact Riemannian manifold M, which are usual parallel rays when M is restricted to Euclidean space R.

本文的第二部分，基于对一些典型的黎曼流形几何性质的观察，结合已有的研究成果，我们首次给出了完备非紧黎曼流形上平行射线的定义，该定义在欧式空间中就是普通的平行射线。

To understand the properties of the transfer function of parallel tube-manifold system in wind tunnel test,an analysis is made of several parameters related to the transfer function on the basis of the dissipative model with some qualitative rules on perallel tube-manifold system obtained.

风洞刚性模型测压试验是获得建筑结构风荷载的重要方法。刚性模型的测压管路系统一般包括模型表面的金属短管及连接金属管和传感器的PVC管等管道元件。为了得到结构风压的完整信息，应在模型表面布置尽可能密集的测点。

In this paper, the regular domain of traditional parametric surface is generalized to manifold, and a new method is proposed to construct smooth surface based on this domain manifold.

将传统参数曲面的规则定义域推广到一般的二维流形上，并基于定义域微分流形提出了一种新的光滑曲面构造方法。

Lastly, we study the conditions of linearization for symmetric system, from which we can see that a symmetric system is linearizable on manifold M if and only if this system is linearizable on quotient manifold M/G.

最后讨论了对称非线性系统线性化问题，从中可以看出对于具有对称性的非线性系统只要在商流形M／G上能满足线性化条件即能保证在整个流形M上能线性化。

He's a pretty westernised kind of guy.

他是一个非常西化的人。

National spirit is the moral kingpin for a nation to realize common ideal and goal.

一、中华民族精神的基本内涵党的十六大报告指出：在五千多年的发展中，中华民族形成了以爱国主义为核心的团结统一、爱好和平、勤劳勇敢、自强不息的伟大民族精神。