关于S^＊p（β）及H^＊p（β）的不等式

设Ｓ＾＊ｐ（β）表示单位圆│Ｚ│〈１内的一族ｐ次对称，正则，单叶，β级星象函数，且Ｈ＾８ｐ（β）表示单位圆不０〈│ｚ│〈１内的一族ｐ次对称，正则，单叶，β级星象函数。本文得到的一些有关函数族Ｓ＾＊ｐ（β）及Ｈ＾＊ｐ（β）的不等式。这些结果都是精确的。     

Zeros of Differential Polynomial f（z）f（k）（z） -- a and Its Normality

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).     

微分方程组dX/dt=AX＋e~（αt）（cosβt·P_m~（（1））（t）＋sinβt·P_m~（（2））（t））特解结构定理及应用

对于一阶常系数非齐线性微分方程组dX/dt=AX＋e~（αt）（cosβt·P_m~（（1））（t）＋sinβt·P_m~（（2））（t））式中P（m1）（t）,P（m2）（t）为次数不超过m关于实变量t的n维向量实值多项式,当α＋iβ不是n级实方阵A的特征根时,本文给出了其特解~X（t）的结构定理和计算方法,使求特解...     

Boundedness of the Littlewood—Paley Operator,the Function g（f）,on BMO（T）

Littlewood-Paley operator,the function g(f),is considered as an operator on BMO(T).It is proved that if f∈BMO(T),then g(f)∈BMO(T) and there is a constant C that is independent of f such that ||g(f)||*≤C||f||*.Moreover,we have got the further results.     

Notes on Univalent Functions with Quasiconformal Extensions

We make improvements to some of the constants concerned with univalent functions with quasiconformal extensions that have appeared in the literature. Project supported by the National Natural Science Foundation of China.     

Univalence criterion for meromorphic functions and Loewner chains

The object of the present paper is to obtain a more general condition for univalence of meromorphic functions in the U^∗. The significant relationships and relevance with other results are also given. A number of known univalent conditions would follow upon specializing the parameters involved in our main results.     

On a Relation between the Universal Teichmu¨ller Space and the Grunsky Operator

Being a Strebel point gives a sufficient condition for that the extremal Beltrami coefficient is uniquely determined in a Teichmüller equivalence class.We consider how Strebel points are characterized.In this paper,we will give a new characterization of Strebel points in a certain subset of the universal Teichmüller space by a property of the Grunsky operator.     

On a relation between the universal Teichmüller space and the Grunsky operator

Being a Strebel point gives a sufficient condition for that the extremal Beltrami coefficient is uniquely determined in a Teichmiiller equivalence class. We consider how Strebel points are characterized. In this paper, we will give a new characterization of Strebel points in a certain subset of the universal Teichmfiller space by a property of the Grunsky operator.     

An improvement of Montel's criterion

Let F be a family of holomorphic functions in a domain D, and let a(z), b(z) be two holomorphic functions in D such that a(z)?b(z), and a(z)?a^′(z) or b(z)?b^′(z). In this paper, we prove that: if, for each f∈F, f(z)−a(z) and f(z)−b(z) have no common zeros, f^′(z)=a(z) whenever f(z)=a(z), and f^′(z)=b(z) whenever f(z)=b(z) in D, then F is normal in D. This result improves and generalizes the classical Montel's normality criterion, and the related results of Pang, Fang and the first author. Some examples are given to show the sharpness of our result.     

可拓集合及其应用研究

介绍了扩展的可拓集合概念 ,提出了可拓集合论需要进一步研究的内容 ,并综述了可拓集合在人工智能、市场、资源、检测和控制等领域的应用 .     

有界星形域上的Poincaré不等式

本文得到了有界星形域上的Poincar啨不等式 ,证明了Poincar啨域在满足一定条件的拟共形映照下是不变的 .     

On the univalence of an integral operator defined by Hadamard product

In this paper, we introduce a new general integral operator defined by the Hadamard product. Furthermore, we obtained new sufficient conditions for this operator to be univalent in the open unit disk.