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	1. 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


	2. 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

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	3. 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


	4. On Pseudo-BCI Algebras with Condition (pP)
	Lu Yinfeng,Zhang Xiaohong
	Mathematics 27 September 2010
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	Abstract:As a generalization of BCI-algebras with condition (S) and pseudo-BCK algebras with condition (pP), the notion of pseudo-BCI algebras with condition (pP) is introduced. An example of pseudo-BCI algebras with condition (pP) is given, the result that every anti-grouped pseudo-BCI algebras is with condition (pP) is proved. Some properties of pseudo-BCI algebras with condition (pP) are investigated and the branch properties of pseudo-BCI algebras with condition (pP) are discussed.
	TO cite this article:Lu Yinfeng,Zhang Xiaohong . On Pseudo-BCI Algebras with Condition (pP)[OL].[27 September 2010] http://en.paper.edu.cn/en_releasepaper/content/4386761


	5. Principally Small Injective Rings
	Xiang yueming
	Mathematics 20 September 2010
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	Abstract:A right ideal I of a ring R is small in case for every proper right ideal K of R, K + I ≠ R. A right R-module M is called PS-injective if every R-homomorphism f : aR → M for every principally small right ideal aR can be extended to R → M. A ring R is called right PS-injective if R is PS-injective as a right R-module. We develop, in this article, PS-injectivity as a generalization of P-injectivity and small injectivity. Many characterizations of right PS-injective rings are studied. In light of these facts, we get several new properties of a right GPF ring and a semiprimitive ring in terms of right PS-injectivity. Related examples are given as well
	TO cite this article:Xiang yueming. Principally Small Injective Rings[OL].[20 September 2010] http://en.paper.edu.cn/en_releasepaper/content/4386202


	6. Canonical Factorization of cyclotomic polynomials
	Wu Genqiang,Li Yanchao,Qi Yu
	Mathematics 08 June 2010
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	Abstract:In this article, we studied the order of an integer q modulo integer m, and then studied the factorization of the mth cyclotomic polynomial over a field K. We discussed the order of q modulo m by the prime-power factorization of m and then gave explicit result of order of q modulo m. We also gave the factorization theorem and then the explicit factorization of the mth cyclotomic polynomial over a field K by the result of q modulo m. Although we gave only some special case of the factorization theorem and the explicit factorization of the mth cyclotomic polynomial, our theory and methods can be used to discuss and give the factorization of the mth cyclotomic polynomial when m is any positive integer.
	TO cite this article:Wu Genqiang,Li Yanchao,Qi Yu. Canonical Factorization of cyclotomic polynomials[OL].[ 8 June 2010] http://en.paper.edu.cn/en_releasepaper/content/4375600


	7. On Primitive Optimal Normal Elements of Finite Fields
	Qunying Liao
	Mathematics 19 January 2010
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	Abstract:Let q be a prime or prime power and F_{q^{n}} the extension of q elements finite field F_{q} with degree n(n>1). Davenport, Lenstra and Schoof proved that there exists a primitive element \\alpha\\in F_{q^{n}}such that \\alpha generates a normal basis of F_{q^{n}} over F_{q}. Later, Mullin, Gao and Lenstra, etc., raised the definition of optimal normal bases and constructed such bases. In this paper, we determine all primitive type I optimal normal bases and all finite fields in which there exists a pair of reciprocal elements \\alpha and \\alpha^{-1} such that both of them generate optimal normal bases of F_{q^{n}} over F_{q}. Furthermore, we obtain a sufficient condition for the existence of primitive type II optimal normal bases over finite fields and prove that all primitive optimal normal elements are conjugate to each other.
	TO cite this article:Qunying Liao. On Primitive Optimal Normal Elements of Finite Fields[OL].[19 January 2010] http://en.paper.edu.cn/en_releasepaper/content/39180


	8. eu_2-Lie admissible algebras and Steinberg unitary Lie Algebra
	Shang Shikui ,Gao Yun
	Mathematics 12 January 2010
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	Abstract:In this paper, we study the algebra eu_2(R,-,r) and give a necessary and sufficient condition for (R,-) such that eu_2(R,-,r) becomes a Lie algebra. Moreover, we define the Steinberg unitary Lie algebra stu_2(R,-,r), which is the universal covering of eu_2(R,-,r) when R is an eu_2-Lie admissible algebra satisfying some assumptions.Finally,we compute the second homology group of the Lie algebra eu_2(R,-,r).
	TO cite this article:Shang Shikui ,Gao Yun . eu_2-Lie admissible algebras and Steinberg unitary Lie Algebra[OL].[12 January 2010] http://en.paper.edu.cn/en_releasepaper/content/38829


	9. A counter-example to a conjecture of Lusztig
	Shi Jianyi
	Mathematics 12 January 2010
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	Abstract:Lusztig defined two functions a and a\
	TO cite this article:Shi Jianyi. A counter-example to a conjecture of Lusztig[OL].[12 January 2010] http://en.paper.edu.cn/en_releasepaper/content/38811


	10. A Note on the w-Global Transform of Mori Domains
	Wang Fanggui
	Mathematics 11 January 2010
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	Abstract:Let R be a domain and let R^{wg} be the w-global transform of R. In this note it is shown that if R is a Mori domain, then the t-dimension formula t-dim(R^{wg})=t-dim(R)-1 holds.
	TO cite this article:Wang Fanggui. A Note on the w-Global Transform of Mori Domains[OL].[11 January 2010] http://en.paper.edu.cn/en_releasepaper/content/38734

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