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The research indicated that if the least common multiple between the slot and pole is 2pQ,and the greatest common divisor is 1,the cogging torque can be greatly reduced.

研究表明：当定子槽与转子极的最小公倍数为2pQ、最大公约数为1时，齿槽转矩最小。

Based on a formal analysis of lifting decomposition, the hierarchical structure concept of the decomposition set, as well as the lifting decomposition technique of the polyphase matrix' greatest mth-order common divisor, is proposed to conquer the difficulties in the practical computation of and the optimal search in the huge decomposition set.

本文在形式化分析Lifting分解原理的基础上，提出了分解集合的分级结构概念以及多相矩阵的m阶最大公因子Lifling分解技术，克服了分解集合求解问题的高复杂性所带来的实际计算与搜索困难；进一步地，从数值稳定性及计算代价两方面研究了分解的评价问题，设计出两种实用的分解稳定性准则；最后，结合分级结构技术提出一种最优分解算法。

Tang Gaohua, Su Huadong, Commutative ring and zero-divisor semigroups of regular polyhedrons.

乔晓云，唐高华，郑学谦。单圈图的全图谱半径，广西科学15（2008），No.3， 224-227 4。

Using properties of zero-divisors, regular elements and subdirectly irreducible ring , we obtain some results on the commutativity of semi-prime ring and Jacobson semi-simple ring as follows 1 Let R be a semi-prime ring ,a∈R and 2a is not zero-divisor,If R satisfies one of the conditions in this paper , then R is commutative.

在某些特殊环的交换性方面取得了进一步的结果，并得到了一些新的结论，主要有一设R 为半质环，a∈R ，且2a 为非零因子，如果R 满足论文中八个条件之一，则可以证明环R 为交换环。

We establish a relation between μ and the stucture of the group G, and obtain the lower bound of the ratio by the mininal prime divisor of the order and commutator of the group G, and give a necessary and sufficient condition under which this lower bound is attained.

第一部分，记有限群G的阶与不可约特征标个数的比值为μ，我们研究了一般的非交换有限群G的结构和μ之间的关系，通过群G的阶的最小素因子和换位子群G′的最小素因子得到了μ的一个下界，同时给出了达到下界的一个充分必要条件。

The divisor class group, often called Jacobian group, based on which hyperelliptic curve cryptosystems are constructed, is much complicated than the elliptic curve rational point group.

但由于可以在一个很小的基域上构造具有较大素数因子阶的Jacobian群，且可应用于密码体制的超椭圆曲线比较丰富，这使得超椭圆曲线密码体制也逐渐受到人们的重视。

N be a divisor function of n.

τ表示 n的除数函数。

Smarandache LCM function and the divisor function,a mean value of composite function which involving the pseudo-Smarandache functions is given,and obtain some interesting identities and asymptotic formulae for them.

Smarandache无平方因子函数Zw和新的伪Smarandache函数K的复合函数的均值问题，并给出一些有趣的恒等式及渐近公式。

Software Description: XCCalc is a Floating-Point calculator program with the following features:- Can calculate with complex numbers like z = x + i*y - Extra precision to millions of decimal places - Uses Fast Hartley Transform to speed-up long multiplies - Separate input and output notation, base 2 to base 36 - Efficient Transcendental functions - Hyperbolic functions - Greatest Common Divisor function.

XCCalc XPCalc 是一款带有下列功能的浮点计算器软件：可以计算诸如 z = x + i*y 这样的复杂算术公式；带有数百万小数位的额外精度；使用 Fast Hartley Transform 以加速长乘法计算；基于2到36个单独的输入和输出表记法；高效的验算函数；双曲线函数；最大公约数函数。

At present the main research and the application public key the system crypto-algorithm has two kinds: The RSA algorithm and the ECC algorithm, former based on the great divisor of integers decomposition difficult problem, latter is separated the logarithmic computation difficult problem based on the elliptic curve in.

目前主要研究和应用的公开密钥系统的密码算法有两种：RSA算法和ECC算法，前者基于大整数因子分解难题，后者基于椭圆曲线上离散对数计算难题。

If you are unfortunate enough to the lovelorn, please tell me, I will help you out, really, please contact me!

如果你不幸失恋了，请告诉我，我会帮助你摆脱困境，真的，请联系我啦！

China's plan to cut energy intensity by 20 percent and pollutant discharges by 10 percent between 2006 and 2010 is a case in point.

中国计划在2006年到2010间降低20%的能源强度和减少10%的主要污染物排放，就是一个这样的例子。