In this paper, we consider two dimensional singular integral equation with two shifts.
本文研究带两个位移的二维奇异积分方程。
The commutator generated by BMO functions and singular integral operators with homogeneous kernel is studied.
本文研究带有齐性核的奇异积分算子与BMO函数的交换子。
The singular integral problems emerged in calculations were solved through triangular polar coordinate transformation;
利用三角极坐标变换处理数值计算中的奇异积分问题；
In this paper, the embedded crack in transversely isotropic body is studied by means of the singular integral equation method.
本文采用奇异积分方程法分析了横观各向同性体中的埋藏裂纹。
The problem is reduced to a singular integral equation on cracks. The formulas for the stress intensity factors are also derived.
问题化为了裂纹上的奇异积分方程，并导出了应力强度因子公式。
The singular integral equation technique is used to determine the normal modes of propagation in asymmetrical bilateral finlines.
本文利用奇异积分方程法计算出了非对称双面鳍线的传播常数。
In this paper, the solvability for a class of nonlinear two-dimensional singular integral equation is considered in unit circular.
研究复平面单位圆域内一类非线性二维奇异积分方程的可解性。
The solution will lead to solve a hyper singular integral equation, when a double layer potential distribution formulation is used.
采用双层位势来表示解，要导至求解超强奇异型积分方程。
By using the method of spherical harmonic, the boundedness of a kind of singular integral operator in product domains is given in this paper.
用球调和的方法研究了一类乘积空间上奇异积分算子的有界性，所获得的结果给出了以往奇异积分算子有界性的应用。
In this paper, we study the direct method of solution for a class of singular integral equations with solutions having singularities of order one.
本文研究了一类具有一阶奇异性解的完全奇异积分方程的直接解法。
By the singular integral equation theory we obtain the resolvable sufficient and necessary condition and the formula of counting index for the problem.
同时利用带位的奇异积分方程理论得到了这一问题可解的主要条件及指数计算公式。
The edge internal branch crack problems for half-plane in antiplane elasticity are solved with complex potentials and singular integral equation approach.
利用复变函数和奇异积分方程方法，求解反平面弹性中半平面边缘内分叉裂纹问题。
The edge internal branch crack problems for half-plane in antiplane elasticity are solved with complex potentials and singular integral equation approach.
运用复变函数及积分方程方法，求解了半平面域多圆孔多裂纹反平面问题。
As an application we utilize the results presented in this paper to study the existence problem of solutions for a class of weakly singular integral equations.
作为所得结果的应用，讨论了弱奇异积分方程解的存在性问题。
So far, the numerical techniques solving the hyper-singular integral equations are established, and these are called finite-part integral-boundary element method.
从而完成了超奇异积分方程组数值法的建立，这一方法现称之为有限部积分——边界元法。
In physical application, there is a singular integral which is difficult to solve. Therefore, a common singular integral is derived by gamma function in this paper.
针对物理学中常常遇到的一个令人感到棘手的反常积分，运用伽马函数推导出了一个求解此类积分的普遍公式。
Especially, we give a calculation method for higher order singular integral by equation (3.1) when the wavelet function is unknown. At last, we create a convergence theorem.
特别是当小波函数未知时，借助于方程(3.1)，对高阶奇异积分作数值计算，建立了收敛性定理。
A new analytical integral algorithm is proposed and applied to the evaluation of the nearly singular integrals in the Boundary Element Method for 2d anisotropic potential problems.
导出了一种解析积分算法，精确计算了二维各向异性位势问题边界元法中近边界点的几乎奇异积分。
The problem of a cylindrical interface crack is reduced to a system of singular integral equations with the aid of two unknown dislocation functions at the interface crack surface.
以裂纹面上的位错函数为未知量将圆柱型界面裂纹问题化成一组奇异积分方程的求解问题。
Boundary element method (BEM) is a simple and effective numerical method to solve potential problems, but usually requires calculation of singular integral, even hyper-singular integrals.
边界元方法求解位势问题有效而简单，但通常需要数值计算奇异积分甚至超强奇异积分。
Using proper decomposition of the functions and integral transformation, the problem is reduced to a singular integral equation, whose solution is given of the theory of integral equation.
笔者通过适当的函数分解和积分变换，将寻求复应力函数的问题转化为求解一正则型奇异积分方程，并借助积分方程理论给出了方程的求解方法。
A formulation for the equivalent circuit parameters of the discontinuities with superior convergency is derived by the transverse resonance method with the singular integral equation technique.
利用横向谐振法结合奇异积分方程技术，导出了具有快速收敛特性的不连续性等效电路参量计算公式。
To begin with, a regularized boundary integral equation with indirect formulation is adopted to deal with the singular integrals and the boundary unknown quantities can be calculated accurately.
首先，采用间接制定正规化边界积分方程的奇异积分处理，可以计算出准确的边界未知量。
The nonsingular integrals are popularly calculated by the Gauss numerical integral, and they are low in precision when the source points approach the element, and the singular integrals are complex.
非奇异积分一般采用数值积分，当配置点接近积分单元时，计算精度较低，奇异积分的计算也很复杂。
The posteriori error estimators in the collocation method for integral equation eigenvalue problem with a weakly singular kernel are presented.
给出矩形域上弱奇异积分算子本征值问题分片零次多项式配置法的后验误差估计式。
Avoiding singular fundamental solution, the paper using non-singular fundamental solution to establish the boundary integral equation.
本文避开奇异基本解，用非奇异基本解建立边界积分方程。
By the first integral method, the existence, uniqueness and nonexistence of solutions for some nonlinear ordinary differential equations with singular boundary condition are discussed.
用首次积分法，讨论了带奇异边界条件的非线性常微分方程解的存在性、不存在性和唯一性。
A class of singular perturbation of nonlinear boundary value problem for integral differential equation involving two parameters is considered.
考虑了一类关于两个参数的微分积分方程非线性边值问题的奇摄动。
INTEGRAL J_I, which is referred to as a parameter of singular stress field at the front of crack-tip, has its practical value.
i积分作为裂缝前缘奇异应力场的参数量，是有实际应用价值的。
INTEGRAL J_I, which is referred to as a parameter of singular stress field at the front of crack-tip, has its practical value.
i积分作为裂缝前缘奇异应力场的参数量，是有实际应用价值的。
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