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Point Groups and Single Forms of Quasicrystals with Eightfold and Twelvefold Symmetry

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Acta Geologica Sinica(English Edition) 1989年第1期63卷 39-43页

作者： Shi Nicheng and Liao Libing Beijing graduate school, China University of Geosiences, Beijing Beijing graduate school China University of Geosiences Beijing

This paper mainly deals with the point groups and single forms of octagonal quasicrystals and the description of one-dimensional quasilattice. The authors present a new sequence for describing the arrangement of quasiperiods in one-dimensional quasilattice. The first ten numbers of quasiperiods of this sequence are 1, 1, 2, 5, 12, 29, 70, 169, 408 and 985. The arrangement of quasiperiods in the first five steps are a, b, ab. babab and babababbabab. Seven p(?)nt groups and nine single forms for the octagonal system have been deduced, They are as follows: Point groups: 8.8m, 82, 8/m, 8/mmm, 8 and 82m; single forms: octagonal prism, dioctagonal prism. octagonal pyramid. dioctagonal pyramid. octagonal dipyramid, dioctagonal dipyramid, octagonal scalenohedron, dioctagonal scalenohedron and octagonal trapezohedron. Besides seven point groups and nine single forms for the dodecahegonal system have also been deduced.

关键词： Point Groups and Single Forms of Quasicrystals with Eightfold and Twelvefold Symmetry

THE　4~Σ-　STATES　OF　THE　FO　RADICAL

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Chinese Chemical Letters 1996年第5期7卷 475-478页

作者： Ming Bao HUANG (Department of Chemistry, graduate school, Academia Sinica, Beijing 100039) Department of Chemistry Graduate School Academia Sinica Beijing 100039

Abstract: For investigating the 4Σ- 4Σ- transition in the FO radical to which an observed 268 nm ASE line has been attributed. the potential energy energy of the four lowest-lying 4A2 states of FO have been calculated using the NIRSDCI method. The results indicate that the first 4Σ- (14A2) and the upper 4Σ- (44A2) States are weakly bound and bound states respectively, and the 24A2 and 34A2 States are both repulsive States which are not relevant to the emission. The predicted Te value for the 4Σ-→4Σ- transition is 4.62 eV, which is in excellent agreement with the photon energy value (4.63 eV) of the ASE line. The procedure of our MRSDCI calculations for excited states is described in detail, and the previous calculation results for these States are discussed.

关键词： ENERGY EXTRAPOLATION CI CALCULATIONS

Effect of Crystallinity on Electrochemical Insertion/Extraction of Li in Transition Metal Oxides Part I: LiMn_2O_4 and LiCo_(0.5)Ni_(0.5)O_2

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Journal of Materials Science & Technology 1999年第6期15卷 509-514页

作者： Tomoki TSUMURA and Michio INAGAKI (graduate school of Engineering, Hokkaido University Kita-ku, Sapporo, 060-8628 Japan) Hokkaido Univ Grad Sch Engn Kita Ku Sapporo Hokkaido 0608628 Japan

Electrochemical insertion/extraction of Li on cathode materials of spinel type LiMn2O4 and ordered rock-salt type LiCo0.5 Ni0.5O2 was measured on samples of which structures were well characterized. On the basis of experimental results on structure, morphology and charge-discharge characteristics, the effect of crystallinity of the cathode materiaIs on electrochemical Li insertion/extraction performance was discussed. These two transition metal oxides belong to onegroup that the crystallinity of these oxides affects to the performance.

关键词： LiMn2O4 and LiCo Effect of Crystallinity on Electrochemical Insertion/Extraction of Li in Transition Metal Oxides Part I O2 Ni

Effect of Crystallinity on Electrochemical Insertion/Extraction of Li in Transition Metal Oxides Part Ⅱ: TiO_2, V_2O_5 and MoO_3

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Journal of Materials Science & Technology 2000年第1期16卷 5-14页

作者： Tomoki TSUMURA and Michio INAGAKI (graduate school of Engineering, Hokkaido University Kita-ku, Sapporo, 060-8628, Japan) graduate school of Engineering Hokkaido University Kita-ku Sapporo 060-8628 Japan NARD Institute Ltd. 2 Nishinagasu Amagasaki 660-0805 Japan Aichi Institute of Technology Yakusa Toyota 470-0392 Japan

Electrochemical insertion/extraction of Li on cathode materials of anatase type TiO_2, quasilayered structure V_2O_5 and layered structure MoO_3 was measured on samples of which structures were well characterized and showed a wide range of crystallinity. On the basis of experimental results on structure, morphology and charge-discharge characteristics, the effect of crystallinity of the cathode materials on electrochemical Li insertion/extraction pedermance was discussed. These three transition metal oxides were classified as one group on the basis of whether the crystallinity of these oxides affects to the performance or not; LiMn_2O_4 and LiCo_(0.5)O_2 belongs to the former group and TiO_2, V_2O_5 and MoO_3 to the latter.

关键词： Li Effect of Crystallinity on Electrochemical Insertion/Extraction of Li in Transition Metal Oxides Part V2O5 and MoO3

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

Adaptive quasi-likelihood estimate in generalized linear models

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Science China Mathematics 2005年第6期48卷 829-846页

作者： CHEN Xia & CHEN Xiru school of Mathematics and Statistics, Wuhan University, Wuhan 430072, China graduate school, Chinese Academy of Science, Beijing 100049, China 1. school of Mathematics and Statistics Wuhan University 430072 Wuhan China 2. graduate school Chinese Academy of Science 100049 Beijing China

This paper gives a thorough theoretical treatment on the adaptive quasilikelihood estimate of the parameters in the generalized linear models. The unknown covariance matrix of the response variable is estimated by the sample. It is shown that the adaptive estimator defined in this paper is asymptotically most efficient in the sense that it is asymptotic normal, and the covariance matrix of the limit distribution coincides with the one for the quasi-likelihood estimator for the case that the covariance matrix of the response variable is completely known.

关键词： generalized linear models, quasi likelihood estimate, adaptive estimate.

Valuations on arithmetic surfaces

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Science China Mathematics 2009年第1期52卷 66-76页

作者： XU Ning Department of Mathematics, graduate school of Chinese Academy of Sciences, Beijing 100049, China Department of Mathematics Graduate School of Chinese Academy of Sciences Beijing 100049 China

In this paper, we give the definition of the height of a valuation and the definition of the big field ? p,G , where p is a prime and G ? ? is an additive subgroup containing 1. We conclude that ? p,G is a field and ? p,G is algebraically closed. Based on this the author obtains the complete classification of valuations on arithmetic surfaces. Furthermore, for any m ? p,G n ∈ ?, let V m,n be an ∝-vector space of dimension n - m + 1, whose coordinates are indexed from m to n. We generalize the definition of ? p,G , where p is a prime and G ? V m,n is an additive subgroup containing 1. We also conclude that ? p,G is a field if m ? 0 ? n.

关键词： valuation height rank totally ordered group big field transcendental number 14J10

ON THE PAUCITY OF EVIDENCE FOR NONSYSTEMATIC VARIABILITY IN INTERLANGUAGE STUDY

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中国科学院大学学报 1997年第2期 195-202页

作者： Wu Bo(graduate school, Academia Sinica)

In early studies on Interlanguage,it is believed that Interlanguage is a system which functions according to its own rules. This idea is best presented in the works by the noted scholars as S. P. Corder,Selinker and Nemser. However,James1 later challenged this view with good reason. Indeed,if there are all sorts of variabilities within the Interlanguage system,with all sorts of causes,what point is there in arguing that Interlanguage is systematic? By the term "strong theory",I refer to a theory that makes strong claims without adducing adequate empirical evidence from either quantitative data or qualitative data. In this paper,it is demonstrated that although Ellis,2-4 strong theory 0f InterIanguage development, which lays great emphasis on the role of nonsystematic variability,seems to hold water theoreticalIy,i.e. it has ha validity,it is weak in empirical terms. Along with the theoretical introduction,empirical evidence is reviewed. This leads to the final conclusion that strong theory needs strong evidence. Ellis’ position urgently needs empirical work to back lt up.

关键词： nonsystematic variability Interlanguage second language acquisition

A NOTE ON THE CONSISTENCY OF LS ESTIMATES IN LINEAR MODELS

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Chinese Annals of Mathematics,Series B 2001年第4期22卷 471-474页

作者： CHEN XIRU The graduate school at Beijing, University of Science and Technology of China, Beijing 100039, China. The graduate school at Beijing University of Science and Technology of China Beijing 100039 China

It is well known that when the random errors are iid. with finite variance, the week and the strong consiStency of LS estimate of multiple regression coefficients are equivalent. This note, by constructing a counter-example, shows that this equivalence no longer holds true in case that the random errors possess only the r-th moment with 1≤5 T ＜ 2.

关键词： Linear regression model Consistency LS estimate