解析开拓

The content of this course is: analytic function (the definition of analytic function, elementary functions, etc.), conformal mapping (the definition if conformal mapping, fractional linear functions, elementary mappings, etc.), complex integration (Cauchy's integral formula, Cauchy's theorem, etc.), Series (Laurent Series, singularities, local property, etc.), residues and its applications (the Residues Theorem, integration by residues, the Argument Principle, the Maximum Principle, Schwarz's Lemma, etc.), analytic continuation and harmonic functions, etc.

本课程内容主要包括：解析函数(解析函数的定义、初等函数等)、共形映射(共形映射的定义、分式线性变换及初等映射等)、复积分(Cauchy 积分公式、 Cauchy 定理等)、级数(Laurent 级数、孤立奇点、局部映射等)、留数及其应用(留数定理、利用留数计算积分、幅角原理、最大模原理、 Schwarz 引理等)、解析开拓和调和函数等内容。

In this paper,at first we transformed the nonlinear elliptic system of 2m first order equations into the complex form, then by use the results on the Riemann-Hilbert problem for nonlinear elliptic complex equation of first order, the method of continuity, the Schauder fixed-point theorem and the Leray-Schauder theorem, we proved that the modified Riemann-Hilbert boundary value problem for the complex system with some conditions is solvable.

本文先将较一般的多个未知函数的一阶椭圆型实方程组化为复方程组，然后讨论这些复方程组在某些条件下的一些边值问题的可解性。这里所考虑的方程组既包含线性的，也包含非线性的，比广义超解析函数所满足的方程组还要广，又本文主要研究较一般的Riemann-Hilbert边值问题，先给出这种边值问题解的先验估计式，然后用参数开拓法及Leray-Schauder定理证明这种边值问题的可解性结果。

The main contents of this course include: complex number and planar point set, function of complex variable, complex integral, series, residue, conformal mapping, analytic extension, harmonic function.

本课程的基本内容有：复数与平面点集、复变函数、复积分、级数、留数、保形映射、解析开拓、调和函数。

The eigenvalue problem of Dirac operator with perturbation Parameter is studied,the analyticity of perturbation parameter is discussed,and the analytic extension is done,at last,the expansion formulas of power serier about preradical expansion into perturbation parameter are got.

针对带有微扰参数的Dirac算子特征值问题，讨论了对微扰参数的解析性，并进行了解开拓，最后得到了预解核对微扰因子的幂级数展开式。

She gently rebuff ed him, but agreed that they could be friends

她婉言拒绝了，但同意作为朋友相处。

If in the penal farm, you were sure to be criticized.

要是在劳改农场，你等着挨绳子吧！