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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 100049, 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.

Linear EV model with replicate observations on independent variables

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Science china mathematics 2006年第6期49卷 752-769页

作者： LIU Jixue, ZHANG Sanguo & 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 100049, china 1. department of Statistics and Finance University of Science and Technology of China Hefei 230026 China 2. department of mathematics Graduate School of Chinese Academy of Sciences Beijing 100049 China

This paper studies the linear EV model when replicate observations are made only on independent variables. We construct the estimates of regression coefficients and prove the consistency and asymptotic normality under some proper conditions. Results obtained reveal the difference between the case where the independent and dependent variables are observed repeatedly and simultaneously and the case studied in this article.

关键词： linear EV model, consistency, asymptotic normality.

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, 100049 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

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.

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 100049,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

Non-Gaussianity of Racetrack Inflation Models

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Communications in Theoretical Physics 2007年第7期48卷 189-192页

作者： SUN Cheng-Yit ZHANG De-Hai department of Physics,The graduate school of The chinese academy of sciences,beijing 100049,china department of Physics The Graduate School of The Chinese Academy of Sciences Beijing 100049 China

In this paper,we use the result in[*** and ***,arXiv:astro-ph/0510709]to calculate thenon-Gaussianity of the racetrack models in[***-Pillado,et al.,JHEP 0411(2004)063;arXiv:hep-th/0406230]and[***-Pillado,et al.,arXiv:hep-th/0603129].The two models give different *** of themare ***,we find that,for multi-field inflationary models with the non-trivial metric of the field space,the condition of the slow-roll cannot guarantee small non-Gaussianities.

关键词： non-Gaussianity non-linear parameter racetrack inflation

Geometry of Broad Line Regions of Active Galactic Nuclei

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chinese Journal of Astronomy and Astrophysics 2008年第1期8卷 50-62页

作者： Xiao-Rong Lü1 Key Laboratory for Particle Astrophysics, Institute of High Energy Physics, chinese academy of sciences, beijing 100049 2 graduate school of chinese academy of sciences, beijing 100049 Key Laboratory for Particle Astrophysics Institute of High Energy Physics Chinese Academy of Sciences Beijing 100049 and graduate school of chinese academy of sciences Beijing 100049

It has long remained an open question as to the geometry of the broad line region （BLR） in active galactic nuclei （AGNs）. The reverberation mapping technique which measures the response of the broad emission lines to the ionizing continuum, when combined with multiwavelength continuum fitted by sophisticated accretion disks, provides a way of probing the BLR geometry. We analyze a sample of 35 AGNs, which have been monitored by the reverberation mapping campaign. In view of energy budget, the reverberation-based BH masses are found to be in agreement with those obtained by accretion disk models in two thirds of the present sample while the reverberation mapping methods underestimate the BH masses in about one third of objects, as also suggested by CoUin et al. in a recent work. We point out that there are obviously two kinds of BLR geometry, which are strongly dependent on the Eddington ratio, and separated by the value LBol/LEdd - 0.1. These results prefer a scenario of the disk and wind configuration of the BLR and identify the Eddington ratio as the physical driver regulating the wind in the BLR.

关键词： accretion, accretion disks - galaxies active - galaxies Seyfert - quasars general

Structure of augmentation quotients of finite homocyclic abelian groups

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Science china mathematics 2007年第9期50卷 1280-1288页

作者： Guo-ping TANG school of Mathematical sciences,graduate University of chinese academy of sciences,beijing 100049,china 1. school of Mathematical sciences Graduate University of Chinese Academy of Sciences Beijing 100049 China

Let G be a finite abelian group and its Sylow p-subgroup a direct product of copies of a cyclic group of order p r , i.e., a finite homocyclic abelian group. Let Δ n (G) denote the n-th power of the augmentation ideal Δ(G) of the integral group ring ?G. The paper gives an explicit structure of the consecutive quotient group Q n (G) = Δ n (G)/Δ n+1(G) for any natural number n and as a consequence settles a problem of Karpilovsky for this particular class of finite abelian groups.

关键词： integral group ring augmentation ideal consecutive quotient of augmentation ideal 16S34 20C05

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.