乘法的

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。

So 2/4=1/2. Here we have used the associative law or the cancellation law for multiplication, which are satisfied for natural numbers, now we assume they are satisfied with fraction numbers.

2的数，所以2/4=1/2。这里我们用到了乘法结合律也可以用消去律，本来这些运算律是对正整数乘法适用的，但对于有分数参加的乘法我们也规定适用。

Derive recursive least squares method, recursive general least squares method, recursive augmented matrix method, recursive multiple-stage least squares method and recursive maximum likelihood method based on recursive Householder transformation by applying the three real-time solutions of overdetermined linear equation to difference model.

将线性矛盾方程组的三种实时解法应用于差分模型，导出了基于Househol-der变换的递推最小二乘法、递推广义最小二乘法、递推增广矩阵法、递推多级最小二乘法和递推极大似然法。

"A set of elements having two operations, designated addition and multiplication , satisfying the conditions that multiplication is distributive over addition and that both operations are associative and commutative for all elements of the set, with the exception of the additive identity element, which is not commutative in respect to multiplication ."

"一组元素，进行加法和乘法两种运算，满足条件：乘法运算需分配于加法之中，这组元素要将这两种运算结合且换进行，附加的就乘法而言不可交换的恒等元素除外。"

Mathematics A set of elements having two operations, designated addition and multiplication, satisfying the conditions that multiplication is distributive over addition and that both operations are associative and commutative for all elements of the set, with the exception of the additive identity element, which is not commutative in respect to multiplication.

域，体：进行加法和乘法两种运算的一组数，满足如下条件，即乘法分配律同样适用于加法分配律，各数在做加法和乘法两种运算中可相互结合并交换，但在乘法中不可交换的加性恒等幺元除外

The improved multiplication algorithm, can be a sign five multiplication, just change a few numbers can be easily extended to more digits multiplication process.

详细说明：采用改进的乘法算法，可进行有符号5位乘法运算，只需更改几个数字便可轻松扩展成更多位数乘法运算程序。

Finite Multiplicative Group In cryptography, we often use the multiplicative finite group: G = in which the operation is multiplication.

有限乘法群在密码学中，我们经常运用乘法有限群：G =，其中的运算是乘法。

With addition and multiplication defined componentwise, both R and R{D, C} are rings.Its clear that R is a subring of ?

R中加法和乘法分别定义为对应分量的加法与乘法，则R关于所定义的加法与乘法构成一个环，显然是？

Wehave obtained two formulas to express thire relation in different view;at the same time,wegive an explicit description of multiplicative unitary operators corresponding to compactquantum group 〓 and 〓 on concrete Hilbert spaces.

我们首先在第四章讨论了紧量子群对应的乘法酉算子和紧量子群与离散群的交叉积对应乘法酉算子的关系，我们得到了在不同观点下的它们之间的关系式；同时给出了紧量子群〓对应的乘法酉算子和〓对应的乘法酉算子在具体的Hilbert空间上它们之间的表达式。

The major achievement of this paper is: Based on characteristics of the traffic data distribution, execute pattern recognition operations on traffic condition on two dimensions by clustering, then use BP neural network to describe and forecast traffic flow aiming at each pattern. Making use of classic flow-occupancy inverse "V" model, implement polynomial fitting using least-squares algorithm and statistics method on flow curves to detect outliers which are proved to be not accord with practice through the actual implement, then use the moving average model to recorrect the outliers and absent. Make correlation analysis on muti-direction flow queues of the intersection and ones of upriver intersections, choose flow queue with high correlation as assistant one to improve the error tolerance of the prediction system, at the same time we can use the method to give an estimation of flow in intersection with out sensors. We design and implement an SOA(Service-Oriented Architecture)-based UTDD(urban traffic data mining development) with high expansibility and performance, which implement unified management and call of the data-mining application though defining a XML-based description of data-mining process and a common interface to call data-mining process, finally we build traffic flow prediction application model on UTDD.

根据交通流量数据分布的特征，提出基于k-means的二次聚类方法，对交通流量在流量大小和时间上进行模式划分，进而对各个交通流模式进行基于BP神经网络的描述和预测，从而提高模型对流量预测的精度； 2）根据流量/时间占有率倒&V&字形曲线分布模型，提出基于最小二乘法的三次多项式曲线拟合和统计方法的异常检测方法，实际应用表明该方法能够有效识别异常数据，然后根据移动平均算法对异常数据进行修正； 3）基于序列相关性分析，分别对预测方向的交通流量数据序列、上游路口相关序列以及预测路口其它各个方向上的交通流量序列进行分析，选择相似性流量序列，作为辅助序列提供其他没有检测器路口的流量估计； 4）设计和实现了基于SOA（Service-Oriented Achitecture）的高性能、可扩展的智能交通数据挖掘系统UTDD，该系统通过定义基于XML的数据挖掘过程描述和通用的过程模型接口，实现数据挖掘应用的统一管理和调用，最后在UTDD上建立了基于路口流量预测的应用模型。

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。