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Tubular algebras and affine Kac-Moody algebras

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Science china mathematics 2007年第4期50卷 521-532页

作者： Zheng-xin CHEN & Ya-nan LIN school of mathematics and Computer Science, Pujian normal university, Fuzhou 350007, china school of Mathematical sciences, Xiamen university, Xiamen 361005, china 1. school of mathematics and Computer Science Fujian Normal University Fuzhou 350007 China 2. school of Mathematical sciences Xiamen University Xiamen 361005 China

The purpose of this paper is to construct quotient algebras L(A) 1 ? /I(A) of complex degenerate composition Lie algebras L(A) 1 ? by some ideals, where L(A 1 ? is defined via Hall algebras of tubular algebras A, and to prove that the quotient algebras L(A) 1 ? /I(A) are isomorphic to the corresponding affine Kac-Moody algebras. Moreover, it is shown that the Lie algebra L re(A) 1 ? generated by A-modules with a real root coincides with the degenerate composition Lie algebra L(A) 1 ? generated by simple A-modules.

关键词： tubular algebras affine Kac-Moody algebras Hall algebras degenerate composition Lie algebras modules with real root 16G70 17B67

Estimates on Bloch constants for planar harmonic mappings

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Science china mathematics 2009年第1期52卷 87-93页

作者： LIU MingSheng school of Mathematical sciences, South china normal university, Guangzhou 510631, china school of Mathematical sciences South China Normal University Guangzhou 510631 China

The Bloch constants for quasiregular harmonic mappings and open planar harmonic mappings are considered. Better estimates are obtained. The results, presented in this paper, improve the one made by Chen et al. and Gri... 详细信息

关键词： Bloch constant quasiregular harmonic mapping open planar harmonic mapping 30C99 30C62

Joint efficient ordering method for group multiobjective programming

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Progress in Natural Science:Materials International 2006年第1期16卷 90-95页

作者： HU Yuda and HU Didi (school of mathematics and information Science, Wenzhou university, Wenzhou 325035, china) school of mathematics and information Science Wenzhou University Wenzhou 325035 China

This paper introduces the concepts of individual efficient pair and group efficient pair for each alternative in group multi-objective programming, and corresponding to these concepts defines the concepts of individual joint efficient preference and group joint efficient preference, respectively. Based on the fundamental properties of the mapping from individual joint efficient preference to group joint efficient preference and group efficient number of alternative, a method of ordering alternatives for group multiobjective programming problems is given.

关键词： group multiobjective programming efficient pair joint efficient preference joint efficient mapping group efficient number.

On conformal measures for infinitely renormalizable quadratic polynomials

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Science china mathematics 2005年第10期48卷 1411-1420页

作者： HUANG Zhiyong~1 JIANG Yunping~(2,3) & WANG Yuefei~3 1. school of information,Renmin university of china,Beijing 100872,china 2. Department of mathematics,Queens College,City university of New York,NY 11367,USA Department of mathematics,Graduate school,City university of New York,New York,NY 10016,USA 3. Academy of mathematics and Systems Science,Chinese Academy of sciences,Beijing 100080,china 1. school of information Renmin University of China 100872 Beijing China 2. Department of mathematics Queens College City University of New York 11367 NY USA 3. Department of mathematics Graduate School City University of New York 10016 New York NY USA 4. Academy of mathematics and Systems Science Chinese Academy of Sciences 100080 Beijing China

We study a conformal measure for an infinitely renormalizable quadratic polynomial. We prove that the conformal measure is ergodic if the polynomial is unbranched and has complex bounds. The main technique we use in t... 详细信息

关键词： Julia set, conformal measure, three-dimensional puzzle, infinitely renormalizable quadratic polynomial.

On several families of elliptic curves with arbitrary large Selmer groups

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Science china mathematics 2010年第9期53卷 2329-2340页

作者： LI Fei & QIU DeRong school of Mathematical sciences,Institute of mathematics and Interdisciplinary Science,Capital normal university,Beijing 100048,china 1. school of Mathematical sciences Institute of Mathematics and Interdisciplinary Science Capital Normal University Beijing 100048 China

In this paper,we calculate the ()-Selmer groups S()(E/Q) and S()(E/Q) of elliptic curves y2 = x(x + εpD)(x + εqD) via the descent *** particular,we show that the Selmer groups of several families of such ell... 详细信息

关键词： elliptic curve Selmer group Mordell-Weil group

A theorem of Fong's type for graded algebras

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Science china mathematics 2005年第5期48卷 577-582页

作者： FAN Yun & ZHU Ping school of mathematics and Statistics, Central china normal university, Wuhan 430079, china school of Mathematical Science, Nankai university, Tianjin 300071, china 1. school of mathematics and Statistics Central China Normal University 430079 Wuhan China 2. school of Mathematical Science Nankai University 300071 Tianjin China

Let G be a finite p-solvable group and k be an algebraic closed field of characteristic p. It is proved that any projective indecomposable module of a G-graded k-algebra is an induced module of a module of the subalgebra graded by a Hall p′-subgroup. A necessary and sufficient condition for the indecomposability of an induced module from a Hall p′-subgroup is obtained.

关键词： group graded algebra indecomposable induced module primitive idempotent.

Development and application of ergodicity model with FRCM and FLAR for hydrological process

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Science china(Technological sciences) 2009年第2期52卷 379-386页

作者： WANG HongRui1, FENG QiLei2, LIN Xin3 & ZENG WenYi4 1 College of Water Science, Key Laboratory for Water and Sediment sciences of the Ministry of Education, Beijing normal university, Beijing 100875, china 2 school of Science, Beijing Institute of Education, Beijing 100011, china 3 school of Mathematical sciences, Beijing normal university, Beijing 100875, china 4 College of information Science and Technology, Beijing normal university, Beijing 100875, china 1. College of Water Science Key Laboratory for Water and Sediment Sciences of the Ministry of Education Beijing Normal University Beijing 100875 China 2. school of Science Beijing Institute of Education Beijing 100011 China 3. school of Mathematical sciences Beijing Normal University Beijing 100875 China 4. College of information Science and Technology Beijing Normal University Beijing 100875 China

In this paper, a new ergodic property analysis model of hydrological process is proposed based on fuzzy-rough c-means clustering (FRCM), autocorrelogram, and fuzzy least absolute regression (FLAR). A precipitation time series (1951―2004) from Shanghai Hydrology Station is then analyzed with the model. The results show that the precipitation time series of April, May, June, and September has er-godic property. We conclude that in the long run, the precipitation of April, May, June, and September will not keep decreasing; it will converge to its mean value in some period.

关键词： hydrological process ergodic autocorrelogram fuzzy-rough c-means clustering fuzzy least absolute regression

Optical pulse compression using a nonlinear optical loop mirror constructed from dispersion decreasing fiber

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Science china(Technological sciences) 2004年第1期47卷 33-50页

作者： CAO Wenhua & LIU Songhaoschool of information, Wuyi university, Jiangmen 529020, china school for information and Optoelectronic Science and Engineering, South china normal university, Guangzhou 510631, china 1. school of information Wuyi University 529020 Jiangmen China 2. school for information and Optoelectronic Science and Engineering South China Normal University 510631 Guangzhou China

A novel scheme to compress optical pulses is proposed and demonstrated numerically, which is based on a nonlinear optical loop mirror constructed from dispersion decreasing fiber (DDF). We show that, in contrast to the conventional soliton-effect pulse compression in which compressed pulses are always accompanied by pedestals and frequency chirps owning to nonlinear effects, the proposed scheme can completely suppress pulse pedestals and frequency chirps. Unlike the adiabatic compression technique in which DDF length must increase exponentially with input pulsewidth, the proposed scheme does not require adiabatic condition and therefore can be used to compress long pulses by using reasonable fiber lengths. For input pulses with peak powers higher than a threshold value, the compressed pulses can propagate like fundamental solitons. Furthermore, the scheme is fairly insensitive to small variations in the loop length and is more robust to higher-order nonlinear effects and initial frequency chirps than the adiabatic compression technique.

关键词： dispersion decreasing fiber (DDF), optical pulse compression, optical solitons.

Checking for normality in linear mixed models

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Science china mathematics 2012年第4期55卷 787-804页

作者： WU Ping 1,,ZHU LiXing 2,3 & FANG Yun 4 1 school of Finance and Statistics,East china normal university,Shanghai 200241,china 2 school of Statistics and mathematics,Yunnan university of Finance and Economics,Yunnan 650221,china 3 The Department of mathematics,Hong Kong Baptist university,Hong Kong 999077,china 4 mathematics and Science College,Shanghai normal university,Shanghai 200234,china 1. school of Finance and Statistics East China Normal University Shanghai 200241 China2. School of Statistics and Mathematics Yunnan University of Finance and Economics Yunnan 650221 China3. The Department of Mathematics Hong Kong Baptist University Hong Kong 999077 China4. Mathematics and Science College Shanghai Normal University Shanghai 200234 China

Linear mixed models are popularly used to fit continuous longitudinal data, and the random effects are commonly assumed to have normal distribution. However, this assumption needs to be tested so that further analysis can be proceeded well. In this paper, we consider the Baringhaus-Henze-Epps-Pulley （BHEP） tests, which are based on an empirical characteristic function. Differing from their case, we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors. The test is consistent against global alternatives, and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1/V~ where n is sample size. ^-hlrthermore, to overcome the problem that the limiting null distribution of the test is not tractable, we suggest a new method： use a conditional Monte Carlo test （CMCT） to approximate the null distribution, and then to simulate p-values. The test is compared with existing methods, the power is examined, and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.

关键词： linear mixed models estimated best linear unbiased predictors BHEP tests conditional MonteCarlo test