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A new smoothing scheme for mathematical programs with complementarity constraints

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Science china Mathematics 2010年第7期53卷 1881-1890页

作者： YAN Taodepartment of information and Computational Sciences, College of Science, {2. {3. of Science and technology, {2. 2.0094, china department of information and Computational Sciences College of Science Nanjing University of Science and Technology Nanjing China

In this paper, we consider a mathematical program with complementarity constraints (MPCC). We present a new smoothing scheme for this problem, which makes the primal structure of the complementarity part unchanged mostly. For the new smoothing problem, we show that the linear independence constraint qualification (LICQ) holds under some conditions. We also analyze the convergence behavior of the smoothing problem, and get some sufficient conditions such that an accumulation point of stationary points of the smoothing problems is C (M, B)-stationarity respectively. Based on the smoothing problem, we establish an algorithm to solve the primal MPCC problem. Some numerical experiments are given in the paper.

关键词： mathematical program with complementarity constrains MPEC-LICQ B-stationarity C-stationarity M-stationarity

Heuristic for no-wait flow shops with makespan minimization based on total idle-time increments

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Science in china(Series F) 2008年第7期51卷 896-909页

作者： LI XiaoPing1,2.& WU Cheng3.1 School of Computer Science & Engineering, Southeast university, nanjing 2.0096,{2. 2.Key Laboratory of Computer Network and information Integration (Southeast university), Ministry of Education, nanjing 2.0096,{2. 3.department of Automation, Tsinghua university, Beijing 100084,{2. School of Computer Science & Engineering Southeast University Nanjing China Key Laboratory of Computer Network and information Integration (Southeast university) Ministry of Education Nanjing China department of Automation Tsinghua University Beijing China

No-wait flow shops with makespan minimization are classified as NP-hard. In this paper, the optimization objective is equivalently transformed to total idle-time minimization. The independence relationship between tasks is analyzed, and objective increment properties are established for the fundamental operators of the heuristics. The quality of the new schedules generated during a heuristic is judged only by objective increments and not by the traditional method, which computes and compares the objective of a whole schedule. Based on objective increments, the time complexity of the heuristic can be decreased by one order. A seed phase is presented to generate an initial solution according to the transformed objective. Construction and improvement phases are introduced by experimental analysis. The FCH （fast composite heuristic） is proposed and compared with the most effective algorithms currently available for the considered problem. Experimental results show that the effectiveness of the FCH is similar to that of the best methods but requires far less computation time. The FCH can also be efficient in real time scheduling and rescheduling for no-wait flow shops.

关键词： no-wait flow shops heuristic makespan Tabu search

Travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation

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Science china Mathematics 2011年第3期54卷 555-572页

作者： DENG ShengFu1, GUO BoLing2.& WANG TingChun2.3.1department of Mathematics, Zhanjiang Normal {3., Zhanjiang 52.048,{2. 2.nstitute of Applied Physics and Computational Mathematics, Beijing 100088,{2. 3.College of Math and Physics, nanjing {3. of information Science and technology, nanjing 2.0044,{2. department of Mathematics Zhanjiang Normal University Zhanjiang China Institute of Applied Physics and Computational Mathematics Beijing China College of Math and Physics Nanjing University of Information Science and Technology Nanjing China

The travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation ut-uxxt + (1 + b)umux = buxuxx + uuxxx are considered where b > 1 and m are positive integers. The qualitative analysis methods of planar autonomous systems yield its phase portraits. Its soliton wave solutions, kink or antikink wave solutions, peakon wave solutions, compacton wave solutions, periodic wave solutions and periodic cusp wave solutions are obtained. Some numerical simulations of these solutions are also given.

关键词： homoclinic orbits heteroclinic orbits peakon wave solutions compacton wave solutions periodic cusp wave solutions

A Note on the Completeness of an Exponential Type Sequence

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Chinese Annals of Mathematics,Series B 2011年第4期32卷 527-532页

作者： Jinhui FANG department of Mathematics Nanjing University of Information Science and Technology Nanjing 210044 China

For any given coprime integers p and q greater than 1, in 1959, B proved that all sufficiently large integers can be expressed as a sum of pairwise terms of the form p^aq^b. As Davenport observed, Birch＇s proof can be modified that the exponent b can be bounded in terms of p and q. In 2.00, N. Hegyvari effective version of this bound. The author improves this bound.

关键词： Complete sequence Coprime Residue J. Birch distinct to show gave an

Robustness and breakup of the spiral wave in a two-dimensional lattice network of neurons

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Science china(Physics,Mechanics & Astronomy) 2010年第4期53卷 672-679页

作者： MA Jun 1,2. TANG Jun 2., ZHANG AiHua 3.& JIA Ya 2.1 {3. of Physics, Lanzhou university of {2., Lanzhou 73.050, china 2.{3. of Physics, Central china Normal university, Wuhan 43.079, china 3.College of Electrical and information Engineering, Lanzhou university of {2., Lanzhou 73.050, china department of Physics Lanzhou University of Technology Lanzhou China department of Physics Central China Normal University Wuhan China College of Electrical and information Engineering Lanzhou University of Technology Lanzhou China

The robustness and breakup of spiral wave in a two-dimensional lattice networks of neurons are investigated. The effect of small- world type connection is often simplified with local regular connection and the long-range connection with certain probability. The network effect on the development of spiral wave can be better described by local regular connection and changeable long-range connection probability than fixed long-range connection probability because the long-range probability could be changeable in realistic biological system. The effect from the changeable probability for long-range connection is simplified by multiplicative noise. At first, a stable rotating spiral wave is developed by using appropriate initial values, parameters and no-flux boundary conditions, and then the effect of networks is investigated. Extensive numerical studies show that spiral wave keeps its alive and robust when the intensity of multiplicative noise is below a certain threshold, otherwise, the breakup of spiral wave occurs. A statistical factor of synchronization in two-dimensional array is defined to study the phase transition of spiral wave by checking the membrane potentials of all neurons corresponding to the critical parameters(the intensity of noise or forcing current)in the curve for factor of synchronization. The Hindmarsh-Rose model is investigated, the Hodgkin-Huxley neuron model in the presence of the channel noise is also studied to check the model independence of our conclusions. And it is found that breakup of spiral wave is easier to be induced by the multiplicative noise in presence of channel noise.

关键词： spiral wave factor of synchronization breakup multiplicative noise robustness

Simulation study of phase retrieval for hard X-ray in-line phase contrast imaging

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Science china(Physics,Mechanics & Astronomy) 2005年第4期48卷 450-458页

作者： YU Bin1,2. PENG Xiang1,2. TIAN Jindong1, NIU Hanben1, DIAO Luhong3.& LI Hua3.1. Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education, Institute of Optoelec- tronics, Shenzhen university, Shenzhen 518060,{3. 2. State Key Laboratory of Precision Measuring {2. and Instruments, Tianjin university, Tianjin 3.0072.china 3. Key Laboratory of Intelligent information Processing, Institute of Computing {2., Chinese Academy of Sciences, Beijing 100080,china Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education Institute of Optoelectronics Shenzhen University Shenzhen China State Key Laboratory of Precision Measuring technology and Instruments Tianjin University Tianjin China Key Laboratory of Intelligent information Processing Institute of Computing Technology Chinese Academy of Sciences Beijing China

Two algorithms for the phase retrieval of hard X-ray in-line phase contrast imaging are presented. One is referred to as Iterative Angular Spectrum Algorithm (IASA) and the other is a hybrid algorithm that combines IASA with TIE (transport of intensity equation). The calculations of the algorithms are based on free space propagation of the angular spectrum. The new approaches are demonstrated with numerical simulations. Comparisons with other phase retrieval algorithms are also performed. It is shown that the phase retrieval method combining the IASA and TIE is a promising technique for the application of hard X-ray phase contrast imaging.

关键词： X-ray optics, phase contrast imaging, phase retrieval, angular spectrum, hard X-ray.

Study on NDVI-T_s space by combining LAI and evapotranspiration

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Science china Earth Sciences 2006年第7期49卷 747-754页

作者： HAN Lijuan1,2.3. WANG Pengxin4, YANG Hua1,2.3. LIU Shaomin1,2.3.& WANG Jindi1,2.3.1. Research Center for Remote Sensing and GIS, School of Geography, Beijing Normal university, Beijing 100875, china 2. State Key Laboratory of Remote Sensing Science, Beijing 100875, china 3. Beijing Key Laboratory for Remote Sensing of Environment and Digital Cities, Beijing 100875, china 4. department of information Management, College of information and Electronic Engineering, china Agricultural university, Beijing 100083. china Research Center for Remote Sensing and GIS School of Geography Beijing Normal University Beijing China State Key Laboratory of Remote Sensing Science Beijing China Beijing Key Laboratory for Remote Sensing of Environment and Digital Cities Beijing China department of information Management College of Information and Electronic Engineering China Agricultural University Beijing China

This paper focuses on interpreting the different spatial relationships between NDVI and Ts, a triangular or a trapezoid, and on analyzing transformation conditions, the physical and ecological meanings of the vegetation index-surface temperature space as well. Further, we use the Tempera-ture-Vegetation Dryness Index (TVDI) to explain the existent meaning of a triangular space after NDVI reaches its saturated state by employing the relationships between NDVI, LAI and evapotranspiration. The specific relations between NDVI and Ts are useful for describing, validating and updating land surface models.

关键词： NDVI, land surface temperature, evapotranspiration, leave area index.

Sufficient and necessary conditions for Lyapunov stability of Lorenz system and their application

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Science china(information Sciences) 2010年第8期53卷 1574-1583页

作者： LUO Qi 1 , LIAO XiaoXin 2.& ZENG ZhiGang 2.1 College of information and Control, {3. {2. of information Science and technology, nanjing 2.0044, china 2.department of Control Science and Engineering, Huazhong {2. of Science and technology, Image Processing and Intelligent Control Key Laboratory of Education Ministry of china, Wuhan 43.074, china College of information and Control Nanjing University of Information Science and Technology Nanjing China department of Control Science and Engineering Huazhong University of Science and Technology Image Processing and Intelligent Control Key Laboratory of Education Ministry of China Wuhan China

The sufficient and necessary conditions for Lyapunov stability of the zero equilibrium point of Lorenz system are discussed, and some brief criteria are presented for globally exponential stability, globally asymptotical stability and instability. Furthermore, the behavior of the non-zero equilibrium point of Lorenz system is also investigated, and several sufficient and necessary conditions are provided for locally exponential stability and instability. The established theorems in this paper develop and extend the existing achievements on Lyapunov stability of Lorenz system. In conclusion, by applying the obtained results, some less conservative feedback-control laws are derived to guarantee the globally exponential stability of the chaos control of Chen system, Lu¨ system, Yang-Chen system and Yu-Xia Li system.

关键词： Lorenz system Lyapunov stability sufficient and necessary condition bifurcation values globally exponential synchronization

On the new results of global attractive set and positive invariant set of the Lorenz chaotic system and the applications to chaos control and synchronization

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Science in china(Series F) 2005年第3期48卷 304-321页

作者： LIAO Xiaoxin 1, 2. 3., FU Yuli 4 & XIE Shengli 4 1. department of Control Science & Control Engineering, Huazhong university of Science & {2., Wuhan 43.074, china 2. School of Automation, Wuhan university of Science & {2., Wuhan 43.070, china 3. School of information, Central South university of Economy, Politics and Law, Wuhan 43.064, china 4. School of Electronics & information Engineering, South china university of {2., Guangzhou 510640, china Correspondence should be addressed to Liao Xiaoxin (email: xiaoxin_liao@***) department of Control Science & Control Engineering Huazhong University of Science & Technology Wuhan China School of Automation Wuhan University of Science & Technology Wuhan China School of information Central South University of Economy Politics and Law Wuhan China School of Electronics & information Engineering South China University of Technology Guangzhou China

Constructing a family of generalized Lyapunov functions, a new method is proposed to obtain new global attractive set and positive invariant set of the Lorenz chaotic system. The method we proposed greatly simplifies the complex proofs of the two famous estimations presented by the Russian scholar Leonov. Our uniform formula can derive a series of the new estimations. Employing the idea of intersection in set theory, we extract a new Leonov formula-like estimation from the family of the estimations. With our method and the new estimation, one can confirm that there are no equilibrium, periodic solutions, almost periodic motions, wandering motions or other chaotic attractors outside the global attractive set. The Lorenz butterfly-like singular attractors are located in the global attractive set only. This result is applied to the chaos control and chaos synchronization. Some feedback control laws are obtained to guarantee that all the trajectories of the Lorenz systems track a periodic solution, or globally stabilize an unstable (or locally stable but not globally asymptotically stable) equilibrium. Further, some new global exponential chaos synchronization results are presented. Our new method and the new results are expected to be applied in real secure communication systems.

关键词： Lorenz chaotic system global attractive set positive invariant set globally exponential tracking globally exponential synchronization.