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Cartesian closedness of categories of completely distributive lattices

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Chinese Science Bulletin 1998年第24期43卷 2059-2063页

作者： ZHANG Dexue 1 and YANG Zhongqiang 2.1. department of mathematics, Sichuan {2., Chengdu 610064, China 2. department of mathematics, Shaanxi Normal {2., Xi’an 710062. China department of mathematics Sichuan University Chengdu China department of mathematics Shaanxi Normal University Xi’an China

The category of completely distributive lattices with Scott continuous functions is cartesian closed. Neither the category of completely distributive lattices with arbitrary union preserving mappings nor the category ... 详细信息

关键词： completely distributive lattice continuous lattice cartesian closedness.

CYCLES CONTAINING MANY VERTICES OF SUBSETS IN GRAPHS WITH LARGE DEGREE SUMS AND NEIGHBORHOOD UNIONS

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Systems Science and Mathematical Sciences 2000年第4期13卷 432-445页

作者： LI Jianping (Institute of mathematics and department of mathematics, yunnan university, kunming 650091. China) 云南大学数学所云南昆明 650091

Let G be a graph of order n and X V(G). G is called X-cyclable if G has an X-cycle, i.e., a cycle containing all vertices of X. Define the parameters a(X) = max{|S| S is an independent vertex set in G[X] induced by X}, σk(X) = min{∑ki=1dG(x.i| {x1, x1…, xk} is an independent vertex set in G[X]} and NCk(X) = min{|∪ki=1 NG(xi)| | {x1, x2.,xk} is an independent vertex set in G[X] }. Our main result is as follows: If G is a 1-tough graph and X V(G) with σ3(X)≥ n, then for every integer t ≥ 1, G has a cycle C containing at least min{|X|, (2.X| - n + 3δ + 1 - t), |X| + NCt(X) - a(X)} venices of X, where δ(X) = [σ3(X)]. This result further extends previous results in H.J. Broersma et al. in terms of X-cyclability. We also obtain that if G is a 1-tough graph with σ3 (X) ≥ n, then for every integer t ≥ 1, G has a cycle containing at least min{|X|, (4|X|- 2.+4δ(X) + 1 - 2.), NCt (X) +NCt (X)} vertices of X, where NCt (X) = min{|N(I) ∩X|| I is an independent set of t vertices of X}. Analogous results are established for 2.connected graphs.

关键词： (X-)longest cycle (X-)dominating cycle hamiltonian graph vertex degree large degree sums neighborhood unions.

CMC surfaces in the hyperbolic 3-space

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Chinese Science Bulletin 1998年第7期43卷 547-550页

作者： YU Zuhuan 1, 2.and LI Zhenqi 1, 3 1. Institute of mathematics, Fudan university, Shanghai 2.0433, China {2.,Sichuan Union university, Chengdu 610064, China 3. department of mathematics, Nanchang university, Nanchang 33 nstitute of Mathemalics Fudan University Shanghai China department of mathematics Sichuan Union University Chengdu China department of mathematics Nanchang University Nanchang China

CMC-H surfaces satisfying H≥1 are studied. It is proved that these surfaces possess a natural representation which is a generalization of the Bryant’s result.

关键词： hyperbolic space CMC surface Weierstrass representation.

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 {2., Hangzhou 310036, China 2. department of Applied mathematics, School of Mathematical Sciences, South China {2. 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.

GLOBAL ATTRACTIVITY IN A PERIODIC DELAY SINGLE SPECIES MODEL

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Systems Science and Mathematical Sciences 2000年第1期13卷 1-6页

作者： LI Yong kun (department of mathematics,{2., kunming 650091. China) 云南大学数学系云南昆明 650091

***[1]illtroducedthefollowingdelayLotka-Volterratypesinglespeciespopulationgrowthmodel:wherea,b,ctTarerealconstants,anda>0,c>0,***>0,b0,(l.1)exhibitstheso--calledAlic... 详细信息

***[1]illtroducedthefollowingdelayLotka-Volterratypesinglespeciespopulationgrowthmodel:wherea,b,ctTarerealconstants,anda>0,c>0,***>0,b0,(l.1)exhibitstheso--calledAlic...

关键词： Single species population growth positive periodic solution global attractivity foedholm mapping.

OUTLIERS AND INFLUENTIAL OBSERVATIONS IN A RIDGE MEAN SHIFT REGRESSION

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Systems Science and Mathematical Sciences 1995年第1期8卷 12-26页

作者： PAN Jianxin (Institute of Applied mathematics, yunnan Province, {2. 650091. China)XIONG Haiyan (department of mathematics, yunnan university, {2. 650091. China) 云南省应用数学所云南昆明 650091 云南大学数学系云南昆明

ＯＵＴＬＩＥＲＳＡＮＤＩＮＦＬＵＥＮＴＩＡＬＯＢＳＥＲＶＡＴＩＯＮＳＩＮＡＲＩＤＧＥＭＥＡＮＳＨＩＦＴＲＥＧＲＥＳＳＩＯＮＰＡＮＪｉａｎｘｉｎ（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，Ｙｕｎｎａｎ... 详细信息

ＯＵＴＬＩＥＲＳＡＮＤＩＮＦＬＵＥＮＴＩＡＬＯＢＳＥＲＶＡＴＩＯＮＳＩＮＡＲＩＤＧＥＭＥＡＮＳＨＩＦＴＲＥＧＲＥＳＳＩＯＮＰＡＮＪｉａｎｘｉｎ（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＹｕｎｎａｎＰｒｏｖｉｎｃｅ，Ｋｕｎｍｉｎｇ６...

关键词： Outliers influential observations ridge mean shift regression ridge residuals.

Existence of the solutions and the attractors for the large-scale atmospheric equations

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Science China Earth Sciences 2006年第6期49卷 650-660页

作者： HUANG Haiyang1 & GUO Boling2.1. department of mathematics, Beijing Normal {2., Beijing 100875, China 2. Institute of Applied Physics and Computational mathematics, Beijing 100080, China 1. department of mathematics Beijing Normal University Beijing 100875 China 2. Institute of Applied Physics and Computational mathematics Beijing 100080 China

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.

Planar cubic hybrid hyperbolic polynomial curve and its shape classification

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Progress in Natural Science:Materials International 2004年第1期14卷 42-47页

作者： WANG Guozhao 1,2. * and YANG Qinmin 1,2. (1. Institute of Computer Graphics and Image Processing, 2. department of mathematics, Zhejiang university, Hangzhou 31002., China) Zhejiang Univ Inst Comp Graph & Image Proc Hangzhou 310027 Peoples R China Zhejiang Univ Dept Math Hangzhou 310027 Peoples R China

The planar cubic hybrid hyperbolic polynomial curves and cubic H Bézier curves are presented. The conditions leading to inflection points and singularities (cusps and loops) are investigated and the shape of these curves is classified. The conclusions enable us to detect inflection points and singularities and get an idea of how to preserve the fair shape when designing such curves.

关键词： hybrid hyperbolic polynomial curve H-Bézier curve shape classification inflection points singularities

Lipschitz continuity of best approximations and Chebyshev centers

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Chinese Science Bulletin 1998年第3期43卷 185-188页

作者： LI Chong 1 and WANG Xinghua 2.1. Center for Mathematical Sciences, Zhejiang university, Hangzhou 31002., China 2. department of mathematics, Hangzhou university, Hangzhou 31002., China Center for Mathematical Sciences Zhejiang University Hangzhou China department of mathematics Hangzhou University Hangzhou China

The Lipschitz continuity results are given for best approximations and Chebyshev centers. Consequently, the open problem presented by Septycki and Vleck is solved completely.

关键词： best approximation Chebyshev center uniform convexity.