ON UNIQUENESS FOR ALGEBROID FUNCTIONS OF FINITE ORDER

Guided by Lo.Yang's method,we concern the question that how algebroid functions are determined by their multiple values and deficient values and we prove an at most3v-valued theorem for algebroid functions.The results are complemented by an example for completeness.     

THE UNIQUENESS FOR ALGEBROID FUNCTIONS OF FINITE ORDER

In this article, we discuss, by Nevanlinna theory, the influence of multiple values and deficiencies on the uniqueness problem of algebroid functions. We get several uniqueness theorems of algebroid functions which include an at most 3 v-valued theorem. These results extend the existing achievements of some scholars.     

ON NEVANLINNA DIRECTIONS OF ALGEBROID FUNCTIONS

In this paper, a notation δχ(ω) is derived from the counting function Nχ(r,w) of branch points of algebriod functions. With this notation, the authors give the definition of the Nevanlinna direction for algebriod functions and discuss its existence in certain condition. By this notation the authors also obtain the numbers of exceptional value of the Julia direction and Borel direction of algebriod functions are not more than 2 [δχ(ω)],here [x] implies an maximum integer number which does not exceed x.     

ON THE OPERATIONS OF ALGEBROID FUNCTIONS

In this article, we first investigate the operational properties of algebroid functions. Then we prove two uniqueness theorems for algebroid functions.     

关于代数体函数的微分多项式

本文证明υ值代数函数的微分多项式是一λ值（1≤λ≤υ）代数体函数,即υ值代数体函数ω=ω（z)的微分多项式p(ω）可以被如下方程确定：[ελ（z）p^λ ελ-1(z)p^λ-1 … ε0(z)]^k=0这里ε0(z),ε1(z),…,ελ（z)为整函数且无公共零点,λ和k为正整数且λk=υ。     

关于代数体函数的重值

<正> 关于亚纯函数或全纯函数的重值问题,首先为卡拉德峨多利(Caratheodory)、蒙德耳(Montel)所研究,并获得重要的结果,其后G.伐理隆(Valiron)、R.奈望利纳(Nevanlinna),以及较近熊庆来等就重值对值分布的影响进行了进一步的研究,获得新结的果.     

ON THE NEVANLINNA DIRECTION OF ALGEBROID FUNCTIONS

In this paper, we prove that for an algebroid function w(z), the singular direction arg z =φ0 , satisfying that for arbitrary ε(0 < ε < π 2 ) and any given a ∈ C, lim r → + ∞ n(r,φ0-ε,φ0 +ε,w=a)/ log r = +∞ holds with at most 2v possible exceptional values of a, is the Nevanlinna direction of w(z).     

代数体函数的性质

本文研究了亚纯函数的几个性质推广到多值的代数体函数.利用代数体函数的循环加,循环乘运算及特征的性质,证明了代数体函数的级与下级的几个性质,并研究了两个代数体函数的公共a值点的度量,且得到代数体函数的两个唯一性定理.     

ON THE SHARING VALUES OF ALGEBROID FUNCTIONS AND THEIR DERIVATIVES

In this paper,we define the shared value of an algebroid function and its derivative on its Riemann surface.By considering the relationship between the shared values and the branch points of algebroid functions and their derivatives,we obtain some uniqueness theorems of algebroid functions sharing values with their derivatives,which extend 3 IM shared values theorem of nonconstant meromorphic functions and their derivatives obtained by Mues-Steinmetz and Gundersen.     

ON ALGEBROID FUNCTIONS IN A SUBDOMAIN OF THE COMPLEX PLANE

AnalgebroidfunctioninthewholecomplexplaneCisconsideredasanaturalextensionofanalgebraicfunction.ItismeaninglesstodistinguishalgebraicfunctionsinasubdolnainofCfromalgebraicfunctionBinthewholeCsinceWpolynomialswithcomplexcoefficientsarealwsysdefinedinthewholeC.Butforordinarymeromorphicfunctions,theirdomainsofdespitioncannotgenerallyfillupthewholeC.SoitisworthwhileconsideringalgebroidfunctionsinasubdolnainofCalthoughwewillfindthattheyaresaggartoalgebroidfunctionsinCinmanyaspects.InfaCt,afewOf…     

关于p除环结构的几个定理

本文讨论了强ｐ除环的结构与赋值，并且给出了ｐ除环是广义四元数体的一个子体的充要条件。     

关于亚纯函数的唯一性问题

本文应用 Ｎｅｖａｎｌｉｎｎａ理论研究亚纯函数的重值与唯一性问题,所得结果推广了某些已知的定理,并回答了Ｃ．Ｃ．Ｙａｎｇ的一个猜测．     

关于多元复函数的正规族

研究函数族的正规性定则是复变函数论中的一个重要且有意义的工作,本文通过引进多元Ｋ－拟亚纯函数（或Ｋ－全纯函数）的定义,得到了多元Ｋ－拟亚纯函数（或Ｋ－全纯函数）族的一个正规定则,据此讨论了多元纯函数（族的若干正规性定则。     

ON THE COEFFICIENTS OF SEVERAL CLASSES OF BI-UNIVALENT FUNCTIONS

In this paper, we investigate the bounds of the coefficients of several classes of bi-univalent functions. The results presented in this paper improve of generalize the recent works of other authors.     

NORMALITY CRITERIA FOR FAMILIES OF MEROMORPHIC ALGEBROID FUNCTIONS

By using the definition of Hausdorff distance, we prove some normality criteria for families of meromorphic algebroid functions. Some examples are given to complement the theory in this article.     

NORMAL THEOREMS ON SEVERAL COMPLEX VARIABLES

Suppose that V is a memanll 8phere with unit diameter. It is an one-to-one correspondenceto the close complex plane C. In this paper, they are identified. Let V" be a Riemann sphereof m dimension.Definition 1 Suppose that A = (a1,' t a.,), B = (b1,' l b.) E V". Define sphericaldistallce between two points A, B{lA, Bl. = thet A, B / oc,lA, bol,. = the, B = co,where lAl =.Definition 2 Suppose tl1at f(z) is a homeomorphism from domain D C V to don1ainDl C V. If on the spherical di…     

关于解析函数的一个唯一性定理及其应用

<正> §1.在近代解析函数论中边界值的唯一性定理有许多的研究,其中有我们所习知著名的(?)氏唯一性定理,即:若 D 是某一可求长约当曲线Γ所范围的内域,而 f(z)是 D 内的半纯函数,如在Γ上存在某一测度大于零的集 E_z,对 E_z 任一点 z_0 上,f(z)的角形边界值为零.则必致f(z)≡0于 D 内.同时,卢洵(?)与普里瓦洛夫还指出:存在有单位圆域内非常数的解析函数,而在一个正测度的集(?)上具有等于零的射形边界值.除此之外还有一个很有用的 Koebe 氏定理.即:     

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].     

牛顿插值级数与解析函数惟一性定理

将插补基点为ｚ＝ｎ的牛顿插值级数的一些性质推广到一般的基点ｚ＝λｎ,并建立起半平面内的一条解析函数惟一性定理。     

UNIQUENESS OF DIFFERENCE POLYNOMIALS OF MEROMORPHIC FUNCTIONS

In this article, we investigate the uniqueness problems of difference polynomials of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Shibazaki. Some examples are given to show the results in this article are best possible.