The method of using node theorem to solve the one-dimensional harmonic oscillator with a deta potential was presented and the reliable accurate eigenenergies and eigen- wave functions were given.
探讨了用节点法求解存在势时的一维谐振子势，并给出精确可靠的能级及本征波函数。
A generalized KAM theorem for lower dimensional tori in Hamiltonian systems is obtained, which applies to the case where there are normal frequencies and hyperbolic normal components simultaneously.
本文给出了关于哈密顿系统低维环面的一个推广的KAM定理，它适用于同时存在法向频率和双曲法向分量的情况。
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。
This theorem simplifies greatly the analysis of the function approximation ability of FFMLNN because one needs only to study the one dimensional function approximation ability of FFMLNN.
也就是说我们只需研究其一维函数逼近能力，所得的结论完全适合于多维情形，该定理大大简化了前馈多层神经网络函数逼近问题的分析难度。
We also use the method in Theorem 1.2 to prove that there exists a smooth 2-dimensional radical symmetric solution for this problem.
与原来的方程相比，它增加了一个非线性极强的阻尼项。我们同样用定理1．2介绍过的方法，证明了径向对称解的存在性。
This note takes a sketch of a proof of a characterization theorem for diffeomorphisms oa a compact 3-dimensional smooth manifold to be structurally stable.
本文摘要叙述有关三维紧致光滑流形上结构稳定的微分同胚的一个特征性定理的证明。
The basic theorem for constructing a kind of 4-dimensional chaotic system is presented based on the feedback control method under discontinuous state.
提出了基于不连续的状态反馈方法，构造一类四维混沌系统的基本定理，实现了类四维简单线性系统的混沌反控制。
The basic theorem for constructing a kind of 4-dimensional chaotic system is presented based on the feedback control method under discontinuous state.
提出了基于不连续的状态反馈方法，构造一类四维混沌系统的基本定理，实现了类四维简单线性系统的混沌反控制。
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