平面多项式系统及其相伴系统

引进平面多项式系统的相伴系统的概念 ,分析了多项式系统与其相伴系统之间在极限环不存在性 ,唯一性 ,中心焦点的判定等问题上的相似之处和不同之处 ,提出了几个公开问题 .     

函数类(?)_∞~r在Orlicz空间内的n宽度

讨论了由非退化的全正核K(x,y)和具有特定性质的函数系{ki(x)}ri=1所确定的某一函数类 (?)∞在Orlicz空间内的n-K宽度,n-G宽度,n-L宽度的精确估计问题.     

A generalized Dedekind-Mertens lemma and its converse

We study content ideals of polynomials and their behavior under multiplication. We give a generalization of the Lemma of Dedekind-Mertens and prove the converse under suitable dimensionality restrictions.

     

The analysis of correlation integrals in terms of extremal value theory

In this paper we first give an overview of the methods of analysis of time series in terms of correlation integrals, which were developed for time series generated by deterministic systems. From the extremal value theory one obtains asymptotic information on the behaviour of the correlation integrals of time series generated by non-deterministic (mixing) systems. This leads to an analysis in terms of correlation integrals which is complementary to the estimation of dimension and entropy.Dedicated to the memory of Ricardo Mañé     

涉及微分多项式的亚纯函数的唯一性

设ｆ（ｚ）是非常数的整函数，ｎ是正整数，Ｆ（ｚ）＝ｆ￣（ｎ）（ｚ）＋ａ＿１（ｚ）ｆ￣（ｎ－１）（ｚ）＋…＋ａ＿ｎ（ｚ）ｆ（ｘ），其中ａ＿１（ｚ），ａ＿２（ｚ），…，ａ＿ｎ（ｚ）均是ｆ（ｚ）的小函数，本文证明了：若ｆ（ｚ）和Ｆ（ｚ）几乎ＣＭ分担两个不同的有穷复数ａ和ｂ，则ｆ（ｚ）≡Ｆ（ｚ）．     

Primal-Dual Interior-Point Algorithms for Semidefinite Optimization Based on a Simple Kernel Function

Interior-point methods (IPMs) for semidefinite optimization (SDO) have been studied intensively, due to their polynomial complexity and practical efficiency. Recently, J. Peng et al. introduced so-called self-regular kernel (and barrier) functions and designed primal-dual interior-point algorithms based on self-regular proximities for linear optimization (LO) problems. They also extended the approach for LO to SDO. In this paper we present a primal-dual interior-point algorithm for SDO problems based on a simple kernel function which was first presented at the Proceedings of Industrial Symposium and Optimization Day, Australia, November 2002; the function is not self-regular. We derive the complexity analysis for algorithms based on this kernel function, both with large- and small-updates. The complexity bounds are and , respectively, which are as good as those in the linear case. Mathematics Subject Classifications (2000) 90C22, 90C31.     

Solving problems of discrete tomography

This is a summary of the most important results presented in the author's PhD thesis. This thesis, written in French, was defended on 24 November 2004 and supervised by Marie-Christine Costa and Christophe Picouleau. This thesis consists in developing the study of discrete tomography problems. It aims at reconstructing discrete objects (matrices, images, discrete sets, etc) that are accessible only through few projections. A copy of the thesis is available on "http: //cedric.cnam.fr/AfficheArticle.php?id = 698". Received: April 2005 AMS classification: 90B70, 68Q17, 52C15, 05B50     

Polynomial functions and permutation polynomials over some finite commutative rings

We extend some classical results on polynomial functions . We prove all results in algebraic methods avoiding any combinatorial calculation. As applications of our methods, we obtain some interesting new results on permutation polynomials in several variables over some finite commutative rings.