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Applications of the theory of Grbner bases to the study of linear recurring arrays

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chinese Science Bulletin 2001年第14期46卷 1149-1152页

作者： LIU MulanThe academy of mathematics of systems sciences, chinese academy of sciences, beijing 100080, china The academy of mathematics of systems sciences Chinese Academy of Sciences Beijing China

This is a small survey of applications of the theory of Grobner bases to the study of linear recurring arrays. It applies some properties of Grobner bases to studying linear recurring arrays and contains recent new re... 详细信息

关键词： Grobner bases linear recurring arrays module structure localization.

Profitless delays for extinction in nonautonomous Lotka-Volterra system

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Communications in Nonlinear Science and Numerical Simulation 2001年第4期6卷 210-216页

作者： Shengqiang LIU and Lansun CHEN academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china e-mail: Lsq@math03. math. ac. cn academy of mathematics and system sciences Chinese Academy of Sciences Beijing 100080 China

We study the delayed periodic n-species Lotka-Volterra systems where the growth rate of each species is not always positive. The sufficient conditions for the extinction that are independent of the delays are obtained. Some known results are improved and generalized. Our results suggest that under some conditions, the introduction and the variance of the time delays can be both harmless and profitless. Discussion about the effect of time delays on the extinction of the system is also advanced.

关键词： competitive Lotka-Volterra system periodic profitless delays extinction

A nontrivial product in the stable homotopy groups of spheres

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Science china mathematics 2004年第6期47卷 831-841页

作者： LIU XiuguiInstitute of mathematics, chinese academy of sciences, beijing 100080, china Institute of mathematics Chinese Academy of Sciences Beijing China

Let A be the mod p Steenrod algebra for p an arbitrary odd prime. In 1962, Liulevicius described h i and b k in Ext* A ’*(Zp,Zp) having bigrading (1, sui— 1) and (2, 2p k+1 x(p— 1)), respectively. In this paper we prove that for p ≥ 7, n ≥ 4 and $3 \leqslant s < p - 1, h_0 b_{n - 1} \tilde \gamma _s \in Ext_A^{s + 3,p^n q + sp^2 q + (s - 1)pq + (s - 1)q + s - 3} (Z_p ,Z_p )$ survives to E∞ in the Adams spectral sequence, where q = 2(p — 1).

关键词： stable homotopy groups of spheres Adams spectral sequence Toda-Smith spectra May spectral sequence

CONVERGENCE RATES TO TRAVELLING WAVES FOR A RELAXATION MODEL WITH LARGE INITIAL DISTURBANCE

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Acta Mathematica Scientia 2004年第2期24卷 213-227页

作者：张辉赵引川 Departmentofmathematics BeijingNormalUniversityBeijing100825China

This paper is concerned with the convergence rates to travelling waves for a relaxation model with general flux functions. Compared with former results in this direction, the main novelty in this paper lies in the fact that the initial disturbance can be chosen large in suitable norm. Our analysis is based on the L^1-stability results obtained by C. Mascia and R. Natalini in [12].

关键词： Convergence rate relaxation travelling waves large initial disturbance

Analysis of a SIS epidemic model with stage structure and a delay

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Communications in Nonlinear Science and Numerical Simulation 2001年第1期6卷 35-39页

作者： Yanni XIAO and Lansun CHEN (academy of mathematics & system sciences, Academic Sinica, beijing 100080, china ) academy of mathematics & system sciences Academia Sinica Beijing 100080 China

A disease transmission model of SIS type with Stage structure and a delay corresponding to the infectious period is formulated. By constructing the difference operator and using global convergence theorem, we show that the disease-free equilibrium is globally asymp- totically stable. The Stability of an endemic equilibrium are investigated for the differential- difference equations.

关键词： SIS epidemic model delay threshold globally asymptotically stable

Relations between Lipschitz functions and convex functions

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Science china mathematics 2005年第5期48卷 703-710页

作者： RUAN Yingbin Department of mathematics, Fujian Normal University, Fuzhou 350007, china academy of mathematics and systems Science, chinese academy of sciences, beijing 100080, china Department of mathematics Fujian Normal University Fuzhou China academy of mathematics and systems Science Chinese Academy of Sciences Beijing China

We discuss the relationship between Lipschitz functions and convex functions. By these relations, we give a sufficient condition for the set of points where Lipschitz functions on a Hilbert space is Frechet differenti... 详细信息

关键词： Lipschitz functions convex functions the Frechet differentiability.

Nonlinear autoregressive models with heavy-tailed innovation

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Science china mathematics 2005年第3期48卷 333-340页

作者： JIN Yang & AN Hongzhi School of Statistics, Renmin University of china, beijing 100872, china academy of mathematics and systems Science, chinese academy of sciences, beijing 100080, china Sch. of Statistics Renmin Univ. of China Beijing 100872 China Acad. of mathematics and Syst. Sci. Chinese Acad. of Sci. Beijing 100080 China

In this paper, we discuss the relationship between the stationary marginal tail probability and the innovation's tail probability of nonlinear autoregressive models. We show that under certain conditions that ensure the stationarity and ergodicity, one dimension stationary marginal distribution has the heavy-tailed probability property with the same index as that of the innovation's tail probability.

关键词： nonlinear autoregressive model, innovation, tail probability.

Hopf bifurcation of nonlinear incidence rates SIR epidemiological models with stage structure

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Communications in Nonlinear Science and Numerical Simulation 2001年第4期6卷 205-209页

作者： Zhonghua LU, Xianning LIU and Lansun CHEN Institute of mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china e-mail: lschen@*** Xi'an Statistic College, Xi'an 710061, china e-mail: lzh Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China Xi'an Statistic College Xi'an 710061 China Department of mathematics Southwest China Normal University Chongging 400715 China

A nonlinear incidence rates SIR epidemiological model with stage structure is considered. Different to bilinear incidence rates models, there exist two positive equilibria and whether or not the disease will eventuall... 详细信息

关键词： Hopf bifurcation SIR epidemiological model. disease-free equilibrium endemic equilibrium

BOUNDARY FEEDBACK STABILIZATION OF NONUNIFORM TIMOSHENKO BEAM WITH A TIPLOAD

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chinese Annals of mathematics,Series B 2001年第4期22卷 485-494页

作者： YAN QINGXU, FENG DEXING Institute of systems Science, academy of mathematics and systems Science, chinese academy of sciences, beijing 100080, china. Institute of systems Science, academy of mathematics and systems Science, chinese academy of sciences, Be Institute of systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

The boundary stabilization problem of a Timoshenko beam attached with a mass at one end is studied. First, with linear boundary force feedback and moment control simultaneously at the end attached with the load, the energy corresponding to the closed loop system is proven to be exponentially convergent to zero as time t →∞. Then, some counterexamples are given to show that, in other casest the corresponding closed loop system is, in general, not stable asymtotically, let alone exponentially.

关键词： Timoshenko beam Boundary feedback control C0 semigroups Exponential stability Multiplier method