| 1. | Unique solutions of linear impulsive fredholm integral equations
型积分方程的唯一解 |
| 2. | The coupled quasi - solution and the solution of nonlinear impulsive fredholm integral equations
积分方程的耦合拟解及解 |
| 3. | To get so - called c - best - approximate solutin on a certain constrained set c , we employ the constrained regularization method to solve fredholm integral equation of the first kind with nonnegative constraints
为得到所谓的带约束的反问题在特定约束集c上的最优解，我们采用约束正则化方法解决非负约束情况下的第一类fredholm积分方程。 |
| 4. | In this thesis , we present a fast self - adaptive algorithm for fredholm integral equations of the second kind with weakly singular kernels . briefly speaking , we design an algorithm which can determine the correlated parameters such that the corresponding numerical solution has given accuracy
本文考虑核函数有弱奇性的第二类fredholm积分方程的自适应快速数值解法，即事先给定数值解的精度，设计算法确定相关的参数使得数值解满足精度要求。 |
| 5. | Furthermore , the dual integral equations can be reduced to the fredholm integral equations of the second kind and solved by numerical procedure . at the end of this chapter , the numerical analysis for dynamic interaction characters of saturated half - space / layered ground and circular plate is evaluated . finally , the solutions for 3 - d dynamic responding of elastic rect
基于横观各向同性饱和半空间/有限层地基非轴对称波动方程的通解，按混合边值问题建立饱和地基与弹性圆板非轴对称动力相互作用的积分方程，求解积分方程后得到横观各向同性饱和地基上圆板非轴对称动力响应的一般解，并分析了饱和地基上圆薄板和中厚板振动的若干特征。 |
| 6. | By means of " conjunction " , the model of this problem is established . and then a series of fredholm integral equations of first kind can be set up in terms of the green ' s function , furthermore the scattering problem of sh - wave by cavity in the interface is transformed into a series of algebraic equations based on the direct - discrete method
按“契合”的方式构造出在两个性质不同的弹性半空间交界面上的任意形孔洞对sh波散射的模型，利用green函数建立求解问题的定解积分方程组，并用直接离散的方法将其转化为代数方程组进行求解。 |
| 7. | The main work includes : for the torsional vibrations of a rigid disk on saturated media , first , the dynamic governing equations are solved by the use of hankel transform and the general solutions in the hankel transform fields are formulated . then , considering the mixed boundary - value condition , the dual integral equations of the torsional vibrations of a rigid disk on saturated grounds are obtained , which can be reduced to the fredholm integral equations of the second kind and solved by numerical procedures . consequently , the dynamic compliance coefficient curves and the torsional angle amplitude curves versus the dimensionless frequency are presented and contrasted to that of the elastic one
在前人研究的基础上，本文基于陈龙珠等曾提出的一组实用饱和土波动方程，用解析或半解析的方法首次较系统而深入地研究了饱和半空间地基与基础的扭转振动问题，主要工作有：对于饱和地基上刚性圆板的扭转振动，作者首先采用hankel变换求解了动力控制方程，得到了该控制方程在hankel变换域内的通解，然后由混合边值条件建立了饱和地基上刚性基础扭转振动时的对偶积分方程，并将其化为易于数值求解的第二类fredholm积分方程，用数值方法计算了基础的动柔度和扭转角幅值与振动频率的关系曲线，并将其与单相弹性介质情况进行了对比分析。 |
| 8. | Finally , a series of fredholm integral equations of first kind for determining the unknown forces can be set up through continuity conditions that are expressed in terms of the green ' s function , finally the integral equations can be transformed into a series of algebraic equations based on the direct - discrete method and solved numerically
利用green函数写出界面位移连续条件，建立求解未知外力系的第一类fredholm积分方程组，采用直接离散的方法将定解积分方程组转化为代数方程组进行求解。本文的具体工作如下： 1 |
| 9. | The model of the problem is composed of two half spaces with half circular lining inclusion . horizontal surfaces of the half spaces are loaded with undetermined anti - plane force in order to satisfy continuity conditions at linking section , or with some certain forces to appear cracks . a series of fredholm integral equations of the first kind for determining the unknown forces can be set up through continuity conditions that expressed by using of the green " function
然后将问题的模型视为“契合”问题，即将其剖分为两个含半圆环形衬砌的弹性半空间，分别在其剖分面上加置未知的出平面荷载，并在欲出现裂纹位置加置出平面反力使之产生裂纹，接下去利用green函数表示出界面连续条件，建立决定待解外力系的第一类fredholm积分方程组。 |
