UNIQUENESS AND VALUE DISTRIBUTION ON DIFFERENCE POLYNOMIALS OF MEROMORPHIC FUNCTIONS

In this paper, we study the value distribution question of certain difference polynomials of meromorphic functions, and investigate the uniqueness questions of meromorphic functions whose certain difference polynomials share a small functions. The results in this paper improve and extend the corresponding results in Zhang [16] and Chen [1].     

Some remarks on the genericity of unique range sets for meromorphic functions

In this paper we relate the study of unique range sets for meromorphic functions (URSM) with the hyperbolic hypersurfaces and give some remarks on the genericity of unique range sets for meromorphic functions.     

Hyperbolic metric and normal family

In this paper, we study the normality of the family of meromorphic functions from the viewpoint of hyperbolic metric. Then, a new sufficient and necessary condition is obtained, which can determine a given family of meromorphic functions is normal or not.     

Expression of meromorphic solutions of systems of algebraic differential equations with exponential coefficients

Using the Nevanlinna theory of the value distribution of meromorphic functions and theory of differential algebra, we investigate the problem of the forms of meromorphic solutions of some specific systems of generalized higher order algebraic differential equations with exponential coefficients and obtain some results.     

The Expression of Slow-growing Meromorphic Functions Sharing One Value CM with Their Derivatives

In this paper, we study the relations between meromorphic functions and their derivatives with one shared values, and obtain a concrete expression of meromorphic functions of zero order that share one value CM with their derivatives by a new method. Our main result is the supplementary of a related result due to Li and Yi(Li X M, Yi H X. Uniqueness of meromorphic functions sharing a meromorphic function of a small order with their derivatives. Ann. Polon. Math., 2010, 98(3):201–219).     

用S\v{a}l\v{a}gean算子定义的某些新多叶亚纯函数类的优化性质

In the present paper, we investigate the majorization property for certain new class of multivalent meromorphic analytic functions defined by Salagean operator. Moreover, we point out some new and interesting applications of our main result to the other classes of multivalent meromorphic functions.     

二阶代数微分方程超越亚纯解

Using Nevanlinna theory of the value distribution of meromorphic functions,we discuss some properties of the transcendental meromorphic solutions of second-order algebraic differential equations,and generalize some results of some authors.     

Majorization Properties for Certain New Classes of Multivalent Meromorphic Functions Defined by Slgean Operator

In the present paper, we investigate the majorization property for certain new class of multivalent meromorphic analytic functions defined by Slgean operator. Moreover,we point out some new and interesting applications of our main result to the other classes of multivalent meromorphic functions.     

Complex and p-Adic Meromorphic Functions f′P′( f ),g′P′(g) Sharing a Small Function

Let K be a complete algebraically closed p-adic field of characteristic zero.We apply results in algebraic geometry and a new Nevanlinna theorem for p-adic meromorphic functions in order to prove results of uniqueness in value sharing problems, both on K and on C. Let P be a polynomial of uniqueness for meromorphic functions in K or C or in an open disk. Let f, g be two transcendental meromorphic functions in the whole field K or in C or meromorphic functions in an open disk of K that are not quotients of bounded analytic functions. We show that if f′P′( f) and g′P′(g) share a small function α counting multiplicity, then f = g, provided that the multiplicity order of zeros of P′satisfy certain inequalities. A breakthrough in this paper consists of replacing inequalities n ≥ k+2 or n ≥ k+3 used in previous papers by Hypothesis(G). In the p-adic context, another consists of giving a lower bound for a sum of q counting functions of zeros with(q-1) times the characteristic function of the considered meromorphic function.     

MEROMORPHIC FUNCTIONS WITH BOUNDED BOUNDARY ROTATION

In this article, we generalize the class of meromorphic functions with bounded boundary rotation and related classes. Characterizations and some properties of these classes of functions are given.     

Normal criteria on the family of meromorphic functions with shared set

In this paper, we investigate the general normality criteria for a family of meromorphic functions using a geometric method. We obtain the necessary and sufficient conditions used for determining the normality of a family of meromorphic functions and some normal criteria on the family of meromorphic functions with shared set by using the fundamental theorem of a covering surface.     

The uniqueness of meromorphic functions concerning small functions

We prove that the Nevanlinna five-point-theorem on the uniqueness of meromorphic functions is valid for five small meromorphic functions.     

On the behaviour of the successive derivatives of meromorphic functions on the final set

We study the behaviour of the sequence of successive derivatives of meromorphic functions at points of the so-called final set. We prove that, whereas in many cases this sequence tends to ∞, for a special class of meromorphic functions, it may have extremely wild behaviour. We also prove a connection between the derivatives of meromorphic functions from this class and so-called Dirichlet sets.     

与其导数具有分担值的亚纯函数唯一性

为进一步丰富亚纯函数唯一性理论,寻求更佳的唯一性条件,利用亚纯函数Nevanlinna理论更精确地估计亚纯函数的n重值点的计数函数,得到两个亚纯函数与其导数具有某些分担值时的唯一性定理,推广和改进了相关文献的相关结果.     

亚纯函数结合导数的辐角分布

本文研究了亚纯函数结合导数的辐角分布. 利用覆盖曲面的方法, 获得了平面上一类零级亚纯函数结合其导数的奇异方向的存在性, 推广了杨乐等关于有限正级亚纯函数的相关结果.     

Shared Values of Certain Nonlinear Differential Polynomials of Meromorphic Functions

In this paper,by using the idea of truncated counting functions of meromorphic functions,we deal with the problem of uniqueness of the meromorphic functions whose certain nonlinear differential polynomials share one finite nonzero value.     

涉及零点重数的亚纯函数的值分布

本文研究涉及零点重数的亚纯函数的值分布，证明了几个一般的模分布定理及相应的亚纯函数族的正规定则．     

一类亚纯函数的正规定则

该文研究了一类亚纯函数的一般性的正规定则.其结果推广了以前与之相关的一系列结果.     

Leafwise Brownian Motions and Some Function Theoretic Properties of Laminations

We discuss the value distribution of Borel measurable functions which are subharmonic or meromorphic along leaves on laminations. They are called leafwise subharmonic functions or meromorphic functions respectively. We consider cases that each leaf is a negatively curved Riemannian manifold or Kähler manifold. We first consider the case when leaves are Riemannian with a harmonic measure in L.Garnett sense. We show some Liouville type theorem holds for leafwise subharmonic functions in this case. In the case of laminations whose leaves are Kähler manifolds with some curvature condition we consider the value distribution of leafwise meromorphic functions. If a lamination has an ergodic harmonic measure, a variant of defect relation in Nevanlinna theory is obtained for almost all leaves. It gives a bound of the number of omitted points by those functions. Consequently we have a Picard type theorem for leafwise meromorphic functions.     

亚纯函数族的几个正规定则

研究了亚纯函数族的正规族问题.利用Zalcman引理的方法,获得了亚纯函数族的几个正规定则.并改进了相关文献的结论.