F_(-m)-流产生的WKI尖孤子方程族解的表示

本文将WKI尖孤子方程族的Lax表示及其共轭部分非线性化为复空间中的F_m-流,进而在一类复的辛变换之下,证实该系统恰为实的辛空间的Liouville意义下的完全可积系,因此由可换流的对合解给出复的尖孤子系统解的表示.     

复Finsler流形上的Koppelman-Leray-Norguet公式

利用不变积分核(Berndtsson核),复Finsler度量和联系于Chern-Finsler联络的非线性联络,研究复Finsler流形上具有逐块光滑C~((1))边界的有界域上(p,q)型微分形式的积分表示,得到了(p,q)型微分形式的Koppelman-Leray-Norguet公式和■-方程的解．作为应用,利用复Finsler度量和联系于Chern-Finsler联络的非线性联络,给出了Stein流形上具有逐块光滑C~((1))边界的有界域上(p,q)型微分形式的Koppelman- Leray-Norguet公式以及■-方程的解,并且得到了Stein流形上实非退化强拟凸多面体上(p,q)型微分形式的积分表示式和■-方程的解．     

六类典型的非线性常微分方程的亚纯解(Ⅰ)

本文主要讨论非线性的复常微分方程的亚纯解的因子分解性质,其中R(z,y)表示变量为z和y的有理函数。     

复Finsler流形上(p,q)型微分形式的积分公式

利用Demailly和Laurent-Thiebaut不变积分核,复Finsler度量和联系于Chern-Finsler联络的非线性联络来研究复Finsler流形上的积分表示理论,得到了Koppelman和Koppelman-Leray公式, 并给出了 ∂-方程的解.     

复Finsler流形上的Koppelman-Leray公式

利用不变积分核(Berndtsson核)、复Finsler度量和联系于Chern-Finsler联络的非线性联络来研究复Finsler流形上的积分表示理论,得到了Koppelman公式和Koppelman-Leray公式,并给出了∂-方程的解.     

一类非线性二维奇异积分方程

本文研究复平面单位圆域内一类非线性二维奇异积分方程的可解性。文中应用泛函分析方法,在某些假设条件下,我们得到了此类非线性方程可解的几个充分条件,同时给出方程的解的表示式。     

单级零点较少的亚纯函数的一个界囿不等式

本文证明了:若.f(z)为复平面上的非线性亚纯函数,满足N1(r,1/f)=S(r,f),则对任何非零复数c,成立T(r,f)<11N(r,f)+11N(r,1/f'-c)+S(r,f).这里N1(r,1/f)表示f(z)的单级零点的计数函数.     

一类新的酉不变度量

<正>1引言和预备知识本文使用下了符号:Cmxn表示mxn复矩阵的集合.Crmxn表示Cmxn中秩为r的复矩阵的集合.     

关于两个矩阵乘积的特征值与奇异值的最佳估计

用A表示复矩阵A的共轭转置矩阵。用λ_i(A)表示n阶复矩阵A的特征值,i=1,…,n对于n阶Hermite矩阵A,在没有特别指出的情况下,本文均约定A的n个(实)特征值按降     

一类多个未知函数的二阶非线性椭圆型方程组于多连通区域上的非线性边值问题

§1.问题的提法本文研究形如下的一类多个未知函数的二阶非线性椭圆型复方程组     

二阶复椭圆Riemann—Hilbert边值问题

讨论了一般二阶非线性椭圆复方程的Riemann-Hilbert边值问题,首先给出Riemann-Hilbert问题及其适应性的概念,其次给出改进后的边值问题解的表述并证明了它的可解性,最后导出原Rremann-Hilbert边值问题的可解条件。     

Connection between holomorphic vector bundles and cohomology on a Riemann surface and conjugation boundary value problems

This paper studies interconnections between holomorphic vector bundles on compact Riemann surfaces and the solution of the homogeneous conjugation boundary value problem for analytic functions on the one hand, and cohomology and the solution of the inhomogeneous problem on the other. We establish that constructing the general solution to the homogeneous problem with arbitrary coefficients in the boundary conditions is equivalent to classifying holomorphic vector bundles. Solving the inhomogeneous problem is equivalent to checking the solvability of 1-cocycles with coefficients in the sheaf of sections of a bundle; in particular, the solvability conditions in the inhomogeneous problem determine obstructions to the solvability of 1-cocycles, i.e. the first cohomology group. Using this connection, we can apply the methods of boundary value problems to vector bundles. The results enable us to elucidate the role of boundary value problems in the general theory of Riemann surfaces.     

关于实轴上多解析函数Riemann边值问题的可解性

本文研究了实轴上具有不同因子的多解析函数的Riemann边值问题的可解性．利用所谓的转化法．建立了Riemann问题的可解性与其相联问题的解之间的关系。该结果推广了解析函数的相应理论。     

The Riemann Hilbert Problem for General Elliptic Complex Equations of Fourth Order

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The Discontinuous Riemann–Hilbert Problem for Elliptic Complex Equations of First Order

In this article, we first transform the general uniformly elliptic systems of first order equations with certain conditions into the complex equations, and propose the discontinuous Riemann- Hilbert problem and its modified well-posedness for the complex equations. Then we give a priori estimates of solutions of the modified discontinuous Riemann-Hilbert problem for the complex equations and verify its solvability. Finally the solvability results of the original discontinuous Riemann-Hilbert boundary value problem can be derived. The discontinuous boundary value problem possesses many applications in mechanics and physics etc.     

Non‐linear singular integral equations on a finite interval

A class of nonlinear singular integral equations of Cauchy type on a finite interval is transformed to an equivalent class of (discontinuous) boundary value problems for holomorphic functions in the complex unit disk. Using recent results on the solvability of explicit Riemann–Hilbert problems, we prove the existence of solutions to the integral equation with bounded piecewise continuous nonlinearities. We discuss the influence of parameters and additional conditions and demonstrate the approach for a free boundary problem arising from seepage near a channel. Copyright © 2001 John Wiley & Sons, Ltd.     

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–Hilbert-type Boundary Value Problems on a Half Hexagon

In this article we discuss the explicit solvability of both Schwarz boundary value problem and Riemann–Hilbert boundary value problem on a half hexagon in the complex plane. Schwarz-type and Pompeiu-type integrals are obtained. The boundary behavior of these operators is discussed.Finally, we investigate the Schwarz problem and the Riemann–Hilbert problem for inhomogeneous Cauchy–Riemann equations.     

某些类具有反射与平移移位的卷积型奇异积分方程的解法（英文）

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 Riemann problems for single‐periodic polyanalytic functions

In this article, Riemann‐type boundary‐value problem of single‐periodic polyanalytic functions has been investigated. By the decomposition of single‐periodic polyanalytic functions, the problem is transformed into n equivalent and independent Riemann boundary‐value problems of single‐periodic analytic functions, which has been discussed in details according to two growth orders of functions. Finally, we obtain the explicit expression of the solution and the conditions of solvability for Riemann problem of the single‐periodic polyanalytic functions.