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Mean size formula of wavelet subdivision tree on Heisenberg group

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Applied mathematics(A Journal of Chinese Universities) 2008年第3期23卷 303-312页

作者： WANG Guo-mao department of mathematics,Zhejiang university,Hangzhou 310027,china.department of mathematics,Hangzhou Dianzi university,Hangzhou 310018,china. department of mathematics Zhejiang University Hangzhou 310027 China department of mathematics Hangzhou Dianzi University Hangzhou 310018 China

The purpose of this paper is to investigate the mean size formula of wavelet packets （wavelet subdivision tree） on Heisenberg group. The formula is given in terms of the p-norm joint spectral radius. The vector refinement equations on Heisenberg group and the subdivision tree on the Heisenberg group are discussed. The mean size formula of wavelet packets can be used to describe the asymptotic behavior of norm of the subdivision tree.

关键词： Heisenberg group wavelet packets subdivision tree joint spectral radius stability

STABILITY OF IMPULSIVE LINEAR HYBRID SYSTEMS WITH TIME DELAY

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Journal of Systems Science & Complexity 2010年第4期23卷 738-747页

作者： Yu ZHANG·Jitao SUN department of mathematics,Tongji university,Shanghai 200092,china. JitaoSUN department of mathematics Tongji University

This paper investigates the stability of impulsive linear hybrid systems with time *** a number of delay-independent/delay-dependent stability criteria are obtained by using Lyapunovfunctions or Lyapunov *** examples ... 详细信息

关键词： Impulsive linear hybrid system Lyapunov function Lyapunov functional time delay.

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

Sharpness on the Lower Bound of the Lifespan of Solutions to Nonlinear Wave Equations

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Chinese Annals of mathematics,Series B 2011年第4期32卷 521-526页

作者： Yi ZHOU 1 Wei HAN 2 1 Nonlinear Mathematical Modeling and Methods Laboratory Shanghai Key Laboratory for Contem- porary Applied mathematics School of Mathematical Sciences, Fudan university, Shanghai 200433, china. 2 School of Mathematical Sciences, Fudan university, Shanghai 200433, china.department of mathematics, north university of china, taiyuan 03.051, china. Nonlinear Mathematical Modeling and Methods Laboratory Shanghai Key Laboratory for Contemporary Applied Mathematics School of Mathematical Sciences Fudan University Shanghai 200433 China

This paper is devoted to proving the sharpness on the lower bound of the lifespan of classical solutions to general nonlinear wave equations with small initial data in the case n = 2 and cubic nonlinearity （see the results of T. T. Li and Y. M. Chen in 1992）. For this purpose, the authors consider the following Cauchy problem： { where □=δt^2-∑i=1n δx^^2 is the wave operator, g（x）（≡/） 0 is a smooth non-negative function with compact support, and ε 〉 0 is a small parameter. It is shown that the solution blows up in a finite time, and the lifespan T（ε） of solutions has an upper bound T（ε） ≤ exp（Aε-2） with a positive constant A independent of ε, which belongs to the same kind of the lower bound of the lifespan.

关键词： Nonlinear wave equation Cauchy problem Lifespan

A RANDOM FUNCTIONAL CENTRAL LIMIT THEOREM FOR PROCESSES OF PRODUCT SUMS OF LINEAR PROCESSES GENERATED BY MARTINGALE DIFFERENCES

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Chinese Annals of mathematics,Series B 2003年第4期24卷 449-456页

作者： WANG YUEBAO YANG YANG ZHOU HAIYANG department of mathematics, Suzhou university, Suzhou 215006, Jiangsu, china. department of mathematics, Suzhou university, Suzhou 215006, Jiangsu, china. Suzhou Univ Dept Math Suzhou 215006 Peoples R China

A random functional central limit theorem is obtained for processes of partial sums andproduct sums of linear processes generated by non-stationary martingale differences. It devel-ops and improves some corresponding results on processes of partial sums of linear processesgenerated by strictly stationary martingale differences, which can be found in [5].

关键词： Ilandom functional central limit theorem Processes of product sums

SPECTRUM-PRESERVING ELEMENTARY OPERATORS ON B(X)

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Chinese Annals of mathematics,Series B 1998年第4期19卷 511-516页

作者： HOU JINCHUAN (department of mathematics, Shanxi Teachers university, Linfen 041004, china.) Shanxi Teachers Univ Dept Math Linfen 041004 Peoples R China

Characterizations for elementary operators of length 2 to be invertibility-preserving,spectrum-preserving or spectrum-compressing are obtained.

关键词： Elementary operators Spectrum-preserving linear maps Positive maps

MATHER SETS FOR SUBLINEAR DUFFING EQUATIONS

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Chinese Annals of mathematics,Series B 1994年第4期15卷 421-434页

作者： QIAN DINGBIAN(department of mathematics, Suzhou university, 215006, china.) SUZHOU UNIV DEPT MATHSUZHOU 215006PEOPLES R CHINA

The existence of Mather sets(generalized quasiperiodic solutions and uNlinked periodicsolutions)for sublinear Duffing equations is shown. Here the approach is based on the use ofaction-angle variables and the applicat... 详细信息

关键词： Sublinear Duffing equation Finite twist Aubry-Mather theorem Mather sets.

LIFE SPAN OF A SMOOTH SOLUTION FOR THE SURFACE DIFFUSION FLOW

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Chinese Annals of mathematics,Series B 2003年第3期24卷 331-342页

作者： LIU ZUHAN department of mathematics, Yangzhou university, Yangzhou 225002, Jiangsu, china. Yangzhou Univ Dept Math Yangzhou 225002 Jiangsu Peoples R China

Consider the motion of immersed hypersurfaces driven by surface diffusion flow and give anlower bound on the life span of a smooth immersed solution, which depends only on how muchthe curvature of the initial surface ... 详细信息

关键词： Surface diffusion flow Mean curvature Second fundamental form Fourth order equation

REDUCTIONS OF ADJOINT REPRESENTATIONS TO LAX REPRESENTATIONS FOR CONSTRAINED FLOWS

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Chinese Annals of mathematics,Series B 1996年第2期17卷 187-198页

作者： ZENG YUNBO department of Applied mathematics, Tsinghua university, Beijing 100084, china. TSING HUA UNIV DEPT APPL MATHBEIJING 100084PEOPLES R CHINA

Within framework of zero-curvature representation theory, the Lax representations for x- andtn-constrained flows of soliton hierarchy are obtained from reductions of adjoint representationsof the auxiliary linear problems. This method is applied to the third order spectral problem bytaking modified Boussinesq hierarchy as an illustrative example.

关键词： Constrained flow Lax representation Adjoint representation Soliton hierarchy