Distortion theorem for Bloch mappings on the unit ball <Emphasis Type="Italic">ℬ</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

In this paper, we obtain a version of subordination lemma for hyperbolic disk relative to hyperbolic geometry on the unit disk D. This subordination lemma yields the distortion theorem for Bloch mappings f ∈ H（B^n） satisfying ｜｜f｜｜0 = 1 and det f＇（0） = α ∈ （0, 1], where｜｜f｜｜0 = sup{（1 - ｜z｜^2 ）n＋1/2n det（f＇（z））[1/n ： z ∈ B^n}. Here we establish the distortion theorem from a unified perspective and generalize some known results. This distortion theorem enables us to obtain a lower bound for the radius of the largest univalent ball in the image of f centered at f（0）. When a = 1, the lower bound reduces to that of Bloch constant found by Liu. When n = 1, our distortion theorem coincides with that of Bonk, Minda and Yanagihara.     

Subordination in the sense of Bochner of L p -semigroups and associated Markov processes

We show that the subordination induced by a convolution semigroup（subordination in the sense of Bochner）of a C0-semigroup of sub-Markovian operators on an Lpspace is actually associated to the subordination of a right（Markov）process.As a consequence,we solve the martingale problem associate with the Lp-infinitesimal generator of the subordinate semigroup.We also prove quasi continuity properties for the elements of the domain of the Lp-generator of the subordinate semigroup.It turns out that an enlargement of the base space is necessary.A main step in the proof is the preservation under such a subordination of the property of a Markov process to be a Borel right process.We use several analytic and probabilistic potential theoretical tools.     

一类由CHEBYSHEV多项式定义的双向单叶解析函数的系数估计

利用Chebyshev多项式定义了一类双向单叶解析函数,并得到了该函数类的系数估计及Fekete-Szeg?不等式问题.     

对具有从属关系的社会选择函数进一步的探讨

分析了Hattori给出的三个条件的合理性，并建立了一个仅满足非限制域条件而不满足存在一个独裁与无关个人影响力独立性条件的具有从属关系的社会选择函数，使具有从属关系的社会选择函数族更加完备。     

Bazilevic函数的两个子族

本文讨论了Ｂａｚｉｌｅｖｉｃ函数的两个子族的基本性质，得到了一些新的从属关系以及模，偏差，积分平均和系数的估计。这些估值多数是精确的。     

真压缩算子解析函数的优势原理

发展了Ky Fan中定理4的结果,对复的Hilbert空间H上的真压缩算子A和单位圆盘△内的解析函数f给出了优势原理,与文比较,本文去掉A为正规算子的限制,并改进了相应的结果,对H（△）的某个子类中的f,给出‖f′（A）‖的估值,并讨论了从属关系的优势原理,特别是把Shah-Goluzin关于从属于单叶函数的优势半径拓广到算子函数。     

Ma-Minda型双向单叶螺旋函数类的Fekete-Szeg不等式

引入单位圆盘D={z∈C:|z|1}内Ma-Minda型双向单叶螺旋函数类H_σ~μ(,β,φ),利用从属关系讨论了该类中函数的Fekete-Szego不等式,所得结果推广了一些作者的相关工作.     

一类微分从属性及其应用

记△={|z|<1}.设函数(?):C~2×△→C在区域D(?)C中解析,G是△中的单叶解析函数.若△中的解析函数p(z)满足微分从属关系(?)(p(z),zp’(z);z)(?)G(z),z∈△,则可确定(?)和G的某些条件使之Re p(z)>p(z∈△),并且给出这些结果的某些应用.     

Double Subordination Preserving Properties for a New Generalized Srivastava-Attiya Integral Operator

The authors obtain subordination and superordination preserving properties for a new defined generalized operator involving the Srivastava-Attiya integral operator.Differential sandwich-type theorems f...     

趣谈中国典故中的数学逻辑思维

我国文化历史悠久,哲人辈出.大量的古典巨著记载了中华文化的发展史,当今文化的诸多分支都可以从中得到溯源.数学作为人类文化的重要组成部分,我国先辈很早就在该领域取得了令世界瞩目的辉煌成就,留下许多不朽的巨著.