The cross ratio invariance of interaction system

Algorithm of space plane parameters based on cross ratio invariance

基于交比不变性的空间平面参数算法

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Currently there are two benchmarks for the International oil market, West Texas Intermediate ( WTI) in the U.S. and Brent in the U.K. However, both of them are benchmarks for light crude oil trading, most of the crude oil imported to China is medium.

现在国际原油市场有两个基准，一个是美国的西得克萨斯中质油期货，另一个是布伦特原油期货。然而，这两个基准主要是为轻质原油贸易制定，进口到中国的则大部分是中质原油。

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Poland's unemployment rate has spiked above nine percent, prompting the country's central bank to cut interest rates for the second time in as many months.Most major financial markets saw light pre-holiday trading.

波兰的失业率骤升到9%以上，促使波兰央行在两个月内两次降低利率。世界大部分股市在节日前的交易量清淡。

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Analysts said it was difficult to see what could stop Spanish and Italian rates continuing to climb, particularly in light summer trading.

分析师表示，很难看到有什么措施能够阻止西班牙和意大利国债收益率继续攀升，尤其是在夏季交易清淡时期。

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Most major financial markets saw light pre-holiday trading.

世界大部分股市在节日前的交易量清淡。

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Nevertheless, on Friday, stock markets around the world shrugged off the manufacturing numbers, posting gains in Hong Kong, Seoul and Europe on light trading volume.

不过，上周五全球股市并没有受到制造业数据的影响，香港、首尔、欧洲股市均在淡静的交易中走高。

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But traders said the eleventh-hour plunge came amid relatively light trading volume& a sign there could yet be more sellers waiting on the sidelines.

但交易员们说，股市在收盘前最后一刻大跌是因为市场交投相对清淡，这一迹象显示还可能有更多卖家在场边观望。

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After a year of gut-wrenching losses, stock markets around the world recorded a positive day amid light trading to close out2008.

全球股市经过一年令人心痛的暴跌，在2008年的最后一天以上涨收场。

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The view is long term investor enters the arena when light trading buy, not be to say to be in trade begin delicate when, OK instantly average.

主张长线投资者在交易清淡时进场收购，并不是说在交易开始清淡的时候，就可以立即买进。

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We derived the identity which combines the measure of the path-integral of the generating functional and the effective action of the pure gauge field in the coset space of the Abelian chiral group, and is invariant under chiral transformation.

导出了与阿贝尔手征群陪集空间纯规范场的生成泛函路径积分测度和有效作用量联合起来在手征群变换下具有不变性相应的恒等式。

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With this identity the renormalization equations are established. The renormalization of the pure gauge field theory in coset space of the Abelian chiral group is carried out by solving these equations.

利用此恒等式建造了重整化方程，并由方程的解将阿贝尔手征群陪集纯规范场理论重整化。

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On the quantization of pure gauge fields on coset space of Abelian chiral group

阿贝尔手征群陪集纯规范场的量子化

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This paper proves that the omni-direction permutations constructed by recurring shift Latin square Dp and Latin square Wp on the finite primary field Fp must be complete mappings on Abelian group Fp, and prove that these omni-direction permutations are also linear functions on Fp.

证明了利用有限素域Fp上的循环移位拉丁方Dp和拉丁方Wp产生的全向置换必定是Fp加群上的完全映射，而且这类全向置换一定是F上的线性函数。

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In terms of sub-shifts of finite type determined by an irreducible matrix, affine maps of compacted connected metric abelian group and continuous maps of tree, the two concepts of topologically ergodic map and topologically transitive map are identical.

指出对于由不可约方阵所决定的符号空间有限型子转移而言，或紧致交换群的仿射变换及树上连续自映射而言，拓扑遍历与拓扑可迁这两个概念是一致的。

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The base using elliptic curves as public-key cryptosystem is that because the points set of elliptic curve on finite field can form Abelian group. By this, the discrete logarithm on elliptic curve can be defined.

使用椭圆曲线作为公钥密码体制的基础是由于定义在有限域上的椭圆曲线上的点的集合可构成阿贝尔群，由此可定义其上的离散对数，即椭圆离散对数。

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Let t ( G) be the number of unitary factors of finite Abelian group G. In this paper, we obtain an asymptotic formula of t ( G) with a better error term.

令t（G）为有限阿贝尔群G的单因子个数.本文得到了∑｜G｜≤xt（G）带有更好余项的渐近公式。

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Generalizing a single involutive automorphism to a finite Abelian group of automorphisms of G, we obtain a homogeneous space called generalized symmetric space and some of its properties.

本文把李群的单个对合自同构推广为由李群G的一些自同构组成的有限可换群，从而决定了一个广义对称空间，并讨论了它的某些性质。

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Up to now, for any given finite abelian group, it havn't been found any paper gave a general formula to calculate the order of the automorphism group of the group.

对于任意给定的有限阿贝尔群，迄今尚未见有文献给出其自同构群的群阶的一般计算公式。

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The combination of abstract algebra, combinatorial mathematics and the matrix theory knowledge, we propose a new construction of Jacket matrix based on finite Abelian group, which expand the Jacket matrix family.

结合抽象代数，组合数学，矩阵理论等知识，提出一种有限阿贝尔群上Jacket矩阵的构造方法，扩展了Jacket矩阵家族。

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If the permutation group is not an Abelian group, we can find an Abelian subgroup included in the group, and then we can use the method as above.

若给出的置换群不是一个Abelian群，则我们可以在这个群中，找一个Abelian子群，因此同样可以用上述方法。

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