查询词典 perturbation function

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。

It also researches the application of variational method to solve the perturbation function in the energy principle.

本文还探讨了变分方法在求解能量原理中的扰动函数的应用。

The output chaotic sequence through the perturbation function distributes uniformly in the whole state space.

经过扰动函数的输出混沌序列均匀分布在整个状态空间中。

In Chapter 1, the resonant phenomena of the NEAs' movement are introduced, briefly expounded the concepts of the mean and secular resonances as well as the way of extracting the resonant parts of the expansion of the perturbation function, still well established the corresponding resonant models.

在第一章中，介绍了近地小行星运动中的共振现象，扼要地阐述了轨道共振和长期共振的概念、共振项的析取方法以及建立了相应的共振模型。

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 chapter four, we developed a direct approach for soliton perturbation based on the Green function, This approch get rid of the proof of orthognality for eigenfunctions in a direct approch for soliton perturbation developed by Yan Jiaren etal.

第四章，发展了一种基于格林函数的孤子微扰理论，克服了颜家壬教授微扰直接法中本征函数正交性证明的困难。

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。

As a result of conservative perturbations, the first order Melnikov function for a perturbed system is identically equal to zero, so the second order Melnikov function has to be considered. The perturbation parameters which make no use in the first order Melnikov function may be important in the second order Melnikov function.

此时一阶Melnikov函数恒等于零，必须考虑二阶Melnikov函数，而在一阶Melnikov函数中不起作用的扰动参数在二阶Melnikov函数中却起着非常重要的作用，因此扰动部分极为复杂。

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。

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 absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。