摄动函数

A static interval optimization method for structures was proposed. The matrices of structures with interval parameters were given. Combining the interval extension of function with the perturbation theory of static analysis, the method for interval static analysis was derived.

提出了一种在位移约束下结构静力区间优化方法，给出了区间参数结构矩阵，将结构静力分析的摄动理论与区间函数扩张定理相结合，推导了结构静力分析的区间方法。

Vibro-impact system; Poisson white noise; Perturbation approach; Probability density function; Generalized Fokker-Planck-Kolmogorov equation

碰撞振动系统；泊松白噪声；摄动法；概率密度函数；广义FPK方程

S: In the non-homogeneous semi-infinite medium, the shear modulus varies in the form of exponential function along the depth, by the perturbation method , the wave function solution and phase velocity equation of the Rayleigh surface waves are obtained in the paper.

对剪切弹性模量沿深度以指数函数变化的非均质半空间，本文用摄动法得到了Rayleigh面波的波函数解答及相速度方程。

This paper, using complex function theory,proves the general conclusion that the systemmust be robust stable if its perturbed system is robust diagonal dominance .

本文用复变函数理论，证明了摄动系统为鲁棒对角优势，则系统一定是鲁棒稳定这个一般性结论。

The use of the rational approximation and the Rayleigh quotient leads to that the quality of power-series expansion is significantly improved and the range of approximation is extended with a few of additional operation counts.

在只增加少许计算量的情况下，利用向量值函数的有理逼近方法以及 Rayleigh 商来改善摄动解的逼近质量并扩大其逼近范围。

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。

This paper aims to examine a class of the problems of third order nonlinear boundary value of singular perturbation by way of transforming unknown function.

以变换未知函数的方式研究一类奇摄动三阶非线性微分方程边值问题，在适当条件下，构造出问题的上下解。

The approximate stationary probability density function for the response of multi-degree-of-freedom dissipated Hamiltonian systems to Poisson white noises are obtained by solving the four-order generalized Fokker-Planck-Kolmogorov equation using perturbation approach.

通过用摄动法求解四阶广义福克－普朗克方程，得到泊松白噪声激励的多自由度耗散的哈密顿系统的近似平稳响应概率密度函数。

A proper k total colouring of a graph G is a colouring to its vertices and edges using k colours such that no two adjacent or incident elements of G may be assigned the same colour.

利用梯度投影与罚函数相结合的技巧，将带不等式和等式约束的优化问题化成一个无约束问题，提出了初始点可任意的求解不等式、等式约束优化问题的摄动梯度投影算法；参数δk取不同的数还可以得到一类梯度投影算法，从而得出了在搜索方向和步长不精确条件下的梯度投影法，保证了在实际应用中更容易实现；在较弱条件下，证明了该算法的全局收敛性。

Based on the mind of perturbation,a method which combines transitive closure method with the objective function method is introduced,and the steps of the method is presented.

分析了传统的模糊聚类方法，基于摄动思想，将传递闭包聚类法与目标函数法相结合，得出了一种既满足聚类效果要求又减小聚类失真的简便算法，同时给出了该聚类方法的步骤。

In her eyes, because that is the doorway toher heart * the place where love resides.

女人的漂亮必須從她的眼睛中去看，因為那是她心靈的窗戶和愛居住的地方

I will send some postcards to you.

我会向你发送一些明信片。