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A unified dynamic model for locomotion and manipulation of a snake-like robot based on differential geometry

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Science china(Information sciences) 2011年第2期54卷 318-333页

作者： WANG ZhiFeng1,3, MA ShuGen1,2, LI Bin1 & WANG YueChao1 1State Key Laboratory of Robotics, Shenyang Institute of Automation, chinese academy of sciences, Shenyang 110016, china 2Department of Robotics, Ritsumeikan university, Shiga-ken 525-8577, Japan 3graduate university of chinese academy of sciences, beijing 1.0039, china 1. State Key Laboratory of Robotics Shenyang Institute of Automation Chinese Academy of Sciences Shenyang 110016 China3. Graduate University of Chinese Academy of Sciences Beijing 100039 China2. Department of Robotics Ritsumeikan University Shiga-ken 525-8577 Japan

A snake-like robot, whose body is a seried-wound articulated mechanism, can move in various environments. In addition, when one end is fixed on a base, the robot can manipulate objects. A method of dynamic modeling for locomotion and manipulation of the snake-like robot is developed in order to unify the dynamic equations of two states. The transformation from locomotion to manipulation is a mechanism reconfiguration, that is, the robot in locomotion has not a fixed base, but it in manipulation has one. First, a virtual structure method unifies the two states in mechanism (e.g., an embedding in the configuration space); second, the product-of-exponentials formula describes the kinematics; third, the dynamics of locomotion and manipulation are established in a Riemannian manifold; finally, based on the analysis of the dynamic model, the dynamics of manipulation can be directly degenerated from those of locomotion, and this degeneration relation is proved through using the Gauss equations. In the differential geometry formulation, this method realizes the unification of the dynamics of locomotion and manipulation. According to a geometrical point of view, the unified dynamic model for locomotion and manipulation is considered as a submanifold problem endowed with geometric meaning. In addition, the unified model offers an insight into the dynamics of the snake-like robot beyond the dynamic model separately established for locomotion or manipulation.

关键词： snake-like robot dynamics unified model differential geometry locomotion manipulation

RADIAL BASIS FUNCTION INTERPOLATION IN SOBOLEV SPACES AND ITS APPLICATIONS

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Journal of Computational Mathematics 2007年第2期25卷 201-210页

作者： Manping Zhang (School of Mathematical sciences,Fudan university,Shanghai 200433,china Institute of Computational Mathematics,chinese academy of sciences,beijing 100080,china School of Mathematical sciences Fudan University Shanghai 200433 China Institute of Computational Mathematics Chinese Academy of Sciences Beijing 100080 China

In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space H^k（Ω）（k 〉 1）. With a special kind of radial basis function, we construct a basis in H^k（Ω） and derive a meshless method for solving elliptic partial differential equations. We also propose a method for computing the global data density.

关键词： Sobolev space Radial basis function Global data density Meshless method

Convergence analysis of the adaptive finite element method with the red-green refinement

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Science china Mathematics 2010年第2期53卷 499-512页

作者： ZHAO XuYing 1, 3 , HU Jun 2,? & SHI ZhongCi 1 1 State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, academy of Mathematics and Systems Science, chinese academy of sciences, beijing 100190, china 2 Key Laboratory of Mathematics and Applied Mathematics (Peking university), Ministry of Education and School of Mathematical sciences, Peking university, beijing 100871, china 3 graduate university of chinese academy of sciences, beijing 100190, china 1. State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China3. Graduate University of Chinese Academy of Sciences Beijing 100190 China2. Key Laboratory of Mathematics and Applied Mathematics (Peking University) Ministry of Education and School of Mathematical Sciences Peking University Beijing 100871 China

In this paper, we analyze the convergence of the adaptive conforming P 1 element method with the red-green refinement. Since the mesh after refining is not nested into the one before, the Galerkin-orthogonality does not hold for this case. To overcome such a difficulty, we prove some quasi-orthogonality instead under some mild condition on the initial mesh (Condition A). Consequently, we show convergence of the adaptive method by establishing the reduction of some total error. To weaken the condition on the initial mesh, we propose a modified red-green refinement and prove the convergence of the associated adaptive method under a much weaker condition on the initial mesh (Condition B).

关键词： red-green refinement adaptive finite element method convergence non-nested local refinement

Relationship between Surface Pollen and Modern Vegetation in Southwestern china

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Journal of Mountain Science 2010年第2期7卷 176-186页

作者： PAN Tao DAI Erfu and WU Shaohong Institute of Geographic sciences and Natural Resources Research Chinese Academy of Sciences Beijing 100101 China graduate university of chinese academy of sciences BeO'ing 100049 China Institute of Tibetan Plateau Research Chinese Academy of Sciences Beijing 100085 China

Based on the pollen data obtained from thirty-five surface soil samples and investigated vegetation data from seven plant quadrats,the quantitative relationship between surface soil pollen and modern vegetation are studied in the longitudinal range-gorge region (LRGR) in Southwestern china.R-values (referring to pollen assemblages) are calculated with pollen percentage and plant *** coefficients of similarity between pollen and vegetation are *** results show that the pollen assemblages on surface soil of all vegetation zones can basically represent the native vegetation,but the pollen assemblages are not fully according with the *** is due to the influencing factors including pollen preservation ability,pollen production,amount of exotic pollen and pollen *** pollen representation in surface soil is different in families and *** pollen of woody plants such as Pinus,Tsuga,Alnus,Fagus and Castanopsis are over-representative,but those of Quercus,Carpinus Myrica,Elaeocarpaceae,Ericaceae,Theaceae and Llex are underrepresentative;the pollen of herbaceous plants such as Artemisia and Rubiaceae are over-representative,while those of others including Gramineae and Araliaceae are *** R-values of the same taxon pollen in different vegetation zones are different,depending on their distances from the pollen *** coefficients of the similarity between plant communities and pollen assemblages are mostly over 70%,which indicate again that the surface soil pollen and spores assemblages can represent the *** is concluded that there is a good corresponding relationship between surface pollen assemblages and native vegetation in LRGR,and it is of great significance for reconstructing the past vegetation and paleoclimate using quantitative fossil pollen data in this region.

关键词： Longitudinal range-gorge region (LRGR) Pollen assemblage Vegetation R-value Coefficient of similarity

SiO/CNTs:A new anode composition for lithium-ion battery

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Science china Chemistry 2009年第12期52卷 2047-2050页

作者： REN YuRong1,2,3?,QU MeiZhen1 & YU ZuoLong1 1 Chengdu Institute of Organic Chemistry,chinese academy of sciences,Chengdu 610041,china 2 College of Chemistry,Jilin Normal university,Siping 136000,china 3 graduate university of chinese academy of sciences,beijing 1.0039,china 1. Chengdu Institute of Organic Chemistry Chinese Academy of Sciences Chengdu 610041 China 2. College of Chemistry Jilin Normal University Siping 136000 China 3. graduate university of chinese academy of sciences Beijing 100039 China

A new anode composition SiO/CNTs (carbon nanotubes) has been prepared by chemical vapor deposition (CVD) method. The results of scanning electron microscopy (SEM) confirm that CNTs deposit on small SiO particles,form a cage,and enwrap SiO particles tightly. SiO/CNTs anode composition exhibits an initial discharge and charge capacity of 1171 and 789 mAh/g,and maintains a reversible capacity of 500 mAh/g after 80 cycles. The improvement of the cyclic performance for SiO/CNTs composition is related to the maintaining of the electric network during cycling,which benefits from a tight contact between CNTs and SiO particles.

关键词： SiO/CNTs CVD composition anode Li-ion battery

The red damping wing of Gunn-Peterson trough in the high redshift GRBs

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Science china(Physics,Mechanics & Astronomy) 2009年第9期52卷 1428-1433页

作者： XU Zhou1,2 & WEI DaMing1,3 1 Purple Mountain Observatory, chinese academy of sciences, Nanjing 210008, china 2 graduate university of chinese academy of sciences, beijing 100012, china 3 Joint Center for Particle Nuclear Physics and Cosmology of Purple Mountain Observatory-Nanjing university, Nanjing 210008, china Purple Mountain Observatory Chinese Academy of Sciences Nanjing 210008 China graduate university of chinese academy of sciences Beijing 100012 China Joint Center for Particle Nuclear Physics and Cosmology of Purple Mountain Observatory-Nanjing university Nanjing 210008 China

We calculate the red damping wing of Gunn-Peterson trough taking the evolution of the neutral fraction into consideration and take a clear look at the ionized region around the ionizing sources. We get the result that the damping wing flux feature is mainly determined by the neutral hydrogen outside the ionized bubble and the cut off in the damping wing would be useful to get the size of the ionized bubble. We also fit the red damping wing of the recently discovered high redshift GRB080913 and find that the ionized bubble is too small to create apparent cut off in the spectrum of this burst.

关键词： cosmology theory intergalactic medium gamma ray burst

THE DUAL MIXED METHOD FOR AN UNILATERAL PROBLEM

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Journal of Computational Mathematics 2003年第6期21卷 733-746页

作者： Lie-heng Wang(LSEC, ICMSEC, academy of Mathematics and System sciences, chinese academy of sciences,beijing 100080, china) LSEC ICMSEC Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China

In this paper, the dual mixed method for an unilateral problem, which is the simplified modelling of scalar function for the friction-free contact problem, is considered. The dual mixed problem is introduced, the existence and uniqeness of the solution of the problem are presented, and error bounds O(h3/4) and O(h3/2) are obtained for the dual mixed finite element approximations of Raviart-Thomas elements for k = 0 and k = 1 respectively.

关键词： Dual Mixed Method Unilateral Problem.

A CLASS OF NEW PARALLEL HYBRID ALGEBRAIC MULTILEVEL ITERATIONS

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Journal of Computational Mathematics 2001年第6期19卷 651-672页

作者： Zhong-zhi Bai (LSEC ICMSEC, academy of Mathematics and Systems sciences, chinese academy of sciences, beijing 100080, china) 中科院计算数学与科学工程计算所北京 100080

Presents preconditioning matrices having parallel computing function for the coefficient matrix and a class of parallel hybrid algebraic multilevel iteration methods for solving linear equations. Solution to elliptic ... 详细信息

关键词： elliptic boundary value problem system of linear equations symmetric positive definite matrix multilevel iteration parallel method

Nonlinear autoregressive models with heavy-tailed innovation

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Science china Mathematics 2005年第3期48卷 333-340页

作者： JIN Yang & AN Hongzhi School of Statistics, Renmin university of china, beijing 100872, china academy of Mathematics and Systems Science, chinese academy of sciences, beijing 100080, china Sch. of Statistics Renmin Univ. of China Beijing 100872 China Acad. of Mathematics and Syst. Sci. Chinese Acad. of Sci. Beijing 100080 China

In this paper, we discuss the relationship between the stationary marginal tail probability and the innovation's tail probability of nonlinear autoregressive models. We show that under certain conditions that ensure the stationarity and ergodicity, one dimension stationary marginal distribution has the heavy-tailed probability property with the same index as that of the innovation's tail probability.

关键词： nonlinear autoregressive model, innovation, tail probability.