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Because of the associative law for addition, we can define multiplication based on addition, a b means a+a+…+a,adding a with b times.

正是由于加法的结合律使得我们可以在加法的基础上定义乘法,就是重复加法的简便运算:a b=a+a+…+a,对a重复相加b次。

Similarly, the addition of any three natural numbers must satisfy associative law:+c=a+, and then we can verify that for any n natural numbers, the results of adding is the same in any associative way which keep the order of numbers.

类似地任何三个自然数可以有结合律:+c=a+,进而可以证明任何n个数的任何结合方式进行加法所得的结果是一致的。

Table 2.1 at the end of this chapter summarizes precedence and associativity for all operators.

本章末尾的表2-1完整总结了所有运算符的优先级和结合律

In this paper,we have presented an autonomous guidance strategy based on optimal states feedback technology.First,by utilizing classical Gauss motion equations,we derived the three separate control laws,which could maximize the time rate of change of a desired orbital element.

首先利用传统Gauss型运动方程,推导出三个轨道根数增大最快的独立控制律;然后根据当前根数与目标值的偏差量对独立控制律进行加权组合;最后为高效可靠地获得最优制导律,采用一种遗传算法和逐次二次规划相结合的混合方法对权重进行了优化。

First, by utilizing classical Gauss motion equations, we derived the three separate control laws, which could maximize the time rate of change of a desired orbital element. Then, the separate control laws were blended based on the deficit between current and target value of orbital state. Finally, to obtain the optimal guidance law effectively and reliably, a hybrid method combining genetic algorithm with sequential quadratic programming was used to optimize the weight values.

首先利用传统Gauss型运动方程,推导出三个轨道根数增大最快的独立控制律;然后根据当前根数与目标值的偏差量对独立控制律进行加权组合;最后为高效可靠地获得最优制导律,采用一种遗传算法和逐次二次规划相结合的混合方法对权重进行了优化。

Conversely, if ''S'' is a subgroup of ''G'', then it obeys the axioms of a group.

因此,满足了闭包、单位元和逆元公理,而结合律是继承来的,所以''S''是子群。

And the Montgomery method to realize point multiplication is also efficient by using projective coordinates to reduce the multiplication times and only one time of inversion been needed.

利用Fermatt小定理求逆,根据有限域上元素的乘法满足结合律和交换律,通过重新安排乘法和平方的顺序,可以减少乘法和平方的次数,比按照定义直接实现速度提高了6倍。

It is a total combination of image thinking, a total of materials as a mutual penetration and combination.

形象共殊结合律,即借助于思维想象力的发挥,共象材料与殊象材料相互渗透、相互结合;3。

In chapter Ⅲ, auther analysed the vowel harmony, the consonant combination, the syllable structures and exlplained their characters .

第三章,对杜尔伯特口语的元音和谐律、辅音结合律、音节结构进行了分析,并阐释其规律。

The development from simplex existence of three tuning systems to organic combination of three tuning systems is known as the twelve-tone-equal temperament with multi-frequency flexibility. The harmonious combinations between circle-of-fifths system and rhyme, just intonation and harmonic, and twelve-tone-equal temperament and inflexion, make up a new tuning system which takes full use of advantages of three tuning systems.

从三律的单一存在发展到现代三律的有机结合(即&复频弹性十二平均律&),五度相生律与旋律美相映,纯律与和声美相映,平均律与转调美相映,复频弹性十二平均律综合三律之长,避其之短,构成一个新的律制,使三律融为一个自由变通的统一体,进入相对的自由王国。

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