" if you want to best - selling brand of " natural number , from the survey , a considerable number of dealers expect the coordination maintain “想畅销的品牌”自然很多，从调查来看，有相当数量的经销商对郎酒保持期待。
If we list all the natural numbers below 10 that are multiples of 3 or 5 , we get 3 , 5 , 6 and 9 . the sum of these multiples is 23 如果我们名单上的所有自然数十年以下有倍数为3或5 ，我们从中获得了第3 ，第5 ，第6和第9 。总和的倍数，这是23 。
Note : methods or procedures may be specified for mapping other natural linear orders onto the natural numbers . sequencing for example , may be alphabetic or chronological 注:为把其它自然线性顺序映射成自然数,可以采用各种方法或过程,例如,排序可以按字母或时间。
This paper give some methods of determination about divisibility of integer , and uses them to solve the numbers which can whether or not be divided exactly by natural numbers between one and ten 摘要给出了自然数整除性的若干判别方法，进而解决了被10以内自然数整除的数的判定问题。
We determine those natural numbers for which there are corresponding graphs with the index value equal to them , and those for which there are not any graphs with the index value equal to them 找出了哪些自然数存在对应的分子图使得该分子图的拓扑指标值等于该自然数，哪些自然数不存在对应的分子图。从而避免了人们因试图合成具有这些拓扑指标值的分子而作无用功。
This article used natural number encode , and did feasibility analysis . in connection with premature in genetic algorithm , this article adopted self - adapting adjustment crossover and mutation probability methods , and did simulation 本文采用自然数编码的方式，并分析了可行性；针对算法优化中出现的“早熟”现象，提出了采用自适应交叉、变异概率法，并进行了仿真。
Firstly , a natural number chaotic sequence is created with the key . then the image matrix is transformed with this chaotic sequence , using the magic cube transformation . the results indicate that the proposed algorithm can get a satisfying effect 提出了一种在小波域内的基于混沌序列的模运算数字图像加密解密算法和基于混沌序列的魔方变换数字图象加密解密算法。
In the end of this chapter , we study the wiener index for the ( m , n ) - graph . this may help for the study of the following problem : which graphs have the wiener index equal to the natural numbers besides 2 and 5 , or the extreme value problem of the wiener index 本章最后给出了( m ， n ) -图类的wiener数，这有助于探讨下述问题：以任何2 、 5之外的自然数为其wiener数的图类四北工业大学硕士学位论文的研究，以及wiener数的极值问题的研究。
Abstract : the optimal population size for genetic algorithm based on repeated natural number coding is studied . the existence and a lower boundary of the optimal population size are given . these results supply a guide to genetic algorithm operations in solving practical problems 文摘:研究了可重复自然数编码遗传算法的最优群体规模，证明了最优群体规模存在性，并给出了最优群体规模的一个下限值.本文对研究自然数编码遗传算法具有一定的意义
