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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, beijing 100080, china graduate school, chinese academy of sciences, beijing 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.

Twistor bundle theory and its application

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Science china mathematics 2004年第4期47卷 605-616页

作者： PENG Chia-Kuei & TANG Zizhoudepartment of mathematics, graduate school of chinese academy of sciences, beijing 100039, china department of Mathematical sciences, Tsinghua University, beijing 100084, china 1. department of mathematics Graduate School of Chinese Academy of Sciences 100039 Beijing China 2. department of Mathematical sciences Tsinghua University 100084 Beijing China

Over an oriented even dimensional Riemannian manifold(M 2m ,ds2 ), in terms of the Levi-Civita connection form Ω and the canonical form Θ on the bundle of positive orthonormal frames, we give a detailed description of the twistor bundle Гm = SO(2m)/U(m)? J +(@#@ M,ds2 ) →M. The integrability on an almost complex structureJ compatible with the metric and the orientation, is shown to be equivalent to the fact that the corresponding cross section of the twistor bundle is holomorphic with respect toJ and the canonical almost complex structureJ 1 onJ +(M,ds2 ), by using moving frame theory. Moreover, for various metrics and a fixed orientation onM, a canonical bundle isomorphism is established. As a consequence, we generalize a celebrated theorem of LeBrun.

关键词： almost complex structure, integrability, twistor bundle.

ON ASYMPTOTIC NORMALITY OF PARAMETERS IN LINEAR EV MODEL

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chinese Annals of mathematics,Series B 2002年第4期23卷 495-506页

作者： ZHANG SANGUO CHEN XIRUHua Lee-Keng Institue for applied mathematics and Information Science, graduate school of chineseacademy of sciences, beijing 100039, china. department of mathematics, graduate school of chinese academy of sciences, Hua Lee-Keng Institue for applied mathematics and Information Science Graduate School of Chinese Academy of Sciences Beijing 100039 China department of mathematics Graduate School of Chinese Academy of Sciences Beijing 100039 China

This paper studies the parameter estimation of one dimensional linear errors-in-variables(EV) models in the case that replicated observations are available in some experimental *** normality is established under mild conditions, and the parameters entering the asymptotic variance are consistently estimated to render the result useable in construction of large-sample confidence regions.

关键词： Errors-in-Variables model Asymptotic normality Replicated observations

Existence of unbiased estimate of regression parameters in simple linear EV models

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Science china mathematics 2005年第7期48卷 915-928页

作者： LIU Jixue & CHEN Xiru department of Statistics and Finance, University of Science and Technology of china, Hefei 230026, china department of mathematics, graduate school of chinese academy of sciences, beijing 10004., china department of Statistics and Finance University of Science and Technology of China Hefei 230026 China department of mathematics Graduate School Chinese Academy of Sciences Beijing 100049 China

It is well known that for one-dimensional normal EV regression model X = x+ u,Y =α+βx+e, where x, u, e are mutually independent normal variables and Eu=Ee=0, the regression parameters a and β are not identifiable without some restriction imposed on the parameters. This paper discusses the problem of existence of unbiased estimate for a and β under some restrictions commonly used in practice. It is proved that the unbiased estimate does not exist under many such restrictions. We also point out one important case in which the unbiased estimates of a and β exist, and the form of the MVUE of a and β are also given.

关键词： EV regression model unbiased estimate identiflability.

Rate of strong consistency of quasi maximum likelihood estimate in generalized linear models

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Science china mathematics 2004年第6期47卷 882-893页

作者： YUE Li & CHEN Xiru school of mathematics and Statistics, Wuhan University, Wuhan 430072, china graduate school, chinese academy of sciences, beijing 100039, china 1. school of mathematics and Statistics Wuhan University 430072 Wuhan China 2. graduate school Chinese Academy of Sciences 100039 Beijing China

Under the assumption that in the generalized linear model (GLM) the expectation of the response variable has a correct specification and some other smooth conditions, it is shown that with probability one the quasi-likelihood equation for the GLM has a solution when the sample size n is sufficiently large. The rate of this solution tending to the true value is determined. In an important special case, this rate is the same as specified in the LIL for iid partial sums and thus cannot be improved anymore.

关键词： quasi-likelihood function generalized linear models strong consistency

ON THE CENTRAL RELAXING SCHEME Ⅱ: SYSTEMS OF HYPERBOLIC CONSERVATION LAWS

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Journal of Computational mathematics 2001年第6期19卷 571-582页

作者： Hua-zhong Tang (school of Mathematical sciences, Peking University, beijing 100871, china) (LSEC,ICMSEC academy of mathematics and Systems sciences, chinese academy of sciences, beijing 100080, china) school of Mathematical sciences Peking University Beijing 100871 China

This paper continues to study the central relaxing schemes for system of hyperbolic conservation laws, based on the local relaxation approximation. Two classes of relaxing systems with stiff source term are introduced to approximate system of conservation laws in curvilinear coordinates. Based on them, the semi-implicit relaxing schemes are con- structed as in [6, 12] without using any linear or nonlinear Riemann solvers. Numerical experiments for one-dimensional and two-dimensional problems are presented to demon- strate the performance and resolution of the current schemes.

关键词： Hyperbolic conservation laws The relaxing system The central relaxing schemes The Euler equations.

Applications of URANS on predicting unsteady turbulent separated flows

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Acta Mechanica Sinica 2009年第3期25卷 319-324页

作者： Jinglei Xu Huiyang Ma department of Physics, graduate University of the chinese academy of sciences, 10004. beijing, china department of Physics Graduate University of the Chinese Academy of Sciences 100049 Beijing China

Accurate prediction of unsteady separated turbulent flows remains one of the toughest tasks and a practi cal challenge for turbulence modeling. In this paper, a 2D flow past a circular cylinder at Reynolds number 3,900 is numerically investigated by using the technique of unsteady RANS （URANS）. Some typical linear and nonlinear eddy viscosity turbulence models （LEVM and NLEVM） and a quadratic explicit algebraic stress model （EASM） are evaluated. Numerical results have shown that a high-performance cubic NLEVM, such as CLS, are superior to the others in simulating turbulent separated flows with unsteady vortex shedding.

关键词： URANS Nonlinear eddy viscosity turbulencemodel ,Separated flows Circular cylinder

CONVERGENCE OF VORTEX METHODS FOR 3-D EULER EQUATIONS

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Journal of Computational mathematics 2000年第3期18卷 239-250页

作者： Jia-fu Lin (Institute of System Science, academy of mathematics and System sciences, chinese academy of sciences, beijing, 100080, china school of Mathematical sciences, Peking University, beijing 100871, china) 中科院系统科学所北京 100080

Presents a study on the convergence of vortex methods for the three-dimensional Euler equations in bounded domains. Related studies on the convergence of vortex methods; Formulation of vortex methods; Convergence for ... 详细信息

关键词： Euler equations vortex methods convergence initial-boundary value problem

Infrared Galaxies in the Nearby Universe

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chinese Journal of Astronomy and Astrophysics 2008年第6期8卷 643-652页

作者： Jian-Ling Wang 1 National Astronomical Observatories,chinese academy of sciences,beijing 100012,china 2 graduate school of chinese academy of sciences,beijing 10004.,china National Astronomical Observatories Chinese Academy of Sciences Beijing 100012 China graduate school of chinese academy of sciences Beijing 100049 China

We used the Sloan Digital Sky Survey （SDSS） Data Release 5 （DR5） to study the morphological properties of 1137 nearby infrared （IR） galaxies, most of which are brighter than 15.9 mag in r-band. This sample was drawn from a cross-correlation of the Infra-Red Astronomical Satellite （IRAS） point source catalog redshift survey with DR5 at z ≤ 0.08. Based on this IR galaxy sample, we constructed five volume-limited sub-samples with IR luminosity ranging from 10^9.5 L⊙ to 10^12L⊙. By deriving the IR luminosity functions （LF） for different morphological types, we found that normal spiral galaxies are the dominant population below LIR ~ 8 ~ 10^10 L⊙; while the fraction of barred spiral galaxies increases with increasing IR luminosity and becomes dominant in spiral galaxies beyond LIR ≈ 5 × 10^10L⊙. As the IR luminosity decreases, the IR galaxies become more compact and have lower stellar masses. The analysis also shows that normal spiral galaxies give the dominant contribution to the total comoving IR energy density in the nearby universe, while, in contrast, the contribution from peculiar galaxies is only 39%.

关键词： galaxies evolution galaxies interactions galaxies starburst infrared galaxies galaxies luminosity function