黎曼

Here we discuss the limitations of the Riemann integral and the greater scope offered by the Lebesgue integral.

在这一章里我们讨论黎曼积分的限制以及勒贝格积分提供的更大的可能性。

Firstly,the article theoretically expounds the superiority of Lebesgue Integral ,then through the detailed cases analyzes its superiority shown in the practical application compared to Riemann Integral.

文章首先从理论上阐明勒贝格积分的优越性，然后通过具体实例详细探讨勒贝格积分相对于黎曼积分，在实际应用中体现出的巨大优越性。

After constrcting the perfective space , prove that this space is just the space of lebesgue integratiable function , thus explain that lebesgue integral is the form of the perfective riemann integral

在构造了完备化空间之后，证明了该空间就是勒贝格可积函数空间，从而说明了黎曼积分的完备化形式是勒贝格积分。

The geometric thinking in the analysis Liman, on the basis of mathematics and physics it focuses on the two areas of the far-reaching implications.

本文在分析黎曼的几何思想的基础上，着重论述了它对数学和物理学两个领域所产生的深远影响。

Chinese language to be picked Liman is one of the 19th century's greatest mathematician, and his very short life, but the contribution of science can not be overlooked.

帮忙翻译一下。谢谢。急！！中文摘要黎曼是十九世纪最伟大的数学家之一，他的一生十分短暂，但对科学的贡献却是不容忽视的。

This limit is called the line integral of f along C from A to B with respect to arc length; that is

时 ，该黎曼和有极限，该极限就叫做沿曲线从 A 到 B 对弧长的曲线积分。

We discussed the compact speudo-umbilical submanifolds in a locally symmetric conformally flat Riemannian manifold.

2中的积分不等式推广到局部对称共形平坦黎曼流形中的伪脐子流形。

In this paper, we discuss the 2-harmonic spacelike submanifolds in a locally symmetric and conformally flat pseudo-riemannian manifold and get two sufficient conditions under which Mn turns into a maximal submanifold,and the results in [2] are improved.

讨论局部对称共形平坦伪黎曼流形的2-调和类空子流形，得到这类子流形成为极大的二个充分条件，推广了文[2]中的结论。

In this paper we will mainly study the gauge fixing Yang-Mills heat flow of a principal bundle For a principle bundle with a compact seme-simple Lie group as its structure group over a compact Riemannian manifold without boundary, the evolutions of the curvature and its higher derivatives under the flow above will be derived, and the energy inequality and the Bochner type estimates will be obtained.

中文摘要：本论文主要讨论主丛上的规范固定Yang-Mills热流我们在紧致无边黎曼流形上的以半单紧致李群为结构群的主丛上，推导了在规范固定Yang-Mills热流下曲率及其高阶导数的演化方程，得到了该热流的能量不等式和Bochner估计，由此可推出单调性公式和小作用量正则性，以及曲率各阶导数的局部一致估计。

In this paper we will mainly study the gauge fixing Yang-Mills heat flow of a principal bundleFor a principle bundle with a compact seme-simple Lie group as its structure group over a compact Riemannian manifold without boundary, the evolutions of the curvature and its higher derivatives under the flow above will be derived, and the energy inequality and the Bochner type estimates will be obtained. Then, the monotonicity formula and the small action regularity theorem can be proved. We will give the locally uniform estimates for the higher derivatives of the curvature.

本论文主要讨论主丛上的规范固定Yang-Mills热流我们在紧致无边黎曼流形上的以半单紧致李群为结构群的主丛上，推导了在规范固定Yang-Mills热流下曲率及其高阶导数的演化方程，得到了该热流的能量不等式和Bochner估计，由此可推出单调性公式和小作用量正则性，以及曲率各阶导数的局部一致估计。

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。