1) transcendental meromorphic solutions
超越亚纯解
1.
In this paper, we investigate the problem of the existence of transcendental meromorphic solutions of a type of algebraic differential equation and obtain a result.
讨论了一类代数微分方程的超越亚纯解的存在性问题 ,得到了一个结果 。
2) transcendental meromorphic function
超越亚纯函数
1.
By using Nevanlinna′s theory on meromorphic function,and studing value distribution(theory of) transcendental meromorphic function,this paper obtained the following conclusion: Let f be a transcendental meromorphic function and c(≠0) be a small function of f.
运用Nevanlinna的亚纯函数理论方法,研究了超越亚纯函数的值分布理论,获得了如下的结论:设f为超越亚纯函数,c为f的不恒等于0的的小函数,则当n≥3时,fnf′-c有无穷多个零点;若附加条件f只有有限多个级≤2的零点,则对一切正整数n,fnf′-c都有无穷多个零点。
2.
The following theorem is proved: Given f is a transcendental meromorphic function, and a 0, a 1,…, a k(a k 0) are some small functions of f , Defined by D=a 0f+a 1f′+…+a kf (k) If all ω with (D) ′=0 are the small functions of f , then for every ε >0,there exists (1-ε)T(r,f)<1+1kNr,1f+1+1kNr,1D-1- Nr,1(D)′+S(r,f) This result includes Haymans and Yang Les inequality.
证明了下述定理：设ｆ是一超越亚纯函数，ａ０，ａ１，…，ａｋ为ｆ的一组小函数，且ａｋ０。
3.
let k be any positive integer and f(z) be a transcendental meromorphic function in the complex plane.
设k∈N,f(z)为复平面上的超越亚纯函数,φ(z)、ak-1(z),…,a0(z)为f(z)的小函数,且φ(z)0。
3) transcendental meromorphic functions
超越亚纯函数
1.
In this paper,the characteristic functions compared with the derivative increment of linear fraction transformation of transcendental meromorphic functions have been studied,and inferred a theorem based on Nevanlinna theory.
研究了超越亚纯函数的分式线性变换的特征函数与其导数的特征函数增长性的比较，并由Ｎｅｖａｎｌｉｎｎａ理论推导出一个定理，其主要结果为：Ｔ（ｒ，Ｆ）＜４０λλ－１ｌｏｇｅλλ－１Ｔ（λｒ，ｆ′）＋ｌｏｇ＋（λｒ）＋ｌｏｇ＋｜ｆ（０）｜＋５＋ｌｏｇ＋ａｄ＋ｌｏｇ＋ｂｄ＋ｌｏｇ２（ｃ＝０）Ｔ（ｒ，Ｆ）＜４０λλ－１ｌｏｇｅλλ－１Ｔ（λｒ，Ｆ′）＋ｌｏｇ＋（λｒ）＋ｌｏｇ＋｜Ｆ（０）｜＋５＋ｌｏｇ＋ａｄ－ｂｃｃ２＋ｌｏｇ＋ｄｃ＋ｌｏｇ２＋ｈ（ｒ）（ｃ≠０
2.
The dynamics of composite transcendental meromorphic functions is investigated in this paper,and some known results was extended to this case.
讨论了两个超越亚纯函数复合的动力学性质,推广了若干已知结果。
4) purely transcendental extension
纯超越扩张
6) meromorphic solution
亚纯解
1.
The problems on the existence of meromorphic solutions of certain second-order complex differential equations with meromorphic coefficients are discussed.
研究了一类二阶亚纯系数复微分方程的亚纯解的存在性问题,得到了几个关于存在亚纯解的结果,这些结果完善了亚纯系数的线性复微分方程理论。
2.
We obtain explicit formulae giving all the meromorphic solutions.
研究了何时一个函数的某次迭代等于它的倒数,给出该函数方程所有亚纯解的精确公式。
3.
This paper investigates the characteristic estimation of meromorphic solutions of a class of systems of complex differential equations.
本文讨论了一类复微分方程组的亚纯解的分量的Nevanlinna特征估计,利用亚纯函数Nevanlinna值分布理论,得到了一个有关方程组亚纯解的分量的Nevanlinna特征估计定理。
补充资料：纯纯
1.诚挚貌。
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