证明

By applying Bendixson-Dulac theroem, we show that the system admits no limit cycle in the first quadrant, thus the global stability of the interior equilibrium is followed.

首先通过运用Bendixson-Dulac定理证明了系统在第一象限没有极限环，从而证明了正平衡点的全局稳定性。

The basic meaning of fishing expedition is that the request for evidence investigation aiming at acquiring inter-related information.

摸索证明的基本含义是指证据声请以获取相关信息为目的。根据古典辩论主义，摸索证明应予禁止。

This test method is called integer-variation test, and it is based on the statistical distribution of the fractional part of a random variable multiplied by an appropriate integer.

证明了首项系数为整数的n个独立随机变量和的小数部分的统计分布性质，并证明了当求和个数趋于无穷时的统计分布性质。

The domain derivative of the Navier-Stokes equations is given in the same manner as the Stokes equatons' domain derivative by reducing to homogeneous equations and proving continuous character and existence of Frechet derivative .

同样利用对非齐次方程的齐次化、证明目标函数对区域的连续性和其导数的存在性，同时给出了定常Navier-Stokes方程的区域导数完整的理论证明。

With proving the isomorph between the function matrix algebra systems and the Boolean algebra s disjunction-conjunction systems,a method of extending the function matrix is proposed,and the expanding theorem of the extended function matrix is proven.

提出了功能矩阵的概念，在证明功能矩阵的代数系统与布尔代数析取合取代数系统同构的基础上，对功能矩阵进行扩展，并证明了扩展功能矩阵的展开定理；利用扩展功能矩阵逐步展开与约简，实现了功能的求解算法。

But he was convinced that one stepping stone that needed confirmation — dubbed the "fundamental lemma"— would be reasonably straightforward. He, his collaborators and his students were able to prove special cases of this fundamental theorem.

朗兰兹知道证明支撑自己构想的假设需要几代人的努力，但证明所有这些首先需要一个垫脚石，它被称作"基本引理"。

The proof of fundamental theorem of algebra involves much algebra knowledge which is difficult to understand.

代数学基本定理的经典证明用到较多的代数知识，且难以理解，文章探讨用数学分析的方法予以证明。

This paper explores ways to prove fundamental theorem of algebra with mathematical analysis.

该证明从复变多项式无非零最小模引入，并在此基础上简单证明了代数学的基本定理。

He, his collaborators and his students were able to prove special cases of this fundamental theorem. But proving the general case proved more difficult than Langlands anticipated — so difficult, in fact, that it took 30 years to finally achieve.

他和同事以及学生虽然能够证明这一基本定理的特殊情况，但证明普通情况所面临的挑战却大大超出朗兰兹的预计——这项工作难度极高，整整历时30年才得以完成。

As for Galvani, although he was proven wrong, his work stimulated research on electricity and the body.

而 Galvani，尽管他被证明是错的，他的工作扔激励在电和身体的研究，这种研究最终证明神经能传递电能，这是医学上一个重要的发现。

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！