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Transformations and non-degenerate maps

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Science China Mathematics 2005年第z1期48卷 195-205页

作者： LI Baokui & WANG Yuefei Institute of Mathematics, academy of Mathematics and System sciences, chinese academy of sciences, {3. 100080, China Graduate School, chinese academy of sciences, {3. 100080, China 1. Institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China 2. Graduate School Chinese Academy of Sciences 100080 Beijing China

We shall prove the equivalences of a non-degenerate circle-preserving map and a M(o)bius transformation in ^Rn, of a non-degenerate geodesic-preserving map and an isometry in Hn of a non-degenerate line-preserving map and an affine transformation in Rn. That a map is non-degenerate means that the image of the whole space under the map is not a circle, or geodesic or line respectively. These results hold without either injective or surjective, or even continuous assumptions, which are new and of a fundamental nature in geometry.

关键词： M(o)bius transformation, circle-preserving map, non-degenerate map.

A Remark on Using Gravitational Lensing Probability as a Probe of the Central Regions of CDM Halos

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chinese Journal of Astronomy and Astrophysics 2002年第5期2卷 399-407页

作者： YunLiNational Astronomical Observatories, chinese academy of sciences, beijing 100012 National Astronomical Observatories Chinese Academy of Sciences Beijing 100012

We calculate the gravitational lensing probabilities by cold dark matter (CDM) halos with different density profiles, and compare them with current observations from the Cosmic Lens All-Sky Survey (CLASS) and the Jodrell-Bank VLA Astrometric Survey (JVAS). We find that the lensing probability is dramatically sensitive to the clumping of the dark matter, or quantitatively, the concentration parameter. We also find that our predicted lensing probabilities in most cases show inconsistency with the observations. It is argued that high lensing probability may not be an effective tool for probing the statistical properties of inner structures of dark matter halos.

关键词： cosmology: dark matter - gravitational lensing - cosmology:theory - galaxies: halos

Investigation of a New Exsolved Cu-Fe-S Phase in“Abnormal Sphalerite”

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Acta Geologica Sinica(English Edition) 1991年第1期65卷 27-36,110-111页

作者： Li Jiuling Wang Su Institute of Mineral Deposits, chinese academy of Geolgical sciences,{3. {3. Laboratory of Electron Microscopy, chinese academy of sciences, {3. Institute of Mineral Deposits Chinese Academy of Geolgical Sciences Beijing China

A new exsolved copper-iron-sulfur phase in sphalerite has been found in the Dajing cassiterite- sulfidecopper-silver-tin deposit, Inner Mongolia, China. After investigating the optical properties, chemical composi-tion, crystal structure and exsolved Characters of the exsolved phase, the authors present important evidencefor its being a new exsolved copper-iron-sulfur phase mineral. Its formation mechenism is discussed in consider-ing heating experiments, phase equilibrium data and the geology of the deposit.

关键词： Ph Fe Abnormal Sphalerite Cu

NONPARAMETRIC APPROACH TO IDENTIFYING NARX SYSTEMS

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Journal of Systems Science & Complexity 2010年第1期23卷 3-21页

作者： Qijiang SONG·Han-Pu CHEN Key Laboratory of Systems and Control,Institute of Systems Science,academy of Mathematics and Systems Science,chinese academy of sciences,beijing 100190,China Key Laboratory of Systems and Control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences

This paper considers identification of the nonlinear autoregression with exogenous inputs(NARX system).The growth rate of the nonlinear function is required be not faster than linear withslope less than *** value of f(·) at any fixed point is recursively estimated by the stochasticapproximation (SA) algorithm with the help of kernel *** consistency of the estimatesis established under reasonable conditions,which,in particular,imply stability of the *** simulation is consistent with the theoretical analysis.

关键词： α-mixing geometrically ergodic Markov chains NARX nonparametric recursive estimate stochastic approximation strongly consistent.

Subspace Search Method for Quadratic Programming With BoxConstraints

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Journal of Computational Mathematics 1999年第3期17卷 307-314页

作者： Zi-luan Wei(ICMSEC, chinese academy of sciences, beijing 100080, China) 中科院计算数学与科学工程计算所北京

A subspace search method for solving quadratic programming with box constraints is presented in this paper. The original problem is divided into many independent subproblem at an initial point, and a search direction is obtained by solving each of the subproblem, as well as a new iterative point is determined such that the value of objective function is decreasing. The convergence of the algorithm is proved under certain assumptions, and the numerical results are also given.

关键词： subspace search method quadratic programing matrix splitting

Ambient noise near the sea-route

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Science China(Physics,Mechanics & Astronomy) 2009年第1期52卷 40-45页

作者： HE Li1,2, LI ZhengLin1,3.& PENG ZhaoHui1 1 National Laboratory of Acoustics, Institute of Acoustics, chinese academy of sciences, beijing 100190, China 2 Institute of Geology and Geophysics, chinese academy of sciences, {3. 100029, China 3.NanHai Laboratory of Acoustics, Institute of Acoustics, chinese academy of sciences, Haikou 570206, China National Laboratory of Acoustics Institute of Acoustics Chinese Academy of Sciences Beijing 100190 China Institute of Geology and Geophysics Chinese Academy of Sciences Beijing 100029 China NanHai Laboratory of Acoustics Institute of Acoustics Chinese Academy of Sciences Haikou 570206 China

Ambient noise data measured in an experiment conducted in shallow water near a sea-route were analyzed. It was observed that, at low frequency, the horizontal correlation has an obvious difference from that predicted by the classical ambient noise model. The theoretical analyses show that this phenomenon is caused by wind noise together with the discrete shipping noise nearby. An ambient noise model was proposed to include the effects caused by both the noise sources. Data measured at different times verify that the proposed model can be used to forecast the ambient noise field in shallow water near the sea-route.

关键词： ambient noise model horizontal correlation discrete ships

GAUSS-SEIDEL-TYPE MULTIGRID METHODS

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Journal of Computational Mathematics 2003年第4期21卷 421-434页

作者： Zhao-hui Huang Qian-shun Chang (academy of Mathematics and System sciences, chinese academy of sciences, {3. 100080, China) academy of Mathematics and System sciences Chinese Academy of Sciences Beijing 100080 China

By making use of the Gauss-Seidel-type solution method, the procedure for computing the interpolation operator of multigrid methods is simplified. This leads to a saving of computational time. Three new kinds of interpolation formulae are obtained by adopting different approximate methods, to try to enhance the accuracy of the interpolatory operator. A theoretical study proves the two-level convergence of these Gauss-Seidel-type MG methods. A series of numerical experiments is presented to evaluate the relative performance of the methods with respect to the convergence factor, CPU-time(for one V-cycle and the setup phase) and computational complexity.

关键词： Multigrid methods Gauss-Seidel solution Interpolation formula Convergence.

PROBABILISTIC NUMERICAL APPROACH FOR PDE AND ITS APPLICATION IN THE VALUATION OF EUROPEAN OPTIONS

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Journal of Computational Mathematics 2001年第6期19卷 591-600页

作者： Dong-sheng Wu (Institute of Systems Science, academy of Mathematics and Systems sciences, chinese academy of sciences, {3. 100080, China ) 中科院系统科学所北京 100080

Presents a probabilistic numerical approach for a class of probabilistic differential equation. Application of the Brownian motion and Monte-Carlo method; Application in the valuation of European Options.

关键词： Brownian motion probabilistic numerical solution European Options

MODELLING AND NUMERICAL SOLUTIONS OF A GAUGE PERIODIC TIME DEPENDENT GINZBURG-LANDAU MODEL FOR TYPE-Ⅱ SUPERCONDUCTORS

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Journal of Computational Mathematics 1997年第4期15卷 365-384页

作者： Zhi-ming Chen (Institute of Mathematics, chinese academy of sciences, beijing, China) 中科院数学所北京

In this paper we seek the solutions of the time dependent Ginzburg-Landau model for type-Ⅱ superconductors such that the associated physical observables are spatially periodic with respect to some lattice whose basic lattice cell is not necessarily rectangular. After appropriately foring the gange, the model can be formulated as a system of nonlinear parabolic partial differential equations with quasi-periodic boundary conditions. We first give some results concerning the existence, uniqueness and regularity of solutions and then we propose a semiimplicit finite element scheme solving the system of nonlinear partial dmerential equations and show the optimal error estimates both in the L2 and energy *** also report on some numerical results at the end of the paper.

关键词： Math QT MODELLING AND NUMERICAL SOLUTIONS OF A GAUGE PERIODIC TIME DEPENDENT GINZBURG-LANDAU MODEL FOR TYPE SUPERCONDUCTORS