关于方程f″+Af′+ Bf=0解的增长性,其中系数A是一个二阶线性微分方程的解

设A(z)是方程f″+P(z)f=0的非零解,其中P(z)是n次多项式,B(z)是一个超越整函数且满足ρ(B)≤1/2,那么方程f″+Af′+Bf =0的每一个非零解都是无穷级.并且方程f″+A(z)f=0两个线性无关解乘积的零点序列收敛指数为无穷.     

一类二阶非齐次线性微分方程解的复振荡

研究了一类二阶非齐次线性微分方程f″+Ae~(az~n)f′+(B_1e~(bz~n)+B_0e~(dz~n))f=F(z)解的增长性和零点分布,其中F为级小于n的非零整函数,A,B1,B0为非零多项式.在复数a,b,d满足一定条件下,得到该方程的每一个解的超级和二级零点收敛指数的精确估计.     

涉及差分算子的亚纯函数的唯一性

本文研究涉及差分算子的亚纯函数的唯一性问题,得到一个唯一性定理:设f是一个级不小于2的有限级整函数,η是非零复数,a(z)是不恒等于0的整函数,满足ρ(a)ρ(f)和λ(f-a)ρ(f).若f-a与Δnηf-a(n=1或2)CM分担0,则f(z)是整数级的,且ρ(a)=1或ρ(a)≥ρ(f)-1,f(z)=a(z)+[Δnηa(z)-a(z)]eA(z),其中A(z)是一个次数和ρ(f)相等的多项式.     

一类二阶非齐次微分方程解的增长性与不动点(英文)

本文研究方程f′′+A(z)f′+B(z)f=F解的增长性、解及其导数的不动点问题,其中A(z),B(z)(不恒等于0),F(z)(不恒等于0)是整函数,F的级为无穷.得到方程解的超级、二级不同零点收敛指数、方程解及其一阶和二阶导数的二级不动点收敛指数等的精确估计.     

一类无穷下级整函数的Julia集的径向分布

主要研究方程f"(z)+A(z)f'(z)+B(z)f(z)=0(A(z)),B(z)为整函数)的解、解的多项式或微分多项式这些具有无穷下级的整函数的Julia集的径向分布问题.     

关于方程f″+Af=F(z)的复振荡

本文讨论了当A(z)为多项式,F(z)为具有无穷多个零点的整函数时,微分方程 f″+A(z)f=F(z)的解f(z)的复振荡的性质.     

一类二阶非齐次微分方程解的增长性与不动点[英文]

研究方程f''+A(z)f'' B(z)f=F解的增长性与解及其导数的不动点问题,其中A(z),B(z),F(z)(不恒等于0)是整函数,F的级为无穷,得到了方程解的超级、二级不同零点收敛指数,方程解及其一阶和二阶导数的二级不动点收敛指数等的精确估计.     

二阶齐次与非齐次线性微分方程亚纯解的零点与增长性质估计(英文)

本文研究了方程f′′+A(z)f′+B(z)f=0与f′′+A(z)f′+B(z)f=F亚纯解的零点与增长性,其中A(z),B(z)(■0),F(z)(■0)为亚纯函数,得到了方程亚纯解的增长级、下级、超级、二级不同零点收敛指数等的精确估计,改进了KwonKi-Ho、陈宗煊与杨重骏、Benharrat Beladi等的结果.     

一类线性差分方程的亚纯解与一个亚纯函数分担3个值的唯一性

主要研究差分方程a_1(z)f(x+1)+a_0(z)f(z)=F(z)的一个有穷级超越亚纯解f(z)与亚纯函数g(z)分担0,1,∞CM时的唯一性问题(其中a_(z),a0(z),F(z)为非零多项式,且满足a_1(z)+a_0(z)■0),得到f(x)≡g(z),或f(z)+g(z)≡f(z)g(z),或存在一个多项式β(z)=az+b_0和一个常数a_0满足e~(a_0)≠e~(b_0),使得f(z)=(1-e~(β(x)))/(e~(β(x))(e~(a_o-b_0)-1))与g(z)=(1-e~(β(x)))/(1-e~(b_o-a_0)),其中a(≠0),b_0为常数.     

限定Borel点的亚纯函数

设E是任意一个非空的闭实数集(mod 2π),ρ(θ)是E上一个上半连续的有界正值函数(0<ρ(θ)相似文献   

多元多项式齐次方程组的一个解法

本文对多元多项式齐次方程组给出一种解法，并给出其解子模的基所含向量的个数在最坏情况时的下界。     

SOLUTION OF A RESEARCH PROBLEM

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The Siegel norm,the length function and character values of finite groups

In this paper we present some new results on the connection between the Siegel norm, the length function and irreducible character values of finite groups. In addition, we provide algorithms to compute the length of a cyclotomic integer and the set of cyclotomic integers with Siegel norm bounded by a given positive real number.     

The Formula of General Term of the Sum of Equal Powers of Natural Numbers

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The diffeomorphic types of the complements of arrangements in ??3 II

For any arrangement of hyperplanes in ℂℙ³, we introduce the soul of this arrangement. The soul, which is a pseudo-complex, is determined by the combinatorics of the arrangement of hyperplanes. In this paper, we give a sufficient combinatoric condition for two arrangements of hyperplanes to be diffeomorphic to each other. In particular we have found sufficient conditions on combinatorics for the arrangement of hyperplanes whose moduli space is connected. This generalizes our previous result on hyperplane point arrangements in ℂℙ³. This work was partially supported by NSA grant and NSF grant     

The diffeomorphic types of the complements of arrangements in CP~3Ⅱ

For any arrangement of hyperplanes in CP~3,we introduce the soul of this arrangement. The soul,which is a pseudo-complex,is determined by the combinatorics of the arrangement of hyper- planes.In this paper,we give a sufficient combinatoric condition for two arrangements of hyperplanes to be diffeomorphic to each other.In particular we have found sufficient conditions on combinatorics for the arrangement of hyperplanes whose moduli space is connected.This generalizes our previous result on hyperplane point arrangements in CP~3.     

A generalization of Alon–Aydinian–Huang theorem

Let $S_{n,k}^m$ be the collection of sets of real numbers of size n, in which every subset of size larger than k has a sum less than m, where $n\ge k+1$, and m is some real number. Denote by $a_{n,k}^m$ the maximum number of nonempty subsets of a set in $S_{n,k}^m$ with a sum at least m. In particular, when $m=0$, Alon, Aydinian, Huang ((2014) [1]) proved that $a_{n,k}^0={\sum }_{i=0}^{k?1}\left(\begin{array}{c}n?1\\ i\end{array}\right)$, where two technical proofs, based on a weighted version of Hall's theorem and an extension of the nonuniform Erd?s–Ko–Rado theorem, were presented. In this note, we extend their elegant result from $m=0$ to any real number m, and show that $a_{n,k}^m=\{\begin{array}{cc}{\sum }_{i=0}^{k?1}\left(\begin{array}{c}n?1\\ i\end{array}\right)\hfill & \text{ if }m\ge 0\hfill \\ {\sum }_{i=1}^k\left(\begin{array}{c}n\\ i\end{array}\right)\hfill & \text{ if }m<0\hfill \end{array}$. Our proof is obtained by exploring the recurrence relation and initial conditions of $a_{n,k}^m$.     

A Note on the Theorems of Church-Turing and Trachtenbrot

We sketch proofs of the theorems of Church-Turing and Trachtenbrot using a semi-monomorphic axiomatization. Mathematics Subject Classification : 03B10, 03B25.     

有向图幂敛指数的Brualdi-Ross型上界

本文证明了n阶恰含i个极小强连通分支的有向图的幂敛指数的一个Brualdi-Ross型上界,并给出了幂敛指数达到此上界的有向图的完全刻划。