数学归纳法

As-samawal used a simple inductive way which played a important role in establishing mathematical induction in this book.

萨玛瓦尔在书中所运用的一种归纳方法，对后世数学归纳法的建立起到了重要的作用。

Finally, the fact is proved using mathematical induction and the character of stochastic matrix.

首先介绍了防御矩阵的概念、物理意义、重要性质及计算方法，分析了防御矩阵满足乘法交换律的重要意义，最后综合运用数学归纳法和随机矩阵性质证明了防御矩阵满足乘法交换律的事实，此结论无论对于多层防御系统的防御效用值研究连是矩阵理论研究都有一定的指导作用。

The clothing of the inductive aggregation is the principle of mathematical induction.

归纳集所具有的这种封闭性质，就是数学归纳法原理。

Based on the technique for unlimitedly generating the corresponding pairs of vertices,this condition is proved with the method of mathematical induction.

基于具有同构关系的对应点无限衍生技术，采用数学归纳法证明了这个充分必要条件的成立。

Based on this, algorithms that consider the earliest emergency time and the least relief points with the pulse need are proposed, respectively, which is proved with mathematical induction.

在此基础上，分别给出了脉冲需求条件下应急时间最早和应急出救点数最少的算法步骤，并应用数学归纳法进行了证明。

From these results, we can see that the Polignac-Xu's number is oscillatingly increased as even number increases. And this not only verified the conjecture mentioned above but offered a distinctly evidence for the former proof of it with mathematical induction also.

从计算结果可以看到，波利那克徐氏数是随着偶数的增大而振荡增大，这不但验证了这个猜测是不成立的，而且也给前期的数学归纳法证明提供了充分的依据。

The quadratic optimal control problem of delay discrete-time linear system is proposed with quadratic performance index. It is transformed intoanother problem by using the Principle of Optimality. The direct expressions of theoptimal control sequence and performance index sequence are given by mathematicalinduction.

针对给定的二次型性能指标，提出了时滞离散系统线性二次最优控制问题，并利用最优性原理将该问题进行了转化，进而利用数学归纳法推出最优有记忆饱和控制序列及最优性能指标序列的直观表达式。

So-called first-order theorem proving may be restricted to a propositional calculus with terms (constants, function names, and free variables) added, making it impossible to express mathematical induction.

所谓一阶定理证明可限于命题演算的条款（常数，函数名，并免费变量）说，无法表达数学归纳法。

This course will introduce the concept of logic, the language of mathematics, mathematical induction, set theory, function, counting methods, the pigeonhole principle, recurrence relation, and graph theory.

内容包括：逻辑引论、数学归纳法、集合理论、函数、排列与组合、鸽笼原理、递回关系及图形理论。

In this we have introduced the application of even formula in making certain equivalent double electrons′ atomic states and the generic way of making certain non-equivalent double electrons′ atomic states,and have got the quantificational connection between atomic states′ number and atomic orbital azimuthally quantum number.

偶数定则是确定非同科双电子形成的原子态的一般方法，根据偶数定则得到了二价原子的原子态数与原子轨道角量子数之间的定量关系；并用数学归纳法证明了有关结论。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。