如果定理的条件被证明为真，则我们可以使用此定理来确定我们的程序的定理结果的正确性。
If the conditions of the theorems are shown to be true, then we can use the theorem to establish the truth of the theorem's result for our program.
由于这个定理的使用条件是非常清楚的，从而分析了一些矛盾。
The clarity of the theorem's service conditions results in the analysis of a few contradictions.
与以往的同一领域的经典定理相比，它的收敛性条件是宽松的。
Its convergent condition is relaxed compared with the classical theorem on the same field.
本文通过群作用和正则覆盖，利用拓扑刚性定理对此问题给出一个判定性条件。
By the use of group action and normal covering we give an answer in some conditions from topological rigidity theorem in this article.
对闭区间套定理的条件作一些变动或增加，可以得到相同的结论。
Change or increase some conditions of the theorem of interlink of close interval, we can reach the same result.
这个存在定理说明只要非线性项满足某种线性增长条件该方程至少有一个解。
The existence theorem shows that the equation has at least one solution provided the nonlinear term satisfies a linear growth condition.
同时，牛顿-莱布尼兹定理的条件可以改进。
另外一大类定理处理不太严励的条件。
Another major class of theorems deals with less stringent conditions.
将应用叠合度理论的延拓定理建立正周期解存在的充分条件。
Sufficient conditions for the existence of positive periodic solutions are established by applying the continuation theorem of coincidence degree theory.
在此基础上，利用微分方程的环域定理获得了所述系统存在极限环的条件。
Then by using Poincare-Bendixson theorem sufficient conditions for the existence of limit cycles are obtained.
其中定理1和2的条件采用带参数的函数，便于运用由方程首次积分构造函数的方法来获得。
The conditions of Theorems 1 and 2 formulated here adopt the Liapunov functions with parameter so that they may be more easily obtained by using Chetaev 's method.
讨论泰勒中值定理中中值点的连续性及可导性问题，给出泰勒中值定理中中值点连续及可导的充分条件，同时给出计算其导数的公式。
The continuity and derivative of the intermediate point in the Taylor mean value theorem are discussed, and some of their sufficient conditions are presented.
定理3X是囿空间的充要条件为：每个从X到Y的一致有界的线性算子族都是等度连续的。
Theorem 3 X is a bornologic space if and only if every uniformly bounded set of linear operators from X to Y is equicontinuous.
此类研究将更多的精力集中在固定理想路网条件下通过交叉口间距合理值的讨论得到路网等级配置比例。
Among these researches, more than half start from the proper road spacing interval discussion based on an given ideal square networks.
此条件具有一般性，主要定理是正常系统相应结果的推广。
The main theorems are the extension of some results of normal systems.
本文利用电流子空间和电压子空间互相正交的条件，得出了各种形式的特勒根定理。
Tellegen's theorem in various forms is derived by the orthogonality relation between the current subspace and voltage subspace.
本文得到了另一广义系统，的同宿轨的存在条件及其相关定理。
The existence and relevant theorems of Homoclinic orbits for another generalized Lienard system are obtained.
本文提出一个一般的分离条件，并建立一些相应的定理，用以统一有关邻域分离性的许多概念和定理；
We advance in this paper a general separation condition and set up corresponding theorems to integrate with the concepts and theorems about the related separateness of neighbourhood.
在较弱的条件下，获得了算法的全局收敛性定理。
Under very mild conditions, the algorithm possesses global-convergency.
设计了一个简单的思想实验，用动量定理对洛伦兹变换成立的条件导出了相对论质量公式。
Based on the theorem of momentum, the mass equation of special relativity is derived using a simple thought experiment.
本文提出并证明了在各向同性强化条件下的安定定理，即在循环载荷作用下，各向同性强化材料的结构，其安定状态总是可以实现的。
Shakedown theorem under isotropic hardening is presented and proved in this paper. Namely, shakedown state is always achievable for structure of isotropic hardening materials under cycling loads.
在微分几何定理证明中，一个定理成立的辅助条件(非退化条件)不是惟一的，但越简单越好。
The subsidiary conditions (or called non-degeneracy conditions) are not one and only that a theorem holds in differential geometry theorem proving.
进而，利用李雅普·诺夫函数和比较定理确定了持续生存的条件。
Conditions for permanence is established via the method of comparison involving multiple Liapunov functions.
运用上确界与下确界存在定理，在一定条件下，研究了连续函数的映射特点，得到一个连续函数所独有的映射规律。
According to the definite condition, the paper USES the theorem of supremum and infimum to study characteristic of mapping function and get its important law of the mapping.
本文通过实例，证明了密勒定理的严格性。文中从工程观点出发，对该定理作出合理的近似处理，并提出了使用该定理的条件及注意点。
The strictness of Miller's Theorem is proved with an example. Approximations from the engineering standpoint and conditions for using this theorem are proposed and precautions are suggested.
本文探讨用向量运算代替串行FORTRAN的DO循环的基本条件，提出了向量化判别定理以及实现向量化的算法。
Conditions for vectorization of FORTRAN DO-loops are discussed in this paper. Based on these conditions, the decision theorems and the algorithm for vectorization are given.
在这一部分中，我们重点讨论了解存在的充分条件，并以定理的形式给出具体的证明。
In this section, we prove the sufficient conditions for the existence of the solutions.
在这一部分中，我们重点讨论了解存在的充分条件，并以定理的形式给出具体的证明。
In this section, we prove the sufficient conditions for the existence of the solutions.
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