On bifurcation points of a complex polynomial

Let be a polynomial of degree . Assume that the set there is a sequence s.t. and is finite. We prove that the set of generalized critical values of (hence in particular the set of bifurcation points of ) has at most points. Moreover, We also compute the set effectively.

     

Ergodic-theoretic properties of certain Bernoulli convolutions

The aim of this paper is to prove some fixed point theorems which generalize well known basic fixed point principles of nonlinear functional analysis. Moreover, we investigate the class of mappings f: X→ X, where X is a Banach space, for which one of the main conditions in the metric fixed point theory, namely the condition (1), is satisfied. We obtain essential applications of this fact. All our results are illustrated by suitable examples. This revised version was published online in June 2006 with corrections to the Cover Date.     

Bounded holomorphic functions and maps with some boundary behavior

Let Ω be a domain of . As a study of boundary behavior of functions and maps in Ω, we consider “the linear cluster set,” which is the cluster set along segment terminating at a boundary point of Ω. We prove that there exist bounded holomorphic functions and maps defined in Ω which have the linear cluster sets of positive measure at every point of a discrete subset of the boundary of Ω under some conditions.     

Minimal number of singular fibers in a Lefschetz fibration

There exists a (relatively minimal) genus Lefschetz fibration with only one singular fiber over a closed (Riemann) surface of genus iff and . The singular fiber can be chosen to be reducible or irreducible. Other results are that every Dehn twist on a closed surface of genus at least three is a product of two commutators and no Dehn twist on any closed surface is equal to a single commutator.

     

Unbounded convex mappings of the ball in

In this paper, we study univalent holomorphic mappings of the unit ball in that have the property that the image contains a line for some , . We show that under certain rather reasonable conditions, up to composition with a holomorphic automorphism of the ball, the mapping is an extension of the strip mapping in the plane to higher dimensions.

     

On the extremality of quasiconformal mappings and quasiconformal deformations

Given a family of quasiconformal deformations such that has a uniform bound , the solution of the Löwner-type differential equation

is an -quasiconformal mapping. An open question is to determine, for each fixed , whether the extremality of is equivalent to that of . The note gives this a negative approach in both directions.

     

一类大气浅水波方程的近似解

研究了一类非线性浅水波方程，利用同论映射理论和方法，得到了相应系统的近似解. 关键词： 浅水波 非线性 同伦映射 近似解     

(2+1)维非对称 Nizhnik-Novikov-Veselov系统的新映射解及其局域结构

映射法是一种非常经典、有效和成熟的求解非线性演化方程的方法，其最大的特点是可以有多种不同形式的设解，使得最终求得的解丰富多彩. 利用改进的 Riccati 方程映射法和变量分离法，得到了(2+1)维非对称 Nizhnik-Novikov-Veselov 系统的新显式精确解.根据得到的孤波解，构造出该系统的峰孤子和分形孤子等局域结构，研究了两个孤立波的“追碰”现象. 关键词： 改进的映射法 (2+1)维非对称 Nizhnik-Novikov-Veselov 系统 局域结构 “追碰”现象     

合肥光源直线加速器BPM系统的研制和测量

合肥光源直线加速器新改造的BPM系统已经安装, 并做了在线的束流位置测量实验. 本文介绍该BPM系统的结构、作为系统核心部分的信号处理模块以及离线标定的实验结果和在线应用的实验结果, 表明该BPM系统具有不小于40dBm的动态范围, 不大于100μm的束流位置分辨率, 水平方向和垂直方向分别具有1.61dB/mm和1.51dB/mm的灵敏度. 校正铁强度与BPM读数关系的实验, 表明该BPM系统能正确地反映束流的位置变化情况, 并且确定了校正铁在水平方向和垂直方向的校正系数分别为0.46mm/A和0.58mm/A, 校正铁设置为默认值时该BPM处的束流中心水平位置和垂直位置分别为0.83mm和－0.57mm.