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Piecewise-Koszul algebras

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Science China mathematics 2007年第12期50卷 1795-1804页

作者： Jia-feng L■~1 Ji-wei HE~2 Di-ming LU~(1+) ~1 department of mathematics,Zhejiang University,Hangzhou 310027,China ~2 department of mathematics,Shaoxing College of Arts and Sciences,Shaoxing 312000,China department of mathematics Zhejiang University Hangzhou China department of mathematics Shaoxing College of Arts and Sciences Shaoxing China

It is a small step toward the Koszul-type *** piecewise-Koszul algebras are, in general,a new class of quadratic algebras but not the classical Koszul ones,simultaneously they agree with both the classical Koszul and higher Koszul algebras in special *** give a criteria theorem for a graded algebra A to be piecewise-Koszul in terms of its Yoneda-Ext algebra E(A),and show an A_∞-structure on E(A).Relations between Koszul algebras and piecewise-Koszul algebras are *** particular,our results are related to the third question of Green-Marcos.

关键词： (d-)Koszul algebras A_∞-algebras Yoneda-Ext algebras

A family of transitive modular Lie superalgebras with depth one

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Science China mathematics 2007年第10期50卷 1451-1466页

作者： Wen-de LIU~(1+) Yong-zheng ZHANG~2 ~1 department of mathematics,Harbin Normal University,Harbin 150080,China ~2 department of mathematics,Northeast Normal University,Changchun 130024,China department of mathematics Harbin Normal University Harbin China department of mathematics Northeast Normal University Changchun China

The embedding theorem is established for Z-graded transitive modular Lie superalgebras g■■■(g-1)satisfying the conditions: (i)g0■■(g-1) and g0-module g-1 is isomorphic to the natural■(g-1)-module; (ii)dim g1=2/3n(2n^2+1),where n=1/2dim g-1. In particular,it is proved that the finite-dimensional simple modular Lie superalgebras satisfying the conditions above are isomorphic to the odd Hamiltonian *** restricted Lie superalgebras are also considered.

关键词： flag, divided power algebra, modular Lie superalgebra, embedding theorem

Transitional function of DG to CA3 in the hippocampus

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Progress in Natural Science:Materials International 2007年第12期17卷 1436-1444页

作者： Yan Chuankui1 and Liu Shenquan2(1. department of mathematics, Hangzhou Normal University, Hangzhou 310036, China 2. department of Applied mathematics, School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China) department of mathematics Hangzhou Normal University Hangzhou 310036 China department of Applied mathematics School of Mathematical Sciences South China University of Technology Guangzhou 510640 China

Using single cell channel model, the transmission features of CA3-DG network in the hippocampus are investigated. The influence of the stimulation on discharge pattern of pyramidal neurons is analyzed, which shows that it starts with period spiking discharges, followed by period-doubling bifurcation to chaos, and period 3 discharge evolving into chaos, and ultimately a period of bursting discharges. By the synaptic model, the CA3-DG network model is constructed, which analyzes the summation of postsynaptic currents in the network, the influence of postsynaptic current on discharge rhythm as well as the mechanism of bursting discharges. The strong capacity of spatiotemporal encoding in the network indicates the features of CA3 network during the information transmission process in the hippocampus. The modeling result with time delay of the synaptic transmission is in accordance with the experimental phenomena of action potential in the hippocampus.

关键词： hippocampus CA3-DG period-doubling bifurcation chaos.

Constructing super Gabor frames:the rational time-frequency lattice case

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Science China mathematics 2010年第12期53卷 3179-3186页

作者： LI ZhongYan 1 & HAN DeGuang 2, 1 department of mathematics and Physics, North China Electric Power University, Beijing 102206, China 2 department of mathematics, University of Central Florida, Orlando, FL 32816, USA department of mathematics and Physics North China Electric Power University Beijing China department of mathematics University of Central Florida Orlando USA

For a time-frequency lattice Λ = A Z d × B Z d , it is known that an orthonormal super Gabor frame of length L exists with respect to this lattice if and only if |det( AB) | = 1 L . The proof of this result involves various techniques from multi-lattice tiling and operator algebra theory, and it is far from constructive. In this paper we present a very general scheme for constructing super Gabor frames for the rational lattice case. Our method is based on partitioning an arbitrary fundamental domain of the lattice in the frequency domain such that each subset in the partition tiles R d by the lattice in the time domain. This approach not only provides us a simple algorithm of constructing various kinds of orthonormal super Gabor frames with flexible length and multiplicity, but also allows us to construct super Gabor (non-Riesz) frames with high order smoothness and regularity. Several examples are also presented.

关键词： super Gabor frame orthonormal super frame full rank lattice tiles

Quasisymmetric property for conjugacies between Anosov diffeomorphisms of the two-torus

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Science China mathematics 2010年第3期53卷 663-670页

作者： HU HuYi 1 & JIANG YunPing 2, 1 department of mathematics, Michigan State University, East Lansing, MI 48824, USA 2 department of mathematics, the Graduate Center and Queens College of CUNY, Flushing, NY 11367, USA department of mathematics Michigan State University East Lansing USA department of mathematics the Graduate Center and Queens College of CUNY Flushing USA

We prove that the restrictions of the conjugacy between two Anosov diffeomorphisms of the twotorus to the stable and unstable manifolds are quasisymmetric homeomorphisms.

关键词： quasisymmetry Anosov diffeomorphisms conjugacy Hlder condition Markov partition

The maximal super-singular integral operators on product spaces

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Science China mathematics 2011年第12期54卷 2615-2626页

作者： WANG Hui1 & CHEN JieCheng2,3, 1department of mathematics, Xidian University, Xi’an 710071, China 2department of mathematics, Zhejiang Normal University, Jinhua 321004, China 3department of mathematics, Zhejiang University, Hangzhou 310027, China department of mathematics Xidian University Xi’an China department of mathematics Zhejiang Normal University Jinhua China department of mathematics Zhejiang University Hangzhou China

We study the maximal super-singular integral operator T＊Ω,α,β（f）（x,y）=sup ∈1〉0,∈2〉0｜∫｜u｜〉ε1,｜v｜〉ε2 b1（｜u｜）b2（｜u｜）Ω（u＇,u＇）/｜u｜^n＋α｜u｜^m＋β-f（x-u,y-u）dudu｜defined on all f ∈ S（R^n ×R^m）, where 0 ≤ α,β〈∞, b1 b2 ∈ L∞（R＋1 ）,Ω satisfies certain cancellation conditions and Ω∈L1（S^n-1×S^m-1）in the case α,β〉0;Ω∈L（log＋L）（S^n-1×S^m-1）in the case αβ=0 and α＋β 〉0. It is proved that, for 1〈p〈∞.T＊Ω,α,βis a bounded operator from the homogeneous Sobolev space Lα,β^p（R^n×R^m）to the Lebesgue space L^p（R^n×R^m）.

关键词： super-singular integral maximal operator product spaces

A New Multisoliton Solution to (2+1)-Dimensional KdV Equation

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Communications in Theoretical Physics 2004年第5期41卷 669-670页

作者： PENG Yan-Ze~(1,2) 1 department of mathematics,Huazhong University of Science and Technology,Wuhan 430074,China2 department of mathematics and Physics,Henan University of Science and Technology,Luoyang 471003,China department of mathematics Huazhong University of Science and Technology Wuhan 430074 China department of mathematics and Physics Henan University of Science and Technology Luoyang 471003 China

A new multisoliton solution to the(2+1)-dimensional KdV equation is obtained by means of the truncatedPainleve expansion method and a direct ansatz *** new exact solution is periodic in the propagating directionx and exponentially decaying in y and thus it is called periodic solitons.A typical spatial structure of it is illustrated bythe figures.

关键词： (2+1)-dimensional KdV equation periodic solitons truncated Painleve expansion method

A blow-up criterion for classical solutions to the compressible Navier-Stokes equations

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Science China mathematics 2010年第3期53卷 671-686页

作者： HUANG XiangDi 1 & XIN ZhouPing 2, 1 department of mathematics, University of Science and Technology of China, Hefei 230026, China 2 department of mathematics, The Chinese University of Hong Kong, Hong Kong, China department of mathematics University of Science and Technology of China Hefei China department of mathematics The Chinese University of Hong Kong Hong Kong China

In this paper, we obtain a blow-up criterion for classical solutions to the 3-D compressible Navier-Stokes equations just in terms of the gradient of the velocity, analogous to the Beal-Kato-Majda criterion for the id... 详细信息

关键词： blow-up classical solutions compressible Navier-Stokes

Parabolic equation of the m-Laplacian with nonlinear boundary condition

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Chinese Science Bulletin 1998年第11期43卷 905-908页

作者： WANG Shu+ 1, 2, WANG Mingxin 3, XIE Chunhong 1 1. department of mathematics, Nanjing University, Nanjing 210093, China 2. department of mathematics, Henan University, Kaifeng 475001, China 3. department of Applied mathematics, Southeast University, department of Mathernntics Nanjing University Nanjing China department of mathematics Henan University Kaifeng China department of Applied mathematics Southeast University Nanjing China

The existence and nonexistence of global positive weak solutions of parabolic equation of the m-Laplician with nonlinear boundary condition are dealt with. The necessary and sufficient conditions on the existence of a... 详细信息

关键词： nonlinear boundary condition parabolic equation of m-Laplacian global solution blow-up.