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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 3.1004, china department of Mathematics, {3. 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.

The geodetic numbers of graphs and digraphs

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Science china Mathematics 2007年第8期50卷 1163-1172页

作者： Chang-hong LU~(1,2) 1 department of Mathematics,east china {3. University,shanghai 200062,china 2 Institute of Theoretical Computing,east china Narnal University,shanghai 200062,china 1. department of Mathematics East China Normal University Shanghai 200062 China 2. Institute of Theoretical Computing East China Narnal University Shanghai 200062 China

For every two vertices u and v in a graph G, a u-v geodesic is a shortest path between u and v. Let I(u, v) denote the set of all vertices lying on a u-v geodesic. For a vertex subset S, let I(S) denote the union of all I(u, v) for u, v ∈ S. The geodetic number g(G) of a graph G is the minimum cardinality of a set S with I(S) = V (G). For a digraph D, there is analogous terminology for the geodetic number g(D). The geodetic spectrum of a graph G, denoted by S(G), is the set of geodetic numbers of all orientations of graph G. The lower geodetic number is g ?(G) = minS(G) and the upper geodetic number is g +(G) = maxS(G). The main purpose of this paper is to study the relations among g(G), g ?(G) and g +(G) for connected graphs G. In addition, a sufficient and necessary condition for the equality of g(G) and g(G × K 2) is presented, which improves a result of Chartrand, Harary and Zhang.

关键词： convex set digraph distance geodesic geodetic number 05C12 05C20

Periodic Solutions of Schrdinger Flow from S^3.to S^2

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Chinese Annals of Mathematics,Series B 2006年第4期27卷 401-410页

作者： Hao YIN department of Mathematics East-China Normal University Shanghai 200062 China.

This paper deals with the periodic solutions of Schrǒdinger flow from S^3.to S^2. It is shown that the periodic solution is related to the variation of some functional and there exist S^1-invariant critical points to... 详细信息

关键词： Schrǒdinger flow Periodic solution Variational method

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 {3. University, shanghai 200062, china College of Mathematics & Information Science, Northwest {3. University, Lanzhou 73.070, 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.

Denitrification in Chongming east tidal flat sediment, Yangtze estuary, china

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Science china Earth Sciences 2006年第10期49卷 1090-1097页

作者： WANG Dongqi1,2, CHEN Zhenlou1,3. XU Shiyuan1,2, HU Lingzhen1 & WANG Jun1,2 1. College of Resources & Environment, east china normal University,{3., china 2. State Key Laboratory of Estuarine and Coastal Sediment Dynamics and Morphodynamics, east china normal University,{3., china 3. Key Laboratory of Geographical Information Science of Ministry of Education,east china normal University,{13. 200062, china 1. College of Resources & Environment East China Normal University Shanghai 200062 China 2. State Key Laboratory of Estuarine and Coastal Sediment Dynamics and Morphodynamics East China Normal University Shanghai 200062 China 3. Key Laboratory of Geographical Information Science of Ministry of Education East China Normal University Shanghai 200062 China

From July 2003.to July 2004, samples were collected on Chongming Island east tidal flat every two months. The research showed that the nitrous oxide (N2O) production rate was very low in the water, Chongming east tidal flat (CM) sediment was the N2O source of the water. Sediment N2O natural production rate was between -0.08 and 1.74 μmolN·m-2·h-1. N2O natural production rate was higher in the summer. The difference of the N2O natural production rate in the different tidal flats, the correlation between the N2O natural production rate and the denitrification rate, and those with the temperature and DO indicate that middle tidal flat sediment denitrification was the main process of the N2O production, while in the low tidal flat sediment, the production of the N2O came from several processes of the nitrogen cycling. Tidal flat sediment denitrification reaction was stronger in summer and winter but relatively lower in the late autumn and early spring. Seasonal change of the sediment denitrification rate was wide, from 1.12 to 3..3. μmolN·m-2·h-1. Temperature, DO and the coactions of them had the prominent effect on the tidal flat sediment denitrification.

关键词： Yangtze estuary, tidal flat sediment, denitrification, nitrous oxide, effect factor.

Tests for nonparametric parts on partially linear single index models

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Science china Mathematics 2007年第3期50卷 439-449页

作者： Ri-quan ZHANG department of Statistics, east china {3. University, shanghai 200062, china department of Mathematics, Shanxi Datong University, Datong 03.009, china department of Statistics East China Normal University Shanghai 200062China

Tests for nonparametric parts on partially linear single index models are considered in this paper. Based on the estimates obtained by the local linear method, the generalized likelihood ratio tests for the models are established. Under the null hypotheses the normalized tests follow asymptotically the χ2-distribution with the scale constants and the degrees of freedom being independent of the nuisance parameters, which is called the Wilks phenomenon. A simulated example is used to evaluate the performances of the testing procedures empirically.

关键词： local linear method partially linear single index models generalized likelihood ratio test Wilks phenomenon χ 2-distribution 62G10 62G20

Issues of the Holocene transgression on the southern plain of the Changjiang Delta

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Acta Oceanologica Sinica 1988年第4期7卷 578-590页

作者： Yan Qinshang and Hong Xueqing department of geography, east china {3. University, shanghai, china Dept. of geography East China Normal Univ. Shanghai China. China

The paper deals with the question of Holocene transgression on the southern plain of the Changjiang *** the beginning of the transgression, the paleovalleys of the Changjiang and Qiantang Rivers were covered by sea water at *** shoreline of 8000-7500 yr BP coincided with the -7m isobath of paleotopography. Sea level had already been the present level about 7000-6500 years ago, and the Holocene transgression reached its maximum extent. During the period, the Changjiang and Qiantang Rivers and the Dongtiaoxi valley were turned into estuaries; the eastern area of shanghai became a shallow sea; some of the bays and lagoons were distributed on the Hang-Jia-Hu and Tao-Ge Plain; the hilly region around the Taihu Lake was coastal marsh and freshwater swamp. Gangshen on the west of shanghai was formed 7000-4000 yr BP, and during the last 4000 years, the eastern coastal plain of shanghai advanced quickly toward the sea, and partial clear land of the western Taihu Lake was enclosed and charged into a fre

关键词： Ho Issues of the Holocene transgression on the southern plain of the Changjiang Delta

A MONOTONE COMPACT IMPLICIT SCHEME FOR NONLINEAR REACTION-DIFFUSION EQUATIONS

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Journal of Computational Mathematics 2008年第2期26卷 123-148页

作者： Yuanming Wang department of Mathematics,east china {3. University,shanghai 200241,china Division of Computational Science,E-Institute of shanghai Universities,shanghai {3. Benyu Guo department of Mathematics,shanghai {3. University,shanghai 20023.,china Division of Computational Science,E-Institute of shanghai Universities,shanghai,china department of Mathematics East China Normal University Shanghai 200241 China Division of Computational Science E-Institute of Shanghai Universities Shanghai Normal University Shanghai 200234 China department of Mathematics Shanghai Normal University Shanghai 200234 China Division of Computational Science E-Institute of Shanghai Universities Shanghai China

A monotone compact implicit finite difference scheme with fourth-order accuracy in space and second-order in time is proposed for solving nonlinear reaction-diffusion equations. An accelerated monotone iterative method for the resulting discrete problem is presented. The sequence of iteration converges monotonically to the unique solution of the discrete problem, and the convergence rate is either quadratic or nearly quadratic, depending on the property of the nonlinear reaction. The numerical results illustrate the high accuracy of the proposed scheme and the rapid convergence rate *** iteration.

关键词： Nonlinear reaction-diffusion equation Monotone compact implicit scheme High accuracy Monotone iteration Rapid convergence rate.

Dispersion of Soluble Matters in Newton-dipolar Stratified Fluid and Effects of Peripheral Layer

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Communications in Nonlinear Science and Numerical Simulation 1998年第4期3卷 236-241页

作者： Zhangji LU, Shousheng DONG, Yu SHEN and Guangping ZHENG (department of Mechanics and Engineering Science, Fudan University, shanghai 20043.,china)(department of Physics, east china normal University, shanghai 200062, china) Dept. of Mechanics and Eng. Science Fudan University Shanghai 200433 China department of Physics East China Normal University Shanghai 200062 China

In the paper, the dispersion law and the concentration distributions of soluble matters in Newton-dipolar fluids flowing through a circular tube have been investigated. Main results are: (1) for the dependence of M on A (or H), the completely opposite trends are obtained in the cases with and without the peripheral layer. (2) effects of δ on　M have the minimum values near 8=0.85-0.9. (3. various models such as couple stress,micropolar, dipolar, Newton-newtonian, Newton-couple stress and Newton-micropolar　model etc. are all special cases of Newton-dipolar fluid (where Mz=0). WhenMz≠ 0,however, there are evident differences between the Newton-dipolar fluid and the Newtoncouple stress fluid, the Newton-micropolar fluid.

关键词： dipolar fluid dispersion effects of a peripheral layer tube flow of complex fluid