In this article,the authors discussed the boundary behavior for the Cauchy- type integrals with values in a Clifford algebra,obtained some Sochocki–Plemelj formulae and Privalov–Muskhelishvili theorems for the Cauch...In this article,the authors discussed the boundary behavior for the Cauchy- type integrals with values in a Clifford algebra,obtained some Sochocki–Plemelj formulae and Privalov–Muskhelishvili theorems for the Cauchy-type integral taken over a smooth surface by rather simple method.展开更多
First, we give a module estimation of the singular integral with a differential element. Then by proving the existences of Cauchy principal value we obtain the transformation formula of the Cauchy-type singular integr...First, we give a module estimation of the singular integral with a differential element. Then by proving the existences of Cauchy principal value we obtain the transformation formula of the Cauchy-type singular integrals with a parameter.展开更多
On the basis of introducing the modified Cauchy kernel, we discuss the Hoelder continuity of the Cauchy-type singular integral operator on unbounded domains for regular functions by dividing into the following three c...On the basis of introducing the modified Cauchy kernel, we discuss the Hoelder continuity of the Cauchy-type singular integral operator on unbounded domains for regular functions by dividing into the following three cases： two points are on the boundary of region; one point is on the boundary and another point is in the interior（or exterior） of the region; two points are in the interior （or exterior） of the region.展开更多
In this work, we study existence theorem of the initial value problem for the system of fractional differential equations where Dα denotes standard Riemann-Liouville fractional derivative, 0 and A ?is a square matrix...In this work, we study existence theorem of the initial value problem for the system of fractional differential equations where Dα denotes standard Riemann-Liouville fractional derivative, 0 and A ?is a square matrix. At the same time, power-type estimate for them has been given.展开更多
In this paper the writer uses Muskhelishvili single-layer potential function solution and single crack solution for the torsion problem of a circular cylinder to discuss the torsion problem of a composite cylinder wit...In this paper the writer uses Muskhelishvili single-layer potential function solution and single crack solution for the torsion problem of a circular cylinder to discuss the torsion problem of a composite cylinder with an internal crack, and the problem is reduced to -a set of mixed-type integral equation with generalized Cauchy-kernel. Then, by using the integration formula of Gauss-Jacobi, the numerical method is established and several numerical examples are calculated. The torsional rigidity and the stress intensity factors are obtained. The results of these examples fit the results obtained by the previous papers better.展开更多
In this paper, we study Riemann boundary value problems on the Curve of Parabola. We characterized the functions which are intergrable on the Curve of Parabola. We also study the asymptotic behaviors of Cauchy-type in...In this paper, we study Riemann boundary value problems on the Curve of Parabola. We characterized the functions which are intergrable on the Curve of Parabola. We also study the asymptotic behaviors of Cauchy-type integral and Cauchy principal value integral on the Curve of Parabola at infinity. At the end, we discuss the Riemann boundary value problems for sectionally holomorphic functions with the Curve of Parabola as their jump curve and obtain the explicit form.展开更多
In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zer...In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zero-points distribution of the solutions and separate the single valued analytic branch of the solutions with square roots,then convert the problem to a Riemann boundary value problem in variable exponent Lebesgue spaces and discuss the singularity of solutions at individual zeros belonging to curve.We consider two types of cases those where the coefficient is Hölder and those where it is piecewise Hölder.Then we solve the Hilbert boundary value problem with square roots in variable exponent Lebesgue spaces.By discussing the distribution of the odd-order zero-points for solutions and the method of symmetric extension,we convert the Hilbert problem to a Riemann boundary value problem.The equivalence of the transformation is discussed.Finally,we get the solvable conditions and the direct expressions of the solutions in variable exponent Lebesgue spaces.展开更多
基金Project supported by NNSF of China(10471107)RFDP of Higher Eduction of China(20060486001)
文摘In this article,the authors discussed the boundary behavior for the Cauchy- type integrals with values in a Clifford algebra,obtained some Sochocki–Plemelj formulae and Privalov–Muskhelishvili theorems for the Cauchy-type integral taken over a smooth surface by rather simple method.
基金Supported by the National Natural Science Foundation of China (Grant No. 10801043)the Natural Science Foundation of Hebei Province (Grant No. A2010000346)the Foundation of Hebei University of Science and Technology (Grant No. QD201028)
文摘First, we give a module estimation of the singular integral with a differential element. Then by proving the existences of Cauchy principal value we obtain the transformation formula of the Cauchy-type singular integrals with a parameter.
基金the National Natural Science Foundation of China(Grant Nos.1140116211301136)the ScienceFoundation of Hebei Province(Grant No.A2014208158)
文摘On the basis of introducing the modified Cauchy kernel, we discuss the Hoelder continuity of the Cauchy-type singular integral operator on unbounded domains for regular functions by dividing into the following three cases： two points are on the boundary of region; one point is on the boundary and another point is in the interior（or exterior） of the region; two points are in the interior （or exterior） of the region.
文摘In this work, we study existence theorem of the initial value problem for the system of fractional differential equations where Dα denotes standard Riemann-Liouville fractional derivative, 0 and A ?is a square matrix. At the same time, power-type estimate for them has been given.
基金P.H.D.Foundation of the State Education Commision of China
文摘In this paper the writer uses Muskhelishvili single-layer potential function solution and single crack solution for the torsion problem of a circular cylinder to discuss the torsion problem of a composite cylinder with an internal crack, and the problem is reduced to -a set of mixed-type integral equation with generalized Cauchy-kernel. Then, by using the integration formula of Gauss-Jacobi, the numerical method is established and several numerical examples are calculated. The torsional rigidity and the stress intensity factors are obtained. The results of these examples fit the results obtained by the previous papers better.
文摘In this paper, we study Riemann boundary value problems on the Curve of Parabola. We characterized the functions which are intergrable on the Curve of Parabola. We also study the asymptotic behaviors of Cauchy-type integral and Cauchy principal value integral on the Curve of Parabola at infinity. At the end, we discuss the Riemann boundary value problems for sectionally holomorphic functions with the Curve of Parabola as their jump curve and obtain the explicit form.
基金supported by the National Natural Science Foundation of China(11601525)the Natural Science Foundation of Hunan Province(2024JJ5412),the Changsha Municipal Natural Science Foundation(kq2402193).
文摘In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zero-points distribution of the solutions and separate the single valued analytic branch of the solutions with square roots,then convert the problem to a Riemann boundary value problem in variable exponent Lebesgue spaces and discuss the singularity of solutions at individual zeros belonging to curve.We consider two types of cases those where the coefficient is Hölder and those where it is piecewise Hölder.Then we solve the Hilbert boundary value problem with square roots in variable exponent Lebesgue spaces.By discussing the distribution of the odd-order zero-points for solutions and the method of symmetric extension,we convert the Hilbert problem to a Riemann boundary value problem.The equivalence of the transformation is discussed.Finally,we get the solvable conditions and the direct expressions of the solutions in variable exponent Lebesgue spaces.
