在一定的条件下，用黏性逼近法证明了序列逼近于这一公共元的强收敛定理。
It is shown that under suitable conditions by the viscosity approximation algorithms, some strong convergence theorems for approximating to this common elements are proved.
一类构造性几何定理的数值并行法证明器。
A prover for parallel numerical verification of a class of constructive geometry theorems.
本文研究了二次标准加入法原理，证明了四个引理和两个定理。
The principle of a double standard addition method is strictly demonstrated. Four lemmas and two theorems are given and proved.
经典圆定理只证明了奇点位于圆外的情况，本文用正则摄动法证明了源和汇位于圆上时，圆定理也是适用的。
This study illustrated that the theorem could be also applied in a case where the sources and sinks are on the circle by means of the regular perturbation method.
证明了广义自洽法与无关性定理的一致性。
The consistency between the generalized self-consistent method and the independence theorem was confirmed.
几何定理证明的前推法能够产生传统形式的可读证明，在定理机器证明领域占有重要的地位。
The forward reasoning for geometry theorem proving can produce the traditional readable proving, thus plays a special role in the mechanical theorem proving.
为了生成传统形式的几何定理可读证明，前推法必不可少。
To produce the traditional readable proving of geometry theorem, the forward reasoning is necessary.
用几何法证明了等视角定理和低副运动可逆性在铰链四杆机构设计中的等价性，以求揭示它们之间的本质联系。
The equivalence between theorem of equal angle of view and reversible property of low pair, applied in synthesis of plane four-bar linkage, is demonstrated to reveal essence of their relation.
本文用待定系数法证明拉格朗日定理与柯西定理。
In this paper, we present the proofs of Lagrange Theory and Cauchy Theory. By this method we may determine coefficient.
类比关于数式的二项式定理，导出关于矩阵的二项式定理，并用数学归纳法予以证明，最后举例说明关于矩阵的二项式定理的应用。
Compared to digital binomial function, matrix binomial function is derived and proved with induction method and the application of it is illustrated with examples.
文中表明用四元数方法证明该定理比矢量法更为简单。
The paper shows that the method of proving the commutative property of composition for the finite rotations by quaternions is simpler than that by vectors.
同时我指出了希伍德对顶点数套用数学归纳法的格式来证明“五色定理”的方法是错误的，从而否定了希伍德证明的“五色定理”。
I is pointed out that Heawood applied the mathematical induction for the vertex number to prove 'The Five Color theorem' is incorrect.
结合评价函数法将带约束的多目标优化问题转化为无约束优化问题，并给出相应的区间扩张，对相关定理进行了证明。
The paper, combined with evaluation function introduces the transformation of constrained problems into unconstrained ones, and offers an interval extension.
结合评价函数法将带约束的多目标优化问题转化为无约束优化问题，并给出相应的区间扩张，对相关定理进行了证明。
The paper, combined with evaluation function introduces the transformation of constrained problems into unconstrained ones, and offers an interval extension.
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