Algebraic values of meromorphic functions on Riemann surfaces

We extend the Schneider-Lang theorem concerning algebraic values of meromorphic functions on the complex plane to meromorphic functions on punctured Riemann surfaces by using Jensen's formula for Riemann surfaces.     

Meromorphic functions of infinite order in the angular domain

We investigate the value distribution of meromorphic functions in the angular domain. In particular, we show a close relationship between radially distributed values and Borel directions of transcendental meromorphic functions of infinite order in some angular domains.     

关于零级亚纯函数的Nevanlinna方向与Borel方向

本文研究了零级亚纯函数Borel方向与Nevanlinna方向的关系.应用Ahlfors覆盖曲面的几何方法,获得了部分零级亚纯函数关于型函数的.Borel方向一定是Nevanlinna方向,而这一结果至今未见有文献研究.     

Meromorphic Functions on a Riemann Surface to a Locally Semi-convex Space

In this article, vector-valued holomorphic and meromorphic functions on a Riemann surface to a complete Hausdorff locally semi-convex space are discussed. By introducing the concepts of vector-valued holomorphic and meromorphic differential forms, Cauchy's theorem and the Residue theorem of a vector-valued differential form on a Riemann surface are proved. Using the theory on the operator and the theory of a cohomology of a sheaf, we give a proof of the Mittag-Leffler theorem for vector-valued meromorphic functions on a non-compact Riemann surface to a complete Hausdorff locally semi-convex space.     

亚纯函数的 Borel 方向与 Tsuji 特征函数

Tsuji特征函数是研究亚纯函数值分布的一个工具之一.本文利用Tsuji特征函数研究亚纯函数的辐角分布,获得了一个刻画亚纯函数Borel方向的充要条件.     

On the Number of Omitted Values by a Meromorphic Function of Finite Energy and Heat Diffusions

We give a bound of the number of omitted values by a meromorphic function of finite energy on parabolic manifolds in terms of Ricci curvature and the energy of the functions. An analogy of Nevanlinna’s theorems based on heat diffusions is used. We also show that meromorphic functions whose energy satisfies some growth condition on algebraic varieties can omit at most two points as a corollary to our main theorems.     

Representations of Meromorphic Functions in Terms of Laurent Expansions and Partial Boundary Values

For any analytic function f on a Riemann surface S with an isolated singularity, we give a "good" formula representing f on a large domain containing any given point on which f is regular in terms of the coefficients of Laurent's expansion around any fixed isolated singular point using a conformal mapping of a doubly-connected domain. Representations of meromorphic functions in terms of partial boundary values will also be referred, clearly.     

亚纯函数族的一个正规定则

本文研究了涉及一类微分多项式的亚纯函数族的正规性问题.利用Zalcman-Pang的方法,得到一个正规定则,推广了2011年袁文俊等得到的结果.     

Two problems in the value distribution theory

This paper includes two parts. In the first part, we deal with the relations between the orders, the lower orders and the number of Julia directions of entire functions. In the second part, we deal with the existence of the zeros of a class of meromorphic functions. This class of meromorphic functions has an interesting physical background.     

On a classification of meromorphic functions defined in the finite plane

We consider a subclass of meromorphic functions in the finite plane ¦z¦ < ∞, which generalizes Yosida's subclass of functions of the first category. We prove necessary and sufficient conditions for a function to belong to this subclass.     

SOME APPLICATIONS OF BOREL TECHNIQUE IN PARTIAL DIFFERENTIAL EQUATIONS

In this work Borel's technique is applied to analyzing the solvability of partial differetialequations.It is proved that if P is analytic-hypoelliptic,f is C~∞,then the problem for Pu=f with any number of conditions on a fixed point is ill-posed.Besides,some other resultson the flat solution to Laplace equation and wave equation are obtained.     

Asymptotic Expansions for Eigenvalues of the Lamé System in the Presence of Small Inclusions

We derive a complete asymptotic expansion for eigenvalues of the Lamé system of the linear elasticity in domains with small inclusions in three dimensions. By an integral equation formulation of the solutions to the harmonic oscillatory linear elastic equation, we reduce this problem to the study of the characteristic values of integral operators in the complex planes. Generalized Rouché's theorem and other techniques from the theory of meromorphic operator-valued functions are combined with asymptotic analysis of integral kernels to obtain full asymptotic expansions for eigenvalues.     

一类非线性时滞微分方程的整函数解

本文研究一类非线性时滞微分方程整函数解的存在性和增长性. 运用Cartan第二基本定理和亚纯函数的Nevanlinna理论, 我们得到超级小于1的整函数解的精确形式.     

Meromorphic functions sharing four small functions on 2CM + 2IM

In this paper, we prove a result that if two meromorphic functions share two small functions CM^* and two other small functions IM^*, then the two meromorphic functions share those four distinct small functions CM^*, and give more detailed results. Which generalizes G. G. Gundersens 2CM+2IM Theorem from sharing values to sharing small functions in detailed form.Received: 5 November 2002     

Meromorphic functions

The author surveys meromorphic functions, with primary emphasis on the distribution of values; the superposition and iteration of meromorphic functions are reviewed, along with meromorphic solutions of functional, differential, and difference equations. The survey covers the period from 1953 through 1971.Translated from Itogi Nauki i Tekhniki (Matematicheskii Analiz), Vol. 10, pp. 5–97, 1973.     

关于具有四个分担值的亚纯函数的唯一性

对具有四个分担值的亚纯函数的唯一性进行了研究,得到：如果两个非常数的亚纯函数具有四个判别的IM分担值,那么要么这两个函数CM分担这四个值,要么这两个函数的这些值的密指量（计数函数）满足不一等式。     

亚纯函数的正规定则与奇异方向

本文讨论了亚纯函数的正规定则与Ｊｕｌｉａ型方向间的联系．     

拟正规与Hayman 选择

本文证明了亚纯函数族的一个拟正规定则, 推广了Xu-Fang, Chang 与Nevo-Pang-Zalcman 的相应结果; 并应用此拟正规定则得到了一个值分布结果, 推广与改进了著名的Hayman 选择, 以及Wang-Fang, Chang 和Nevo-Pang-Zalcman 的相关结论.     

Normality and boundary behaviour of arbitrary and meromorphic functions along simple curves and applications

In this paper, we establish some theorems giving necessary and sufficient conditions for an arbitrary function defined in the unit disc of the complex plane to have boundary values along classes of an equivalence relation over simple curves. Our results generalize the well-known theorems on asymptotic and angular boundary behaviours of meromorphic functions (Lindelölf-, Lehto–Virtanen- and Seidel–Walsh-type theorems). The obtained results are applied to the study of boundary behaviour of meromorphic functions along curves using P-sequences, as well as in the proof of the uniqueness theorem similar to ?aginjan’s one. The constructed examples of functions show that the results cannot be improved.     

关于亚纯函数据有三个公共值以及它们的导函数据有一个公共值的问题

这篇论文研究的是亚纯函数的唯一性。这篇论文的主要结论是：如果两个非常数亚纯函数ｆ和ｇ有三个ＣＭ公共值或四个ＩＭ公共值,并且ｆ’和ｇ’以零为ＩＭ公共值,则ｆ和ｇｒＭｏｂｉｕｓ变换。其中一个结论是Ｋ．Ｔｏｈｇｅ有一个结果的改进,而且我们采用了与Ｋ．Ｔｏｈｇｅ不同的方法。『