Meromorphic p -valent function with fixed second negative coefficients

In this paper we consider the class consisting of analytic functions with negative coefficients and fixed second coefficient. The object of the present paper is to give coefficient estimates, convex linear combinations, some distortion theorems and radii of starlikeness and convexity for f(z) in the class . The work is supported by UKM grant ST-028-2003 and IRPA grant 09-02-02-80 EA208, Malysia. This paper is that of a talk on the “International Conference at Analysis in Theory and Applications” held in Nanjing, P. R. China, July, 2004.     

关于某些调和函数

用H表示形如f(z)=h(z) g(z)的调和函数族,其中h和g是单位圆盘内的解析函数.本文考虑H的三类子族函数.其中的两族为PH(α)=f∶Ref(z)z≥α和NH(α)=f∶Ref(z)θz≥θα,其中0≤α<1和θ=argz.本文得到了函数f属于其中一族的一个充分必要条件,并且获得了一些系数不等式和偏差定理.     

负系数单叶函数的一个新子族

本文引入了一类具有负系数的单叶函数族C_n(α),并且讨论了这类函数族精确的系数估计,偏差定理及闭包定理,推广了一些已有结果.     

Fourier coefficients of Zygmund functions and analytic functions with quasiconformal deformation extensions

An open problem is to characterize the Fourier coefficients of Zygmund functions.This problem was also explicitly suggested by Nag and later by Teo and Takhtajan-Teo in the course of study of the universal Teichmu¨ller space.By a complex analysis approach,we give a characterization for the Fourier coefficients of a Zygmund function by a quadratic form.Some related topics are also discussed,including those analytic functions with quasiconformal deformation extensions.     

关于Bloch函数的性质

研究了Bloch函数族B中的两个子族Bα与B0,给出了它们的函数之间的关系;作为应用建立了Bα与B0中函数的偏差定理,从而刻画了Bα与B0中函数的有关性质.     

关于多值解析函数的教学研究

复变函数论中的多值函数教学是一个难点.钟玉泉先生的教材在这一难点的处理方面是较成功的.他通过例题,介绍多值函数分成单值分支的方法,介绍求函数值的方法,并对这些方法进行了总结,得出的结论是:当给定初值后,只有通过连续变化才能得到其它点的函数值.这一点和传统的代入法求函数值完全不同.然而该教材就在这一总结之后,又用代入法求Arcsin2.我们认为这自我否定了刚刚建立起来的求值方法,扰乱了读者的思想.本文通过对Arcsinz分成单值解析分支的讨论,对求Arcsin2提出了新的教材处理方案,以期和读者商榷.     

等概离散无记忆信源率失真函数的计算方法

研究了等概信源的率失真函数计算问题,得到了等概信源在对称失真与列对称失真下率失真函数的计算方法,并举例说明了其具体应用.     

Analytic Discs and Extension of CR Functions

Let M be a manifold of X = C ⁿ , A a small analytic disc attached to M, z ^o a point of A where A is tangent to M, z ¹ another point of A where M extends to a germ of manifold M ₁ with boundary M. We prove that CR functions on M which extend to M ₁ at z ¹ also extend at z ^o to a new manifold M ₂. The directions M ₁ and M ₂ point to, are related by a sort of connection associated to A which is dual to the connection obtained by attaching 'partial analytic lifts' of A to the co-normal bundle to M in X.     

几类亚纯双单叶函数的系数估计

研究了几类亚纯双单叶函数的系数估计,所得结果改进或推广了部分作者的结论.     

On continuous solutions of a generalized Cauchy-Riemann system with more than one singularity

We study the solvability of the Riemann-Hilbert problem for a generalized Cauchy-Riemann system with several singularities and reveal several new phenomenon. For the number of continuous solutions we shall show that it depends not only on the index but also on the location and type of the singularities; moreover, it does not depend continuously on the coefficients of the equation.     

A New Approach to Analytic Multifunctions

We show how the theory of analytic multifunctions can be developed in an elementary and self-contained fashion, using the abstract notions of gauge and multigauge. This approach also yields new information about the metric properties of analytic multifunctions, leading to analogues of Schwarz's lemma and the Schwarz–Pick theorem.     

近于凸函数新子类的偏差定理和卷积性质

引进了近于凸函数的新子类.利用从属关系得到了偏差定理和卷积性质.所得结果推广了一些作者的相关结果,并得到有趣的新结果.     

复变函数中刘维尔定理的新证明

利用截断函数的性质给出了复变函数中刘维尔定理的一种新的证明方法.     

A UNIFIED CLASS OF ANALYTIC FUNCTIONS WITH FIXED ARGUMENT OF COEFFICIENTS

In this paper we introduce new classes of analytic functions with fixed argument of coefficients defined by subordination. Coefficient estimates, distortion theorems, integral means inequalities, and the radii of convexity and starlikeness are investigated. Convolution properties are also pointed out.     

P-叶星像函数类的一些充分条件

令Hn(p)表示形如f(z)=zp ∑ ∞k=n pakzk,且在单位圆U={z;|z|<1}内解析的函数f(z) 的全体所成的函数类.本文应用微分从属技巧得到了p-叶β级星像函数的一些充分条件,所得结果推广了一些作者的相关结果.     

Noncommutative plurisubharmonic polynomials part I: Global assumptions

We consider symmetric polynomials, p, in the noncommutative (nc) free variables {x₁,x₂,…,xg}. We define the nc complex hessian of p as the second directional derivative (replacing xT by y)

     

Certain Sufficient Conditions for Starlikeness and Convexity of Meromorphically Multivalent Functions

In this paper we derive certain sufficient conditions for starlikeness and convexity of order α of meromorphically multivalent functions in the punctured unit disk.     

CERTAIN SUFFICIENT CONDITIONS FOR STARLIKENESS AND CONVEXITY OF MEROMORPHICALLY MULTIVALENT FUNCTIONS

In this paper we derive certain suffcient conditions for starlikeness and con-vexity of orderαof meromorphically multivalent functions in the punctured unit disk.     

某些星象函数子类的优化问题

In this article, we study several majorizaton properties for the subclasses SL~*,SR~*(a, b), BS~*(α), S_c~*, S_q~* and S_R~* of starlike functions. Meanwhile, some special cases of our main results are given.     

A short proof of Hara and Nakai's theorem

We give a short proof of the following theorem of Hara and Nakai: for a finitely bordered Riemann surface , one can find an upper bound of the corona constant of that depends only on the genus and the number of boundary components of .