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Population-size-dependent branching processes in Markovian random environments

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Chinese Science Bulletin 1998年第8期43卷 635-638页

作者： WANG Hanxing 1 and DAI Yonglong 2 1. department of mathematics, Shanghai University, Shanghai 201800, China 2. department of mathematics, Zhongshan University, Guangzhou 510275, China department of mathematics Shanghai University Shanghai China department of mathematics Zhongshan University Gunngzhou China

A branching model {Z n} n≥0is considered where the offspring distribution of the population’s evolution is not only dependent on the population size, but also controlled by a Markovian environmental process {ξ n} n≥0. For this model, asymptotic behaviour is studied such as limn→∞Z n and limn→∞Z n/m n in the case that the mean m k, θof the offspring distribution converges to m>1 as the population size k grows to ∞. In the case that {ξ n} n≥0is an irreducible positive recurrent Markov chain, certain extinction (i.e. P(Z n=0 for some n)=1) and noncertain extinction (i.e. P(Z n=0 for some n)<1) are studied.

关键词： Markov chains in random environments stochastic population models branching processes.

Automorphisms with order three of affine Lie algebras

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Chinese Science Bulletin 1998年第21期43卷 1793-1798页

作者： JIN Quanqin 1,2 and HOU Zixin 2 1. department of mathematics, Hebei University, Baoding 071002, China 2. department of mathematics, Nankai University, Tianjin 300071, China department of mathematics Hebei University Baoding China department of mathematics Nankai University Tianjin China

Some properties of automorphisms of affine Lie algebras are presented. Automorphisms with order three are classified up to conjugacy, and their fixed point sets are also computed. As a corollary, it is proved that two... 详细信息

关键词： affine Lie algebra automorphism of order three first (second) kind of automorphism.

Perturbations of the radical of nest algebras

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Chinese Science Bulletin 1998年第7期43卷 556-560页

作者： LU Fangyan 1 and LU Shijie 2 1. department of mathematics, Suzhou University, Suzhou 215006, China 2. department of mathematics, Zhejiang University, Hangzhou 310027, China department of mathematics Suzhou University Suzhou China department of mathematics Zhejiang University Hangzhou China

Let R N and K-N be the radical ideal and the compact operator ideal of nest algebra T(N) respectively. It is proved thatR-N+K-N=span{T∈T(N)∶TT(N)NCT}=span{T∈T(N): #σ′(ST)≤1, S∈T(N)}.

关键词： nest algebras radical perturbation.

Congruences on ideal nil-extension of completely regular semigroups

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Chinese Science Bulletin 1998年第5期43卷 379-381页

作者： REN Xueming 1, 2 GUO Yuqi 2 and CEN Jiaping (Shum Kar-ping) 31. department of mathematics, Xi’an University of Architecture & Technology, Xi’an 710055, China 2. department of mathematics, Yunnan University, Kunming 650091, China 3. department of department of mathematics Xi’an University of Architecture & Technology Xi’an China department of mathematics Yunnan University Kunming China department of mathematics Chinese University of Hong Kong Hong Kong

Let S be an ideal nil-extension of a completely regular semigroup K by a nil semigroup Q with zero. A concept of admissible congruence pairs (δ,ω) of S is introduced, where δ and ω are a congruence on Q and a congruence on K respectively. It is proved that every congruence on S can be uniquely respresented by an admissible congruence pair (δ,ω) of S. Suppose that ρ K denotes the Rees congruence induced by the ideal K of S. Then it is shown that for any congruence σ on S,a mapping Γ:σ|→(σ Q,σ K) is an order-preserving bijection from the set of all congruences on S onto the set of all admissible congruence pairs of S,where σ K is the restriction of σ to K and σ Q=(σ∨ρ K)/ρ K. Moreover,the lattice of congruences of S is also discussed. As a special case,every congruence on completely Archimedean semigroups S is described by an admissible quarterple of S. The following question is asked: Is the lattice of congruences of the completely Archimedean semigroup a semimodular lattice?

关键词： completely regular semigroups ideal nil-extension congruences.

Hierarchy of Combined TL-RTL Equations and an Associated (2+1)-Dimensional Lattice Equation

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Communications in Theoretical Physics 2006年第11期46卷 773-778页

作者： JIANG Qiao-Yun~1 and ZHOU Ru-Guang~(2,+) ~1department of mathematics, Nantong University, Nantong 226007, China ~2department of mathematics, Xuzhou Normal University, Xuzhou 221116, China department of mathematics Nantong University Nantong 226007 China department of mathematics Xuzhou Normal University Xuzhou 221116 China

A new (2+1)-dimensional lattice equation is presented based upon the first two members in the hierarchy of the combined Toda lattice and relativistic Toda lattice (TL-RTL) equations in (1+1) dimensions. A Darboux transformation for the hierarchy of the combined TL-RTL equations is constructed. Solutions of the first two members in the hierarchy of the combined TL-RTL equations, as well as the new (2+1)-dimensional lattice equation are explicitly obtained by the Darboux transformation.

关键词： combined TL-RTL equation integrable system Darboux transformation T0da lattice equation relativistic Toda lattice equation

p-th moment exponential stability of stochastic differential equations with impulse effect

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Science China(Information Sciences) 2011年第8期54卷 1702-1711页

作者： SHEN LiJuan 1,2 & SUN JiTao 11 department of mathematics, Tongji University,Shanghai 200092,China 2 department of mathematics,Luoyang Normal University, Luoyang 471022,China department of mathematics Tongji University Shanghai China department of mathematics Luoyang Normal University Luoyang China

The p-th moment exponential stability of stochastic differential equations with impulse effect is *** employing the method of vector Lyapunov functions,some sufficient conditions for the p-th moment exponential stability are *** addition,the usual restriction of the growth rate of Lyapunov function is replaced by the condition of the drift and diffusion coefficients to study the p-th moment exponential *** examples are also discussed to illustrate the effectiremess of the results obtained.

关键词： stochastic differential equations impulse p-th moment exponential stability vector Lyapunov functions

Schwarz-Pick estimates for positive real part holomorphic functions on unit ball and polydisc

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Science China mathematics 2010年第4期53卷 1017-1024页

作者： LIU Yang 1,& CHEN ZhiHua 2 1 department of mathematics,Zhejiang Normal University,Jinhua 321004,China 2 department of mathematics,Tongji University,Shanghai 200092,China department of mathematics Zhejiang Normal University Jinhua China department of mathematics Tongji University Shanghai China

We give higher order derivatives Schwarz-Pick estimates for all positive real part holomorphic functions on Bn and D n,and generalize early work on Schwarz-Pick estimate of higher order derivatives for holomorphic fun... 详细信息

关键词： Schwarz-Pick estimate holomorphic function Taylor expansion

A New Lie Algebra and a Way to Generate Multiple Integrable Couplings

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Communications in Theoretical Physics 2007年第12期48卷 979-982页

作者： FENG Bin-Lu~(1,2)and HAN Bo~1~1 department of mathematics,Harbin Institute of Technology,Harbin 150001,China~2 department of mathematics,Weifang University,Weifang 261000,China department of mathematics Harbin Institute of Technology Harbin 150001 China department of mathematics Weifang University Weifang 261000 China

A new higher-dimensional Lie algebra is constructed,which is used to generate multiple integrable *** this,we come to a general approach for seeking multi-integrable couplings of the known integrablesoliton equations.

关键词： Lie algebra integrable hierarchy Hamiltonian structure

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.