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Highest weight representations of a Lie algebra of Block type

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Science china mathematics 2007年第4期50卷 549-560页

作者： Yue-zhu WU & Yu-cai SU department of mathematics, shanghai Jiaotong university, shanghai 200240, china department of mathematics, Qufu normal university, Qufu 273165, china department of mathematics, university of Science and Technology of china, Hefei 230026, china 1. department of mathematics Shanghai Jiaotong University Shanghai 200240 China 2. department of mathematics Qufu Normal University Qufu 273165 China 3. department of mathematics University of Science and Technology of China Hefei 230026 China

For a field $\mathbb{F}$ of characteristic zero and an additive subgroup G of $\mathbb{F}$ , a Lie algebra B(G) of the Block type is defined with the basis {L α,i , c | α ∈ G ?1 ≤ i ∈ ?} and the relations [L α,i , L β,j ] = ((i + 1)β ? (j + 1)α)L α+β,i+j + αδ α, ?β δ i+j,?2 c, [c, L α,i ] = 0. Given a total order ? on G compatible with its group structure, and any Λ ∈ B(G) 0 * , a Verma B(G)-module M(Λ, ?) is defined, and the irreducibility of M(Λ, ?) is completely determined. Furthermore, it is proved that an irreducible highest weight B(?)-module is quasifinite if and only if it is a proper quotient of a Verma module.

关键词： Verma modules Lie algebras of Block type irreducibility 17B10 17B65 17B68

An investigation on a novel PDLC film's fabrication and its electro-optical properties

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Science china Chemistry 2007年第3期50卷 358-363页

作者： DING HongLiu, ZHAO Ting, CHENG YuXiao, PANG YueHong, XU He, SHI GuoYue & JIN LiTong Chemistry department of east china normal university, shanghai 200062, china 1. Chemistry department of east china normal university Shanghai 200062 China

A polymer dispersed liquid crystal (PDLC) film that has good electro-optical properties is produced by the method of polymerized-induced phase separation. Based on the application foreground, its capability parameters, such as contrast ratio, work voltage, and visual angle, are characterized for the first time by a white light but not a fixed wavelength light. The results show the PDLC film has a low work-voltage of 20 V, more than 150° visual angle, high stability, and long lifetime. The differences between plastic and glass ITO-coated substrates of PDLC films are also studied in this paper. The plastic substrate has better property and will have a wider perspective especially in the portable, tender and folded display devices. Due to adjustable properties of film by electric field, PDLC has the potential application for display device, sensor, switch, grating, and new generation analytical apparatus.

关键词： polymer dispersed liquid crystal (PDLC) bisphenol-A epoxy resin nematic liquid crystal electro-optical properties

Controllability of Non-densely Defined Neutral Functional Differential Systems in Abstract Space

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Chinese Annals of mathematics,Series B 2007年第2期28卷 243-252页

作者： Xianlong FU Xingbo LIU department of mathematics East China Normal University Shanghai 200062 China.

In this paper, by means of Sadovskii fixed point theorem, the authors establish a result concerning the controllability for a class of abstract neutral functional differential systems where the linear part is non-densely defined and satisfies the Hille-Yosida condition. As an application, an example is provided to illustrate the obtained result.

关键词： Controllability Non-densely defined Integral solution Sadovskii fixed point theorem

THE STABILITY ANALYSIS OF THE θ-METHODS FOR DELAY DIFFERENTIAL EQUMIONS

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Journal of Computational mathematics 1996年第3期14卷 203-212页

作者： H.J.Tian J-X.Kuang(department of mathematics, shanghai normal university, shanghai, china) shanghai normal UNIV DEPT MATH SHANGHAI PEOPLES R CHINA

This paper deals with the stability analysis of θ-methods for the numericalsolution of delny dmerential equations (DDEs). We focus on the behavioux of suchmethods in the solution of the linear test equation y'(t) = a(t)y(t) + b(t)y(t - T),where T > o, a(t) and b(t) are functions from R to C. It is proved that the linearθ-method and the one-leg θ-method are TGP-stable if and only if θ = 1.

关键词： METHODS FOR DELAY DIFFERENTIAL EQUMIONS THE STABILITY ANALYSIS OF THE Math

Extremal problems on the Hua domain of the first type

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Science china mathematics 2005年第z1期48卷 343-354页

作者： SU Jianbing & YIN Weiping mathematics department, Xuzhou normal university, Xuzhou 221116, china mathematics department, Capital normal university, Beijing 100037, china 1. mathematics department Xuzhou Normal University 221116 Xuzhou China 2. mathematics department Capital Normal University 100037 Beijing China

In this paper we study some extremal problems between the Hua domain of the first type and the unit ball.

关键词： extremal problem, Hua domain of the first type, minimal circumscribed Hermitian ellipsoid.

Extremal problems on the generalized Hua domain of the first type

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Progress in Natural Science:Materials International 2006年第4期16卷 352-358页

作者： SU Jianbing and YIN Weiping department of mathematics, Xuzhou normal university, Xuzhou 221116, china department of mathematics, Capital normal university, Beijing 100037, china [a]department of mathematics Xuzhou Normal University Xuzhou China [b]department of mathematics Capital Normal University Beijing China

Some extremal problems between the generalized Hua domain of the first type and the unit ball are studied. The extremal mapping and extremal value in explicit formulas are also obtained.

关键词： extremal problem generalized Hua domain of the first type minimal circumscribed Hermitian ellipsoid.

A categorical interpretation of Yetter-Drinfel'd modules

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Chinese Science Bulletin 1999年第9期44卷 771-778页

作者： KAN Haibin and WANG ShuanhongInstitute of mathematics , Fudan university , shanghai 200433 , china department of mathematics , Henan normal university, Xinxiang 453002, china Institute of mathematics Fudan Univrrsity Shanghai China Dcpartment of mathematics Henun Normal University Xinxiang China

It is known that any strict tensor category （C, I） can determine a strict braided tensor category Z （ C）, the centre of C. When A is a finite Hopf algebra, Drinfel’d has proved that Z（AM） is equivalent to D（A）M as a braided tensor category, where AM is the left A-module category, and D （A） is the Drinfel’d double of A. This is the categorical interpretation of D （A）.Z（4M） is proved to be equivalent to the Yetter-Drinfel’ d module category AY D4 as a braided tensor category for any Hopf algebra A. Furthermore, for right A-comodule category MA , Z（MA） is proved to be equivalent to the Yetter-Drinfel’ d module category AY D4 as a braided tensor category. But, in the two cases, the Yetter-Drinfel’ d module category AY DA has different braided tensor structures.

关键词： Yetter-Drinfel’d module tensor category equivalence.

ON THE UNIQUE SOLVABILITY OF THE NONLINEAR SYSTEMS IN MDBM

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Journal of Computational mathematics 1994年第1期12卷 55-60页

作者： Kuang Jiao-xun Lu Lian-hua (department of mathematics, shanghai normal university, shanghai, china) shanghai normal UNIV DEPT MATHSHANGHAIPEOPLES R CHINA

To obtain the approximate solution of the nonlinear ordinary differential equations requires the solution to systems of nonlinear equations. The authors study the conditions for the existence and uniqueness of the sol... 详细信息

关键词： DL ON THE UNIQUE SOLVABILITY OF THE NONLINEAR SYSTEMS IN MDBM

SUPER HYPERBOLIC TYPE KAC-MOODY LIEALGEBRA

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Systems Science and Mathematical Sciences 1997年第4期10卷 329-332页

作者： CHEN Hongji(department of mathematics, Huizhou university, Huizhou, Guangdong 516015, china)LIU Bin(department of mathematics, east china normal university, shanghai 200062, china)

In this paper we give the definition of super hyperbolic type Kac-MoodyLie algebra and discuss its imaginary roots systems. Finally, we give the necessary andsufficient condition for Cartan matrices to be of super hyp... 详细信息

关键词： Super hyperbolic type affine type finite type hyperbolic type Kac-Moody Lie algebra.