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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 {2. & Engineering, nanjing university of Aeronautics & Astronautics, nanjing 2.0016, China 2.School of mathematics, Yunnan normal university, Kunming 650092. China 1. School of computer {2. & 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

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 {2. and Technology,Shanghai 2.02.7,China 2.chool of mathematics and computer science,nanjing normal university,nanjing 2.0097,China 3Center of Nonlinear {2.,nanjing university,nanjing 2.0093,China 4College of mathematics and Physics,nanjing university of Posts and Telecommunications,nanjing 2.0046,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

An unconstrained optimization method using nonmonotone second order Goldstein's line search

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science China mathematics 2007年第10期50卷 1389-1400页

作者： Wen-yu SUN~(1+) Qun-yan ZHOU~(1,2. ~1 School of mathematics and {2. science,nanjing normal university,nanjing 2.0097,China ~2.Department of Basic Courses,Jiangsu Teachers university of Technology,Changzhou 2.3001,China 1. School of mathematics and {2. science Nanjing Normal University Nanjing 210097 China 2. Department of Basic Courses Jiangsu Teachers University of Technology Changzhou 213001 China

In this paper, an unconstrained optimization method using the nonmonotone second order Goldstein's line search is proposed. By using the negative curvature information from the Hessian,the sequence generated is shown to converge to a stationary point with the second order optimality conditions. Numerical tests on a set of standard test problems confirm the efficiency of our new method.

关键词： nonmonotone method, direction of negative curvature, line search, descent pair,unconstrained optimization

Weighted composition operators between μ-Bloch spaces on the unit ball

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science China mathematics 2005年第10期48卷 1349-1368页

作者： ZHANG Xuejun~1 & XIAO Jianbin~2.1. College of mathematics and computer {2.,Hunan normal university,Changsha 410006,China(email:xuejunttt@2.3. net) 2. The School of {2.,Hangzhou Dianzi university,Hangzhou 310037,China 1. College of mathematics and computer {2. Hunan Normal University 410006 Changsha China 2. The School of science Hangzhou Dianzi University 310037 Hangzhou China

In this paper,necessary and sufficient conditions are given for the weighted composition operator T_(ψ,ψ) to be bounded or compact from the space β_μ to β_ν (or β_(μ,0) to β_(ν,0) ) on the unit ball of C^***... 详细信息

关键词： μ-Bloch space, weighted composition operator, boundedness, compactness.

HAJOS' CONJECTURE AND CONNECTIVITY OF EULERIAN GRAPHS

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Journal of Systems science & Complexity 2002年第3期15卷 295-298页

作者： XU Baogang (School of mathematics and {2. science, nanjing normal university, nanjing 2.0097, China) School of mathematics and {2. science Nanjing Normal University Nanjing 210097

Hajos' conjecture asserts that a simple eulerian graph on n vertices can be decomposed into at most n-1/2.circuits. In this paper, we propose a new conjecture which is equivalent to Hajos' conjecture, and show that to prove Hajos' conjecture, it is sufficient to prove this new conjecture for 3-connected graphs. Furthermore, a special 3-cut is considered also.

关键词： Circuit decomposition connectivity eulerian graph.

Multisymplectic five-point scheme for the nonlinear wave equation

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Chinese science Bulletin 2003年第S2期48卷 24-29页

作者： WANG Yushun~(1,2., WANG Bin~1, YANG Hongwei~1 & WANG Yunfeng~1 1. LASG, Institute of Atmospheric Physics, Chinese Academy of sciences, Beijing 10002.. China 2. Permanent address: School of {2. and computer science, nanjing normal university, nanjing 2.0097. China Chinese Acad Sci Inst Atmospher Phys LASG Beijing 100029 Peoples R China nanjing normal Univ Sch Math & Comp Sci Nanjing 210097 Peoples R China

In this paper, we introduce the multisymplecticstructure of the nonlinear wave equation, and prove that theclassical five-point scheme for the equation is multisymplec-tic. Numerical simulations of this multisymplectic scheme onhighly oscillatory waves of the nonlinear Klein-Gordonequation and the collisions between kink and anti-kink soli-tons of the sine-Gordon equation are also provided. The mul-tisymplectic schemes do not need to discrete PDEs in thespace first as the symplectic schemes do and preserve notonly the geometric structure of the PDEs accurately, but alsotheir first integrals approximately such as the energy, themomentum and so on. Thus the multisymplectic schemeshave better numerical stability and long-time numerical be-havior than the energy-conserving scheme and the symplec-tic scheme.

关键词： symplectic schelne energy-conserving scheme multisymplectic scheme nonlinear wave equation.

Concatenating construction of the multisymplectic schemes for 2.1-dimensional sine-Gordon equation

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science China mathematics 2004年第1期47卷 18-30页

作者： WANG Yushun, WANG Bin & QIN MengzhaoLASG, Institute of Atmospheric Physics, Chinese Academy of sciences, Beijing 10002., China School of {2. and computer science, nanjing normal university, nanjing 2.0097, China School of {2. and System science, Chinese Academy of sciences, Beijing 100080, China 1. LASG Institute of Atmospheric Physics Chinese Academy of Sciences 100029 Beijing China 2. School of mathematics and {2. science Nanjing Normal University 210097 Nanjing China 3. School of mathematics and System {2. Chinese Academy of Sciences 100080 Beijing China

In this paper, taking the 2.1-dimensional sine-Gordon equation as an example, we present the concatenating method to construct the multisymplectic schemes. The method is to discretizee independently the PDEs in different directions with symplectic schemes, so that the multisymplectic schemes can be constructed by concatenating those symplectic schemes. By this method, we can construct multisymplectic schemes, including some widely used schemes with an accuracy of any order. The numerical simulation on the collisions of solitons are also proposed to illustrate the efficiency of the multisymplectic schemes.

关键词： 2.l-climensional sine-Gordon equation multisymplectic scheme concatenating method solitons

The Alternating-Direction Schemes and Numerical Analysis for the Three-dimensional Seawater Intrusion Simulation

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Acta Mathematicae Applicatae Sinica 2002年第3期18卷 389-404页

作者： Zhi-yue ZhangLASG, Institute of Atmospheric Physics, Chinese Academy of sciences, Beijing 10002., China & School of {2. and computer science, nanjing normal university, nanjing 2.0097, China LASG Institute of Atmospheric Physics Chinese Academy of Sciences Beijing China School of mathematics and {2. science Nanjing Normal University Nanjing China

Both numerical simulation and theoretical analysis of seawater intrusion in coastal regions are of great theoretical importance in environmental sciences. The mathematical model can be described as a coupled system of three dimensional nonlinear partial differential equations with initial-boundary value problems. In this paper, according to the actual conditions of molecular and three-dimensional characteristic of the problem, we construct the characteristic finite element alternating-direction schemes which can be divided into three continuous one-dimensional problems. By making use of tensor product algorithm, and priori estimation theory and techniques, the optimal order estimates in H1 norm are derived for the error in the approximate solution.

关键词： Three-dimensional seawater intrusion characteristic finite element alternating-direction optimal order estimate in H^1

On characterizations of isometries on function spaces

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science China mathematics 2008年第4期51卷 620-631页

作者： LI SongYing~(1+) RUAN YingBin~2.1 Department of mathematics university of California Irvine CA 92.97 USA 2.S{2. of mathematics and computer science Fujian normal university Fuzhou 350007 China 1. Department of mathematics University of California Irvine CA 92697 USA 2. School of mathematics and {2. science Fujian Normal University Fuzhou 350007 China

The paper gives characterization for an isometric isomorphism on little Bloch space, VMOA and holomorphic Besov space over the unit ball B n in ? n .

关键词： ismometry Besov spaces 32.17 47A15