N-Widths and Average Widths of Besov Classes in Sobolev Spaces

In this paper, we consider the n-widths and average widths of Besov classes in the usual Sobolev spaces. The weak asymptotic results concerning the Kolmogorov n-widths, the linear n-widths, the Gel＇fand n-widths, in the Sobolev spaces on T^d, and the infinite-dimensional widths and the average widths in the Sobolev spaces on Ra are obtained, respectively.     

单位球上全纯函数空间的系数乘子

本文给出了C^n中超球B上Hardy空间H^p,Bergman空间Lα^p,Bloch空间β，Besov空间Bp及Lipschitz空间Ak^p之间的系数乘子。     

常型Sturm-Liouville问题的左定空间

本文刻画了常型Sturm-Liouville问题的左定空间的一般形式．根据自伴边值条件的分类,确切地给出了所有可能的左定空间描述．     

The Generalized West Decomposition of Operators and Other Compact Perturbation Problems

This paper introduces the concept of the generalized Riesz operators and the concept of the generalized West decomposition of a general operator which generalizes the definition of the West decomposition of Riesz operators, and proves that the following three statements are equivalent on a general Banach space： （a） Every generalized Riesz operator has the generalized West decomposition; （b） Every operator makes strong Stampfli theorem true; Every operator has Apostol＇s compact correction.     

Feature Selection using Fuzzy Support Vector Machines

The feature selection consists of obtaining a subset of these features to optimally realize the task without the irrelevant ones. Since it can provide faster and cost-effective learning machines and also improve the prediction performance of the predictors, it is a crucial step in machine learning. The feature selection methods using support machines have obtained satisfactory results, but the noises and outliers often reduce the performance. In this paper, we propose a feature selection approach using fuzzy support vector machines and compare it with the previous work, the results of experiments on the UCI data sets show that feature selection using fuzzy SVM obtains better results than using SVM.     

Adaptive application of operators in standard representation

Recently adaptive wavelet methods have been developed which can be shown to exhibit an asymptotically optimal accuracy/work balance for a wide class of variational problems including classical elliptic boundary value problems, boundary integral equations as well as certain classes of noncoercive problems such as saddle point problems. A core ingredient of these schemes is the approximate application of the involved operators in standard wavelet representation. Optimal computational complexity could be shown under the assumption that the entries in properly compressed standard representations are known or computable in average at unit cost. In this paper we propose concrete computational strategies and show under which circumstances this assumption is justified in the context of elliptic boundary value problems. Dedicated to Charles A. Micchelli on the occasion of his 60th birthday Mathematics subject classifications (2000) 41A25, 41A46, 65F99, 65N12, 65N55. This work has been supported in part by the Deutsche Forschungsgemeinschaft SFB 401, the first and third author are supported in part by the European Community's Human Potential Programme under contract HPRN-CT-202-00286 (BREAKING COMPLEXITY). The second author acknowledges the financial support provided through the European Union's Human Potential Programme, under contract HPRN-CT-2002-00285 (HASSIP) and through DFG grant DA 360/4–1.     

Pro-torus actions on Poincaré duality spaces

In this paper, it is shown that some of the results of torus actions on Poincaré duality spaces, Borel’s dimension formula and topological splitting principle to local weights, hold if ‘torus’ is replaced by ‘pro-torus’.     

几类B值小指标鞅空间的原子分解

本文对几类B值小指标鞅空间建立了原子分解定理,利用原子分解讨论了它们之间的相互嵌入关系,其原子分解的存在性和它们之间的关系均与Banach空间的凸性和光滑性有密切联系.     

Nonparametric Density Estimation in Hidden Markov Models

Let { X n} be a Markov chain that is either f -mixing or satisfies the Poisson equation.In this note we obtain the convergence rate under L 1 -criterion for bounded functions of the X k 's. And in the hidden Markov model setup { (X n ,Y n ) }we study the kernel estimate of the density of the observed variables { Y n }when a 'stable' status is reached.     

基于改善空间关联性的混沌控制

基于混沌信号的统计特性，提出了一种通过改善混沌信号的空间关联性实现混沌控制的方法.以Hénon离散混沌系统和四阶Chua's电路超混沌连续系统为例进行了数值研究，验证了这种控制方法的有效性.结果表明， 通过改善混沌信号之间的空间关联性， 混沌系统能以较快的速度收敛到它的平衡点或多种周期轨道. 关键词： 混沌控制 空间关联性 Hénon系统 四阶Chua's电路