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A relative local variational principle for topological pressure

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science china mathematics 2010年第6期53卷 1491-1506页

作者： MA XianFeng1,chen ErCai2,3,& ZHANG AiHua2,4 1Department of mathematics,East china university of science and Technology,Shanghai 200237,china 2school of mathematics and computer science,nanjing normal university,nanjing 210097,china 3Center of Nonlinear science,nanjing university,nanjing 210093,china 4College of mathematics and Physics,nanjing university of Posts and Telecommunications,nanjing 210046,china 1. Department of mathematics East China University of Science and Technology Shanghai 200237 China2. School of Mathematics and Computer Science Nanjing Normal University Nanjing 210097 China3. Center of Nonlinear Science Nanjing University Nanjing 210093 China4. College of Mathematics and Physics Nanjing University of Posts and Telecommunications Nanjing 210046 China

We define the relative local topological pressure for any given factor map and open cover,and prove the relative local variational principle of this *** precisely,for a given factor map π:(X,T)→(Y,S) between two topological dynamical systems,an open cover U of X,a continuous,real-valued function f on X and an S-invariant measure ν on Y,we show that the corresponding relative local pressure P(T,f,U,y) satisfies sup μ∈M(X,T){ hμ(T,U|Y)+∫X f(x)dμ(x) :πμ=ν}=∫Y P(T,f,U,y)dν(y),where M(X,T) denotes the family of all T-invariant measures on ***,the supremum can be attained by a T-invariant measure.

关键词： pressure conditional entropy relative local variational principle

Manifold contraction for semi-supervised classification

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science china(Information sciences) 2010年第6期53卷 1170-1187页

作者： HU EnLiang 1,2 , chen SongCan 1 & YIN XueSong 1 1 school of computer science & Engineering, nanjing university of Aeronautics & Astronautics, nanjing 210016, china 2 school of mathematics, Yunnan normal university, Kunming 650092, china 1. school of computer science & Engineering Nanjing University of Aeronautics & Astronautics Nanjing 210016 China2. School of Mathematics Yunnan Normal University Kunming 650092 China

The generalization ability of classification is often closely related to both the intra-class compactness and the inter-class *** to the fact that many current dimensionality reduction methods, regarded as a pre-processor, often lead to the poor classification performance on real-life data, in this paper, a new data preprocessing technique called manifold contraction(MC) is proposed for the classification-oriented learning *** main motivation behind MC lies in seeking a proper mapping of contracting the given multiple-manifold data such that the ratio of the intra-class to the inter-class scatters is ***, in order to properly control the contraction level in MC, an adaptive MC(AMC) criterion is developed in the semi-supervised *** to its generality, MC can be not only applied in original space and reproducing kernel Hilbert space(RKHS), but also easily incorporated with dimensionality reduction method for further improvement of classification *** final experimental results show that MC, as a data preprocessor, is effective and promising in the subsequent classification learning, especially in small-size labeled sample case.

关键词： manifold learning dimensionality reduction lower-dimensional embedding semi-supervised learning classification manifold contraction adaptive manifold contraction

THERMODYNAMIC FORMALISM FOR SUBADDITIVE SEQUENCE OF DISCONTINUOUS FUNCTIONS

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Analysis in Theory and Applications 2010年第2期26卷 174-185页

作者： Xianfeng Ma (nanjing normal university/East china university of science and Technology, china) Ercai chen (nanjing normal university/nanjing university, china) Yu Pei (nanjing normal university, china) 1. school of mathematics and computer science Nanjing Normal Uniersity Nanjing 210097 P. R. China2. Department of Mathematics East China University of Science and Technology Shanghai 200237 P. R. China3. Center of Nonlinear Science Nanjing University Nanjing 210093 P. R. China

The topological pressure for subadditive sequence of discontinuous functions is defined on any invariant subset having a nested family of subsets in the compact metric space. Two subadditive variational principles associated with two different relatively weak conditions are developed for the defined topological pressure. As an application, we give an example on systems with nonzero Lyapunov exponents.

关键词： thermodynamic formalism variational principle topological pressure subadditive sequence of functions

The high order Schwarz-Pick lemma on complex Hilbert balls

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science china mathematics 2010年第10期53卷 2649-2656页

作者： DAI ShaoYu1,2,chen huaihui1 & PAN YiFei3,4 1Department of mathematics,nanjing normal university,nanjing 210097,china 2Department of General Study Program,Jinling Institute of Technology,nanjing 211169,china 3school of mathematics and Informatics,Jiangxi normal university,Nanchang 330022,china 4Department of Mathematical sciences,Indiana university-Purdue university Fort Wayne,Fort Wayne,IN 46805-1499,USA 1. Department of mathematics Nanjing Normal University Nanjing 210097 China2. Department of General Study Program Jinling Institute of Technology Nanjing 211169 China3. School of Mathematics and Informatics Jiangxi Normal University Nanchang 330022 China4. Department of Mathematical Sciences Indiana University-Purdue University Fort Wayne Fort Wayne IN 46805-1499 USA

In this paper we prove a high order Schwarz-Pick lemma for holomorphic mappings between unit balls in complex Hilbert *** addition,a Schwarz-Pick estimate for high order Fréchet derivatives of a holomorphic function ... 详细信息

关键词： complex Hilbert ball high order Schwarz-Pick lemma

Geometric double-entity model for recognizing far-near relations of clusters

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science china(Information sciences) 2011年第10期54卷 2040-2050页

作者： WANG KaiJun ,YAN XuanHui & chen LiFei school of mathematics and computer science,Fujian normal university,Fuzhou 350108,china 1. school of mathematics and computer science Fujian Normal University Fuzhou 350108 China

When solving many practical problems,we not only need sample labels given by a clustering algorithm,but also rely on the recognition of far-near relations of *** the difficult condition of many clusters in a high-dimensional data set,the clustering visualization methods based on dimension reductions usually produce the phenomena,e.g.,some clusters are overlapping,interlacing,or pushed away;as a result,the far-near relations of some clusters are displayed wrongly or cannot be *** existing inter-cluster distance methods cannot determine whether two clusters are far away or *** geometric double-entity model method (GDEM) is proposed to describe far-near relations of clusters,and the methods such as the relative border distance,absolute border distance and region dense degree are designed to measure far-near degrees between *** pays attention to both the absolute distance between nearest sample sets and the dense degrees of border regions of two clusters,and it is able to uncover accurately far-near relations of clusters in a high-dimensional space,especially under the difficult condition mentioned *** experimental results on four real data sets show that the proposed method can effectively recognize far-near relations of clusters,while the conventional methods cannot.

关键词： geometric double-entity model far-near relations of clusters distance between clusters partitional clustering algorithms

Tubular algebras and affine Kac-Moody algebras

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science china mathematics 2007年第4期50卷 521-532页

作者： Zheng-xin chen & Ya-nan LIN school of mathematics and computer science, Pujian normal university, Fuzhou 350007, china school of Mathematical sciences, Xiamen university, Xiamen 361005, china 1. school of mathematics and computer science Fujian Normal University Fuzhou 350007 China 2. school of Mathematical sciences Xiamen University Xiamen 361005 China

The purpose of this paper is to construct quotient algebras L(A) 1 ? /I(A) of complex degenerate composition Lie algebras L(A) 1 ? by some ideals, where L(A 1 ? is defined via Hall algebras of tubular algebras A, and to prove that the quotient algebras L(A) 1 ? /I(A) are isomorphic to the corresponding affine Kac-Moody algebras. Moreover, it is shown that the Lie algebra L re(A) 1 ? generated by A-modules with a real root coincides with the degenerate composition Lie algebra L(A) 1 ? generated by simple A-modules.

关键词： tubular algebras affine Kac-Moody algebras Hall algebras degenerate composition Lie algebras modules with real root 16G70 17B67

On the General Weighted-average Consensus Protocol of Multi-agent Systems with Double-integrator Dynamics

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On the General Weighted-average Consensus Protocol of Multi-...

Consensus of linear time-invariant multi-agent systems based on dynamic output feedback

2009中国控制与决策会议

作者： Yushi Shi,Jiandong Zhu,Teng chen school of mathematics and computer science,nanjing normal university,nanjing,210097

＜正＞In this paper,a general weighted-average consensus protocol is proposed for multi-agent systems with double-integrator *** and sufficient conditions for solving the weighted-average consensus problem are obtained,namely,all the gains realizing the weighted-average consensus can be ***,a periodic consensus protocol is obtained as a special case.

关键词： weighted-average consensus double-integrator dynamics

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Consensus of linear time-invariant multi-agent systems based...

基于内容的分布式Web图像检索系统与算法研究

2009中国控制与决策会议

作者： Teng chen,Jiandong Zhu,Yushi Shi school of mathematics and computer science,nanjing normal university,nanjing 210097

＜正＞In this paper,it is researched the consensus problem via dynamic output feedback for linear time-invariant multi-agent systems（LTI-MASs） under fixed topologies.A linear matrix inequality approach for computing... 详细信息

关键词： Consensus Linear time-invariant multi-agent systems Linear matrix inequality(LMI) Dynamic output feedback

来源： cnki会议评论

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计算机工程与应用 2004年第30期40卷 71-73页

作者：方昭辉张明陈冬霞南京师范大学数学与计算机科学学院南京210097

该文提出了分布式基于内容的Web图像检索系统的模型,介绍了系统的分布协作策略,给出了关键的分布协作检索的算法,描述了检索子系统的功能和实现。

关键词：基于内容分布式 CBIR Web