黎曼

2The new cloud physical model is put forward the metric geometry.(3)The generalized cloud equations of cloud is derived on the generalized function and the Sobolev space on the Riemannian manifold.

提出了 大气模式中新一代云方案的动力学：(1)基于拓扑的云分类；(2)基于度量几何的云模型(3)利用黎曼流型上的广义函数和索伯列夫空间，系统建立了云之动力学方程组。

The n-dimensional umbilical submanifolds in a Riemannian manifold of quasi constant curvature are discussed.

摘要讨论拟常曲率黎曼流形中的全脐子流形，得到关于这类子流形的两个定理。

We get some results about the scalar curvature of 2 and n(n≥3)dimensions Einstein manifold :ρ Maybe is constant and ρ is constant, the relation between Einstein Manifold and Riemannian Manifold with constant sectional curvature.

本文对其有关性质进行了讨论，得到了2维和n(n≥3)维爱因斯坦流形的数曲率的一些结果：ρ可能为常数和ρ为常数，以及爱因斯坦流形与常曲率黎曼流形之间的关系

In general cases, the demixing matrix in ICA is not in the standard Euclideanspace but in the Riemannian space. Thus the tradition gradient direction is not the speedest direction.

一般情况下， ICA中的解混合矩阵所在的参数空间并非欧式空间，而是黎曼空间，因此，传统梯度所得到的方向并非最速方向。

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。

In this paper,focusing on the symplectic manifolds,we discuss the Seiberg-Witteninvariants,some basic construction.the existence of symplectic forms,and the existenceof Riemannian metric of positive scalar curvature.

本文主要围绕辛流形，讨论其Seiberg-WItten不变量、辛流形的一些基本构造，辛形式的存在怀及其上是否存在具有正数量曲率的黎曼度量等问题而展开的。

Its main goal is to explore information relating to the large-scale geometrical structure of proper metric spaces, including noncompact complete Riemannian manifolds, finitely generated groups, etc., so as to establish connections among geometry, topology and analysis of the geometric spaces, and furthermore, to solve other important problems such as the Novikov conjecture, the Baum-Connes conjucture, the Gromov-Lawson-Rosenberg conjecture on positive scalar curvature and so on.

其主要目标是通过几何空间（如非紧完备黎曼流形、有限生成群等）大尺度几何结构的信息，建立几何空间的几何、拓扑与分析之间的联系，并应用于解决其他重要问题，如Novikov猜测、Baum-Connes猜测， Gromov-Lawson-Rosenberg正标量曲率猜测等。

Its main goal is to explore information in the K-theory groups of the index C*-algebras, the Roe algebras C*, by using the large-scale geometrical structure of proper metric spaces, including noncompact complete Riemannian manifolds, finitely generated groups, etc., so as to establish connections among geometry, topology and analysis of the geometric spaces, and furthermore, to solve other relating problems, say, the Novikov conjecture, the Gromov-Lawson-Rosenberg conjecture on positive scalar curvature, the idempotent problem in the theory of C*-algebras.

粗几何上的指标理论是"非交换几何"领域九十年代以来发展起来的重要研究方向，它孕育于非紧流形上的指标理论，其主要目标是通过几何空间（如非紧完备黎曼流形、有限生成群等）的大尺度几何结构探索指标代数，即 Roe代数，的K-理论群的信息，从而建立几何空间的几何、拓扑与分析之间的联系，并应用于解决其他重要问题，如Novikov猜测、Gromov-Lawson-Rosenberg正标量曲率猜测、群C*-代数幂等元问题等。

The second variation formula of vertical energy functional for a submersion between Riemannian manifolds is calculated with a simple and direct manner.

对于黎曼流形的浸没建立了垂直能量泛函的二阶变分公式，研究强垂直调和映射的稳定性。

A Riemann sum with uniform interval size d and f evaluated at the left end of each subinterval.

在等区间大小d下，f在每一区间中取左端点所得的黎曼和。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。