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	1. The Representations of Quantum Double of DihedralGroups
	Dong Jingcheng,CHEN Huixiang
	Mathematics 14 February 2012
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	Abstract:Let k be an algebraically closed field ofodd characteristic p, and let Dn be the Dihedral group of order2n such that pmid 2n. Let D(kDn) denote the quantum doubleof the group algebra kDn. In this paper, thestructures of all finite dimensional indecomposable leftD(kDn)-modules are described and classified, equivalently, all finite dimensionalindecomposable Yetter-Drinfeld kDn-modules are described, and classified.
	TO cite this article:Dong Jingcheng,CHEN Huixiang. The Representations of Quantum Double of DihedralGroups[OL].[14 February 2012] http://en.paper.edu.cn/en_releasepaper/content/4466399


	2. Yetter-Drinfeld Modules over The Hopf Ore Extension of The Group Algebra of Dihedral Group
	ZHU Hong,CHEN Huixiang
	Mathematics 14 February 2012
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	Abstract:Let k be an algebraically closed field of characteristic zero, and Dn be the dihedral groupof order 2n, where n is a positive even integer. In this paper, the Yetter-Drinfeld modulesover the Hopf-Ore extension A(n,0) of kDn are investigated. The the structures and properties of simpleYetter-Drinfeld modules over A(n,0) are described, and all simple Yetter-Drinfeld modules over A(n,0) areclassified up to isomorphism.
	TO cite this article:ZHU Hong,CHEN Huixiang. Yetter-Drinfeld Modules over The Hopf Ore Extension of The Group Algebra of Dihedral Group[OL].[14 February 2012] http://en.paper.edu.cn/en_releasepaper/content/4466396

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	3. Alternating groups and flag-transitive $2-(v,k,4)$ symmetric designs
	DONG Huili,ZHOU Shenglin
	Mathematics 26 December 2011
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	Abstract:In this paper, we study the classification offlag-transitive, point-primitive 2-(v,k,4) symmetric designs. Weprove that if the socle of the automorphism group of aflag-transitive, point-primitive nontrivial2-(v,k,4) symmetric design D is an alternating group An for n>=5, then (v,k)=(15,8) and D=(P,B) is one of the following:(i) P is the set of one-dimensional subspaces of V4(2), B is acollection of PX, where X is the set of one-dimensional subspacescontained in one hyperplane of V4(2), G=A7 or A8, andthe stabiliser Gx=L3(2) or AGL3(2) respectively.(ii) P is the set of 2- of Ω6: ={1,2,..., 6}, B is a collection ofPX, where X is Y{Y}U{Z is a 2- of Ω6 Z∩Y=θ}, Y is a 2- of Ω6, G=A6 or S6, and Gx=S4 or S4*Z2 respectively.
	TO cite this article:DONG Huili,ZHOU Shenglin. Alternating groups and flag-transitive $2-(v,k,4)$ symmetric designs[OL].[26 December 2011] http://en.paper.edu.cn/en_releasepaper/content/4457833


	4. On an infinite-dimensional Lie algebra of Virasoro-type
	PEI Yufeng ,BAI Chengming
	Mathematics 13 December 2011
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	Abstract:In this paper, we study an infinite-dimensional Lie algebra of Virasoro-type whichis realized as an affinization of a 2-dimensional Novikov algebra. It is a special deformation ofthe Liealgebra of differential operators on a circle of order at most one.There is an explicit construction of a vertex algebra associated to the Lie algebra.We determine derivations and central extensionsof this Lie algebra in terms of derivations and bilinear formsof the corresponding Novikov algebra respectively.
	TO cite this article:PEI Yufeng ,BAI Chengming. On an infinite-dimensional Lie algebra of Virasoro-type[OL].[13 December 2011] http://en.paper.edu.cn/en_releasepaper/content/4454969


	5. Poisson bialgebras
	NI Xiang,BAI Chengming
	Mathematics 09 December 2011
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	Abstract:We introduce a notion of Poisson bialgebra as an analogue of a Liebialgebra of Drinfeld. Poisson bialgebras exhibit many familiarproperties of Lie bialgebras. In particular, they can be constructedfrom a combination of the classical Yang-Baxter equation and theassociative Yang-Baxter equation and there exists a natural Drinfeldclassical double. Moreover, Poisson bialgebras are related tocertain algebraic structures and they fit naturally into a frameworkto construct compatible Poisson brackets in integrable systems.
	TO cite this article:NI Xiang,BAI Chengming. Poisson bialgebras[OL].[ 9 December 2011] http://en.paper.edu.cn/en_releasepaper/content/4454981


	6. Laplace's Theorem in semirings
	Wang XuePing,Mo Yan
	Mathematics 28 October 2011
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	Abstract:Laplace's Theorem is an important theorem using forcalculating the determinant of matrix in classical linear algebras.This paper tries to generalize it and studies it over semirings, itfirst introduces the notions of a k-order minor and its algebraiccofactor, respectively, then provides an extension of Laplace'sTheorem over commutative semirings with the help of biderminant,i.e., the bideterminant det(D) of matrix D equals to the sum ofall k-order minors det(Mi) multiply their correspondingalgebraic cofactors det(Ai), where 1≤n≤n-1. In the end,we obtain some properties of the bideterminant for matrices oversemirings and show that the bideterminant of an upper triangularblock matrix equals to the product of all the bideterminants ofdiagonal elements.
	TO cite this article:Wang XuePing,Mo Yan. Laplace's Theorem in semirings[OL].[28 October 2011] http://en.paper.edu.cn/en_releasepaper/content/4447687


	7. Optimal H∞ State Estimation for Discrete-Time Delayed Chaotic Systems via a Unified Model
	Meiqin Liu,Senlin Zhang,zhen Fan
	Mathematics 17 May 2011
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	Abstract:This paper is concerned with the problem of state estimation for a class of discrete-time chaotic systems with time delays. A unified model consisting of a linear dynamic system and a bounded static nonlinear operator is employed to describe these systems, such as chaotic neural networks, Chua's circuits, and Hénon map etc. Based on the H∞ performance analysis of this unified model using the linear matrix inequality (LMI) approach, H∞ state estimator are designed for this model with sensors to guarantee the asymptotic stability of the estimation error dynamic systems and to reduce the influence of noise on the estimation error. The parameters of these estimators are obtained by solving the eigenvalue problem (EVP). As most discrete-time chaotic systems with time delays can be transformed into this unified model, H∞ state estimator design for these systems can be done in a unified way. Two numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes.
	TO cite this article:Meiqin Liu,Senlin Zhang,zhen Fan. Optimal H∞ State Estimation for Discrete-Time Delayed Chaotic Systems via a Unified Model[OL].[17 May 2011] http://en.paper.edu.cn/en_releasepaper/content/4428191


	8. On $0$-Schur algebras
	Deng Bangming,Yang Gui-Yu
	Mathematics 26 January 2011
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	Abstract:Based on a geometricconstruction of quantum Schur algebras due to Beilinson, Lusztig andMacPherson and the structure of $0$-Hecke algebras, we give apresentation for $0$-Schur algebras and determine theirrepresentation type.
	TO cite this article:Deng Bangming,Yang Gui-Yu. On $0$-Schur algebras[OL].[26 January 2011] http://en.paper.edu.cn/en_releasepaper/content/4408256


	9. A note on cover-avoiding properties of finite groups
	Liu Jianjun,Guo Xiuyun
	Mathematics 29 November 2010
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	Abstract:A subgroup H of a group G is said to be a CAP-subgroup of a group G if, for any non-Frattini chief factor K/L of G, we have HK=HL or H∩K=H∩L. In this paper, some new characterizations for finite groups are obtained based on the assumption that some subgroups are CAP-subgroups of G.
	TO cite this article:Liu Jianjun,Guo Xiuyun. A note on cover-avoiding properties of finite groups[OL].[29 November 2010] http://en.paper.edu.cn/en_releasepaper/content/4393884


	10. Cyclotomic Polynomials and Factorization Theorems
	Wu Genqiang,LI Yanchao,Qi Yu
	Mathematics 08 November 2010
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	Abstract:Let Qm(x) be the mth cyclotomic polynomial over finite field Fq. The factorization of Qm(x^t) and f(x^t) over Fq are discussed, where t is an positive integer larger than one and f(x) is any irreducible polynomial over Fq. The discussions depend on some results from number theory. We give some detailed explanation of this problem by classification of t. The method this paper introduced can be used to treat every cases of this problem.
	TO cite this article:Wu Genqiang,LI Yanchao,Qi Yu. Cyclotomic Polynomials and Factorization Theorems[OL].[ 8 November 2010] http://en.paper.edu.cn/en_releasepaper/content/4390965

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