证明

For example, we study the properties of the"centroid curve" and the"auxiliary curve", and identify two planes in which these two curves are defined respectively; we also use the idea of homotopy method to prove a fact that the orbit of a differential system has no triple contact point with the line we considered. Another key technique, which we use several times, is deformation argument.

例如研究由Abel积分之比定义的"质心曲线"和"辅助曲线"的几何性质，并把这两条在不同平面上定义的曲线放在同一坐标系中考虑；利用拓扑中同伦的思想来证明微分系统的轨线不可能与某条直线三重相切；利用几何方法与分析计算相结合证明了某一曲线是正则的；以及连续变动参数的技巧。

The boundedness of system is proved by the comparative theme of impulsive differential equation, and the local stability of trivial or semi-trivial positive periodic solution (prey annihilation periodic solution) is tested.

利用脉冲微分方程的比较定理，证明了系统的有界性，讨论了平凡周期解与半平凡周期解的局部稳定性，进而利用重合度理论证明了系统周期正解的存在性。

This paper was concerned with the Dirichlet-Neumann mixed boundary value problem of bipolar quantum hydrodynamic model in thermal equilibrium. By truncation method and Leray-Schauder fixed point theorem, the existence of solution to the problem is proved. In addition, the uniqueness of the solution was proved as the Plank constant was large enough.

研究了热平衡状态下双极量子流体动力学模型的Dirichlet-Neumann混合边值问题，利用截断方法和Leray-Schauder不动点定理证明了其解的存在性，另外还证明了当普朗克常数充分大时其解是唯一的。

In the condition of no loop and no twoness, the auto update theorem is justified. At the same time, a locally best algorithm is given and additional validation is conducted.

在没有回路问题和二重性问题的条件下，本文证明了自动更新定理，并进一步提出了一个局部最优的自动更新算法，还给出了这个算法的证明。

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在此情况下，在请求人一方的选择下，请求书须附有下列各项之一：得要求经政府公证机构或其他政府主管机关证明为真实之授权契约之摘要，该摘要中须写明双方当事人和被授权的权利；未经证明的授权声明，该声明须按附於本附件中的授权声明书格式所规定的形式和内容写成，并由注册持有人和被授权人二者签名。

The paper introduces several important notions such as uncountability and halting problem firstly,the fact is proved by contradiction that halting problem is impossible problem,and the same to other relative issues in computer is proved by reduction.

本文先介绍了不可数性和停机问题等重要概念，用反证法证明了停机问题是不可解的，并使用归约法对计算机中的相关问题的不可解性进行了证明。

The question of whether two lambda calculus expressions are equivalent cannot be solved by a general algorithm, and this was the first question, even before the halting problem, for which undecidability could be proved.

两个lambda演算表达式是否相等的问题不能够被一个通用的算法解决，这是第一个问题，它甚至排在停机问题之前。为了证明停机问题是没有答案的，不可判定性能够被证明。

Cohen argues that voluntary transactions don't always necessarily lead to just results and voluntary transactions results in the unfreedom of non-parties.

柯亨论证道，诺齐克的转让正义理论不仅没有证明社会主义是不正义的，而且没有证明社会主义是与自由相对立的。

We discussed the stability of the system balance, used the Poincare-Bendixson's annular region theorem to prove the existence, and used the Zhang Zhifen unicity theorem to prove the uniqueness of limit cycle, at the same time give meaning to the corresponding conclusions on the ecology.

讨论了系统平衡点的稳定性，用Bendixson环域定理证明极限环的存在性，借助张芷芬唯一性定理证明极限环的唯一性，同时对相应结论的生态学意义给予说明。

The conclusion such arguments hope to draw is not a refutation of some variety of epistemic skepticism via a demonstration of the alternative, but rather a demonstration of the unintelligibility of the skeptical position.

这样的论证所希望获得的，不是通过对其他选项的证明来实现对怀疑论的拒绝，而是证明怀疑论立场的unintelligibility。

She gently rebuff ed him, but agreed that they could be friends

她婉言拒绝了，但同意作为朋友相处。

If in the penal farm, you were sure to be criticized.

要是在劳改农场，你等着挨绳子吧！