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Non-Homogeneous Riemann Boundary Value Problem with Radicals 被引量:6
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作者 Lu Jian-ke School of Mathematics and Statistics,Wuhan University,Wuhan 430072, Hubei,China 《Wuhan University Journal of Natural Sciences》 EI CAS 2002年第4期379-382,共4页
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 t... 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. 展开更多
关键词 riemann boundary value problem branch points of radicals INDEX order at infinity sectionally holomorphic functions
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RIEMANN BOUNDARY VALUE PROBLEMS FOR SOME K-REGULAR FUNCTIONS IN CLIFFORD ANALYSIS 被引量:3
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作者 姜乐 杜金元 《Acta Mathematica Scientia》 SCIE CSCD 2012年第5期2029-2049,共21页
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,... 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. 展开更多
关键词 riemann boundary value problem harmonic function bi-harmonic function Plemelj formula
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Riemann Boundary Value Problem of Non-Normal Type on the Infinite Straight Line 被引量:2
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作者 Lixia Cao 《Applied Mathematics》 2013年第8期1226-1230,共5页
Various kinds of Riemann boundary value problems (BVPs) for analytic functions on closed curves or on open arc, doubly periodic Riemann BVPs, doubly quasi-periodic Riemann BVPs, and BVPs for polyanalytic functions hav... Various kinds of Riemann boundary value problems (BVPs) for analytic functions on closed curves or on open arc, doubly periodic Riemann BVPs, doubly quasi-periodic Riemann BVPs, and BVPs for polyanalytic functions have been widely investigated in [1-8]. The main ap- proach is to use the decomposition of polyanalytic functions and their generalization to transform the boundary value problems to their corresponding boundary value problems for analytic functions. Recently, inverse Riemann BVPs for generalized analytic functions or bianalytic functions have been investigated in [9-12]. In this paper, we consider a kind of Riemann BVP of non-normal type on the infinite straight line and discuss the solvable conditions and the general solution for it. 展开更多
关键词 Non-Normal Type riemann boundary value problem The INFINITE STRAIGHT Line
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THE RIEMANN-HILBERT BOUNDARY VALUE PROBLEM FOR THE MOISIL-THEODORSCO SYSTEM 被引量:8
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作者 杨丕文 《数学物理学报(A辑)》 CSCD 北大核心 2006年第B12期1057-1063,共7页
This article studies the inhomogeneous Moisil-Theodorsco system in the space R3, gives the integral expression of its solution, proves the Holder continuity of the solution. Moreover the author studies the Riemann-Hil... This article studies the inhomogeneous Moisil-Theodorsco system in the space R3, gives the integral expression of its solution, proves the Holder continuity of the solution. Moreover the author studies the Riemann-Hilbert boundary value problem for the Moisil-Theodorsco system in a cylindrical domain of R3, and gives the solvability conditions and the integral expressions of solutions. The Holder continuity of the solutions is proved. 展开更多
关键词 黎曼-希尔伯特边界值问题 Moisil-Theodorsco系统 整式 算子 HOELDER连续
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Nonregular Boundary Value Problem for the Cauchy-Riemann Operator
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作者 Ibrahim Ly Sadou Tao 《Advances in Pure Mathematics》 2020年第11期623-630,共8页
The purpose of the research is to assign a formally exact elliptic complex of length two to the Cauchy-Riemann Operator. The Neumann problem for this complex in a bounded domain with smooth boundary in R<sup>2&l... The purpose of the research is to assign a formally exact elliptic complex of length two to the Cauchy-Riemann Operator. The Neumann problem for this complex in a bounded domain with smooth boundary in R<sup>2</sup> will be studied, helping therefore to solve a usual boundary value problem for the Cauchy-Riemann operator. 展开更多
关键词 Cauchy-riemann Operator boundary value problem Normal Solvability
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ON SOLUTION OF A KIND OF RIEMANN BOUNDARY VALUE PROBLEM WITH SQUARE ROOTS 被引量:19
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作者 路见可 《Acta Mathematica Scientia》 SCIE CSCD 2002年第2期145-149,共5页
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
关键词 riemann boundary value problem branch points INDEX order at infinity sectionally holomorphic functions
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A Generalized Riemann Boundary Value Problem 被引量:10
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作者 LIU Hua LU Jian 《Wuhan University Journal of Natural Sciences》 CAS 2000年第2期147-149,共3页
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 th... 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. 展开更多
关键词 riemann boundary value problem sectionally holomorphic function order at infinily INDEX
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ON RIEMANN BOUNDARY VALUE PROBLEM FOR POLYANALYTIC FUNCTIONS ON THE REAL AXIS 被引量:9
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作者 汪玉峰 杜金元 《Acta Mathematica Scientia》 SCIE CSCD 2004年第4期663-671,共9页
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 n... 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. 展开更多
关键词 Polyanalytic function riemann boundary value problem
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RIEMANN BOUNDARY VALUE PROBLEM WITH RESPECT TO THE PERTURBATION OF BOUNDARY CURVE TO BE AN OPEN ARC 被引量:4
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作者 林娟 王传荣 《Acta Mathematica Scientia》 SCIE CSCD 2009年第5期1481-1488,共8页
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
关键词 open arc riemann boundary value problem smooth perturbation STABILITY
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ON HOMOGENEOUS RIEMANN BOUNDARY VALUE PROBLEMS OF HIGHER DEGREE 被引量:2
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作者 路见可 《Acta Mathematica Scientia》 SCIE CSCD 1997年第1期12-21,共10页
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
关键词 riemann boundary value problems LOOP cross-point
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EXTENSION OF SOLUTIONS TO RIEMANN BOUNDARY VALUE PROBLEMS AND ITS APPLICATION 被引量:2
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作者 路见可 《Acta Mathematica Scientia》 SCIE CSCD 2007年第4期694-702,共9页
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
关键词 riemann boundary value problem class KN index and canonical function in class KN almost bounded almost of order k characteristic singular integral equation
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RIEMANN BOUNDARY VALUE PROBLEMS WITH GIVEN PRINCIPAL PART 被引量:2
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作者 李卫峰 杜金元 《Acta Mathematica Scientia》 SCIE CSCD 2009年第1期25-32,共8页
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 ... 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. 展开更多
关键词 riemann boundary value problems principal part riemann-Hilbert analysis for orthogonal polynomials
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Reconsideration on Homogeneous Quadratic Riemann Boundary Value Problem 被引量:2
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作者 LuJian-ke 《Wuhan University Journal of Natural Sciences》 EI CAS 2004年第1期1-5,共5页
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 gene... 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. 展开更多
关键词 homogeneous quadratic riemann boundary value problem ordinary and special nodes INDEX sectionally holomorphic function
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Jacobi-Sobolev Orthogonal Polynomialsand Spectral Methods for Elliptic Boundary Value Problems
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作者 Xuhong Yu Zhongqing Wang Huiyuan Li 《Communications on Applied Mathematics and Computation》 2019年第2期283-308,共26页
Generalized Jacobi polynomials with indexes α,β∈ R are introduced and some basic properties are established. As examples of applications,the second- and fourth-order elliptic boundary value problems with Dirichlet ... Generalized Jacobi polynomials with indexes α,β∈ R are introduced and some basic properties are established. As examples of applications,the second- and fourth-order elliptic boundary value problems with Dirichlet or Robin boundary conditions are considered,and the generalized Jacobi spectral schemes are proposed. For the diagonalization of discrete systems,the Jacobi-Sobolev orthogonal basis functions are constructed,which allow the exact solutions and the approximate solutions to be represented in the forms of infinite and truncated Jacobi series. Error estimates are obtained and numerical results are provided to illustrate the effectiveness and the spectral accuracy. 展开更多
关键词 Generalized JACOBI POLYNOMIALS Spectral method - Jacobi-Sobolev ORTHOGONAL BASIS functions ELLIPTIC boundary value problems Error analysis
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A RIEMANN-HILBERT APPROACH TO THE INITIAL-BOUNDARY PROBLEM FOR DERIVATIVE NONLINEAR SCHRDINGER EQUATION 被引量:4
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作者 徐建 范恩贵 《Acta Mathematica Scientia》 SCIE CSCD 2014年第4期973-994,共22页
We use the Fokas method to analyze the derivative nonlinear Schrodinger (DNLS) equation iqt (x, t) = -qxx (x, t)+(rq^2)x on the interval [0, L]. Assuming that the solution q(x, t) exists, we show that it ca... We use the Fokas method to analyze the derivative nonlinear Schrodinger (DNLS) equation iqt (x, t) = -qxx (x, t)+(rq^2)x on the interval [0, L]. Assuming that the solution q(x, t) exists, we show that it can be represented in terms of the solution of a matrix Riemann- Hilbert problem formulated in the plane of the complex spectral parameter ξ. This problem has explicit (x, t) dependence, and it has jumps across {ξ∈C|Imξ^4 = 0}. The relevant jump matrices are explicitely given in terms of the spectral functions {a(ξ), b(ξ)}, {A(ξ), B(ξ)}, and {A(ξ), B(ξ)}, which in turn are defined in terms of the initial data q0(x) = q(x, 0), the bound- ary data g0(t)= q(0, t), g1(t) = qx(0, t), and another boundary values f0(t) = q(L, t), f1(t) = qx(L, t). The spectral functions are not independent, but related by a compatibility condition, the so-called global relation. 展开更多
关键词 riemann-Hilbert problem DNLS equation global relation finite interval initial-boundary value problem
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Compound Boundary Value Problems for Hyperanalytic Functions 被引量:1
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作者 HE Fu-li 《Chinese Quarterly Journal of Mathematics》 CSCD 2013年第1期1-10,共10页
In this paper, the so-called Riemann-Hilbert compound boundary value problems for hyperanalytic functions are considered, include the compound value problems for simply connected regions and open arcs, we get these so... In this paper, the so-called Riemann-Hilbert compound boundary value problems for hyperanalytic functions are considered, include the compound value problems for simply connected regions and open arcs, we get these solutions. 展开更多
关键词 compound boundary value problems riemann-Hilbert boundary value problems Douglis analysis hyperanalytic function
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ON SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR THE POISSON EQUATION WITH A NONLOCAL BOUNDARY OPERATOR
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作者 B.J.KADIRKULOV M.KIRANE 《Acta Mathematica Scientia》 SCIE CSCD 2015年第5期970-980,共11页
In this work, we investigate the solvability of the boundary value problem for the Poisson equation, involving a generalized Riemann-Liouville and the Caputo derivative of fractional order in the class of smooth funct... In this work, we investigate the solvability of the boundary value problem for the Poisson equation, involving a generalized Riemann-Liouville and the Caputo derivative of fractional order in the class of smooth functions. The considered problems are generalization of the known Dirichlet and Neumann oroblems with operators of a fractional order. 展开更多
关键词 operator of fractional integration and differentiation SOLVABILITY boundary value problem riemann-Liouville operator Caputo fractional derivative Poisson equation Dirichlet and Neumann problems
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k-正则函数的非正则型Riemann边值问题 被引量:8
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作者 曾伟 杨丕文 《四川师范大学学报(自然科学版)》 CAS CSCD 北大核心 2007年第3期291-294,共4页
研究k-正则函数u(z)(即(ku)/(z-k)=0的解)的非正则型Riemann边值问题,讨论了它的可解性,并得出了可解性定理.
关键词 κ-正则函数 非正则 可解性 riemann边值问题
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K-解析函数的Riemann边值问题 被引量:3
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作者 张建元 赵书芬 韩艳 《应用数学和力学》 CSCD 北大核心 2014年第7期805-814,共10页
引入了(分片)K-解析函数和Cauchy型K-积分的概念.利用K-对称变换的方法研究了Cauchy型K-积分的某些性质,然后借助函数在曲线上的指标与这些Cauchy型K-积分的性质,得到了K-解析函数类中的Riemann边值问题的可解条件和解的表达式以及它们... 引入了(分片)K-解析函数和Cauchy型K-积分的概念.利用K-对称变换的方法研究了Cauchy型K-积分的某些性质,然后借助函数在曲线上的指标与这些Cauchy型K-积分的性质,得到了K-解析函数类中的Riemann边值问题的可解条件和解的表达式以及它们与指标之间的关系.而解析函数和共轭解析函数都是K-解析函数的特例,文中所得结果,推广了解析函数和共轭解析函数中的相应结论. 展开更多
关键词 Cauchy型K-积分 (分片)K-解析函数 K-对称变换 边界值公式 riemann 边值问题 指标
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一类Riemann-Hilbert边值逆问题 被引量:18
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作者 王明华 《纯粹数学与应用数学》 CSCD 北大核心 2006年第4期532-537,共6页
给出解析函数的一类R iem ann-H ilbert边值逆问题的数学提法,依据解析函数R iem ann-H ilbert边值问题的经典理论,讨论了此边值问题的可解性,给出了该边值问题的可解条件和解的表示式.
关键词 riemann-Hilbert边值逆问题 riemann-HILBERT边值问题 标数 可解性
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