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The method of Ricci flow is applied to study the metric deformation on Rimannian manifold with boundary.

Hamilton的Ricci流方法被广泛地应用于研究流形的几何和拓朴。

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。

Endowed with a Riemannian metric derived from the gray scale information of a given image, the image space became a Riemannian manifold. On this Riemannian manifold, we evolved a curve by the mean curvature flow using the level set methods.

在图像空间上直接赋予一种由图像灰度信息导出的黎曼度量，使之成为黎曼流形，然后在此黎曼流形上利用水平集方法对曲线以平均曲率流进行演化。

A flexible, imaginative performance requires a minute but continuous modification of the metric values printed in the music; it includes color gradation and variety in the use of dynamics, pedaling, and rubato, elements that are indicated in the score only rudimentarily.

灵活的、富于想象力的演奏只是一瞬间，但印刷在乐谱里的音量长度却是在不断地修改；它包括音色的渐变，以及使用力度强弱、踏板和自由节奏时的多样性，乐谱中所标明的基本动作是最初步的。

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。

What this paper discusses rainbow gravitation to fall is cruel bilge model, derived of metric field and scalar quantity field disturb equation, analysed the property that density disturbs to change along with time.

本论文讨论彩虹引力下的暴胀模型，导出了度规场和标量场的扰动方程，分析了密度扰动随时间变化的性质。

Total invest-ment of the 1st and scend plan of this project is USD18,650,000,annual production capacity-40,000 metric tons wire products (including Cold Heading Wire and cold forging Wire).

项目一期总投资1365万美元，年产紧固件用冷镦钢丝和弹簧用弹簧钢丝25，000吨。

In this note, various definitions of lower semicontinuous set- valued mapping are extended to topological spaces without any metric topological and are compared.

文章的目的是要把各类下半连续型集值映射的定义推广到不带有任何度量的拓扑空间中并且作仔细的比较。

Listen,point and check your answers.

听，指出并且检查你的答案。

Warming needle is one of effective treatment methods for knee arthralgia aggravated by cold,and it is simple,safety,so it should be developed in clinical acupuncture and moxibustion extensively.

但以本院科针灸门诊在2005年1月—2006年6月期间共收治膝痛患者100余例，经过临床的诊断后，其中施以温针治疗的48例，疗效显著，报道如下。1临床资料本组病例48