数值方程

In the second part,we have mainly discussed the error es-timates of the numerical methods for solving ill-posed problem,including the error estimate of finite-dimensional regulariza-tion method in Chapter 5,and the error estimate of regulariza-tion-spline method for solving Fredholm integral equation ofthe first kind.

在第二部分，我们主要讨论了不适定问题数值方法的误差估计，包括有限维正则化方法求解不适定问题的误差估计以及用样条正则化方法求解第一类Fredholm积分方程的误差估计，两者均是目前还未有的结果。

In previous paper1-3, from the results of the electronic computer simulation experiments and the analysis of the corresponding optical properties, we presented a stabilization condition for numerically solving a Fredholm Integral equation of the first kindσ2σ1kBdσ=I in Fabry-Perot interferencespectroscopy.

在以前的论文中，我们从计算机模拟实验及相关的光学现象出发提出了Fabry—Perot干涉光谱技术中的积分方程数值求解的稳定条件。

The inversion of particle size distribution from measured data of light scattering, as a typical inverse problem, has been studied by many reseachers and solved by several numerical methods. Among which, direct Tikhonov regularization method with Morozov discrepancy principle, is often used to overcome the ill-posedness linked with the Fredholm integral equation of the first kind, so the stability of inversion has been heightened. But there has much room for improvement of the inversion accuaracy, especially for the double-peak problems.

由测量得到的散射光强数据来反演颗粒粒径分布是一个典型的反问题，它已为许多的学者所研究，并用多种数值方法来求解，其中带Morozov偏差原理的直接Tikhonov正则化方法经常被采用，以便用来克服与上述反演相联系的第一类Fredholm积分方程的不适定性带来的困难，因而反演的精度得到了提高；然而仍有许多改进的余地，特别是对于所谓"双峰"问题更是如此。

Through establishing the functional of the source pulse which is based on the concept of "usable energy" in the received pulse and then extremizing the functional by means of the calculus of variations, the mathematical models of the optimized source pulse waveforms are shown to be associated with the eigenfunctions of a homogeneous Fredholm linear integral equation of the second kind. An efficient algorithm is developed for numerically solving the integral equation models.

论文研究了基于延迟反射脉冲序列无源标签的UWB RFID系统的基本工作原理并进行了详细的信号描述和分析，通过建立基于接收脉冲"有效能量"概念的源脉冲波形函数的泛函和使用变分计算泛函极值，得到了相关于第二类齐次Fredholm线性积分方程特征函数的源脉冲波形最优解数学公式模型，并开发了一套有效的数值求解算法。

Finally, based on the fundamental solutions of Biots consolidation of transversely isotropic saturated multi-layered soils, the Fredholm integral equation of second kind for the interaction between transversely isotropic saturated multi-layered soils and rectangular piles is established, the relevant numerical analysis is also carried out.

最后，基于横观各向同性层状饱和地基Biot固结问题的基本解答，建立了横观各向同性层状饱和地基与方形单桩、群桩共同作用问题的第二类Fredholm积分方程，并进行了数值分析与计算；通过将矩形刚性基础基底划分成若干个大小相等的矩形网格，用矩形均布荷载表示网格的基底反力，并利用已获得的横观各向同性层状饱和地基Biot固结问题的基本解来求解每个矩形网格的柔度系数，然后根据刚性基础与层状饱和地基的接触条件和其本身的静力平衡条件，求解分析了横观各向同性层状饱和地基与刚性矩形板的共同作用问题。

In this paper the fundamental equations are derived and the finite element software ABAQUS is adopted to calculate the time history of pore pressure.

本文通过对基本方程的推导，借助于大型有限元软件ABAQUS，进行了饱和土体在动力作用下孔隙水压变化的数值模拟。

The discrete heat and moisture transfer equation and control conditions are obtained with finite volume method. The temperature and moisture distribution and transient heat and moisture absorbing and desorbing of porous envelop are calculated with numerical method. The program for porous envelop heat and moisture transfer are developed by use of FORTRAN. The heat and moisture transfer model is verified using the examples given out in the reference [41] and testing data of funk hole located in A zone Chongqing university.

采用有限体积法对多孔材料热湿传递方程及控制条件进行离散，用数值方法求解多孔围护结构温湿度分布和壁面的瞬时热湿吸放量，采用FORTRAN语言编写了围护结构热湿传递计算程序，并用文献[41]给出的算例和重庆大学A区防空洞的测试数据对模型进行了验证。

It lay emphasis on the research of Galerkin FEM equations for multiaquifers and its solution, and on the research of basic ideas and implementation of visual mesh auto-generation .

重点研究了潜水——承压水多层结构含水层系统的伽辽金FEM方程，并探讨了其数值解法，提出了基于可视化理念的FEM剖分软件系统设计的基本思想及其实现的方法。

By Galerkin meshless method, the equations of motion of static rectangular membrane is established. The first ten natural frequencies of the different aspect ratios and the different pull ratios of rectangular membrane with four clamped edges, three clamped edges and one free edge, two opposite free edges and other two clamped edges were calculated. It is feasible and valid to solve the transverse vibration problem of membrane by Galerkin meshless method.

采用伽辽金无网格法，建立了矩形薄膜横向自由振动的运动方程，并对四边固支、三边固支一边自由、一对边固支另一对边自由三种边界条件下，薄膜的不同长宽比及不同单位长度拉力比作用下的矩形薄膜的前十阶固有频率进行了数值计算，结果说明伽辽金无网格法用于求解薄膜横向振动问题是切实可行的。

In general, this equation can not be solved analytically, so we need deal with it numerically.

该方程一般情况下不适合于解析求解，通常需做数值处理。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新