On Additive Partitions of Type ( a, b, k) of the Set of Natural Numbers

1、

An edge-labelling f of a graph G is a 1-1 map from E ( G) into the natural numbers.

图G的边的一个标号f是指边集E（G）到自然数的子集的一个一一映射。

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2、

A recurrence formula of the coefficient of the sum of natural numbers power and the calculating formula of Bernoulli Number

自然数幂和公式系数的递推公式和有关Bernoulli数的计算公式

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3、

Some properties of the Fibonacci sequence are discussed and some probability relations between the Fibonacci sequence and the natural number sequence are obtained.

讨论了Fibonacci序列的一些性质，得到Fibonacci序列与自然数序列的某些概率联系。

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4、

Secondly, by using of the medium axiomatic set theory ( MS), a natural number system in MS is constructed, and it is proved that five axioms of Peano ′ s natural number system are theorems is MS.

其次，利用中介公理集合论MS的相关理论，构造了MS中的自然数系统，证明了Peano5条公理为MS中的定理。

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5、

Deduces the operational formula of the function between the third power Cartesian product of the natural number set N& N × N × N and N, and further researches into complex computation of countably infinite sets.

文中推导出了自然数集合N的三次笛卡尔积运算&N×N×N与自然数集合N之间的双射函数运算公式，对可数无穷集合的复杂计算作了进一步研究。

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6、

A Generalization of Preceding N-trmed Power Sum for Natural Number

自然数前n项方幂和推广

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7、

All of these indicate that the system of Peano ′ s natural number can be generated in MS and a theoretical foundation provided to prove that MS is a foundation of classical mathematics.

这表明Peano自然数系统能在MS中产生，为最终证明精确性经典数学能奠基于MS提供了理论基础。

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8、

Several precise expressions involving Stirling numbers as coefficients for the power sum of natural numbers are given. Some new properties of the Stirling number and counting formulae of the Bernoulli number are obtained.

给出了自然数方幂和的包含Stirling数的几种精确表示式，得到了Stirling数的一些新的性质和Bernouli数的计数式。

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9、

The Stirling Numbers of the Second Kind and Multiple Sums of Powers of Natural Numbers

第二类Stirling数与多重自然数方幂和

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10、

K Difference of k Power of Arbitrary k+ 1 Adjacent Natural Numbers Equal to k Factorial

任意k+1个相邻自然数k次方的k次差等于k阶乘

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11、

Eratosthenes sieve method is a method to search for all prime numbers less than natural number N ( N> 1).

埃拉托斯特尼筛法是求不超过自然数N（N>1）的所有质数的一种方法。

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12、

The Explicit Expression involving Bernoulli Numbers for the Power Sum of Natural Numbers

自然数方幂和的包含Bernoulli数的精确表示式

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13、

Natural Number K Power Sum Once

关于自然数K次幂和的讨论

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14、

He tried to cram as many things as possible into his traveling bag.

他尽量把东西都塞进旅行包.

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15、

Here it is, the red traveling bag, but I can't find the other one.

在这里, 红的旅行包, 但是我找不到另一件行李.

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16、

A canvas or leather traveling bag designed to be carried while strapped to the shoulders.

带有衣物的可移动的矩形的旅行包.

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17、

Go and pack your traveling bag at once.

去把旅行包收拾好吧.

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18、

B : Yes, this is all mine, two suitcases and a traveling bag.

B: 是的, 这全是我的.两个箱子和一只旅行包.

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19、

His traveling bag is crammed full of old clothes.

他的马桶包被塞得满满的,都是一些旧衣服.

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20、

Produce and sell pramoxine hydrochloride rubber promoting agent TMTD, TMTM , rubber sulphuretted agent DTDM, etc.

生产销售盐酸丙吗卡因、橡胶促进剂TMTD、橡胶促进剂TMTM 、橡胶硫化剂DTDM等.

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