By the use of the circle method , and then treating the singular integral carefully , the best qualitative results are obtained . a natural necessary and sufficient condition for the solvability to the equation is given explicitly 利用圆法并通过对奇异积分的详细讨论，我们得到了最好的定性结果，并且明确地给出有解的充分必要条件。
In this paper , the method of solution in the vector format for a kind of dual singular integral equation with two convolution kernels is discussed , and the general explicit solution and the related conditions of solvability are obtained 摘要本文对文[ 2 ]中的含两个卷积核的对偶型奇异积分方程给出了向量形式求解方法，并且给出了一般解的显式及相应的可解条件。
This dissertation introduces a regularization algorithm to tackle the problems of the nearly singular integrals . in the algorithm , the singular factor is removed from the kernel functions in the singular integrals by means of integration by parts 该算法通过对积分核进行一系列的分部积分，将引起几乎奇异积分的因子变换到积分号之外，从而可以克服几乎奇异积分的困难。
Due to the importance of the accuracy of the time - domain impedance matrix elements , the techniques by which treating of the singular integrals and near singular integrals arose from the tdie - mom solving process are analyzed in detail , and these techniques are utilized to solve the tdie . in the end , using triangle patches discretizing arbitrarily 3 - d dielectric objects and metal - nonmetal composite objects surface and utilizing spatial rwg and temporal triangular bases , the tdie are solved by mot algorithm 最后,分别对三维介质目标、金属非金属组合目标散射体表面用三角贴片离散,并在空间上采用rwg基函数,在时间上采用三角型时间基函数、利用阻抗元素的精确算法计算出阻抗矩阵,再运用mot法分别求解了介质体目标,金属非金属组合目标的时域积分方程,并分析了金属非金属组合目标分界面上的等效电流与等效磁流的特性。
In this dissertation , the numerical computation for the acoustic radiation problem ( arp ) is studied deeply and systematically in the theory , method and the application technique , based on analyzing the situation of the home and abroad on the numerical computation for the acoustic radiation problem . the calculation formulas of the boundary element method ( bem ) for the exterior acoustic radiation problem in the full - space and half - space are deduced , based on the wave propagation theorem ; the arising of the non - unique solutions , which is associated with the application of the boundary integral equation ( bie ) in acoustic radiation problem , is analyzed and proofed ; the improved combined helmholtz integral equation formulation ( ichief ) is presented to overcome the non - uniqueness problem more effectively and reliably ; the determination of the singular integral coefficients on various occasions is analyzed ; the properties and treatments of the singular integrals with different orders axe studied ; the computation program of the cubic spline ichief is developed and its ability to overcome the non - uniqueness problem and feasibility to discrete the surface coarsely with the sufficient calculation precision are examined through examples 第二章在声波动理论基础上，详细地推导出对应于无限域和半无限域的外部振动声辐射问题的边界积分方程计算公式；根据fredholm积分理论，对利用边界积分方程计算振动声辐射问题过程中解的非唯一性的产生进行了分析和证明；改进了chief法以提高其克服解的非唯一性的有效性和可靠性；对不同条件下奇性系数的计算、强奇性积分的收敛性及其在变量替换时与普通积分的差异性、不同阶奇性积分的计算、数值求积分等进行了研究；开发了三次样条改进chief法计算软件，并通过算例考核了该方法在特征波数处克服解的非唯一性的有效性和在保证计算精度的前提下实现剖分粗化以提高计算效率的可行性。
In the first part of this paper , resorting to the idea of hadamard principle value and induction , we discuss the inductive definition , existence of hadamard principle value , recursive formula , computation formula , differential formula on the sense of hadamard principle value for several kinds of quasi - bochner - martinelli - type high order singular integrals with one singular point 本文借助于高阶奇异积分的hadamard主值的思想以及归纳法的思想，在第一部分讨论了几类含一个奇点的拟bochner - martinelli型高阶奇异积分的归纳定义， hadmard主值的存在性，递推公式，计算公式，以及在hadamard主值意义下的微分公式。
The stability of cauchy singular integral when the integral curve has a smooth perturbation is discussed in our first partition ; we apply some results of the first partition to the second partition and solve the stability of the solution to the cauchy singular integral equation . finally , on the basis of the stability of the cauchy type integral , we study the stability of the solution to the riemann boundary value problem when the contour perturbs smoothly 在第一部分中，我们主要讨论了cauchy奇异积分在积分曲线发生光滑扰动时的稳定性问题；而在第二部分中，我们把第一部分的结果应用到cauchy奇异积分方程，导出了其关于积分曲线摄动的稳定性的研究及其一些结果；最后，在第三部分中，我们在研究cauchy型积分关于积分曲线的稳定性问题的基础上，探讨了riemann边值问题的稳定性问题。
