反证法

Based on the fundamental theory of impulsive differential systems, employing Green formula, Gauss divergence theorem, Jensen inequality and Gronwall-Bellman inequality with impulse, we discuss the oscillation of impulsive partial differential systems by adopting reduction to absurdity and the stability in via of comparison theorem, respectively. Especially, we take an in-depth study on the oscillation of neutral impulsive parabolic systems and the stability of a class of nonlinear impulsive partial differential equations and obtain some useful conclusions.

本学位论文以脉冲微分系统基本理论为基础，利用反证法的分析方法和比较定理，结合Green公式、Gauss散度定理、Jensen不等式、含脉冲的Gronwall-Bellman不等式以及相关数学工具研究了脉冲偏微分系统的振动理论和稳定性理论，特别对中立型脉冲时滞抛物系统的振动性和一类非线性脉冲偏微分系统的稳定性作了较为深入的研究，给出了一些有用的结论。

Secondly,by reduction to absurdity and the sequentially compactness of the space,the minimality of a homeomorphism on a sequentially compact space is discussed.

其次，利用反证法结合空间的序列紧致性对序列紧致空间上的同胚映射的极小性进行讨论。

Mathematics proved to be direct and two indirect method, the reduction to absurdity is a kind of indirect proof, it is mathematical proof of Dafa.

帮我翻译：数学证明有直接法和间接法两，反证法是间接证法的一种，它是数学证明的大法。

The chapter two, by using reduction to absurdity and estimating the differential inequality, we investigate the oscillation of a kind of even order half- linear differential equation, and we give an example to validate the theorem.

在第二章中，我们利用反证法及对微分不等式的估计研究了一种偶数阶半线性微分方程解的振动性，接着举了例子验证所得定理。

It says that under certain assumptions, composite massless spin-2 particle do not exist.

一起在80年左右在physics letters A上发表过一篇短文，说是为什么不可能存在高自旋的基本粒子，用的是反证法。

To prove the inequality involving for negative proposition, the proposition "or at least",""," nonexistence "and" impossible "words, can consider to use when required.

凡涉及到的证明不等式为否定命题、惟一性命题或含有"至多"、"至少"、"不存在"、"不可能"等词语时，可以考虑用反证法。

Chapter 3 emphasizes on the case that the considered systems contain not only impulse but also time delay. We mainly investigate impulsive parabolic systems with time delay and neutral impulsive parabolic systems. Section 3.1 discusses the oscillation of impulsive parabolic systems with time delay under Robin boundary condition and obtains some useful criteria via first order impulsive differential inequalities with time delay. Section 3.2 studies the oscillation of neutral impulsive parabolic systems under Neumann boundary condition and Robin boundary condition, respectively, and obtains some sufficient conditions for oscillation and strong oscillation via first order neutral impulsive differential inequalities.

第三章针对于"脉冲"与"时滞"共存的复杂情形，仍采用反证法讨论了含时滞的脉冲偏微分系统的振动理论，具体研究了脉冲时滞抛物系统和中立型脉冲时滞抛物系统。3.1节考虑了脉冲时滞抛物系统的振动理论，借助于一阶脉冲时滞微分不等式的解的性质，得到了满足Robin边界条件的脉冲时滞抛物系统的若干振动准则；3.2节考虑了中立型脉冲时滞抛物系统的振动理论，借助于一阶中立型脉冲时滞微分不等式的解的性质，分别给出了满足Neumann边界条件和Robin边界条件的中立型脉冲时滞抛物系统的若干振动和强振动准则。

Many steps were reached using the long-cherished method of Proof by Induction, others by Proof by Reductio ad Absurdum, and still others using Proof by Graduate Student.

许多步骤是用各种经典的逻辑证明方法推导得到的，包括归纳法、反证法等，甚至有些部分还是由旁听的研究生证明的。

The reductio ad absurdum of these unbridled speculations can be seen in the Pitis Sophia, which is light-maidens, paralemptores, spheres, Heimarmene, thirteen ons, light-treasures, realms of the midst, realms of the right and of the left, Jaldabaoth, Adamas, Michael, Gabriel, Christ, the Saviour, and mysteries without number whirl past and return like witches in a dance.

该反证法这些肆无忌惮的投机活动可以看出，在pitis索菲亚，这是轻少女， paralemptores ，领域， heimarmene ， 13 ons ，轻宝藏，境界之中，境界的权利和左， jaldabaoth ， adamas ，迈克尔，加布里埃尔，基督救世主，并没有多少的奥秘，旋转过去和回报一样，巫婆在舞蹈。

The key of our method is to reduce the exact controllability of a semilinear system to the observability estimate for the dual system of its linearized system.

另一方面，我们注意到，上述的两种方法无法给出任何能观性不等式中出现的常数的显式估计，因为它们采用的是反证法来吸收低阶项的。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。