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这个密码是由自然数组成的。This code is made up of natural numbers.

密码是由自然数组成的。This code is made up of natural numbers.

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算法采用自然数编码的方法来提高搜索效率，并进行了仿真。And it uses the natural number coding method to improve search efficiency effectively.

本文利用函数项级数，微分及排列组合等工具推导出了一个求自然数等幂和的一个一般公式。In this paper, a general formula of sum of equal power series of natural number is given.

自然数可以分为奇数、偶数、质数、合数。The natural number is not bad mark is an odd number , even number , prime number , compound number.

如改变前提，是可以得到连续统与自然数集合间的一个一一对应的。If it was changed, a one-one correspondence between continuum and natural number set can be received.

通过对自然数一些基本性质的分析论证，得出一个简明的梵塔移动的通项公式。It derives a simplified general team formula by analyzing the basic characteristics of natural numbers.

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借助牛顿公式和韦达定理，采用迭代的方法求解类似于自然数等幂和的问题。With the help of Newton formula and Vieta theorem, iterative method was used to solve problems of power sum.

最后，介绍上述结果在求解自然数幂和公式方面的应用。Finally, a little applications of above results for solving powers sum formulas of natural numbers are introduced.

小数由十，十的倍数和十分位的倍数组成。小数点把自然数与小数部分分开。Decimals are based on ten, multiples of ten, and tenths. A decimal point separates natural numbers from decimal fractions.

“自动矢量处理”实现了在自然数据基础上网状径路数据自动产生、快速运算。The way of automatic vector processing accomplishes automatically generation of reticulation route data and quick operation.

当你把孩子的成绩性别，你看到的没有发现男性优势在构建自然数的概念。When you compare children's performance by sex, you see no hint of a superiority of males in constructing natural number concepts.

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部分问题在于，根据定义，质数不能被分解，而后者通常是研究一个自然数的起点。Part of the problem is that, by definition, they have no factors, which is normally the first foothold in investigating a number problem.

可以把这种对应看作是各负责另一人之安全的两人同行制，每一个自然数都与某个正分数配对，反之亦然。You could think of this correspondence as a buddy system in which each natural number is paired with some positive fraction, and vice versa.

例如，0到1之间的实数集合是“不可数的”——无法与自然数作一一对应。Specifically, the set of real numbers between 0 and 1 is “uncountable” — it can’t be put in one-to-one correspondence with the natural numbers.

同学们，我们已经学习了整数、自然数、小数，已初步认识了分数，你能说出几个分数吗？Students, We have learned whole numbers, nature numbers, decimals, and know a little about fractions . Who can give me some example about fractions.

对于有时间窗的非满载VSP问题，将货运量约束和软时间窗约束转化为目标约束，建立了非满载VSP模型，设计了基于自然数编码，使用最大保留交叉、改进的反转变异等技术的遗传算法。On the VSP with time window, while the restraints of capacity and time windows are changed into object restraints, a mathematic model is established.

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以前通常使用方格计算纸，用起始自然数1按所要求的图形顺序依次排列求得。In the past, this problem could be solved by means of square calculation paper, with the initial natural number 1 arranged in required graphic sequence.

在分析基于二进制编码的遗传算法基础上，对基于自然数编码的遗传算法作了初步的探讨。In this paper, based on the analysis of the genetic algorithm on binary coding, a preliminary discussion is made on the genetic algorithm of natural number coding.

采用自然数和二进制互换的编码方式，应用N皇后的约束条件构造适应度函数，保证了算法的全局收敛性。The transform coding between integer and binary, fitness function based on constraint of N-Queens problem are designed to ensure the global convergence of algorithm.