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In addition, by utilizing Jacobi two square numbers theorem and Lagrange four square numbers theorem and some theta function identities, we also prove the known results of number theory: two triangular number theorem, four triangular number theorem, and the number of representations of a positive integer by various quadratic forms in terms of divisor functions

包括Jacobi二平方数定理，Lagrange四平方数定理等，然后利用这些结果结合几个theta函数恒等式，我们获得了把任意一个正整数表示成两个三角数或四个三角数的和以及其他的二次形式的方法数，这些方法数都是用因子函数来表示的。

In this paper, we introduce the concepts of the great common P-divisor, least common P-multiple of two distinct nonzero elements x, y in arbitrary unique factorization domain R, and denote them byp, and p respectively.

在本文中，作为通常的整数环Z上的最大公因子和最小公倍数的推广，我们在惟一分解整环R上定义了最大公P-因子和最小公P-倍元，分别记为_P和_P。

The purposes of this study are to develop two concrete teaching activities and to see students' learning situations from practicing the activities of divisor's unit.

本研究旨在发展因数教学活动设计以帮助学生理解因数的意义，并从实践中了解此教学活动的学习情形。

The purposes of this study were to develop and to practice innovative teaching activity and to examine students' learning situations from practicing the activity of poker game on divisor's unit.

本研究将扑克牌游戏融入小学因数教学，做为因数教学初期的练习与检验的活动，以强化学生因数的概念，并藉由实践了解此教学活动的学习效果。

Can be general computing, will be zero divisor error.

可以进行一般四则运算，除数为零时会报错。

From the graph, we can know that the graph of y=kx+b, is crossing the point of (0,b), and is parallel with the line of y=kx. And in the point of (0,b), o is x and b is y . In this situation, zero can be the divisor. It can be the scientific gist.

从正比例函数和一次函数的图象可知，一次函数y=kx+b在坐标平面上的函数图象是经过(0，b)且平行于正比例函数y=kx的一条直线，这其中的点(0，b)，0表示x，b表示y，在这样的情况下就成了零作除数的情景，这可说是零能作除数的科学依据。

An ring R is said to be the middle superprime ring, if every non - zero ideal of R contains an non - zero element c, which is not middle divisor of zero.

一个环R称为中间超素环，如果它的每个非零理想都包含一个非零元素，它不是中间零因子。

Floored division is integer division in which the remainder carries the sign of the divisor or is zero, and the quotient is rounded to its arithmetic floor.

底限除法是余数携带著除数符号或零的整数除法，而商是四舍五入到它的算术底。

In mathematics , a division is called a division by zero if the divisor is zero . Such a division can be formally expressed as a /0 where a is the dividend. Whether this expression can be assigned a well-defined value depends upon the mathematical setting. In ordinary arithmetic, the expression has no meaning .

如果某一上市公司宣布派发红利股份、红利认股权证、以折让价供股或派发其它有价权益，在除权日之前一日持有它的股票的人士可享有该等权益，在除权日当日或以后才买入该公司股票的人则不能享有该等权益。

In this paper,we discuss the Walsh spectral characteristics of partially-bent functions over ring Znq(q=p1*p2,p1、p2 are primes),propose two new concepts―nonzero factor variant-permanently linear structure and zero divisor variant―permanently linear structure,classify the variant-permanently linear structure of partially-bent functions and show their correlation,obtain several new equivalent conditions of partially-bent functions on ring Znq,finally,point out the correlations among balance, linear structure and points taking nonzero spectrum.

本文在环Znq上讨论了部分bent函数的谱特征(q=p1*p2，p1，p2是素数)，得到了Znq上部分bent函数的几个新的刻划，揭示了部分bent函数的平衡性、线性结构点及非零谱值点之间的相互关系，并对部分bent函数的恒变线性结构点进行了分类，指出了它们之间的相互关系，提出了零因子恒变线性结构点和非零因子恒变线性结构两个新概念。

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。