近似积分

Using the Green function theory, the integral equation of perturbational parameters was obtained.

基于非均匀介质中波函数的局部理论和射线理论，引入了全波场的广义射线近似形式，通过定义介质参数函数，把反演目标归结为其第一类Fredholm积分方程。

Based on Born approximationmethod and the local principles of wave function in inhomogeneous medium and theray theory and the integral equation theory,this dissertation researches the theory andsimulation of the inversion method of large perturbational medium parameters andbreaks through the approximation condition of the small perturbational parametersand the weak scattering in traditional inversion method.

本文在Born近似方法的基础之上，基于非均匀介质中波函数局部理论和射线理论及积分方程等理论方法，对大扰动参数反演方法的理论和数值模拟进行了研究，突破了传统反演方法要求的参数小扰动和弱散射条件。

Although the EPRI give a set of the approximate engineering solution method, actually the crack of parts in engineering project mostly presents inner 3D effect. If using 2D elastic-plastic or 3D elastic analysis, the result can't be precise. Because these methods have neglected the reassignation of the stress and strain which happened at nearly the top of cracks, carrying on 3D elastic-plastic analysis and J-integral calculation become the foundational work to study the expander and safety assessment of the pressure vessel cracks.

虽然EPRI给出了一套近似的工程解法，但实际上工程中构件的裂纹大多呈现内在的三维效应，若使用二维弹塑性或三维弹性分析必然不够精确，因为对裂纹的&等效&二维表达忽视了发生在靠近裂纹端部的应力和应变的再分配，所以对压力容器裂纹进行三维弹塑性分析及其J积分是研究压力容器裂纹扩展和安全评定的基础工作之一。

For soil surface the IEM model was used, and the specula surface approximation was used for flooded field.

利用矢量辐射传输理论建立了水稻微波后向散射模型，模型中考虑了稻田土壤无水的情况，用积分方程模型模拟土壤下垫面，而对稻田积水情况下的垫面用镜面反射近似。

The collision term is two bi-velocity non-dimensionalized reduced ngle tri-velocity model equation is transformed into a bi- h integrating weightedly the non-dimensionalized model equation about the third component of molecule velocity.

采用BGK模型和Shakov模型近似碰撞项，进而引入两个二速度无量纲简化分布函数，通过关于分子速度第三分量取矩积分，将三速度单一模型方程变换为二速度微分方程组。

An approximative mathematical model of the temperature controlling system has been constituted and simulated with various controlling strategy, according to the demanded function of the running Microwave Heating Asphalt Pavement Regenerate Repairer. From the result of simulation, it suggests that FPID Controller, which is of superior anti-jamming capability, overmatches Ordinary PI Controller, Traditional PID controller and Integration Separation PID Controller in dynamic characteristic. Consequently, this simulation of model offers a kind of valid method for the constitution of complicated system.

根据沥青路面修复要求实现的功能建立了温度控制系统的近似数学模型，对系统先后进行各种控制仿真，通过仿真发现，系统中模糊整定PID控制算法的动态性能比PI、PID和可积分分离的PID控制的性能要好，且具有较强的抗干扰能力，为复杂系统建模提供了一个有效途径。

Because the curve radius of easement curve gradually changes, the formula for calculating the coordinates can not be obtained with the method of integration.

由于缓和曲线的曲率半径是逐渐变化的，不能用积分的方法求得其上点位坐标的计算公式，以往都是用级数展开进行近似计算。

Simultaneously, the exports of ionization rate and nonionzed concentration are set up as a powerful tool for studying thoroughly the freeze-out effect. dN〓/dp and dN〓/dn are neglected in the linearized equation system of the iteration methods of Newton and Gummel, due to having lower 15 orders or more than dN〓/dn and dN〓/dp, thus the computing effort is cut down with no effect on precision. A new cut-off technique is adopted to accelerate the convergence speed, about twice reduced for Newton iteration method and six times or so for Gummel iteration method. The approximate formulae of Fermi-Dirac statistics are also put forward with simpler form and higher precision. 3. A term dependent on time is added to the electron and hole current succession equations respectively. It is only this model that conservation of charge in transient analysis and alternating small-signal analysis at low temperature can be kept by. 4. The performance of SE-PISCES is explained by the simulation example of PISCES-2B, diode.

研究了低温半导体器件模拟的数值方法：对载流子浓度进行了新的归一化；编制了不考虑掺杂所引进的内建电场时的电离率计算程序；由于低温杂质电离率随偏压状态而变化，为此编制了每次求解迭代时的电离浓度计算程序，并将其插入到求解迭代程序中；同时，设置了杂质电离率和未电离杂质浓度的出口点，为更深入地研究冻析效应提供了有力工具；在Newton迭代法和Gummel迭代法的线性化方程组中忽略了dN〓/dp、dN〓/dn，是因为它们比dN〓/dn、dN〓/dp低15个数量级以上，这样减小了计算量又不影响模拟精度；对Newton迭代法和Gummel迭代法采取了新的截断技术，提高了收敛速度，Newton法迭代法和两次左右，Gummel法减少六次左右；给出了表达式更简单而精度更高的Fermi-Dirac积分近似计算公式。

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%。

In this paper we present the results of a theoretical study of the focusingproperties of a symmetrical two-cylinder lens with identical radii and negligibleseparation for relativistic electron beams.

本文提出相对论情况下双圆筒静电透镜的聚焦性质，得出在薄透镜近似下的解析公式，并给出计算实例及与数值积分计算相比较。

Objective To investigate the effects of interleukin-1 β converting enzyme gene on the biologic characteristics of ovarian cancer cells.

目的 探讨白细胞介素-1 β转换酶的表达，对卵巢癌细胞生物学特性的影响。

Campylobacter: This illness is the most commonly identified cause of diarrheal illness in the world.

弯曲：这种病是最常见的原因查明腹泻病，在世界上。