循环图能量的一个上界

本文讨论循环图的能量,得到循环图能量上界的一个估计值.进一步得到整循环图能量的两个计算公式.     

循环准整环的构造

研究了一类特殊循环环即循环准整环的构造,得到的主要结论有:1)所有的无限循环准整环就是M~0和 1)的标准分解式为n=p₁^α₁p₂^α₂…p_s^α_s,ⅰ)若s=1,则n阶循环准整环共有α₁+1个,它们是dZ/ndZ,其中d=p₁^β₁,0≤β₁≤α₁;ⅱ)若s>1,则n阶循环准整环共有α₁α₂…α_s个,它们是dZ/ndZ,其中d=p₁^β₁p₂^β₂…p_s^β_s,...     

关于整表代数的同构

对任意整表基为T 的整表代数, 研究了代数整数环的一个子环R上的整R-代数RT, 证明了两个整表代数之间的一个R-代数同构必是一个整表代数同构, 只要它与一种标准化变换相容.     

一类整函数的非正规点集

1.引言设f(z)为一超越整函数,考虑由这个函数经过逐次迭代所得到的函数:这个函数序列构成一个函数族。我们记J(f)为这个函数族的非正规点集。这个点集与f的各阶不动点有密切关系,因而引起了关于这个点集的一些研究工作。在这方面,     

关于f(k)f-a的零点之猜测

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。     

Q整图新类

对于一个简单图G, 方阵Q(G)=D(G)+A(G)称为G的无符号拉普拉斯矩阵,其中D(G)和A(G)分别为G的度对角矩阵和邻接矩阵. 一个图是Q整图是指该图的无符号拉普拉斯矩阵的特征值全部为整数.首先通过Stanic 得到的六个顶点数目较小的Q整图,构造出了六类具有无穷多个的非正则的Q整图. 进而,通过图的笛卡尔积运算得到了很多的Q整图类. 最后, 得到了一些正则的Q整图.     

整函数与其两个导数CM共享一个值

该文研究了与两个导数共享一个非零、有穷值的整函数的唯一性问题，给出了函数确定的表达式，回答了仪洪勋，杨重骏提出的一个问题     

关于外汇汇率的非线性协整分析

不同汇率的波动特征及其之间存在的相互关系是金融研究领域的一个热点。本文以人民币对美元汇率和人民币对欧元汇率为研究对象,检验出它们之间存在着非线性的协整关系,并建立了分数维非线性协整模型来定量地描述这种长期均衡关系。     

整值随机变量数学期望的一个简洁解法

给出了求整值随机变量数学期望的一个技巧,以简化计算。     

导数具有相同1值点的亚纯函数的唯一性定理

本文给出了一个导数具有相同1值点的亚纯函数唯一性定理,回答了C.C.Yang的一个问题,纠正了K.Shibazaki的一个结果.例子表明本文结果是精确的.     

复指数Dirichlet 级数表示的整函数

该文对一个由复指数Dirichlet 级数表示的，其系数满足一给定增长条件且在一固定水平带形有界不恒为零的整函数的存在性， 给出了充分必要条件。     

Value sharing results for shifts of meromorphic functions

In this paper, we deal with the value distribution of difference products of entire functions, and present some result on two difference products of entire functions sharing one value with the same multiplicities. The research findings also include an analogue for shift of a well-known conjecture by Brück. Our theorems improve the results of I. Laine and C.C. Yang [I. Laine, C.C. Yang, Value distribution of difference polynomials, Proc. Japan Acad. Ser. A Math. Sci. 83 (2007) 148-151], K. Liu and L.Z. Yang [K. Liu, L.Z. Yang, Value distribution of the difference operator, Arch. Math. 92 (2009) 270-278], and J. Heittokangas et al. [J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, J.L. Zhang, Value sharing results for shifts of meromorphic function, and sufficient conditions for periodicity, J. Math. Anal. Appl. 355 (2009) 352-363]. Moreover, we show by illustrating a number of examples that our results are best possible in certain senses.     

ON ENTIRE FUNCTIONS, BLOCH AND NORMAL FUNCTIONS

New criteria for an analytic function to be Bloch and for a meromorphic function to benormal are given. These criteria generalize the recently introduced area integral conditionsinvolving a Green's function.     

Complete systems of partial derivatives of entire functions and frequently hypercyclic operators

We find some sufficient conditions for a system of partial derivatives of an entire function to be complete in the space H(C^d)$H({\mathbb{C}}^d)$ of all entire functions of d   variables. As an application of this result we describe new classes of frequently hypercyclic operators on H(C^d)$H({\mathbb{C}}^d)$.     

关于一类复微分-差分方程组的解

作者主要研究了一类复微分-差分方程组的有限级整函数解,得到了一有趣的结果,将复微分(或差分)方程中相关结果推广至复微分-差分方程组中.     

复指数Dirichlet 级数所表示的整函数的增长性

由Dirichlet 级数表示的整函数f(z)在带形中有界,其系数{a_n}和指数 {λ_n}(n=1,2,... )是复数列.文中引入 φ-级 和下φ -级,讨论f(z) 具有φ -级和下φ -级的条件.     

Optimal uniform approximation on angles by entire functions

The paper discusses the best or optimal uniform approximation problem by entire functions on a closed angle Δ. This problem has been studied by M.V. Keldysch in [4], under the assumption that the functions ? subject to approximation are holomorphic in a larger angle containing Δ and there is no restriction on the growth of ? at infinity. In [8], the problem was investigated for a wider class of functions ? continuously complex differentiable on Δ, with sharper estimates on the growth of approximating entire functions, linked with the growth of ? on Δ and the differential properties of ? on the boundary of Δ. In this paper, we improve some of the results on entire approximation on angles, using new approximation ideas partially presented in [9] and [10].     

Entire functions that share a small function with their derivatives

Let f be an entire function of finite order and a an entire function of order less than f's. If f−a and f^′−a have the same zeros with the same multiplicities, then f^′−a≡c(f−a) for some non-zero constant c.     

论一类整函数的牛顿级数展式

本文给出级小于1的整函数的牛顿级数展式的充要条件．     

Normal families and uniqueness theorems for entire functions

There exists a set S with 3 elements such that if f is a non-constant entire function satisfying E(S,f)=E(S,f′), then f≡f′. The number 3 is best possible. The proof uses the theory of normal families in an essential way.