查询词典 manifold without boundary

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。

Do some tentative analysis of the tunnel lining by numerical manifold method. the idea is given that combining regular mesh with finite element mesh and using low-order and high-order cover displacement function in numerical manifold method, it make preprocess and program analysis, precision and efficiency for coordination.

4利用数值流形方法对隧道工程中衬砌结构进行了尝试性的分析，提出了结合规则网格和有限网格并行、高低阶覆盖位移函数混合计算的思想，以达到前处理和程序计算、计算效率和求解精度的协调。

Objective:To explore the feasibility of laparoscopy in diagnosing and treating of abdominal diseases.

目的：探讨腹腔镜用以诊断腹部外科疾病及选择治疗方案的可行性。

The lifetime of nylon 1010 and nylon 1010/POSS composites decreased with increasing temperature.

热重-红外联用分析表明尼龙1010在氮气气氛下的降解产物主要为小分子的低聚物，POSS并不改变尼龙1010降解产物的组成。