共查询到20条相似文献,搜索用时 0 毫秒
1.
《中国科学A辑(英文版)》2008,(7)
Let f be a transcendental meromorphic function,a a nonzero finite complex number,and n 2 a positive integer.Then f a(f')n assumes every complex value infinitely often.This answers a question of Ye for n = 2.A related normality criterion is also given. 相似文献
2.
关于f~((k))-af~n的零点 总被引:2,自引:0,他引:2
张占亮 《数学的实践与认识》2004,34(11):129-134
设 f (z) 为平面内超越亚纯函数 ,a≠ 0 为常数 ,证明了当 n≥ k+3 时 ,f( k) -afn有无穷多个零点 . 相似文献
3.
本文完全证明了[1]中的一个猜测,设f为超越整函数,k为非负整数,则f^(k)f仅可能有的Picard例外值是0,由此还得到整函数族的一个正规定则。 相似文献
4.
5.
关于f~(k)f-a的零点 总被引:1,自引:0,他引:1
本文部分证明了[1]中的一个猜测:设f(z)为开平面上有穷级的超越整函数,k为非负整数,则f(k)f仅可能有的Picard例外值是0. 相似文献
6.
对于函数方程f1n1+af1m1f2m2+f2n2=1,其中a∈C/{0},n1,n2,m1,m2∈N,给出存在非常数亚纯函数解和整函数解的必要条件. 相似文献
7.
WANG YOU-MING 《东北数学》2009,25(3):277-281
In this paper we derive the fundamental inequality of the theorem of meromorphic functions. It extends some results of Yi Hong-xun et al. As one of its application, we then study the value distribution of f^(k)f^n-c(z). 相似文献
8.
Further Extension of a Theorem of Values Distribution of Meromorphic Function $f^{(k)}f^n$ 下载免费PDF全文
Youming Wang 《数学研究通讯:英文版》2009,25(3):277-281
In this paper we derive the fundamental inequality of the theorem of meromorphic functions. It extends some results of Yi Hong-xun et al. As one of its applications, we then study the value distribution of $f^{(k)} f^n - c(z)$. 相似文献
9.
10.
本文讨论f(f~(k))~n的值分布的定量估计并改进了C.K.Tse与C.C.Yang的一个结果. 相似文献
11.
HAYMAN W. K. 《中国科学 数学(英文版)》2010,(3)
Value distribution theory is concerned with the position and frequency of solutions of the equation f(z) = a. Here f may be entire, i.e. an everywhere convergent power series or meromorphic, i.e. the ratio of two such series, or a function in some other domains, such as an angle or a disk. Yang Lo’s significant contributions to this area will be highlighted. Some of his important contributions to normal families will also be described. 相似文献
12.
研究了亚纯函数结合其导数的值分布问题,得到了一个有趣的不等式,此不等式概括了方-杨和I.Lahiri和S.Dewan的结果,应用此不等式还得到关于θ(a(z);φ)的一个估计,这里φ(z)=α(z)f~nM[f],M[f]=(f′)~(n_1)(f″)~(n_2)…(f~((k)))~(n_k),n_1,n_2,…,n_k,n为非负整数满足:n_1+n_2+…+n_k≥1,α(z),a(z)(≠00,∞)为f的小函数. 相似文献
13.
Suppose that function f(z) is transcendental and meromorphic in the plane. The aim of this work is to investigate the conditions in which differential monomials f(z)f(k)(z) takes any non-zero finite complex number infinitely times and to consider the normality relation to differential monomials f(z)f(k)(z). 相似文献
14.
Let ƒ be a transcendental meromorphic function, a a nonzero finite complex number, and n ⩾ 2 a positive integer. Then ƒ + a(ƒ′)
n
assumes every complex value infinitely often. This answers a question of Ye for n = 2. A related normality criterion is also given.
This work was supported by the National Natural Science Foundation of China (Grant No. 10771076), the Natural Science Foundation
of Guangdong Province, China (Grant No. 07006700) and by the German-Israeli Foundation for Scientific Research and Development
(Grant No. G-809-234.6/2003) 相似文献
15.
By a classical observation in analysis, lacunary subsequences of the trigonometric system behave like independent random variables: they satisfy the central limit theorem, the law of the iterated logarithm and several related probability limit theorems. For subsequences of the system ( f (nx)) n≥1 with 2π-periodic ${f\in L^2}$ this phenomenon is generally not valid and the asymptotic behavior of ( f (n k x)) k≥1 is determined by a complicated interplay between the analytic properties of f (e.g., the behavior of its Fourier coefficients) and the number theoretic properties of n k . By the classical theory, the central limit theorem holds for f (n k x) if n k = 2 k , or if n k+1/n k → α with a transcendental α, but it fails e.g., for n k = 2 k ? 1. The purpose of our paper is to give a necessary and sufficient condition for f (n k x) to satisfy the central limit theorem. We will also study the critical CLT behavior of f (n k x), i.e., the question what happens when the arithmetic condition of the central limit theorem is weakened “infinitesimally”. 相似文献
16.
关于Smarandache二重阶乘函数的值分布问题 总被引:1,自引:0,他引:1
葛键 《纯粹数学与应用数学》2008,24(3)
对任意正整数n,著名的Smarandache二重阶乘函数SDF(n)定义为最小的正整数m使得m!!能够被n整除,其中二重阶乘函数m!!=1·3·5…m,如果m是奇数;m!!=2.4.6…m,如果m是偶数.本文的主要目的是利用初等方法研究函数SDF(n)的值分布性质,并给出一个有趣的均值公式. 相似文献
17.
李华仙 《纯粹数学与应用数学》2013,(3):318-324,330
利用亚纯函数的Nevanlinna值分布理论和方法,研究了一类代数体函数微分多项式的值分布问题,推广和改进了相关文献的结论. 相似文献
18.
In this note it is proved that entire functions of the form Fa(z)=H(z)-aα(z)
where H andα are entire functions, with α having at least one zero, H' and α'having no common zeros and T(r, α) = S(r, H), are prime in entire sense for most values of a. The class of these functions is seen to contain examples of both periodic and non-periodic prime entire functions found by Noda, Qiao, Urabe and by Singh and Charak. Another result due to Singh and Charak will be improved as well. 相似文献
where H andα are entire functions, with α having at least one zero, H' and α'having no common zeros and T(r, α) = S(r, H), are prime in entire sense for most values of a. The class of these functions is seen to contain examples of both periodic and non-periodic prime entire functions found by Noda, Qiao, Urabe and by Singh and Charak. Another result due to Singh and Charak will be improved as well. 相似文献
19.
设A(n,k)表示不定方程的非负整数解的个数,P(n,k)为整数n分为k个部分的无序分拆的个数,每个分部不小于1.本文给出了A(n,k)和P(n,k)的精确表达式. 相似文献
20.
该文在有关相应线性算子特征值的条件下,讨论非线性(k,n-k)共轭边值问题允许h(x)在x=0和x=1奇异.利用锥上的不动点指数理论获得了正解和多重正解的存在性. 相似文献