Applying the theorem to conical curve, one can get a new "Butterfly Theorem" which makes up for the deficiencies of the classical one and widens its scope of application.
将“蝴蝶定理”推广到一般二次曲线上进行讨论，并给出了新的“蝴蝶定理” ，它弥补了古典“蝴蝶定理”的不足，使“蝴蝶定理”得到了更加广泛的应用。
By applying a fixed point theorem, the authors study the existence of positive periodic solutions to a class of differential equations with stated-dependent delay.
运用不动点定理，研究一类具状态依赖时滞的微分方程周期正解的存在性。
Furthermore, the superposition theorem is then adopted in the approach, which overcomes the difficulties when applying the symmetrical components to the short circuit calculation.
采用基于叠加原理的短路电流计算方法，克服了传统的对称分量法应用于配电网短路电流计算时所遇到的困难。
Applying the Markov renewal theorem, it is shown that certain reasonable conditions of the QBD process lead to the geometric decay of the tail probabilities as the level goes to infinity.
通过对QBD过程某些条件的限定，应用马尔可夫更新定理，得出在一定合理的条件下，当水平趋于无穷时的尾概率的几何衰变。
In this paper we mentioned a new way of applying the reciprocal theorem of work, which is clear in concept and simple in procedure.
本文提出的计算方法是功的互等定理的新应用，具有概念清晰、步骤简捷的特点。
We proved the intermediate value theorem for continuous function at closed interval by constructing auxiliary sequence ingeniously and applying compact theorem as well as Cauchy convergence criterion.
通过巧妙地构造辅助数列，应用致密性定理、柯西收敛准则来证明闭区间上连续函数的介值性定理。
Secondly, we design an approximated delay feedback control method by applying Taylor theorem; it can make the controlled system stabilize the expected periodic orbits or equilibrium points.
其次，应用泰勒展开定理，设计了一种近似的延迟反馈控制方法，将受控的系统稳定到希望的周期轨道或平衡点上。
On applying the diffraction theory and with the aid of the reciprocity theorem, an approximate formula for the radiation field of a slot cut in a metal sheet of finite size is derived.
本文应用绕射理论并借助于互易定理，导出了一个在有限尺寸金属平板上割出的一条裂缝的近似辐射埸公式。
Sufficient conditions for the existence of positive periodic solutions are established by applying the continuation theorem of coincidence degree theory.
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。
A new existence theorem is obtained by applying the degree theory on cone.
利用锥上的度数理论获得了一个新的存在定理。
By applying the fixed point theorem, several new existence theorems of solutions for quasi-equilibrium problems are given under noncompact setting of topological Spaces.
应用此不动点定理，在非紧的一般拓扑空间中给出了几个关于拟平衡问题的解的存在性定理。
Applying fixed points theorem, we give the sufficient conditions of the existence of positive ergodic solutions for a class of infinite nonlinear integral equations.
利用不动点理论，给出了一类非线性积分方程正的遍历解存在的充分条件。
Applying fixed points theorem, we give the sufficient conditions of the existence of positive ergodic solutions for a class of infinite nonlinear integral equations.
利用不动点理论，给出了一类非线性积分方程正的遍历解存在的充分条件。
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