数值函数

If you do need to iterate over a sequence of numbers, the built-in function range comes in handy.

如果你需要一个数值序列，内置函数range可能会很有用，它生成一个等差级数链表。

If you do need to iterate over a sequence of numbers, the built-infunction range comes in handy.

如果你需要一个数值序列，内置函数range可能会很有用，它生成一个等差级数链表。

If you do need to iterate over a sequence of numbers, the built-in function range comes in handy. It generates lists

如果你需要一个数值序列，内置函数range可能会很有用，它生成一个等差级数链表。

If you do need to iterate over a sequence of numbers, the built-in function range comes in handy. It generates

如果你需要一个数值序列，内置函数range可能会很有用，它生成一个等差级数链表。

Chapter four studies the chaotic responses in a system consisting of simple pendulum and harmonic oscillator under bounded noise excitation. Firstly, the Melnikov function of the two-degree-of-freedom system under Hamiltonian perturbation is derived. The essential condition of the autonomous system for the probable onset of chaos is obtained, the Poincare maps of the system under small Hamiltonian perturbation and the effect of increasing perturbation on the Poincare maps are studies. Then for the non-autonomous system under damping and harmonic or bounded noise excitation, the largest Lyapunov exponent and Poincare maps are calculated. From the analysis of the largest Lyapunov exponent, the critical criterion for the onset of chaos, and the conclusion that the threshold of bounded noise amplitude for the onset of chaos in the system increases as the intensity parameter of Wiener process increases are obtained. The result from the analysis of Poincare maps is in agreement with that obtained from the Largest Lyapunov exponent. The effect of varying damping coefficient and intensity parameter of Wiener process is also analyzed.

第四章研究了有界噪声激励下的两自由度单摆—谐振子系统的混沌运动，首先推导了该两自由度系统仅在Hamilton扰动下的Melnikov函数，得到该自治系统可能产生混沌的必要条件；研究了该系统在小的Hamilton扰动和增大摄动情形下的Poincare截面；然后对有阻尼、谐和或有界噪声激励下的非自治系统数值计算了其最大Lyapunov指数和Poincare截面；从Lyapunov指数分析得到了这个两自由度系统产生混沌运动的临界条件及产生混沌的临界激励幅值随Wiener过程强度参数值的增大而增大的结论，Poincare截面分析的结果亦符合Lyapunov指数分析的结论；研究了Wiener过程强度参数、阻尼系数变化对Poincare截面的影响。

With the use of the dislocation method of complex potential function, this paper studies the interaction between the interface macrocrack and the interface or beneath-interface microcracks by the construction and numerical solution of singular integral equations .

采用复势函数的位错解方法，通过对奇异积分方程的建立和数值求解，研究了界面主裂纹同界面及基体微裂纹之间的干涉。结果表明远场载荷角ψ同Dunder's参数α对界面微裂纹及基体中水平微裂纹同主裂纹干涉的影响都很显著，而ψ对屏蔽区的影响则远小于α对其的影

Finally we derive the equivalent transfer functions using reduction rules and interesting important performance indices, for example, steady probability, mean first and nth passage time, mean recurrence time, the mean sojourn time, and counters of the transition and place can be find.

最后用化简规则获得等效传递函数，求出我们关心的重要参数的数值。

With the same idea for thin film test, a method was proposed to determine the yield strength and hardening index of small volume of material by indentation loading curve using spherical indenter.

通过对小体积材料球压入过程的数值研究，获得了小体积材料基本力学性能与球压入响应间的函数关系，并据此提出用球形压头的纳米压入加载曲线确定小体积材料屈服强度与硬化指数的新方法。

In this paper, a new numerical method, the coupling method of spherical harmonic function spectral and streamline diffusion finite element method for unsteady Boltzmann equation in the neutron logging field is discussed, and the convegrence and error estimations of this scheme are proved.

针对中子测井问题，研究非定常Boltamann中子输运方程的确定型数值求解方法，给出了求解Boltzmann方程的球谐函数展开和流线扩散有限元耦合方法，证明了这种耦合方法的收敛性和误差估计·实际算例表明此方法是有效

The false scattering and ray effect in spherical harmonics method ,including P-1 and P-3 approximation,is studied.

从辐射传输方程的近似求解过程出发，在定性分析的基础上构造物理模型，通过数值模拟研究球谐函数法(P1和P3近似法)的假散射和射线效应。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。