Methods Using the theorem of center manifold and bifurcation theory of planar system.
方法利用中心流形定理并结合平面系统的分支理论。
A new way to prove Lagrange's mean value theorem is given using the theorem of interval nest.
应用区间套定理给出了拉格朗日中值定理一个新的证明。
Using the theorem of linear Diophantine equations and the Chinese remainder theorem, we have constructed a class of trap-door knapsack public-key cryptosystems, which have a better security.
利用不定方程理论及中国剩余定理，我们设计了一类陷门背包公开钥密码系统，它们具有更好的安全性。
This is a useful theorem for the existence of efficient estimate can efficiently be discussed by using the theorem, and an efficient estimate can be obtained immediately when it comes into existence.
它是有效地讨论有效估计的存在性以及当有效估计存在时立即得到这个有效估计的一个有用的定理。
So, that's by the divergence theorem using the fact that s is a closed surface.
所以那是通过散度定理得到的，其中使用了S是封闭曲面这一事实。
Or, if you really don't like that line integral, you could close the path by adding some other line integral to it, and then compute using Green's theorem.
如果不喜欢计算线积分，可以通过增加一条线积分让曲线封闭起来，然后就可以用格林公式来计算了。
So, using Green's theorem, the way we'll do it is I will, instead, compute a double integral.
那么，使用格林公式，我们去计算二重积分。
Using separation theorem of convex set and the time terminal value function equation, we obtain the determining method of optimal terminal time as well as the Maximum principle.
由凸集分离定理及终端时间阈值函数方程，我们获得了最大值原理及最优控制时间的确定方法。
Using CBL technique, the theorem of momentum with changing force is tested. The experimental principle and procedure are introduced.
利用CBL技术在变力作用下验证了动量定理，并介绍了实验原理及实验步骤。
By using a new three-solution theorem, we obtain the existence and multiplicity of positive solutions for fourth-order boundary value problem.
讨论了四阶边值问题，通过应用一个新的三解定理，得到了其解的存在性与多重性。
By using the collectively fixed point theorem, the existence theorems of some new system of vector equilibrium problems are obtained.
作为应用，给出了聚合不动点定理在矢量平衡问题组中的应用。
Helping students to comprehend contents of theorem is the urgent problem that we will solve using effective way.
采用行之有效的教学方法帮助学生理解定理内容，是我们迫切要解决的问题。
The validity of simulating star map is verified by using the angle-distance of stars and projection theorem.
利用星间角距和投影原理的性质来验证星图模拟的有效性。
Then relative interior is introduced and an alternative theorem of generalized convex set-valued maps is established by using the separation theorem.
引进了相对内部，应用凸集分离定理建立了一个广义凸集值映射的择一性定理。
The attitude dynamic equations of a spacecraft with flexible appendages are obtained by using the momentum theorem.
利用动量矩定理推导出带挠性伸展附件航天器的动力学方程。
According to the central limit theorem the writer analyses the using case of air splicer and clarifies the using distribution of air splicer obtains the statistic on air consumption of air splicer.
运用中心极限定理对空气捻接器的使用情况进行分析，明确了空气捻接器的使用分布情况，得出了空气捻接器耗气量的统计数据。
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。
Using cone fixed point theorem we get the existence of one and two positive solutions.
利用锥上的不动点定理得到了一个正解和两个正解的存在性。
Using the Gauss-Bonnet theorem, Stephen Hawking proved that the topology of the event horizon of a (four dimensional) black hole is a 2-sphere.
使用高斯-博内定理， 史蒂芬·霍金证明一个（四维）黑洞活动视界的拓扑结构是2个球体。
Using this theorem, the replacement theorem was discussed and its representations were improved.
运用这一定理，本文还讨论了网络的置换定理，给出其改进了的表述形式。
By using the continuation theorem of topology degree theory and properties of nonsingular M-matrix, we obtain sufficient conditions for the existence of positive periodic solutions of this system.
利用拓扑度理论中的连续定理以及M -矩阵的性质获得了该系统正周期解存在的充分条件。
By using the contain theory and partition theorem of symmetric matrix, three conjectures about YANG Hui matrix are cetified.
它使用了对称矩阵特征根的包含原理和分隔定理，并利用了正矩阵特征根的性质。
The existence of co-exist periodic solution is investigated by using the bifurcation theory, the implicit function theorem and the method of asymptotic expansion.
运用分歧理论，隐函数定理，以及渐近展开的方法，获得了非平凡周期解的存在性。
Using the uniqueness theorem for boundary value problem of steady magnetic field and Weierstrass theorem, the unique choice of image electric current is discussed.
利用稳恒磁场边值问题解答的唯一性定理和维尔斯特拉斯定理讨论了镜象电流选择的唯一性。
The implications of the Minimax theorem are tested using field data.
本文利用田野数据对最小最大定理进行验证。
By using the fixed point theorem on cone, this paper studies the existence of positive solutions for first order periodic boundary value problem with impulses.
利用锥上的不动点定理讨论了一阶脉冲微分方程周期边值问题的正解的存在性。
The market share or the choice probability is evaluated by using the approaches from the GEV theorem.
该模型满足GEV定理，给出了市场占有率、即产品选择概率的估计、评价和分析方法。
Using the principal curvature formula, we prove an existence theorem of Weingarten hypersurface.
并利用主曲率计算公式证明了W-超曲面的一个存在性定理。
Using the principal curvature formula, we prove an existence theorem of Weingarten hypersurface.
并利用主曲率计算公式证明了W-超曲面的一个存在性定理。
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