交换律

We then can verify the associative law and the commutative law for multiplication, and the uniqueness of the result of addition indicates the uniqueness and the cancellation law for multiplication.

我们容易验证乘法满足结合律和交换律，并且由加法结果的唯一性得出乘法结果的唯一性和乘法消去律。

The combination rule of the method satisfies commutative law and associative law, fully uses information of conflict evidences, and solves three kinds of problems appeared in conflict evidences combination process.

该组合方法满足结合律和交换律，充分利用冲突证据信息，解决了冲突证据组合中的三类问题。

In the 2nd one we have already a+(b+1)= a+b'='=+1,this is the first step of associative law for addition,further more we can verify the associative law and commutative law for addition.

而在第二条中已经有a+(b+1)= a+b'='=+1，就是加法结合律的第一步，进而可以验证加法交换律和结合律。

As a branch of modern algebra , finite fields is an abstract system in algebra which satisfies operational laws such as associative law, commutative law, distributive law etc.

作为近世代数学的一个分支，有限域是一个拥有传统算术四则运算的抽象代数系统，它满足结合律、交换律、分配律、消去律等运算法则。

The operation laws including:commutative law, associative law, cancellation law, unity of operation, inverse element, and distributive law between two operations,here we just omit them.

这些运算律包括：交换律，结合律，消去律，运算单位元，运算逆元，两个运算之间的分配律等，在此不再一一说明详细过程。

According to analyzing on the consistent degree of addition modulo 2∧n with XOR addition for commutative law, the computation formulas of the probability distribution of the noise function and the square sum of the probability values were presented, which is applied on the distinguishing attack on Py. The data complexity of our attack is about 2019∧（-1）times of the data complexity of the distinguishing attack on Py proposed by Sekar et al..

通过对模2∧n加与模2加相对于交换律的相容程度的分析，给出了模2n加与模2加相对于交换律所产生的噪声函数的概率分布及其取值平方和的计算公式，并利用此结果提出了一种对Estream候选算法Py的新的区分攻击方法，该方法所需的数据复杂性约为Sekar等提出的区分攻击所需数据复杂性的2019∧（-1）。

Clearly, the sum of games is a commutative and associative operation, as is the nim sum operation.

无疑，游戏的求和是满足交换律和结合律的运算，nim和运算也是。

Unfortunately, it is not generally possible to determine whether or not an operation is associative simply by glancing at its Cayley table, as is the case with commutativity.

不幸的是，一般不可能象交换律那样通过简单查看凯莱表来确定一个运算是否符合结合律。

The trick about floating point numbers is that although they are extremely useful for representing real-life quantities, operations on them do not obey the arithmetic rules we learned in middle school: associativity, transitivity, commutativity; moreover, many very ordinary-seeming numbers can be represented only approximately with floating point numbers.

For example：有关浮点数的诀窍是，尽管他们是用来代表我们生活中的数，但操作却不符合我们从中学学到的运算法则：结合律，交换律等等，另外许多时候浮点数只是近似值。

Finally, the fact is proved using mathematical induction and the character of stochastic matrix.

首先介绍了防御矩阵的概念、物理意义、重要性质及计算方法，分析了防御矩阵满足乘法交换律的重要意义，最后综合运用数学归纳法和随机矩阵性质证明了防御矩阵满足乘法交换律的事实，此结论无论对于多层防御系统的防御效用值研究连是矩阵理论研究都有一定的指导作用。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。