A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integr...A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.展开更多
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
We transform the singular integral equations with solutions simultaneously having singularities of higher order at infinite point and at several finite points on the real axis into ones along a closed contour with sol...We transform the singular integral equations with solutions simultaneously having singularities of higher order at infinite point and at several finite points on the real axis into ones along a closed contour with solutions having singularities of higher order, and for the former obtain the extended Neother theorem of complete equation as well as the solutions and the solvable conditions of characteristic equation from the latter. The conclusions drawn by this article contain special cases discussed before.展开更多
Using integration by parts and Stokes' formula, the authors give a new definition of Hadamard principal value of higher order singular integrals with Bochner-Martinelli kernel on smooth closed orientable manifolds...Using integration by parts and Stokes' formula, the authors give a new definition of Hadamard principal value of higher order singular integrals with Bochner-Martinelli kernel on smooth closed orientable manifolds in C-n. The Plemelj formula and composite formula of higher order singular integral are obtained. Differential integral equations on smooth closed orientable manifolds are treated by using the composite formula.展开更多
Under the appropriate hypotheses subject to the unknown function and the free term, by means of our Lemma, we prove the rationality of order at x = ∞ on two sides for the characteristic singular integral equations wi...Under the appropriate hypotheses subject to the unknown function and the free term, by means of our Lemma, we prove the rationality of order at x = ∞ on two sides for the characteristic singular integral equations with solutions having singularities of higher order on the real axis X. We transform the equations into solving equivalent Riemann boundary value problems with solutions having singularities of higher order and with additional conditions on X. The solutions and the solvable conditions for the former are obtained from the latter.展开更多
In this paper, we discuss the locally topological structure for nonlinear homogeneous n-degree system with zero characteristic roots, and give a criteria by the coefficients of the polynonmials.
基金supported by the Natural Science Foundation of Fujian Province of China(S0850029,2008J0206)Innovation Foundation of Xiamen University(XDKJCX20063019),the National Science Foundation of China (10771174)
文摘A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.
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 the NNSF of China (10471107)RFDP of Higher Education of China (20060486001)
文摘We transform the singular integral equations with solutions simultaneously having singularities of higher order at infinite point and at several finite points on the real axis into ones along a closed contour with solutions having singularities of higher order, and for the former obtain the extended Neother theorem of complete equation as well as the solutions and the solvable conditions of characteristic equation from the latter. The conclusions drawn by this article contain special cases discussed before.
基金the Bilateral Science and Technology Collaboration Program of Australia 1998 the Natural Science Foundation of China (No. 1
文摘Using integration by parts and Stokes' formula, the authors give a new definition of Hadamard principal value of higher order singular integrals with Bochner-Martinelli kernel on smooth closed orientable manifolds in C-n. The Plemelj formula and composite formula of higher order singular integral are obtained. Differential integral equations on smooth closed orientable manifolds are treated by using the composite formula.
基金Supported by the National Natural Science Foundation of China (10471107)the Specialized Research Fund for the Doctoral Program of Higher Education of China (20060486001)
文摘Under the appropriate hypotheses subject to the unknown function and the free term, by means of our Lemma, we prove the rationality of order at x = ∞ on two sides for the characteristic singular integral equations with solutions having singularities of higher order on the real axis X. We transform the equations into solving equivalent Riemann boundary value problems with solutions having singularities of higher order and with additional conditions on X. The solutions and the solvable conditions for the former are obtained from the latter.
文摘In this paper, we discuss the locally topological structure for nonlinear homogeneous n-degree system with zero characteristic roots, and give a criteria by the coefficients of the polynonmials.
