里德

We prove that an n-dimensional complete open Riemannian manifold M with Ricci curvature Ric_M ≥ 0 is diffeomorphic to an Euclidean n-space if M satisfies some volume growth conditions.

第二章，我们研究了Ricci益率有一定下界的完备非紧n维Riemann流形，证明了这样的流形在满足一定体积增长条件下微分同胚于n维欧几里德空间。

Finite dimensional euclidean spaces Scalar products, norms, orthonormal basis and orthonormalization.

有限维欧几里德空间标量的产品，规范，标准正交基和正交化。

The metaphor of a flat world is worked relentlessly throughout this overlong book, but it is not its incessant repetition that is most troublesome. It is Friedman's failure to recognize that in many ways, some of them not difficult to observe, the world is becoming distinctly less flat.

扁平世界的暗喻从头到尾贯穿于这部大部头著作中，但这还不是这部著作最令人讨厌的地方，最让人讨厌的地方是：弗里德曼没有发现，在很多方面，其中的一些并不难观察到，世界很明显正变得越来越不扁平化了。

Analysis was done for the parameter selection of Montgomery algorithm in ringF_p /x·p(x. Through suitable algorithm parameter and representation change in ring, wereduce the complexity of multiplication in F_p /x.

分析了一类商环F_p／x·p(x上乘法的快速实现问题，通过选择合适的参数，并基于欧几里德算法改变了商环中元素的表示形式，降低了商环F_p／x·p(x上乘法运算的复杂度。

Meanwhile the recording industry was hit with a major scandal over payola schemes between record labels and disc jockeys, a controversy that would bring down some of the most innovative independent studios and revered jockeys, including the legendary Alan Freed himself.

而与此同时，唱片业遭受到一个有关唱片公司与DJ之间贿赂丑闻的巨大打击。一场争论就此展开，而这场争论使得许多最具创新精神的独立工作室和最值得崇敬的DJ成为牺牲品，其中就包括传奇的摇滚先生——艾伦·弗里德。

Philemon and Basilides are but two of the spirit guides that were in contact with Jung.

腓利门和巴西里德是两位与容格接触的精神导师。

In this paper,the decoder is designed using modified Euclidean algorithm,the public extraction algorithm is used to optimize the muhi- plier,and the complexity and the power consumption of RS decoder are reduced by using the iteration and multiple methods.

文中设计的译码器采用修正的欧几里德算法，并在实现中采用公共项提取算法有效地优化了乘法器，以迭代、复用等方法降低了RS码译码硬件实现的复杂度。

You ought to be aware, miss, that you are under obligations to Mrs Reed: she keeps you: if she were to turn you off you would have to go to the poorhouse.

"小姐，你该明白，你受了里德太太的恩惠，是她养着你的。要是她把你赶走，你就得进贫民院了。"

As I knew from my postbag, part of his appeal lay in his willingness to come out with home truths which had occurred to many other people who had not dared to utter them.

我从读者来信中得知，弗里德曼的部分吸引力在于，他愿意说出其他许多人想到、但不敢说出来的逆耳忠言。

Astrid becomes a precociously sexual creature at fourteen when she seduces a man in his fifties, then turns off that sexuality as if it never existed, but the reader is never told why.

在十四岁时，阿斯特里德就显出了性方面的早熟，她引诱了一名五十多岁的男子，随后又了断了这段性关系，仿佛它根本不曾存在过一样，其中的原因也没有对读者阐明。

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。