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We prove that on the localgauge group C∞(M a compact manifold,G a matrix Lie group)there does not exist afinite translationally invariant Borel measure.

我们证明了在局域规范群C∽(M为一紧致流形，G为一矩阵李群)上不存在有限的平移不变的Borel测度。

We first prove a general upper bound in term of the size:〓then derive the exact upper bounds for 3-uniform hypergraphs and (n-2)-uniformhypergraphs of order n.

首先用超图的边数给出了圈示数的一般上界：〓-m+1。随后求出了n阶齐3超图与齐(n-2)超图圈示数的精确上界。

Secondly, for the boundary correspondence of affine stretch on hyperbolic regions, we prove that the above conclusion is also true. Finally, we pose a sufficient and necessary condition for the same conclusion.

最后利用退化的四边形序列，给出了拟对称同胚的极值拟共形延拓的最大伸缩商、四边形模之比的上确界及拟对称同胚的边界伸缩商三者相等的一个充要条件。

SINGAPORE - Australian minerals giant BHP has come a long way from the days more than 120 years ago when a sheep station boundary rider, Charles Rasp, discovered what would prove to be one of the world's richest lead-silver-zinc deposits in the red arid country of central Australia.

提要：澳大利亚矿业巨头必和必拓集团正在计划收购另一家矿业巨头力拓集团。如果并购成功，必和必拓集团将变成一家市值超过3500亿美元、产量规模空前的行业巨无霸。

First, we prove the existence and uniqueness of the global solution to the initial boundary value problem for the stochastic equation.

一方面，我们证明这一随机方程初边值问题的整体解的存在、唯—性。

Prove that if this quantity is bounded above by that value of the Veronese surface then x is either a totally umbilical sphere or a conformal Veronese surface.

最后我们模仿3维的情况，引进一个保角不变量，并证明此保角不变量的上界若为Veronese曲面之值，则x不是全脐球面就是Veronese曲面的保角类。

We then introduce a conformal invariant quantity which is formulated in terms of the square of the length of the trace free part of the second fundamental form and the mean curvature, and prove that if this quantity is bounded above by that value of the Clifford torus then x is either a totally umbilical sphereor a conformal Clifford torus.

接著我们介绍一个由第二基本型式迹为零部份的张量长度平方与平均曲率形成的保角不变量，并证明此保角不变量的上界若为Clifford环面之值，则x不是全脐球面就是Clifford环面的保角类。

But we can prove that the corresponding Eulur\'s function is bounded from below in a proper set S of W_0~(1,p)× W_0~(1,q), and then a minimizer of Eulur\'s function in S gives rise to a solution of the problem.

但是，我们可以证明欧拉泛函在合适的集合S中有下界，因此在该集合中利用变分方法寻找泛函的极小就可以得到原问题的解。

In chapter four, we prove that a complete open Riemmannian manifold with Ricci curvature negatively lower bounded is of finite topological type provided that the conjugate radius is bounded from below by a positive constant and its excess is bounded by some function of its conjugate radius.

第四章，我们证明了对于Ricci曲率具负下界的完备开Riemannian流形，当其共轭半径有正下界且它的Excess被其共轭半径的某个函数所界定时，它就有有限拓扑型。

We prove that a bounded hyperconvex domain D is Bergman complete if the pluricoinplex Green function is symmetric.

我们证明了若一个有界超凸域的多复变量Green函数是对称的，则其是Bergman完备的。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。