查询词典 method of perturbation

In this paper,a systematic direct perturbation method of dark solitons is found.Having analyzed the mistakes in earlier works on perturbation method for dark solitonsand essence of the direct perturbation method for bright solitons,we notice that to in-troduce the adjoint solutions of the squared Jost solutions and to prove the completenessare crucial to the problem.Giving up the unnecessary scheme of introducing the adjointoperator in the bright soliton case,we directly find the adjoint solutions by meetingthe demand for the orthogonality that inner product of the squared Jost solutions andits adjoint should be proportional to a δ function in the case of continuous spectra.The corresponding adjoint operator is thus found.Taking into account the reductiontransformation,we find a correct description for the completeness of the squared Jostsolutions and directly verify its validity with explicit expressions of the squared Jostsolutions.

本论文建立了系统的暗孤子直接微扰方法，在对前人关于暗孤子微扰方法的错误以及亮孤子直接微扰方法的本质作了充分的分析后，认识到引入平方Jost解的伴随解和证明完备性是问题的关键，撇开过去亮孤子情况首先引入伴随算子的非必要作法，直接从平方Jost解与其伴随解的内积在连续谱时正比于δ函数这一正交性要求出发，找出了伴随解，同时得出了应有的伴随算子，在考虑到约化变换性后，得到了暗孤子情况的平方Jost解的完备性的正确表述，并在单个暗孤子的情况利用平方Jost解的显式直接验证了它的正确性。

Instead of the empirical direct substitution method used in former harmonic ex- pansion method for the generation of perturbation base function s,a more rigorous 1~or- der perturbation method was proposed to generate the perturbation base function s.

针对文献提出的用于换料方案快速评价的低阶谐波展开法，提出用一阶微扰方法来替代原先经验性的扰动基函数产生方法，从而使低阶谐波展开法的理论更完善、适用性更广、精度更高。

In part two, the optical spatiotemporal pattern in ring optic cavity is investigated. Using delay feedback with spatial perturbation method, the system shows roll, square, hexagon, homocentric circle,"honeycomb"and"snowflower" pattern with different spatial perturbation functions. Different patterns can be coexist and compete each other with the same perturbation function, which is the new character of this optical system with delay feedback.

第二部分，利用延时反馈的空间微扰方法研究了环形腔中二能级介质的光学时空斑图的控制，在不同的微扰函数作用下，出现了滚筒状、四方形、六角形、蜂窝状、同心圆以及"雪花"状等不同的斑图，并且在相同的微扰函数下出现了不同斑图之间的竞争，这种竞争是我们发现的这一具有空间微扰的延时反馈非线性光学系统光学斑图的新特征。

In part two, the optical spatiotemporal pattern in ring optic cavity is investigated. Using delay feedback with spatial perturbation method, the system shows roll, square, hexagon, homocentric circle,"honeycomb"and"snowflower" pattern with different spatial perturbation functions. Different patterns can be coexist and compete each other with the same perturbation function, which is the new character of this optical system with delay feedback.

第二部分，利用延时反馈的空间微扰方法研究了环形腔中二能级介质的光学时空斑图的控制，在不同的微扰函数作用下，出现了滚筒状、四方形、六角形、蜂窝状、同心圆以及&雪花&状等不同的斑图，并且在相同的微扰函数下出现了不同斑图之间的竞争，这种竞争是我们发现的这一具有空间微扰的延时反馈非线性光学系统光学斑图的新特征。

The perturbation methods are the common analyzing method for studying thevibratory response of the mistuned bladed disk, but different perturbation methodshave their own relying conditions on the system parameters. In this dissertation, threekey perturbation methods are studied for their application conditions. Their relyingconditions on the system parameters are summarized.

本文对三种常用摄动法的构造特点及其适用性进行了研究，总结了它们在分析失谐叶盘系统振动响应时对于系统参数的适用条件；针对自适应摄动法在分析失谐叶盘系统振动响应时，对于基系统模态的选择难以控制的问题，提出了一种模态自动选择法。

In this paper perturbation of eigenvalue and eigenfunction for higher order ordinary differential equation in the case of boundary perturbation combined with operator perturbation we considered.

本文研究了在边界和算子摄动相结合的情况下高阶常微分方程特征值与特征函数的摄动，把摄动问题A_6，μ的特征值λ_ε，μ和特征函数y_6，μ按两参数ε、μ的次幂展开，并且证明这些展开式当ε、μ充分小时是收敛的。

In chapter 3, we given a brief description of the perturbation theory: Time-independent perturbation theory and Time-dependent perturbation theory.

第三章：简略介绍了微扰理论：不含时微扰理论和含时微扰理论。

The eigenvalue problem of Dirac operator with perturbation Parameter is studied,the analyticity of perturbation parameter is discussed,and the analytic extension is done,at last,the expansion formulas of power serier about preradical expansion into perturbation parameter are got.

针对带有微扰参数的Dirac算子特征值问题，讨论了对微扰参数的解析性，并进行了解开拓，最后得到了预解核对微扰因子的幂级数展开式。

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。

The dose enhancement effects and decreasing effects caused by material inhomogeneity were studied quantitatively with a parameter named Dose Perturbation Factor, which was the ratio of the dose at a point in the heterogeneous phantom to the dose of the same spatial location point in the homogeneous phantom. It was showed that the degrees of the dose enhancement or decreasing depended on the energy of radiation, field sizes of the beamlets and compositions of the media. The dose perturbation for high energy X rays is greater than that for low energy X rays. At the same energy condition, the dose perturbation decreased when the field size increased. And the relationship between them was not linear.

模拟结果表明：在小射野情况下，异质组织界面处出现了较大的剂量跃变，剂量扰动效应的强弱程度取决于射线的能量、射野的大小和模体介质的不同等多种因素，高能X射线条件下的剂量扰动效应大于低能X射线条件下的剂量扰动；在入射X射线能量相同的条件下，剂量扰动效应随射野尺寸的减小而增强，并呈现一种非线性关系。

"Please accept this talisman as a token of our thanks."

请收下这个护身符以表达我们的感谢。

If I have that magic, I will be more acceptable in the society.

如果我拥有那种魔法，我将更加被这个社会所容纳。