In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and th...In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and the solutions for singular integral equations possess singularities of higher order, the solution and the solvable condition for characteristic equations as well as the generalized Noether theorem for complete equations are given.展开更多
By dint of the stability of Cauchy-type integral with kernel density of class H＊ for an open arc, this paper discusses the stability of the solution of Riemann boundary value problem with respect to the perturbation ...By dint of the stability of Cauchy-type integral with kernel density of class H＊ for an open arc, this paper discusses the stability of the solution of Riemann boundary value problem with respect to the perturbation of boundary curve to be an open arc.展开更多
The Riemann boundary value problem with square roots in class h0 when the jumping curve is an open arc in the complex plane is considered. It is solved by reducing it to a classical Riemann boundary value problem so t...The Riemann boundary value problem with square roots in class h0 when the jumping curve is an open arc in the complex plane is considered. It is solved by reducing it to a classical Riemann boundary value problem so that its solutions are obtained in closed form. In certain cases, some auxiliary function ω（z）is introduced. With different choices of ω（z）＇s, some interesting examples are illustrated.展开更多
After choosing weight functions suitably, we define a Banach spaceH ω μ (L) and discuss the generalized inverse of singular integral operators on an open arc. Using the generalized inverse, we obtain the solutions f...After choosing weight functions suitably, we define a Banach spaceH ω μ (L) and discuss the generalized inverse of singular integral operators on an open arc. Using the generalized inverse, we obtain the solutions for the following singular integral equation展开更多
The authors examine the relation between the perturbed Cauchy singular integral with its kernel density belong to H＊ and unperturbed one and show that the Cauchy singular integral is stable under perturbation of the ...The authors examine the relation between the perturbed Cauchy singular integral with its kernel density belong to H＊ and unperturbed one and show that the Cauchy singular integral is stable under perturbation of the curve of integration.展开更多
In this paper, we discuss the stability of general compound boundary value prob-lems combining Riemann boundary value problem for an open arc and Hilbert bound-ary value problem for a unit circle with respect to the p...In this paper, we discuss the stability of general compound boundary value prob-lems combining Riemann boundary value problem for an open arc and Hilbert bound-ary value problem for a unit circle with respect to the perturbation of boundary curve.展开更多
基金Foundation item is supported by the NNSF of China(19971064)
文摘In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and the solutions for singular integral equations possess singularities of higher order, the solution and the solvable condition for characteristic equations as well as the generalized Noether theorem for complete equations are given.
基金supported by Natural Science Foundation of China (10071016)the Natural Science Foundation of Fujian Province (2008J0187)the Science and Technology Foundation of Education Department of Fujian Province (JA08255), China
文摘By dint of the stability of Cauchy-type integral with kernel density of class H＊ for an open arc, this paper discusses the stability of the solution of Riemann boundary value problem with respect to the perturbation of boundary curve to be an open arc.
基金Supported by the National Natural Science Foundation of China (10161009)
文摘The Riemann boundary value problem with square roots in class h0 when the jumping curve is an open arc in the complex plane is considered. It is solved by reducing it to a classical Riemann boundary value problem so that its solutions are obtained in closed form. In certain cases, some auxiliary function ω（z）is introduced. With different choices of ω（z）＇s, some interesting examples are illustrated.
基金Supported by the National Natural Science Foundation of China( No.2 0 1980 6 33)
文摘After choosing weight functions suitably, we define a Banach spaceH ω μ (L) and discuss the generalized inverse of singular integral operators on an open arc. Using the generalized inverse, we obtain the solutions for the following singular integral equation
基金Supported by the Natural Science Foundation of Fujian Province（2008J0187）
文摘The authors examine the relation between the perturbed Cauchy singular integral with its kernel density belong to H＊ and unperturbed one and show that the Cauchy singular integral is stable under perturbation of the curve of integration.
基金the Natural Science Foundation of Fujian Province (2008J0187).
文摘In this paper, we discuss the stability of general compound boundary value prob-lems combining Riemann boundary value problem for an open arc and Hilbert bound-ary value problem for a unit circle with respect to the perturbation of boundary curve.
