解析函数

We also use the Schr〓der transformation, Abel transformation, power series and Dirichlet series theory to discuss the existence and uniquness of analytic solutions for an extensive class of nonlinear iterative equations.

进而还利用Schr〓der变换、Abel变换以及幂级数与Dirichlet级数理论研究一类具有相当广泛性的非线性迭代函数方程解析解的存在性和唯一性问题。

This method can overcome the defects of traditional analytical optimization methods: they are hard to suit the conditions of discontinuous objective function and disconnected constrained domain. At the same time, the quantities measured by PMU can fully give play to maximum advantage while limited PMUs are placed.

该方法克服了传统解析优化方法难以适应不连续目标函数和不连通约束域等情况的缺点，同时，在配置有限PMU的情况下使PMU量测量发挥最大效益。

Theoretical analysis was carried out to achieve the analytical expression for Doppler shift and amplitude of liquid surface wave.

对此进行了理论分析，得到了多普勒频移与液体表面波振幅之间的解析关系式，并利用贝塞尔函数分析了频谱分析图中解调出低频液体表面波频率的可行性，设计并实现了一套液体表面波多普勒相干检测的实验装置。

In the second part, we have considered the polariton system described by the model effective Hamiltonian involving single mode photon field interacting with a transverse optical phonon in a more realistic form. On this basis, we have discussed the dynamical evolution of the wave function , the dynamical variables and the non-classical properties for the system in a analytic form for the first time.

第二部分将极化激元系统约化成模型单模光子—横向声子有效相互作用系统，在此基础上以解析形式首次讨论了系统的波函数、力学量和压缩态、亚泊松分布等非经典效应的动力学演化行为。

Standard of will basic electrovalency of simple and easy equivalent makes analytic expression, considered 2 times to supply the parameter quote of function among them.

将基本的简易当量电价法作解析表达，其中考虑了二次供应函数的参数报价。

An exact solution of the scattering by a chiral elliptic cylinder is obtained in terms of Mathieu function and modified Mathieu functions by means of vector wave functions.

对旋波媒质的电磁特性进行分析，基于边界值问题，借助于矢量波函数，首次给出了旋波媒质椭圆柱电磁散射问题的解析形式解。

In the present paper, we shall show that there are many elliptic invariant tori of the equation for a given analytic potential which is not necessary to be constant.

在这篇文章中，证明对于给定的解析势函数，不一定是常数，方程存在许多椭圆不变环面，与 Kuksin 和 Poschel 的文章不同的是，不变环面上承载的是高频的拟周期解。

Double pendulum ; analytic method ; Whittaker's theorem ; elliptic function ; integrable system

双摆；解析方法；惠特克定理；椭圆函数；可积系统

The influences of the shock thickness and Alfven waves on the particle acceleration by diffusive shock waves are numerically studied through solving one-dimensional diffusive equation including the second-order Fermi effect. It is shown that the spectral index of the energetic particles strongly depends on the shock thickness. For example, the spectral index increases from 2.1 to 3.7 in the low energy range of 3-10 MeV and from 2.5 to 5.0 in the high energy range of 20-60 MeV as the thickness increases. The spectral index decreases from 4.3 to 3.1 as the particle injection energy increases. The spectral index decreases from 4.0 to 1.8 at the quasi-steady stage with the enhancement of the compression ratio from 2 to 4. The results indicate that under the influence of Alfven waves, the energetic particle spectrum at lower energy becomes flat and the spectral index decreases from 2.5 to 0.6 in the low energy range of 3-10 MeV and from 11.6 to 5.0 in the high energy range of 20-60 MeV. At the same time, the rollover energy reaches 19.6 MeV. The spectral index decreases from 5.8 to 2.9 as the energy density of Alfven waves increase. All these results are basically consistent with the theoretical models, as well as the observations of typical energetic particle events.

通过数值求解包含二阶费米加速的一维扩散方程，探讨在准平行激波条件下激波厚度和级联阿尔芬波对粒子加速的影响，研究粒子分布函数的演化与激波厚度和阿尔芬波强度的内禀关系，计算结果表明：(1)考虑激波厚度时，谱指数明显依赖于激波厚度，随着厚度从0.32增大到2.56，低能端(3-10MeV)谱指数逐渐从2.1增加到3.7，高能端(20-60MeV)谱指数从2.4增大到5.0，能谱逐渐变软；当初始注入粒子动量增大1.3倍，质子能谱指数从4.3减小到3.1，且与零厚度激波加速的谱指数差值缩小；厚度不变时，随着压缩比从2增加到4，准稳态分布时低能端(3-10MeV)粒子能谱指数逐渐从4.0减小到1.8谱变硬；(2)在级联阿尔芬波的影响下，随着时间的增大，粒子在低能处(3-10MeV)的谱指数从2.5减小到0.6高能端(20-60MeV)谱指数从11.6减小到5.0，能谱变硬，拐点能量值从7.5MeV增大到为19.6MeV；随着波的能量密度增大，谱指数从5.8减小到2.9，这表明阿尔芬波强度越大，加速效率越高，通过与激波厚度解析结果和高能粒子事件的观测能谱比较发现两者是一致的，说明数值模拟结果是可靠的。

In order to solve the thermal effect problem of laser rod by diode laser end-pumped,based on the heat conduct theory,a novel eigenfunction group of heat conduction equation was established and the general solutions of temperature field and thermal distortion field within laser rod were obtained.

为了解决激光二极管端面泵浦激光棒引起的热效应问题，基于热传导理论，建构了热传导方程新的本征函数解，得出了激光棒内温度场与热形变场的一般解析表达式。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失