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.
最简单的真数是自然数，即平时我们口数的一、二、三…。
The simplest real Numbers are the natural Numbers, which are just the ordinary counting number l, 2, 3...
质数是指仅有两个约数的自然数，例如，1不是一个质数。
The prime number is a natural number that has exactly two different divisors, i. e. 1 is not a prime number.
最简单的真数是自然数，即平时我们口数的一、二、三三…。
Thee simplest real numbers are the natural numbers, which are just the ordinary counting number l, 2,3…
对一个图而言，满足此条件的最小的自然数即为此图的覆盖数。
The cover pebbling number for lexicographic product graphs and some strong product graphs were determined.
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.
一些年纪大一点的孩子明白发明数词来满足自然数的续数原则是可能的。
Some of the older children were explicit about the possibility of inventing count words to satisfy the successor principle for natural numbers. For example, A.
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.
在单点交叉过程中引入了逆序数向量进行交叉，简化了自然数序列的交叉过程。
During the single dot cross operation, import the athuard ordinal number arrow, simplify the cross operation of the natural sequence.
这个自然数的流每隔一秒就被发送到 ScaleInt进程的in通道。
This stream of natural numbers one second apart is then fed into the in channel of the ScaleInt process.
如果我们要列出10以下且为3或5的倍数的所有自然数，我们将得到3、5、6和9。
If we list all the natural Numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6, and 9.
比如数字5，在自然数或计数中，它是一个基本的数字：质数，只能被1或它自身整除。
The number 5, for example, when viewed among the natural, or counting, numbers is one of those elemental creatures: a prime number, divisible only by 1 and itself.
算法采用自然数编码，自适应的交叉变异算子，并融入启发式信息有效地提高了搜索效率。
It introduces the natural number coding method, adaptive probabilities of crossover and mutation, and furthermore, makes use of heuristic information to improve search efficiency effectively.
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.
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。
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.
在自然数的集合里，每个数字不是奇数就是偶数，不存在一个偶数或多或少比另一个偶数更像偶数这样的情形。
In the set of natural Numbers, every number is either odd or even, and there is not one even number that is more or less even than any other even number.
在一个与自然数有关的问题中，通过寻找递推关系，由初始值递获得所需结果的方法称之为递推法。
In a problem concerning the natural number, the way of seeking recursion relationship and getting the reseclt from primary value recursion is called recursion method.
康托用此论题来证明有多少自然数（1，2，3，4，…），就有多少正分数（正整数p和q的比率p/q）。
Cantor used it to prove that there are exactly as many positive fractions (ratios p/q of positive whole numbers p and q) as there are natural numbers (1, 2, 3, 4, …).
为了符合应用，关于时间的模型从离散的自然数和整数，延伸到稠密的线性实数，甚至扩展到区间代数和树代数。
The underlying model of time appropriate to the application can range from discrete natural numbers and integers to dense linear real numbers or to algebras of intervals and trees.
编码技术是可扩展标记语言(XML)查询处理的基础，传统编码技术利用自然数进行编码，很难支持XML动态更新。
Labeling scheme is the basis for Extensible Markup Language (XML) query processing. The traditional labeling schemes use Numbers based on natural order, which is hard to support XML updating.
然后就是对其他自然数，其fibonacci数就是它前面两个数字的和，即F(N)=F(N-1)+F(N-2)。
Then we say that for any other natural number, that fibonacci number is the sum of the previous two fibonacci numbers.
如果集合较小，我们可以简单地列出起成员并用正整数记录列出的成员的数目，从1开始，以自然数的次序往下直至结束。
If the set is small, we can simply list the members and number the list with positive integers, starting with 1 and proceeding in the natural order until we reach the end of the list.
它用JCSP提供的类NumbersInt生成一系列自然数，通过temp通道传递给另一个叫作FixedDelayInt的内置类。
It USES the JCSP-provided class NumbersInt to generate a sequence of natural Numbers that are fed through the temp channel to another built-in class, called FixedDelayInt.
它用JCSP提供的类NumbersInt生成一系列自然数，通过temp通道传递给另一个叫作FixedDelayInt的内置类。
It USES the JCSP-provided class NumbersInt to generate a sequence of natural Numbers that are fed through the temp channel to another built-in class, called FixedDelayInt.
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