(F_1,F_2)-攀援集的一些注记

研究(F_1,F_2)-攀援集的迭代不变性.定义了与正整数k相关的Furstenberg族的性质P(k)和Q(k).指出:对任意介于0,1之间的实数s而言,Furstenberg族M(s)具有性质P(k)和Q(k),其中■(s)表示非负整数集的所有上密度不小于s的无限子集构成的集族.据此证明了:对任意正整数k,S为系统(X,f)的(■(s),■(t))-攀援集当且仅当S为系统(X,f~k)的(■(s),■(t))-攀援集,其中s,t是介于0,1之间的任意给定的实数.     

分担函数集的正规定则

本文将亚纯函数正规性与分担函数集相结合,探讨了亚纯函数族F正规与F中任意两个函数f与g分担函数的个数,f与其导数f'分担函数的个数及函数f的重值的个数三者之间的关系,给出了一个综合判定亚纯函数族正规的充分条件.     

On right S-Noetherian rings and S-Noetherian modules

In this paper we study right S-Noetherian rings and modules, extending notions introduced by Anderson and Dumitrescu in commutative algebra to noncommutative rings. Two characterizations of right S-Noetherian rings are given in terms of completely prime right ideals and point annihilator sets. We also prove an existence result for completely prime point annihilators of certain S-Noetherian modules with the following consequence in commutative algebra: If a module M over a commutative ring is S-Noetherian with respect to a multiplicative set S that contains no zero-divisors for M, then M has an associated prime.     

重访听音辩鼓问题

听音辨鼓这个反问题发展至今已经半个世纪,许多数学和物理学家都做出了很多有益的贡献.这个挑战性问题由美国数学家M.Kac 1966年正式提出,用数学语言描述为欧几里得空间中,是否可以找到两个(或更多)非等距单连通区域是等谱的?C.Gordon等人1992年在二维平面上给出一对等谱区域,首次对Kac的问题说"No".问题发展至今,只有17类平面等谱区域.它们都遵循一系列镜像反演规则,成对等谱,保持反演规则不变,改变基本构建块的形状,可以形成无穷多同类的等谱对.本文重访17类等谱区域,探究构建块之间的镜像反演规则.通过折叠方法,建立17类等谱区域特征函数之间的迁移映射关系.结合符号计算,列出17类等谱区域移植矩阵的通解.此外,利用Bernstein-Bézier多项式,计算等谱区域的广义特征值.     

A General Families Index Theorem

We consider the heat operator of a Bismut superconnection for a family of generalized Dirac operators defined along the leaves of a foliation with Hausdorff graph. We assume that the strong Novikov–Shubin invariants of the Dirac operators are greater than three times the codimension of the foliation. We compute the t asymptotics associated to a rescaling of the metric by 1/t and show that the heat operator converges to the Chern character of the index bundle of the operator. Combined with previous results, this gives a general families index theorem for such operators.     

Intersecting Curves in the Plane

 We prove that for every family of n pairwise intersecting simple closed planar curves in general position, at least (4/5)n ²−O(n) points lie on more than one curve. This improves the previous lower bound of (3/4)n ²−O(n) due to Richter and Thomassen. Received: March 29, 2000 Final version received: August 30, 2001 RID="*" ID="*" Research supported in part by NSF grant DMS-9970325 Acknowledgments. I thank Bruce Richter for informing me about this problem, Gelasio Salazar for reading a preliminary version of the paper, and a Referee for useful comments. Current Address: Microsoft Research, One Microsoft Way, Redmond, WA 98052-6399, USA. e-mail: mubayi@microsoft.com 1991 Mathematics Subject Classification. 05C35, 52C10     

Bounded Scott Set Saturation

We examine the relationship between two different notions of a structure being Scott set saturated and identify sufficient conditions which guarantee that a structure is uniquely Scott set saturated. We also consider theories representing Scott sets; in particular, we identify a sufficient condition on a theory T so that for any given countable Scott set there exists a completion of T that is saturated with respect to the given Scott set. These results extend Scott's characterization of countable Scott sets via models and completions of Peano arithmetic.     

Deterministic equivalents of additive functionals of recurrent diffusions and drift estimation

Let X _t be a one-dimensional Harris recurrent diffusion, with a drift depending on an unknown parameter θ belonging to some metric compact Θ. We firstly show that all integrable additive functionals of X _t are asymptotically equivalent in probability to some deterministic process v _t . Then we use this result to study the behavior of the maximum likelihood estimator for the parameter θ. Under mild regularity assumptions, we find an upper rate of its convergence as a function of v _t , extending some recent results for ergodic diffusions.      

一种双目标带约束工件成类的平行机器调度启发式规则

提出了一种快速而有效的启发式规则(fam ily slack,简称FSLACK),来求解极小化总延误时间和极小化最大完工时间两个目标,工件按产品类型成组,带模具数量约束的平行机器生产调度问题.本文提出的FSLACK与EDD、LPT及SLACK进行了比较.随机订单的测试结果表明,本文提出的启发式规则在求解双目标带约束工件成类的平行机器调度问题上是有效的.这表明该算法可以应用在成型加工业的现场作业调度.     

Universal elements for non-linear operators and their applications

We prove that under certain topological conditions on the set of universal elements of a continuous map T acting on a topological space X, that the direct sum T⊕Mg is universal, where Mg is multiplication by a generating element of a compact topological group. We use this result to characterize R₊-supercyclic operators and to show that whenever T is a supercyclic operator and z₁,…,zn are pairwise different non-zero complex numbers, then the operator z₁T⊕?⊕znT is cyclic. The latter answers affirmatively a question of Bayart and Matheron.