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	1. A Note on Relative Flatness and Coherence
	Zhang Xiaoxiang ,Chen Jianlong
	Mathematics 08 May 2006
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	Abstract:Let $R$ be a ring and $M$ a fixed right $R$-module. A new characterization of $M$-flatness is given by certain linear equations. For a left $R$-module $F$ such that the canonical map $M\otimes_RF\rightarrow \mathrm{Hom}_R(M^, F)$ is injective, where $M^ =$ Hom$_R(M, R)$, the $M$-flatness of $F$ is characterized via certain matrix subgroups. An example is given to show that $R$ need not be $M$-coherent even if every left $R$-module is $M$-flat. Moreover, some properties of $M$-coherent rings are discussed.
	TO cite this article:Zhang Xiaoxiang ,Chen Jianlong . A Note on Relative Flatness and Coherence[OL].[ 8 May 2006] http://en.paper.edu.cn/en_releasepaper/content/6517


	2. Imprimitive Complex Reflection Groups G(m,p,n)
	Shi Jianyi,Wang Li
	Mathematics 21 March 2006
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	Abstract:We describe the group Aut(m,p,n) of all the reflection-preserving automorphisms of G(m,p,n). The results are obtained in the cases of p=1, p=m and p\in [2,m-1], separately. Then we study some structural properties of the group Aut(m,p,n).
	TO cite this article:Shi Jianyi,Wang Li . Imprimitive Complex Reflection Groups G(m,p,n)[OL].[21 March 2006] http://en.paper.edu.cn/en_releasepaper/content/5826

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	3. Left cells with a-value 4 in the affine weyl groups Ei(i=6,7,8)
	Shi Jianyi ,Zhang Xigou
	Mathematics 20 March 2006
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	Abstract:In the present paper,we give the respresentative set of left cell with a-value 4 in the affine weyl groups Ei(i=6,7,8),and the distinguished involution.Then we show that these left cells are left-connected,which verify Lustig conjecture in our case.
	TO cite this article:Shi Jianyi ,Zhang Xigou . Left cells with a-value 4 in the affine weyl groups Ei(i=6,7,8)[OL].[20 March 2006] http://en.paper.edu.cn/en_releasepaper/content/5796


	4. Multipartite Entanglement of a Tetrahedron Lattice
	Zhang Rong ,Zhu Shiqun ,Hao Xiang
	Mathematics 14 March 2006
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	Abstract:Three dimensional Heisenberg model in the form of a tetrahedron lattice is investigated. The concurrence and multipartite entanglement are calculated through 2-concurrence $C$ and 4-concurrence $C_4$. The concurrence $C$ and multipartite entanglement $C_4$ depend on different coupling strengths $J_i$ and are decreased when the temperature $T$ is increased. For a symmetric tetrahedron lattice, the concurrence $C$ is symmetric about $J_1$ when $J_2$ is negative while the multipartite entanglement $C_4$ is symmetric about $J_1$ when $J_2<2$. For a regular tetrahedron lattice, the concurrence $C$ of ground state is $\frac{1}{3}$ for ferromagnetic case while $C=0$ for antiferromagnetic case. However, there is no multipartite entanglement since $C_4 =0$ in a regular tetrahedron lattice. The external magnetic field $B$ can increase the maximum value of the concurrence $C_B$ and induce two or three peaks in $C_B$. There is a peak in the multipartite entanglement $C_{4B}$ when $C_{4B}$ is varied as a function of the temperature $T$. This peak is mainly induced by the magnetic field $B$
	TO cite this article:Zhang Rong ,Zhu Shiqun ,Hao Xiang . Multipartite Entanglement of a Tetrahedron Lattice[OL].[14 March 2006] http://en.paper.edu.cn/en_releasepaper/content/5697


	5. System Efficiency vs. Individual Performance in Adaptive Competing Systems
	Gou Chengling
	Mathematics 13 March 2006
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	Abstract:This paper addresses the issue of the relation between the system efficiency and the individual performance with in adaptive competing systems. The adaptive competing systems are modeled by mix-game model which is an extension of minority game (MG). In mix-game, there are two groups of agents; group 1 plays the majority game, but the group 2 plays the minority game. The average winnings of agents can represent the average individual performance and the volatility of a system can represent the efficiency of the system. It is found the correlations between the average winnings of agents and the means of local volatilities are different when agent history memories change under their different configurations. This paper also gives some suggestions for designing complex competing systems.
	TO cite this article:Gou Chengling. System Efficiency vs. Individual Performance in Adaptive Competing Systems[OL].[13 March 2006] http://en.paper.edu.cn/en_releasepaper/content/5647


	6. Generalized Tilting Modules With Finite Injective Dimension
	Huang Zhaoyong
	Mathematics 28 February 2006
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	Abstract:Let $R$ be a left noetherian ring, $S$ a right noetherian ring and $_RU$ a generalized tilting module with $S={\rm End}(_RU)$. The injective dimensions of $_RU$ and $U_S$ are identical provided both of them are finite. Under the assumption that the injective dimensions of $_RU$ and $U_S$ are finite, that the subcategory $\{ {\rm Ext}_S^n(N, U)\|N$ is a finitely generated right $S$-module$\}$ is submodule closed is characterized equivalently. From which, a negative answer to a question posed by Auslander in 1969 is given. Finally, some partial answers to Wakamatsu Tilting Conjecture are given.
	TO cite this article:Huang Zhaoyong. Generalized Tilting Modules With Finite Injective Dimension[OL].[28 February 2006] http://en.paper.edu.cn/en_releasepaper/content/5432


	7. Theoretical and experimental study on two-dimensional binary locally resonant phononic crystals
	Wang Gang,Wen Jihong,Liu Yaozong,Wen Xisen
	Mathematics 13 January 2006
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	Abstract:The theoretical prediction of a locally resonant band gap in two-dimensional binary phononic crystals is verified experimentally. Numerical simulations show that the in-plane subfrequency gap exists in the thin plate of phononic crystal is much wider than that in the bulk of phononic crystal. Theoretical analysis shows that this is due to the different pure shearing/compressing module ratios in the thin plate and the bulk. The band gap edges as well as the mid-gap attenuations of finite samples are studied with different filling fractions, elastic parameters and densities of host medium. Vibration experiments are conducted with two thin plates of two-dimensional binary locally resonant phononic crystal, which are with and without holes respectively. The measured subfrequency gaps are in good agreement with the theoretical predictions.
	TO cite this article:Wang Gang,Wen Jihong,Liu Yaozong, et al. Theoretical and experimental study on two-dimensional binary locally resonant phononic crystals[OL].[13 January 2006] http://en.paper.edu.cn/en_releasepaper/content/4997


	8. A Necessary Condition for Irregular Wavelet Frames
	Yang Shouyuan,Zhou Xingwei
	Mathematics 05 December 2005
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	Abstract:The main purpose of this note is to investigate the admissibility condition of irregular wavelet frames. We prove that if the system {ψ(l) m,n = s.1/2 m ψ(l)(s.1 m · .tn) : m, n ∈ Z, l = 1, 2, · · · ,N} constitute a frame for L2(R), then the integral dξ ξ.1N l=1 \| . ψ(l)(ξ)\|2 is bounded up and below. Furthermore, we give a specific estimate for the upper and lower bounds, which extends Daubechies’ result to irregular wavelet frames.
	TO cite this article:Yang Shouyuan,Zhou Xingwei. A Necessary Condition for Irregular Wavelet Frames[OL].[ 5 December 2005] http://en.paper.edu.cn/en_releasepaper/content/4080


	9. Lower boundary hyperplanes of the canonical left cells in the affine Weyl group Wa（An-1）
	Shi Jianyi
	Mathematics 23 November 2005
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	Abstract:Let F be any canonical left cell of the affine Weyl group Wa of type A. We describe the lower boundary hyperplanes for F, which answer two questions of Humphreys.
	TO cite this article:Shi Jianyi. Lower boundary hyperplanes of the canonical left cells in the affine Weyl group Wa（An-1）[OL].[23 November 2005] http://en.paper.edu.cn/en_releasepaper/content/3751


	10. On $n$-semihereditary Rings and $n$-coherent Rings
	Xiaoxiang Zhang,Jianlong Chen
	Mathematics 14 November 2005
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	Abstract:Let $R$ be a ring. For fixed positive integer $n$, $R$ is said to be left $n$-semihereditary in case every $n$-generated left ideal is projective. $R$ is said to be weakly $n$-semihereditary if each $n$-generated left (and/or right) ideal is flat. Some properties of $n$-semihereditary rings, respectively, weakly $n$-semihereditary rings and $n$-coherent rings are investigated. It is also proved that $R$ is left $n$-semihereditary if and only if it is left $n$-coherent and weakly $n$-semihereditary, if and only if the ring of $n\times n$ matrices over $R$ is left 1-semihereditary if and only if the class of all $n$-flat right $R$-modules form the torsion-free class of a torsion theory. $R$ is left semihereditary if and only if it is left $n$-semihereditary for all positive integers $n$.
	TO cite this article:Xiaoxiang Zhang,Jianlong Chen. On $n$-semihereditary Rings and $n$-coherent Rings[OL].[14 November 2005] http://en.paper.edu.cn/en_releasepaper/content/3631

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