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ON THE APPROXIMATELY SIMILARITY OF OPERATORS

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Chinese Annals of mathematics,Series B 1998年第4期19卷 465-472页

作者： WEI GUOQIANG (department of mathematics, East china normal university, Shanghai 200062, china.) E china normal Univ Dept Math Shanghai 200062 Peoples R China

The author shows that a rank-preserving *-isorporphism between separable C*-algebras with unity is approximately equivalent to the identity representation. Some applications are made for approximately similarity of n-... 详细信息

关键词： C*-algebra Rank-preserving *-isomorphism Approximately equevalent,Approximately similar n-tuples of operators

MULTIPLICITY OF PERIODICSOLUTIONS OF DUFFING'S EQUATIONSWITH LIPSCHITZIAN CONDITIONMULTIPLICITY OF PERIODICSOLUTIONS OF DUFFING'S EQUATIONS WITH LIPSCHITZIAN CONDITION

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Chinese Annals of mathematics,Series B 2000年第4期21卷 479-488页

作者： WANG ZAIHONG (department of mathematics, Capital normal university, Beijing 100037, china.) department of mathematics Capital Normal University Beijing 100037 China

This paper deals with the existence and multiplicity of periodic solutions of Duffing equations x + g(x) = p(t). The author proves an infinity of periodic solutions to the periodically forced nonlinear Duffing equations provided that g(x) satisfies the globally lipschitzian condition and the time-mapping satisfies the weaker oscillating property.

关键词： Periodic solution Time mapping Poincare-Birkhoff twist theorem

Codimension 3 nonresonant bifurcations of homoclinic orbits with two inclination flips

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Science china mathematics 2005年第2期48卷 248-260页

作者： SHUI Shuliang & ZHU Deming College of mathematics and Physics, Zhejiang normal university, Jinhua 321004, china department of mathematics, East china normal university, Shanghai 200062, china 1. College of mathematics and Physics Zhejiang Normal University 321004 Jinhua China 2. department of mathematics East China Normal University 200062 Shanghai China

Homoclinic bifurcations in four-dimensional vector fields are investigated by setting up a local coordinate near a homoclinic orbit. This homoclinic orbit is principal but its stable and unstable foliations take inclination flip. The existence, nonexistence, and uniqueness of the 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the two-fold 1-periodic orbit and three-fold 1 -periodic orbit are also obtained. It is indicated that the number of periodic orbits bifurcated from this kind of homoclinic orbits depends heavily on the strength of the inclination flip.

关键词： bifurcation, homoclinic orbit, non-resonance, inclination flip, 1-periodic orbit.

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Saturated models

Chinese Science Bulletin 1998年第7期43卷 562-564页

作者： CHEN Guolong department of mathematics, Beijing normal university, Beijing 100875, china department of mathematics Beijing Normal University Beijing China

An equivalent description of saturated models is given, and some properties of countable saturated models, almost saturated models and full models are discussed. New proofs of two important theorems of the related doc... 详细信息

关键词： almost saturated model full model power type.

Short cycle structures for graphs on surfaces and an open problem of Mohar and Thomassen

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Science china mathematics 2006年第2期49卷 212-224页

作者： REN Han & DENG Mo department of mathematics, East china normal university, Shanghai 200062, china College of mathematics & Information Science, Northwest normal university, Lanzhou 730070, china 1. department of mathematics East China Normal University Shanghai 200062 China 2. College of mathematics & Information Science Northwest Normal University Lanzhou 730070 China

In this paper we investigate cycle base structures of a (weighted) graph and show that much information of short cycles is contained in an MCB (i.e., minimum cycle base). After setting up a Hall type theorem for base-transformation, we give a sufficient and necessary condition for a cycle base to be an MCB. Furthermore, we show that the structure of MCB in a (weighted)graph is unique. The property is also true for those having a longest length (although much work has been down in evaluating MCB, little is known for those having a longest length). We use those methods to find out some unknown properties for short cycles sharing particular properties in (unweighted) graphs. As applications, we determine the structures of short cycles in an embedded graph and show that there exist polynomially bounded algorithms in finding a shortest contractible cycle and a shortest two-sided cycle provided such cycles exist. Those answer an open problem of B. Mohar and C. Thomassen.

关键词： cycle base facial cycle graph embedding.

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.

Lp integrability of trigonometric series with special varying coefficients

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Applied mathematics:A Journal of Chinese Universities 2009年第4期24卷 402-410页

作者： WEI Bao-rong department of mathematics,Hangzhou normal university,Zhejiang 310036,china department of mathematics Hangzhou Normal University Zhejiang 310036 China

Very recently,Yu,Le and Zhou introduced the so called Δ*B1 and Δ*B2 conditions,which are generalizations of the monotone *** applying these two new conditions,the author essentially generalizes the classical results of Chen on the necessary and sufficient conditions of the Lp integrability of trigonometric *** fact,the present paper gives the first result on the necessary and sufficient conditions of the Lp integrability of trigonometric series,where coefficients may have diffierent signs.

关键词： Lp integrability trigonometric series special varying coefficients

METHOD OF NONCONFORMING MIXED FINITE ELEMENT FOR SECOND ORDER ELLIPTIC PROBLEMS METHOD OF NONCONFORMING MIXED FINITE ELEMENT FOR SECOND ORDER ELLIPTIC PROBLEMS

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Journal of Computational mathematics 2000年第5期18卷 449-456页

作者： Zhen-dong Luo (department of mathematics, Capital normal university, Beijing 100057, china) 首都师范大学北京 100037

In this paper, the method of non-conforming mixed finite element for second order elliptic problems is discussed and a format of real optimal order for the lowest order error estimate.

关键词： Non-conforming mixed finite element Error estimate Second order elliptic problems.

K-uniformly rotund spaces and k-uniformly smooth spaces

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Chinese Science Bulletin 1998年第2期43卷 92-95页

作者： Suyalatu 1 and WU Congxin 2 1. department of mathematics,Inner Mongolia normal university, Huhhot 010022, china 2. department of mathematics, Harbin Institute of Technology, Harbin 150006, china department of mathematics Inner Mongolia Normal University Huhhot China department of mathematics Harbin Institute of Technology Harbin China

The conception of k_uniform smoothness (KUS) is introduced. It is the extension of the conception of uniform smoothness. It is proved that the k_uniform smoothness and Sullivan’s K_uniform rotundity (KUR) are the daul notions. X+* is a KUR space if and only if X is a KUS space, X+* is a KUS space if and only if X is a KUR space. If X is a KUS space, then X is a (K+1)US space. It is also proved that the KUS space includes the Nan’s k_strongly smooth space.

关键词： K_uniform smoothness K_uniform convexity.