natural number

noun

1. 自然数
   a positive whole number such as 1, 2, or 3, and sometimes also zero

1. A research on natural number power summation formula and the contained factors
   自然数方幂求和公式及所含因式的研究
2. In this paper, a general formula of sum of equal power series of natural number is given.
   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。
3. Does the Largest Natural Number Exist?& A new method in infinity theory to eliminate the paradox of transfinite numbers ( 2)
   存在最大的自然数吗？&排除超限数悖论，无穷理论的新方案（2）
4. A new view point to view the basic characteristics of data, particularly to indicate the significance of so-called natural number and integer in researches and forecasting of natural events;
   对数据基本性质的新认识，特别是指出自然数、整数在研究和预测中的重要性；
5. A natural number is the abstraction in quantity of objects of a class, and natural numbers can be used to describe the order of time or location.
   自然数是同类事物个体数量多少的抽象，同时自然数可以自然地用于描述事物所处的时间和位置等次序。
6. On the Proof of the Inconsistency of Natural Number System
   关于自然数系统不相容性证明的分析与研究
7. Our final conclusion is: Except for natural number, other numbers are manmade for the need of operations, and they can not be used for counting objects in real life.
   我们的最后的结论是：除了自然数，其它数都是由于运算的需要而人为制造的，不能直接用于实际生活中事物的数量。
8. Applying this result we obtain the iterative method of m positive solutions where m is an arbitrary natural number.
   使用这个结论获得了m个正解的迭代方法，其中m是一个任意的自然数。
9. And the design and implementation of logistics vehicles dispatching system based on genetic algorithm is discussed in this paper, At the same time the key technologies such as the implementing of the genetic algorithm based on natural number encode in the logistics vehicles dispatching have been expounded.
   文章论述了基于遗传算法的物流车辆配送系统的设计与实现，详细阐述了基于自然数编码的遗传算法在物流车辆调度中的运用等关键技术。
10. The initial lines are gotten by converting chaos sequence into natural number.
    将混沌序列转化为自然数混沌序列，得到信息隐藏的初始列。
11. 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.
    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。
12. An adaptive chaos genetic algorithm was used to solve the model. The algorithm used natural number coding method with dynamically adjustment for the probability coefficients of crossover and mutation, and used chaos optimization method as the mutation operator.
    对于模型的求解方法，构造了一种自适应的混沌遗传算法，采用自然数编码方式，动态的在线调整算法的交叉和变异概率，并采用混沌优化方法作为变异算子。
13. In this paper, two propositions of natural number a's multiple power is given and proved, and some examples in application are also given and explained.
    给出并证明了自然数a的多重幂的两个命题，举例说明了它的应用。
14. This paper proves one of the two important limits with continuous function, which is different from the mathematicians 'demonstration by treating x as natural number.
    本文是对两个重要极限之一的证明，以往数学家们都是对x为自然数的证明，这里是以连续函数来进行证明。
15. An Algorithm for Computering Natural Number Power
    求自然数方幂和的一种计算机算法
16. And it uses the natural number coding method to improve search efficiency effectively.
    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。
17. The array of natural number was used to form the antibody to ensure the diversity and validity of the antibody. And the proliferation and suppress strategy based on the deepness of antibody was introduced.
    介绍了保证抗体的多样性和有效性的基于自然数的抗体编码方法和基于抗体浓度的抗体激增和抑制策略。
18. The Meaning and the Truth of the Collected and Expanded Natural Number
    自然数集扩充的意义和公理化
19. In this paper, on the basis of analysis of the existing genetic algorithms, an improved crossover operator is presented, and a genetic algorithm for solving vehicle routing problems with and without time windows is proposed which is based on a natural number coding scheme.
    在分析现有求解该问题的遗传算法的基础上，对现有的交叉算子进行了改进，并设计了基于自然数编码的遗传算法，用来求解一般的和有时间窗限制的车辆路径问题。
20. This paper is about the summary and development of Article [ 1], Providing further conclusion on summation methods of the power of natural number.
    本文是文〔1〕的概括和发展，为自然数方幂和的研究提供进一步的结论。
21. The natural number coding, the random population selection, the simple crossover strategy of "two-parents-and-one-kid" and the fixed mutation probability were totally adopted.
    在算法中采用了自然数编码、随机选取种群、简单的双亲单子交叉策略和固定的突变概率。
22. A Generalization of Preceding N-trmed Power Sum for Natural Number
    自然数前n项方幂和推广
23. Variety Number of Natural Number Reduction to Sum of Consecutive Odd Numbers
    自然数分拆成若干个连续奇数之和的分拆种数
24. If it was changed, a one-one correspondence between continuum and natural number set can be received.
    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。
25. A number theory PROBLEM-PARTITION of natural number circle in three sections of equal sum
    一个数论问题&自然数圈的等和三段的划分
26. A Formula of the Sum of Equal Power Series of Natural Number Problems
    等幂和计算的一般公式及相关问题
27. Natural Number System in MS
    MS中的自然数系统
28. Natural Number K Power Sum Once
    关于自然数K次幂和的讨论
29. 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。

noun

1. the number 1 and any other number obtained by adding 1 to it repeatedly