查询词典 Riemannian

At many occasions they arise quite natu-rally.For example,they appear in the Iwasawa decomposition of the isometry group ofa non-compact Riemannian symmetric space.Also,every connected homogeneous Rie-mannian manifold of non-positive sectional curvature can be represented as a connectedsolvable Lie group with a left-invariant Riemannian metric.

它们出现在非紧致黎曼对称空间的等距群的Iwasawa分解中；任一非正截面曲率的连通齐性和黎曼流形可以表为带有左不变黎曼度量的连通可解李群等，带有左不变黎曼度量的幂零及可解李群的微分几何，调和分析和谱几何是重要的研究课题。

For H-type groups, explicit equations of shortest sub-Riemannian geodesies and a full characterization of the sub-Riemannian isometry groups are given in this dissertation.

对广义的Heisenberg群，本论文给出了最短次黎曼测地线的明确表达方程，并完全刻画了次黎曼等距群。

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

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

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。

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。

In chapter 2 we recall the basic facts about Riemannian manifold and some notions of the transform theory on Riemannian manifolds.

首先，利用给定流形的向量丛上联络的存在性给出流形上的不可积分布上非完整联络的存在性证明，进而证明了次黎曼联络的存在唯一性，并以此为出发点研究了次黎曼流形中仿射变换、等距变换、共形变换和射影变换下的一些不变性质，给出了相应变换下的一些不变量。

The problem has wide applications to various disciplines such as computational complexity theory, organic chemistry etc., and is also closely related with the problem of how to construct cospectral Riemannian manifold in Riemannian geometry and the problem of 'Can one hear the shape of a drum?

该问题的研究在计算复杂性理论、有机化学等领域有着重要应用，并与Riemann几何里面如何构造同谱Riemann流形及物理学里面的'听鼓辨其形状'等问题密切相关。

We study the nonexistence of stable p-harmonic map from complete non-compact strong-parabolic Riemannian manifold to pinching Riemannian manifold.

文章讨论了从完备非紧强抛物黎曼流形到拼挤黎曼流形的稳定p 调和映照的不存在性。

Riemannian Space. The parameter space in blind source separation is Riemannian Space. Natural gradient has many better characters compared with normal gradient.

自适应盲分离算法中的系数空间是黎曼空间，本文将自然梯度下降法应用于Infomax算法可以改进算法的性能，有利于算法的数值稳定性和提高算法的收敛速度。

This paper proves the existence of utility function by using Riemannian geometry methods, which build a bridge between Riemannian geometry and economics.

运用黎曼几何的方法证明了效用函数的存在性，引进了广义的边际效用趋势概念，该定义揭示了以效用函数为度量与一般的欧氏度量的偏离，并证明了这个定义是内蕴的。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。