Solution of the Riemann boundary value problem with square roots (1.1) for analytic functions proposed in [1] is reconsidered, which was solved under certain assumptions on the branch points appeared. Here the work is...Solution of the Riemann boundary value problem with square roots (1.1) for analytic functions proposed in [1] is reconsidered, which was solved under certain assumptions on the branch points appeared. Here the work is continued without these assumptions and the problem is solved in the general case.展开更多
In this paper,singular integral equations with upper and lower translations arediscussed and the equivalence for solving them in and are shown.Equations with asingle pair of upper and lower translations are studied ...In this paper,singular integral equations with upper and lower translations arediscussed and the equivalence for solving them in and are shown.Equations with asingle pair of upper and lower translations are studied in detail.Their solutions as wellas the conditions of solvability are obtained.The method used consists of transferringthem to boundary value problems of analytic functions in upper and lower half-planesand then solving the latter.展开更多
The Hilbert boundary value problem Re{λ（t） p√ψ＋（t）} = c（t）, t∈L of normal type with Holder continuous coefficients is discussed, where L is the unit circle ｜t｜ = 1,p ≥2 is any definite integer,ψ^＋（t）...The Hilbert boundary value problem Re{λ（t） p√ψ＋（t）} = c（t）, t∈L of normal type with Holder continuous coefficients is discussed, where L is the unit circle ｜t｜ = 1,p ≥2 is any definite integer,ψ^＋（t） is the boundary value of the unknown function ψ（z） holomorphic in ｜z｜ 〈 1 with single-valued continuous p√ψ＋（t） on L.展开更多
In this paper, solutions of Riemann boundary value problems with nodes are extended to the case where they may have singularties of high order at the nodes. Moreover, further extension is discussed when the free term ...In this paper, solutions of Riemann boundary value problems with nodes are extended to the case where they may have singularties of high order at the nodes. Moreover, further extension is discussed when the free term of the problem involved also possesses singularities at the nodes. As an application, certain singular integral equation is discussed.展开更多
In this paper, four kinds of integral equations of convolution type are solved, in which the reflection occurs, that is, besides the unknown f(t),f(-t) is also appeared. Moreover, it is mentioned that the methods or s...In this paper, four kinds of integral equations of convolution type are solved, in which the reflection occurs, that is, besides the unknown f(t),f(-t) is also appeared. Moreover, it is mentioned that the methods or solution for two of them are still effective when translation shifts, i.e., f(t+lambda(j)) or/and f(-t-mu(j)), occur in addition.展开更多
General solution for homogeneous Riemann problems of higher degree is considered. By introducing the concept of loop as well as cross-point, the problem is solved in detail for the quadratic case. The cubic and the qu...General solution for homogeneous Riemann problems of higher degree is considered. By introducing the concept of loop as well as cross-point, the problem is solved in detail for the quadratic case. The cubic and the quartic ones are also analysed.展开更多
The mathematical problem of an infinite elastic plane consisting of three different media with an arbitrary number of cracks is considered. It is reduced to singular integral equations along the interfaces and the cra...The mathematical problem of an infinite elastic plane consisting of three different media with an arbitrary number of cracks is considered. It is reduced to singular integral equations along the interfaces and the cracks by a constructive method. Those along the interfaces are further reduced to Fredholm ones.展开更多
基金Project supported by NNSF of China (No.19871064)
文摘Solution of the Riemann boundary value problem with square roots (1.1) for analytic functions proposed in [1] is reconsidered, which was solved under certain assumptions on the branch points appeared. Here the work is continued without these assumptions and the problem is solved in the general case.
基金Project Supported by the Natural Science Funds of National Committee of Science and Technology.
文摘In this paper,singular integral equations with upper and lower translations arediscussed and the equivalence for solving them in and are shown.Equations with asingle pair of upper and lower translations are studied in detail.Their solutions as wellas the conditions of solvability are obtained.The method used consists of transferringthem to boundary value problems of analytic functions in upper and lower half-planesand then solving the latter.
文摘The Hilbert boundary value problem Re{λ（t） p√ψ＋（t）} = c（t）, t∈L of normal type with Holder continuous coefficients is discussed, where L is the unit circle ｜t｜ = 1,p ≥2 is any definite integer,ψ^＋（t） is the boundary value of the unknown function ψ（z） holomorphic in ｜z｜ 〈 1 with single-valued continuous p√ψ＋（t） on L.
文摘In this paper, solutions of Riemann boundary value problems with nodes are extended to the case where they may have singularties of high order at the nodes. Moreover, further extension is discussed when the free term of the problem involved also possesses singularities at the nodes. As an application, certain singular integral equation is discussed.
文摘In this paper, four kinds of integral equations of convolution type are solved, in which the reflection occurs, that is, besides the unknown f(t),f(-t) is also appeared. Moreover, it is mentioned that the methods or solution for two of them are still effective when translation shifts, i.e., f(t+lambda(j)) or/and f(-t-mu(j)), occur in addition.
文摘General solution for homogeneous Riemann problems of higher degree is considered. By introducing the concept of loop as well as cross-point, the problem is solved in detail for the quadratic case. The cubic and the quartic ones are also analysed.
基金Project supported by the Science Fund of the Chinese Academy of Sciences
文摘The mathematical problem of an infinite elastic plane consisting of three different media with an arbitrary number of cracks is considered. It is reduced to singular integral equations along the interfaces and the cracks by a constructive method. Those along the interfaces are further reduced to Fredholm ones.
