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cauchy kernel
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  cauchy核
     This paper discusses the Noether theorem of complete singular integral equation which containsboth the convolution kernel and the Cauchy kernel, and comes up with the Noether theoremwhich is similar to the Fredholm integral equation, the convolution equation and the singularintegral equation.
     本文讨论了既含卷积核又含Cauchy核的完全奇异积分方程的Noether定理,得到了与Fredholm积分方程、卷积型积分方程、奇异积分方程相类似的Noether定理。
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     In this paper,we construct a Fredholm module by using singular integral operators theory with the quaternionic Cauchy kernel and C~*-algebra theory.
     运用四元数Cauchy核奇异积分算子理论和C*代数理论,建立了一个Fredholm模结构.
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     Some Problems on the Solution of the Singular Integral Equations with Both Cauchy Kernel and Convolution Kernels
     关于Cauchy核和卷积核混合的奇异积分方程求解方法的研究问题
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     On Singular Integral Equation with Hype ranalytic Cauchy Kernel
     具有超解析Cauchy核的奇异积分方程
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     In this paper, we introduce the concept of Hlder conditions in the sense of mean square (metric), establish the concept of the random singulur integral of random process with second order moment, and prove an existence theorem on random singular integral with Cauchy kernel.
     对二阶矩随机过程引进均方度量意义下的H lder条件及其判定,建立二阶矩过程随机奇异积分的概念和关于Cauchy核随机奇异积分存在的一个定理.
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  相似匹配句对
     Cauchy-SzegKernel over Polydisk
     多圆盘上的Cauchy—Szeg核
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     Approximate Method to Slove the Equation with A Cauchy's Kernel
     负指标的Cauchy奇异积分方程的近似法
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     kernel technology?
     NET的实质和一些核心技术、.
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     ON THE SINGULAR CAUCHY PROBLEM
     关于奇异Cauchy问题
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     The(n,k)-Wellposedness of Cauchy Problem
     抽象Cauchy问题的(n,k)-适定性
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  cauchy kernel
The Bochner-Martinelli (B.-M.) kernel inherits, forn≥2, only some of properties of the Cauchy kernel in ?.
      
Norms of the singular integral operator with Cauchy Kernel along certain contours
      
We consider the collocation method with piecewise linear trial functions for systems of singular integral equations with Cauchy kernel and piecewise continuous coefficients.
      
If Φ is a function of one variable, itsnth order Cauchy kernel is defined by
      
The solution of the boundary value problem that one obtains from the mathematical formulation of the current crack problem under thermal loading reduces to an integral equation with a generalized Cauchy kernel.
      
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To find the sectionally holomorphic veclor ■(P)≡(φ_0,φ_1,φ~2,φ~3):1) Which is holomorphic in D~+ and D~-, i.e. satisfying the system of partial differential equations of elliptic-type of the first order in spaceand satisfying on the boundary surface ∑ the boundary condition(H)_l ■~+(P_0)=G(p_0)■~-(p_0)+■(P_0)Where G(p_0)=[G_(ij)(p_0)],ij=1,2,3,4, which is a given nonsingular function matrix on ∑ and (?)(P_0)=(g_1,g_2,g_3,g_4) is a given function vector and they are satisfying the H (Hlder) condition on ∑. By...

To find the sectionally holomorphic veclor ■(P)≡(φ_0,φ_1,φ~2,φ~3):1) Which is holomorphic in D~+ and D~-, i.e. satisfying the system of partial differential equations of elliptic-type of the first order in spaceand satisfying on the boundary surface ∑ the boundary condition(H)_l ■~+(P_0)=G(p_0)■~-(p_0)+■(P_0)Where G(p_0)=[G_(ij)(p_0)],ij=1,2,3,4, which is a given nonsingular function matrix on ∑ and (?)(P_0)=(g_1,g_2,g_3,g_4) is a given function vector and they are satisfying the H (Hlder) condition on ∑. By using the double integral of Cauchy typeWhere be 4×4 matrices, they are transpose of each other.γ_(PQ)=γ(P,Q)=((x-ξ)~2+(y-η)~2+(z-ζ)~2)~(1/2) be the distance of two points p(ξ,η,ζ,) and Q(x,y,z).By ■(α,β,γ) denote the outer normal of D~+ on the surface ∑ at the poinr Q. The matrix M(P,Q) is Called a Cauchy kernel matrix, the point P=Q is an isolated singular point of second order of M(P,Q).Reducing the Hilbert boundary problem in space (H)_l to the System of singulra integral equations with Cauchy kernel matrix;WhereUsing the Banach fixed point theorem to prove the existence and uniqueness theorem for the system of singuler integral equations (I)_l, then the above Hilbert boundary value problem in space (H)_l has a unique solutiou under some conditions.By means of the Schauder fixed-point theorem, which enables us to prove existence theorem for nonliean Hilbert boundary value problem in space:(H)_n G■~+(P_0)+K■~-(P_0)+λ■(P_0,■~+(P_0),■~-(P_0))=0Where G(P_0)=[G_(ij)(P_0)]i,j=1,2,3,4; K(P_0)=[K_(ij)(P_0)]i,j=1,2,3,4, which are the given nonsingular function matrices on ∑, and det|G±K|≠0, λ≠0 is a parameter, ■≡■(f_1,f_2,f_3,f_4) is a given non-linear Continuous function vector of ■~+(P_0) and■~-(P_0) and satisfying H(Hlder) condition on ∑.Supposing that also satisfies some supplementary conditions, it is shown that the non-linear Hilbert boundary value problem in space (H)_n has a uniquc solution also.

本文是研究空间的线性与非线性的Hilbert边值问题,该问题是提出的,但他只解决了常系数的情形。作者首先证得了H((?),Σ)是Banach空间,再用Banach不动点定理证得变系数的空间线性Hilbert边值问题解的存在性与唯一性。同时用Schauder不动点原理证得空间非线性Hilbert边值问题解也是存在的,然后加上适当条件便可证得解亦呈唯一的。

In this note, the well-known Bertrand-Poincare formula for changing order of integration related to singular intergrals with Cauchy kernel has been extended to some cases related to singular integrals of high order. The main results are Theorem 1 to Theorem 3, in which Theorem 1 had already been obtained in literature[5] but both its statement and its proof used here are new and simpler.

本文把关于Cauchy核奇异积分的Bertrand-Poincar换序公式推广到高阶奇异积分的情况。主要结果见定理1至3,其中定理1已见于文献,但这里的表达方式和证法均是新的且较简。

In this paper we consider a class of the higher order singular integral equation. We reduce equation (1) to the reqular singular integral equation with Cauchy Kernel, then we give the necessary and sufficient condifion of the solnbility for (1 ), discnss the number of solution of (1).

本文研究一类Hadamard主值意义下的高价奇异积分方程,给出它可解的一个充分且必要条 件,并在它可解时讨论其解的数目.

 
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