函数的积分

The thesis will introduce, respectively, relevant concepts of residue theorem and its promotion and application in two parts In the basic concepts of chapter II, the definition, classification and relationship between function zero and pole of the isolated singular point are given to lead out relevant definition, theorem and solving method, while the core content of this paper is promotion and application of residue theorem, including calculation of integration by using residues, application in diagonal theorem and argument theorem, application in electromagnetism and theorem promotion and relevant application of extension theorems

本文将从两大部分分别引入和浅析了留数定理的相关概念及其推广和应用在第二章的基本概念部分中，给出了孤立奇点的定义和分类、函数零点与极点的关系，从而引出留数定理的相关定义与定理及其求法而本文的核心内容也就是留数定理的推广和应用，包括运用留数来计算积分、体现在对角定理与辐角定理中的应用、在电磁学中的应用及其定理的推广和推广定理的相关应用

Based upon the general equations of a trans-versely isotropic foundation, the stress functions and the theory of Fourier transforms , the basie displacement so-lutions for a transversely isotropic body under horizontal concentrated loads are obtained.

根据横观各向同性体的基本方程，运用应力函数、傅氏变换和傅氏逆变换理论，得出了横观各向同性地基在水平集中荷载作用下的基本位移解，然后利用积分的方法分别得出了横观各向同性地基在条形面积上水平均布荷载、水平三角形分布荷载及水平梯形分布荷载的位移计算公式，并利用实测的一组弹性参数，将横观各向同性地基中的相对位移与现有的计算理论给出的各向同性地基中的相对位移通过图形作了分析比较，得出了一些有益的结论，以供岩土工程设计人员参考。

The results of numerical experiments, using the four-dimensional variational data assimilation system of the nonhydrostatic mesoscale model MM5, show that: the tangent linear model and adjoint model conducted by keeping the "on-off" switches the same as the basic state, can provide a good approximation of the first-order information to the NLM perturbation and a good descent direction for the minimization procedure; switching on and off at every other time step in the Kuo cumulus parameterization scheme don"t impact the convergence rate of cost function; the existence of the switches don"t impact improvement to the MM5 model rainfall prediction because that not only specific humidity ,but also wind, temperature and pressure are assimilated into the model.

非静力中尺度数值模式MM5的四维变分资料同化系统进行的数值试验结果表明："开关"变量保持与基态一致，所构造的切向线性模式能够提供关于非线性模式扰动的一阶近似，伴随模式所计算的梯度值能够为最小化过程提供较好的下降方向；郭氏降水参数化方案中对流每隔一个积分步的交替发生并不影响目标函数最小化的收敛速度；"开关"变量的存在也不影响将风、温度、气压和比湿结合起来同化对MM5降水预报准确性的提高。

The wave function of the phonon is assumed to take thecoherent state,a self-consistent integrodifferential equationsatisfied by the electron wave function is derived.Solving for thisequation,we get the polaron ground-state energy E=-0.1085α2, whichis very close to these of previous strong-coupling theories.In chap.4,we will apply approaches developed in chaps.2 and 3 to discuss theimportant two-dimensional(2D)polaron problem.

把声子部分取成相干态的形式，我们推导出电子波函数所满足的非线性的微分积分方程，求解这个方程，我们得到基态能为E＝-0.1085α2，它与以前的各种强耦合理论的结果非常接近，在第四章中，我们利用在第二，三章中发展的方法讨论很重要的二维极化子问题。

First, we consider nonholonomic chained systems with modeling error, in this section,based on back-stepping , using the so-called adding a integrator , state-scaling technique , we design discontinuous feedback law,such that the trival solution of the closed-loop systems global strong stable; Second,we consider high-order nonholonomic chained systems with modeling errors and external disturbances, in this section,using input/state-scaling and integrator backstepping methods , we design discontinuous feedback law and give out the switching strategy, such that the closed-loop systems global /C-exponential stable; Finally, we consider a class of more general power chained form systems with particular drift-terms, in this section , using Lyapunov method, we design time-varying feedback law , such that the closed -loop systems p—exponential stable.

第一部分考虑的模型为带有模型误差的高阶非完整链系统，我们运用加幂积分器、State-scaling技巧以及基于Back-stepping方法构造出不连续反馈律，从而使得所讨论系统的闭环系统的平凡解全局强稳定；第二部分考虑的模型为带有模型误差的不确定高阶非完整链系统，这一部分我们运用input／state scaling和integrator backstepping方法构造出不连续反馈律，并给出切换策略，使得所对应的闭环系统全局κ-指数稳定；第三部分考虑的系统是形式更为一般的且带有特殊形式漂移项的幂链系统，利用Lyapunov函数方法，设计出时变反馈律，从而使得相应的闭环系统ρ-指数稳定。

The results show that for the global scale characteristics of the vertically integrated vapor flux fields, which is described in terms of the rotational and divergent components of the stationary parts of the vapor field, both GOALS and FGCM--0 can reproduce the subtropical gyres in each hemisphere, the eastward water va- por transport of the mid--latitude westerlies, and the westward vapor transport of equatorial easterlies reasonably, though the precise positions of the gyres simulated by GOALS, and the intensities of the gyre centers in FGCM--0 do not match the observations accurately.

结果表明：(1)对垂直积分的水汽通量场的流函数及其对应的无辐散水汽通量矢量的模拟，三个耦合模式都能够较为合理地再现副热带大洋的涡旋结构、中纬度西风带的东向水汽输送、赤道东风带的西向水汽输送和东亚夏季风水汽输送等行星尺度特征及其季节变化，只是GOALS的涡旋位置、FGCM-0的涡旋中心强度，较之实际略有偏差。

Based on the experimental data of the strain of the geogrids at different embedments, a three dimensional strain surface that represents a function of coordinate and time is obtained. The time function for pull-out force of geogrids is deduced through integration of friction along total length of geogrids.

通过不同埋设位置的检测点所得到的格栅即时应变数据，拟合出格栅的三维应变曲面ε；对格栅表面上的摩擦力进行全段积分，得到格栅拉拔力的时程函数T。

In order to obtain more exact analytical solution to study the output characteristics of double-clad fiber lasers,according to the continuous-wave rate equations of fiber lasers,using typical parameters of double-clad fiber lasers,the contribution of the re-emission effect arising from the interaction between the upper-level atoms and pump light was estimated.Taking into account the predominant part of the re-emission to improve the accuracy of the integration approximated rate equations,the integration of the product of the loss and radiation should be found and explicit analytical expressions for the output of the DCFLs and gradient efficiency of the pump radiation,were deduced,and certain issues of concern were discussed.

为了求得用于研究双包层光纤激光器输出特性的更为精确的解析解，根据稳态速率方程组，针对典型的双包层光纤激光器参量，在估计了上能级粒子再发射项和抽运光产生的影响后，采用保留再发射贡献主导部分的办法以提高可积分近似方程的精确度，明确地提出了要获得光纤激光器输出功率的解析表达式的关键在于求出损耗系数与光场乘积的积分值，简洁地求得了输出功率和抽运光斜线效率的显函数解析表达式，并对其相关问题进行了讨论，以915nm，920nm和975nm的抽运光为例，当输出激光为1090nm时，得出975nm抽运光产生的斜率效率最高并可高达约87%。

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。