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Insignia in Latin is the plural form of insigne, but it has long been used in English as both a singular and a plural form

Insignia 在拉丁语中是 insigne 的复数形式，但是在英语中很长时间来一直既被用作单数又被用作复数形式

The Latin singular insigne is rare and may strike some readers as pedantic.

拉丁语的单数形式insigue 很罕见，这可能会使一些读者认为是在卖弄学问

A time domain singularity extraction technique is presented to calculate singular integrals in time domain electric field integral equation solver.

介绍了一种基于奇异提取技术的时域积分方程中奇异积分的处理方法，在奇异提取过程中，电磁波传播的延迟效应对积分的贡献包含在内。

The nearly singular integral occurs in the boundary element formulation when a source point is close to the integration element but not on this element.

边界元法中存在几乎奇异积分的计算困难。引起边界单元上几乎奇异积分的因素是源点到其邻近单元的最小距离δ。

What is more, we discuss the existence of positive solutions of singular initial problem. We give the conditions of the existence of function integral.

随后讨论了有奇点的初值问题的解的存在性，本文假设中所给条件是关于函数的积分存在性条件。

The major contributions of this dissertation are as follows:(1) Based on integral inequality, an LMI approach to the robust stability, robust stabilization and robust H_∞control of uncertain continuous-time and discrete-time linear singular systems with time-varying delay is developed.

论文主要工作有以下几个方面：(1)针对一类具有范数有界不确定的线性奇异时变时滞系统，基于积分不等式或有限和不等式，分别讨论连续和离散情形下的鲁棒稳定、鲁棒可镇定问题和鲁棒H_∞控制问题。

Singular perturbation of three-point boundary value problem for third order nonlinear equation is studied by using of Volterra type integral operator and differential inequality techniques.

讨论了三阶非线性微分方程三点边值问题的奇摄动。

The direct method of solution for non-normal type of singular integral equation with Hubert kernel is discussed. Their solution have form of integral and the condition of solution have form of the system of equations.

给出了具有Hilbert核非正则型奇异积分方程的直接解法，对核密度函数k在附加某些条件下，得出了方程积分形式的解和方程组形式的可解条件。

In the second chapter, modefied Taylor\'s expansion method is studied for solving Fredholm-Volterra integral equations, several illustative examples are given to show the efficiency of the proposed method. More over, by simple algebra, the modified Taylor\'s expansion can also be used to solve integral equations with weakly singular kernel, and the corresponding accuracy is dramatically promoted.

第二章重点讨论了应用Taylor展开方法解Fredholm-Volterra积分方程，通过数值例子，表明了该方法的简单有效性，特别应用于具有弱奇异核积分方程获得了更高精度的解。

Firstly, Wavelet-Galerkin algorithm for solving the first kind of singular integral equation with the Hilbert kernel is proposed, we use the characteristic of periodic wavelet on L~2([0,1]) and Hilbert kernel to solve and make stiff matrix lower dimensions and become sparser through thresholding,thus the cost of computation is reduced. Because of the singularity of Hilbert kernel we use Tikhonov regularization method to solve the system of stiff equation. At last the convergence and numerical result of approximate solution are given. Secondly, an approach of regularization based on Fourier is presented for sideways heat equation; we give the theory proof and error estimate.

首先，提出了含Hilbert核的第一类奇异积分方程的小波伽辽金(Wavelet-Galerkin)数值算法，该算法中利用了L~2([0，1])上的周期小波和Hilbert核的特点进行处理，使得刚性矩阵维数降低并且通过阈值使得它更加稀疏，减少了计算量；由于Hilbert核的奇异性，通过Tikhonov正则化方法求解所得到的刚性方程组，给出了收敛性和数值结果；其次，对标准的一维逆热传导方程给出了一种基于Fourier正则化方法，给出了理论证明及其误差估计，解决了文献中算法与理论误差估计的不相匹配的现象，该正则化方法不仅保留了测量数据的部分高频成份，且与文献中的算法具有同样的计算量和误差估计。

That snake Alaric named Archbishop...

庇护。。。那个毒如蛇蝎的Alaric被命名为大教主。。。

You have done lots of magical things to be amazed at.

你做了很多神奇的事物感到惊讶。