黎曼

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

在等区间大小d下，f在每一区间中取右端点所得的黎曼和。

A Riemann sum with uniform interval size d and f evaluated at the maximum point of f in each subinterval.

在等区间大小d下，f在每一区间中取极大值点所对应的点所得的黎曼和。

A Riemann sum with uniform interval size d and f evaluated at the minimum point of f in each subinterval.

在等区间大小d下，f在每一区间中取极小值点所对应的点所得的黎曼和。

In this thesis, we mainly study several problems on geometry and topology of Rieman-nian submanifolds, which contains the geometric rigidity, topological sphere theorems and eigenvalue problems of Laplace-Beltrami operator on Riemannian submanifolds.

本文着重研究黎曼子流形上几何与拓扑的若干问题，主要内容包括子流形的几何刚性、拓扑球面定理和Laplace-Beltrami算子的特征值问题。

In this thesis, we mainly study problems on global geometry and geometricanalysis of Riemannian submanifolds, including vanishing theorem for homologygroups, topological sphere theorem, L~2 harmonic 1-forms, finiteness of end andthe spectrum of the Laplacian. In 1973, by using the Federer-Fleming existence theorem and the techniquesfrom the calculus of variations in the geometric measure theory, H.

本文着重研究黎曼子流形上整体几何与几何分析的若干问题，主要内容包括子流形的同调群消没定理、拓扑球面定理、L~2调和1-形式、端的有限性和Laplace算子谱等问题。

In this paper, two dimensional shallow flow—pollutants coupled model, which applies uninstructed grid finite volume method and Riemann approximate solver, is used to gain the trend of hydrodynamics and water quality change under the condition of driving force. Mechanism of nitrogen and phosphorous circle of WASP5 is considered in the water quality part of the model according to nutrition actuality of shallow lake in the cities.Xuanwu Lake is object of research in this paper.

本文针对城市浅水湖泊富营养化加剧现状，结合WASP5模型中有关氮和磷的循环机理，并将该机理写入已有的二维浅水流体水量模型中加以耦合，应用在无结构网格下的有限体积法与黎曼近似解求解的方法，求解湖泊在外驱动作用下的湖泊水动力和水质因子氮和磷的变化。

However, The RH remains a basically unproved conjecture to this day.

然而，黎曼假设至今始终是一个紧绷为获得证明的猜想。

Wiles, and/or they, must also prove the Riemann Hypothisis!!!

怀尔斯，和／或他们，还必须证明黎曼假设！！！

Of the Reimann Zeta function

黎曼捷塔公式的零

Therefore it seems to us that the falsity of Jiang's 1997 statement is best showed by showing that Balan is all right.

由此，对我们看来通过表明巴兰完全正确是显示蒋1997年声明（译注：否定黎曼假设的声明）虚假的最好方式。

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％。