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Communications in Theoretical Physics 2004年第9期 329-334页

作者： CHEN Yong~(1,2,3. WANG Qi~(2,3. LI Biao~(2,3.1 Department of Physics,Shanghai Jiao Tong university,Shanghai 20003.,china2 Department of Applied Mathematics,Dalian university of Technology,Dalian 116024,china3.Key Laboratory of Mathematics and Mechanization,the Chinese Academy of sciences,Beijing 100080,china

Making use of a new and more general ansatz,we present the generalized algebraic method to uniformlyconstruct a series of new and general travelling wave solution for nonlinear partial differential *** an applicationof the method,we choose a(1+1)-dimensional dispersive long wave equation to illustrate the *** a result,wecan successfully obtain the solutions found by the method proposed by Fan [***,***.153.2003.17]and find other new and more general solutions at the same time,which include polynomial solutions,exponentialsolutions,rational solutions,triangular periodic wave solutions,hyperbolic and soliton solutions,Jacobi and Weierstrassdoubly periodic wave solutions.

关键词： generalized algebraic method symbolic computation solitary wave solution Weierstrass and Jacobi elliptic functions periodic solution

Detecting Lags in nonlinear Models Using General Mutual Information

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Journal of Mathematical Research and Exposition 2010年第1期30卷 87-98页

作者： Wei GAO1,2, Zheng TIAN1,3.1. Department of Applied Mathematics, Northwest Polytechnical university, Shaanxi 710072, P. R. china 2. School of Statistics, Xi’an university of Finance & Economics, Shaanxi 710061, P. R. china 3. National Key Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of sciences, Beijing 100080, P. R. china Department of Applied Mathematics Northwest Polytechnical University Shaanxi P.R.China 710072

The general mutual information （GMI） and general conditional mutual information （GCMI） are considered to measure lag dependences in nonlinear time series. Both of the measures have the property of invariance with transform. The statistics based on GMI and GCMI are estimated using the correlation integral. Under the hypothesis of independent series, the estimators have Gaussian asymptotic distributions. Simulations applied to generated nonlinear series demonstrate that the methods appear to find frequently the correct lags.

关键词： general mutual information general conditional mutual information nonlinear time series lag dependence.

Periodic solutions of a 2nth-order nonlinear difference equation

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science china Mathematics 2010年第1期53卷 41-50页

作者： ZHOU Zhan 1, YU JianShe 1 & CHEN YuMing 21 School of Mathematics and Information science, Guangzhou university, Guangzhou 510006, china 2 Department of Mathematics, Wilfrid Laurier university, Waterloo N2L 3.5, Canada 1. School of Mathematics and Information science Guangzhou University Guangzhou 510006 China2. Department of Mathematics Wilfrid Laurier University Waterloo N2L 3C5 Canada

In this paper, a 2 nth-order nonlinear difference equation is *** the critical point theory, we establish various sets of sufficient conditions of the nonexistence and existence of periodic *** obtained complement or ... 详细信息

关键词： periodic solution nonlinear difference equation critical point theory

The potential effect of variations in climate and agricultural practice on N_2O emissions (Ⅱ)——Variations in agricultural practice

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Chinese science Bulletin 1999年第S2期44卷 97-99页

作者： XU Wenbin~(1,2), HONG Yetang~1, CHEN Xuhui~3. LI Changsheng~4, LIN Qinghua~1 and WANG Yu~1, 1. State Key Laboratory of Environmental Geochemistry, Institute of Geochemistry, Chinese Academy of sciences, Guiyang 550002, china 2. Institute of Environment and Resources Chemistry, Zhejiang university, Hangzhou 3.0027, china 3. Soil and Fertilizer Institute, Guizhou Academy of Agricultural sciences, Guiyang 550013. china 4. Institute for the Study of Earth, Oceans, and Space, university of New Hampshire, Durham, USA State Key Laboratory of Environmental Geochemistry Institute of Geochemistry Chinese Academy of Sciences Guiyang 550002 China Institute of Environment and Resources Chemistry Zhejiang University Hangzhou 310027 China Soil and Fertilizer Institute Guizhou Academy of Agricultural Sciences Guiyang 550013 China Institute for the Study of Earth Oceans and Space University of New Hampshire Durham NH United States

WE expanded Decomposition-Denitrification （DNDC）modeling study to systematically assess the potential effect of farming practice on N2O emission by choosing a corn-rape rotation and a soybean-winterwheat rotation field in Guizhou Province, westsouthern china, asN2O emission from subtropical agricultural soil study plots. These sensitivity studies address questions relevant to issue of how change in fanning practice might be used to mitigate emissions. Manure additions had the most pronounced impact on N2O emissions of farming practice simulatedand the influence of manure addition was nonlinear （fig. 1）. This result is consistent with previous studies for an Iowa corn field. The addition of manure remarkably elevates the level of organic carbon, enhances soil nitrogen mineralization, and increases the efficiency of N2O production. Simulated results alsoshowed that the influence of manure additions on N2O emission from soybean-winter wheat field had

关键词： N2O emission farming practice potential effect agricultural soil.

A fast SVM training algorithm based on the set segmentation and k-means clustering

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Progress in Natural science:Materials International 2003年第10期 30-35页

作者： YANG Xiaowei 1,2 , LIN Daying 1, HAO Zhifeng 1, LIANG Yanchun 3.*, LIU Guirong 2 and HAN Xu 2(1. Department of Applied Mathematics, South china university of Technology, Guangzhou 510640, china 2. Centre for ACES, Department of Mechanical Engineering, National university of Singapore, 119260, Singapore 3. College of Computer science and Technology, Jilin university, Changchun 13.012, china) Department of Applied Mathematics，South china university of Technology，Guangzhou 510640，china Centre for ACES，Department of Mechanical Engineering，National university of Singapore，119260，Singapore Department of Applied Mathematics，South china university of Technology，Guangzhou 510640，china College of Computer science and Technology，Jilin university，Changchun 13.012，china Centre for ACES，Department of Mechanical Engineering，National university of Singapore，119260，Singapore

At present, studies on training algorithms for support vector machines (SVM) are important issues in the field of machine learning. It is a challenging task to improve the efficiency of the algorithm without reducing the generalization performance of SVM. To face this challenge, a new SVM training algorithm based on the set segmentation and k means clustering is presented in this paper. The new idea is to divide all the original training data into many subsets, followed by clustering each subset using k means clustering and finally train SVM using the new data set obtained from clustering centroids. Considering that the decomposition algorithm such as SVM light is one of the major methods for solving support vector machines, the SVM light is used in our experiments. Simulations on different types of problems show that the proposed method can solve efficiently not only large linear classification problems but also large nonlinear ones.

关键词： support vector machines set segmentation k means clustering.

Quasi-periodic solutions with prescribed frequency in a nonlinear Schrdinger equation

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science china Mathematics 2010年第12期53卷 3067-3084页

作者： REN Xiu-Fang Department of Mathematics, Nanjing university, Nanjing 210093, china 1. Department of Mathematics Nanjing University Nanjing 210093 China

In this paper, one-dimensional (1D) nonlinear Schrdinger equation iut-uxx + Mσ u + f ( | u | 2 )u = 0, t, x ∈ R , subject to periodic boundary conditions is considered, where the nonlinearity f is a real analytic function near u = 0 with f (0) = 0, f (0) = 0, and the Floquet multiplier Mσ is defined as Mσe inx = σne inx , with σn = σ, when n 0, otherwise, σn = 0. It is proved that for each given 0 1, the above equation admits a Whitney smooth family of small-amplitude quasi-periodic solutions with b-dimensional Diophantine frequencies, corresponding to b-dimensional invariant tori of an associated infinite-dimensional Hamiltonian system. Moreover, these b-dimensional Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proof is based on a partial Birkhoff normal form reduction and an improved KAM method.

关键词： Schrdinger equation Hamiltonian system Birkhoff normal form quasi-periodic solution

nonlinear properties of fractal growth of thin films at low temperature

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Communications in nonlinear science and Numerical Simulation 2001年第2期6卷 61-67页

作者： Fengmin WU, Jiefang ZHANG, Gen BIAN and Ziqin WU Research Center of science, Zhejiang university of Technology, Hangzhou 3.0014, {3. Institute of nonlinear Physics, Zhejiang Normal university, Jinhua 3.1004, {3. Shao Yifu Hospital of Zhejiang Provin Research Center of science Zhejiang University of Technology Hangzhou 310014 China Institute of nonlinear Physics Zhejiang Normal University Jinhua 321004 China Shao Yifu Hospital of Zhejiang Province Hangzhou 310005 China Department of Astronomy and Applied Physics University of Science and Technology of China Hefei 230026 China

Fractal growth of thin films at low temperature (75-200 K) is simulated by kinetic Monte Carlo method, using realistic growth model-Ag on Pt(111) surface and physical parameters. It is shown that the fractal growth of thin films is nonlinear, i. e., the island size S(t) grows with time t as tk ) where the growth exponent k is slightly less than 1 because of the growth competition of islands and the competition between nucleation and growth of islands. The further results indicate that the branch width of islands b increases with increasing island size S as b -Sa, where a is approximately equal to 1/3.because of the geometrical structure of the triangular substrate.

关键词： fractal growth thin film Monte Carlo method

An Extended Subequation Rational Expansion Method and Solutions of (2+1)-Dimensional Cubic nonlinear Schr(?)dinger Equation

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Communications in Theoretical Physics 2007年第12期48卷 987-992页

作者： GUO Wei-Ming~1 LI Biao~(1,3.and CHEN Yong~(1,2,3.~1 nonlinear science Center and Department of Mathematics,Ningbo {3.,Ningbo 3.5211,china~2 Institute of Theoretical Computing,East china Normal {3.,Shanghai 200062,china~3.Key Laboratory of Mathematics Mechanization,the Chinese Academy of sciences,Beijing 100080,china nonlinear science Center and Department of Mathematics Ningbo University Ningbo 315211 China Key Laboratory of Mathematics Mechanization the Chinese Academy of Sciences Beijing 100080 China Institute of Theoretical Computing East China Normal University Shanghai 200062 China

An extended subequation rational expansion method is presented and used to construct some exact,analyt-ical solutions of the (2+1)-dimensional cubic nonlinear Schrdinger *** our results,many known solutionsof the (2+1)-dimensional cubic nonlinear Schrdinger equation can be recovered by means of some suitable selections ofthe arbitrary functions and arbitrary *** computer simulation,the properties of new non-travelling waveand coefficient function's soliton-like solutions,and elliptic solutions are demonstrated by some plots.

关键词： (2+1)-d cubic nonlinear Schrdinger equation soliton solution elliptic function soltuions

Forecasting of Stock Returns by Using Manifold Wavelet Support Vector Machine

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Journal of Shanghai Jiaotong university(science) 2010年第1期15卷 49-53页

作者：汤凌冰盛焕烨汤凌霄 Department of Computer science and Engineering Shanghai Jiaotong University Department of Computer and Electronic Engineering Hunan Business College School of Economics Changsha University of Science & Technology

An admissible manifold wavelet kernel is proposed to construct manifold wavelet support vector machine(MWSVM) for stock returns *** manifold wavelet kernel is obtained by incorporating manifold theory into wavelet technique in support vector machine(SVM).Since manifold wavelet function can yield features that describe of the stock time series both at various locations and at varying time granularities,the MWSVM can approximate arbitrary nonlinear functions and forecast stock returns *** applicability and validity of MWSVM for stock returns forecasting is confirmed through experiments on real-world stock data.

关键词： stock returns forecasting kernel manifold wavelet support vector machine (MWSVM)