ON SOLUTION OF A KIND OF RIEMANN BOUNDARY VALUE PROBLEM WITH SQUARE ROOTS

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.

A Generalized Riemann Boundary Value Problem

The generalized Riemann boundary value problem for analytic functions is considered, where the unknown function may have branch points of the second order. Under certain assumptions, its general solution as well as the condition of solvability is obtained when the solution is required to be of finite order at infinity.

Non-Homogeneous Riemann Boundary Value Problem with Radicals

The solution of the non-homogeneous Riemann boundary value problem with radicals (1. 2) together with its condition of solvability is obtained for arbitrary positive integersp andq, which generalizes the results for the casep=q=2.

ON RIEMANN BOUNDARY VALUE PROBLEM FOR POLYANALYTIC FUNCTIONS ON THE REAL AXIS

In this article, Riemann boundary value problem with different factors for polyanalytic functions on the real axis is studied. The expression of solution and sufficient and necessary condition for solvability of the non-homogeneous Riemann boundary value problem are obtained.

RIEMANN BOUNDARY VALUE PROBLEM WITH RESPECT TO THE PERTURBATION OF BOUNDARY CURVE TO BE AN OPEN ARC

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.

RIEMANN BOUNDARY VALUE PROBLEMS FOR SOME K-REGULAR FUNCTIONS IN CLIFFORD ANALYSIS

In this paper,we study the R m（m〉0） Riemann boundary value problems for regular functions,harmonic functions and bi-harmonic functions with values in a universal clifford algebra C（Vn,n）.By using Plemelj formula,we get the solutions of R m（m〉0） Riemann boundary value problems for regular functions.Then transforming the Riemann boundary value problems for harmonic functions and bi-harmonic functions into the Riemann boundary value problems for regular functions,we obtain the solutions of R m（m〉0） Riemann boundary value problems for harmonic functions and bi-harmonic functions.

ON HOMOGENEOUS RIEMANN BOUNDARY VALUE PROBLEMS OF HIGHER DEGREE

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.

EXTENSION OF SOLUTIONS TO RIEMANN BOUNDARY VALUE PROBLEMS AND ITS APPLICATION

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.

Reconsideration on Homogeneous Quadratic Riemann Boundary Value Problem

The homogeneous quadratic riemann boundary value problem (1) with H?lder continuous coefficients for the normal case was considered by the author in 1997. But the solutions obtained there are incomplete. Here its general method of solution is obtained. Key words homogeneous quadratic Riemann boundary value problem - ordinary and special nodes - index - sectionally holomorphic function CLC number O 175.5 Foundation item: Supported by the National Natural Science Foundation of China (19871064)Biography: Lu Jian-ke (1922-), male, Professor, research direction: complex analysis and its applications.

RIEMANN BOUNDARY VALUE PROBLEMS WITH GIVEN PRINCIPAL PART

In this article, the authors discuss the Riemann boundary value problems with given principal part. First, authors consider a special case and give a classification of the solution class Rn by the way. And then, they consider the general case. The solvable conditions for this problem and its solutions is obtained when it is solvable.

The Solution of A Compound Periodic Boundary Problem

We have studied the compound periodic boundary problem in the upper halfplane above the real axis. Under proper conditions, we obtain a periodic and sectionallyholo-morphic function in the upper half plane. In addition, we have also solved the compoundboundary problem with discontinuities of the first kind of the coefficients in the Hilbertcondition.

New Formulation for Arbitrary Cracks Problem and Its Stress Intensity Factor of Plane Elasticity

Aim The general arbitrary cracked problem in an elastic plane was discussed. Methods For the purpose of acquiring the solution of the problem, a new formulation on the problem was proposed. Compared with the classical plane elastic crack model, only the known conditions were revised in the new formulation, which are greatly convenient to solve the problem, and no other new condition was given. Results and Conclusion The general exact analytic solution is given here based on the formulation though the problem is very complicated. Furthermore, the stress intensity factors K Ⅰ, K Ⅱ of the problem are also given.

Riemann boundary value problems and reflection of shock for the Chaplygin gas

In this paper,we study two-dimensional Riemann boundary value problems of Euler system for the isentropic and irrotational Chaplygin gas with initial data being two constant states given in two sectors respectively,where one sector is a quadrant and the other one has an acute vertex angle.We prove that the Riemann boundary value problem admits a global self-similar solution,if either the initial states are close,or the smaller sector is also near a quadrant.Our result can be applied to solving the problem of shock reflection by a ramp.

A Class of Inverse Boundary Value Problems for (λ,1) Bi-Analytic Functions

In this paper,a class of inverse boundary value problems for(λ,1)bi-analytic functions is given.Using the method of Riemann boundary value problem for analytic functions,the conditions of solvability and the expression of the solutions for the inverse problems are obtained.

ON THE METHOD OF SOLUTION FOR A KIND OFNONLINEAR SINGULAR INTEGRAL EQUATION

The solutions of the nonlinear singular integral equation , t 6 L, are considered, where L is a closed contour in the complex plane, b ≠ 0 is a constant and f(t) is a polynomial. It is an extension of the results obtained in [1] when f(t) is a constant. Certain special cases are illustrated.

CONVOLUTION EQUATIONS WITH REFLECTION AND TRANSLATION SHIFT

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.

The Method of Solutions for some Kinds of Singular Integral Equations of Convolution Type with Both Reflection and Translation Shift

In this paper,some kinds of singular integral equations of convolution type with reflection and translation shift are discussed and they are turned into Riemann boundary value problems with both discontinuous coefficients and reflection by using the Fourier transform.In spite of the classical method for solution,we are to give another method,therefore the general solution and condition of solvability are obtained in class{0}.

On a Class of Two Dimensional Singular Integral Equations

We mainly consider a class of two dimensional normal type singular integral equations, the solutions as well as the conditions of solvability of which are obtained .The methods used consist of transferring them to several one dimensional Riemann boundary value problems, and then solving the latter.

Stability of a Kind of Welding Problem under Different Materials with Same Shearing Modulus

This paper discusses the stability of the welding problems under different materials with same shearing modulus. Using the stability of Cauchy type integral while the smooth perturbation for the integral curve and Sobolev perturbation for the kernel density happening, the stability of complex stress functions are studied and errors of stress and displacement are given.

Characteristic Singular Integral Equations with Solutions Having Singularities of Higher Order on the Real Axis

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.