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Highest weight representations of a Lie algebra of Block type

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Science china mathematics 2007年第4期50卷 549-560页

作者： Yue-zhu WU & Yu-cai SU department of mathematics, Shanghai Jiaotong university, Shanghai 200240, china department of mathematics, Qufu normal university, Qufu 273165, china department of mathematics, university of Science and Technology of china, Hefei 230026, china department of mathematics Shanghai Jiaotong University Shanghai China department of mathematics Qufu Normal University Qufu China department of mathematics University of Science and Technology of China Hefei China

For a field $\mathbb{F}$ of characteristic zero and an additive subgroup G of $\mathbb{F}$ , a Lie algebra B(G) of the Block type is defined with the basis {L α,i , c | α ∈ G ?1 ≤ i ∈ ?} and the relations [L α,i , L β,j ] = ((i + 1)β ? (j + 1)α)L α+β,i+j + αδ α, ?β δ i+j,?2 c, [c, L α,i ] = 0. Given a total order ? on G compatible with its group structure, and any Λ ∈ B(G) 0 * , a Verma B(G)-module M(Λ, ?) is defined, and the irreducibility of M(Λ, ?) is completely determined. Furthermore, it is proved that an irreducible highest weight B(?)-module is quasifinite if and only if it is a proper quotient of a Verma module.

关键词： Verma modules Lie algebras of Block type irreducibility 17B10 17B65 17B68

A FINITE DIFFERENCE METHOD FOR THE MODEL OF WHEEZES

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Journal of Computational mathematics 1995年第2期13卷 123-129页

作者： Lu Bai-nian (department of mathematics, Shaanxi normal university, Xi’an, Shaanxi, china) 陕西师范大学数学系陕西西安

In this paper, a finite difference scheme for the linear and nonlinear models of wheezes are given. The stability of the finite difference scheme for the linear model is obtained by using of von Neumann method. Moreover, the convergence and stability of the finite difference scheme for the nonlinear model are studied by the energy inequalities method. By some numerical computations, the relationships between angular frequency and wall position, fluid speed and amplitude are discussed. Finally, the author shows that the numerical results are coincided with Grotberg's theoretical results.

关键词： Math A FINITE DIFFERENCE METHOD FOR THE MODEL OF WHEEZES

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 normal university,Shanghai 200062,china 2 Institute of Theoretical Computing,East china Narnal university,Shanghai 200062,china department of mathematics East China Normal University Shanghai China Institute of Theoretical Computing East China Narnal University Shanghai 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

A lower bound on the total signed domination numbers of graphs

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Science china mathematics 2007年第8期50卷 1157-1162页

作者： Xin-zhong LU department of mathematics,Zhejiang normal university,Jinhua 321004,china department of mathematics Zhejiang Normal University Jinhua China

Let G be a finite connected simple graph with a vertex set V (G) and an edge set E(G). A total signed domination function of G is a function f : V (G) ∪ E(G) → {?1, 1}. The weight of f is w(f) = Σ x∈V(G)∪E(G) f(x). For an element x ∈ V (G) ∪ E(G), we define $f[x] = \sum\nolimits_{y \in N_T [x]} {f(y)} $ . A total signed domination function of G is a function f : V (G) ∪ E(G) → {?1, 1} such that f[x] ? 1 for all x ∈ V (G) ∪ E(G). The total signed domination number γ s * (G) of G is the minimum weight of a total signed domination function on G.In this paper, we obtain some lower bounds for the total signed domination number of a graph G and compute the exact values of γ s * (G) when G is C n and P n .

关键词： total signed domination function total signed domination number 26A33

ON THE INVERSE IMAGE SET OF RATIONAL FUNCTIONS

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Acta Mathematica Scientia 2007年第3期27卷 541-548页

作者：孙道椿 department of mathematics South China Normal University

This article studies the inverse image of rational functions. Several theorems are obtained on the Julia set expressed by the inverse image, and a mistake is pointed out in ***＇ theorem incidentally.

关键词： Rational dynamical system Julila set Fatou component

Integral spinor norms in dyadic local fields Ⅲ

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Science china mathematics 2010年第9期53卷 2425-2446页

作者： L JianRui1 & XU Fei2,1department of mathematics,Jinan university,Guangzhou 510632,china 2School of mathematics,Capital normal university,Beijing 100048,china department of mathematics Jinan University Guangzhou China School of mathematics Capital Normal University Beijing China

In this paper we give an alternative computation of integral spinor norms over dyadic local fields by using the Jordan decomposition of *** particular,we emphasize the striking similarity between the theory over dyadi... 详细信息

关键词： integral lattice spinor norm Jordan decomposition

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.

Fredholm operators in Toeplitz algebras associated with discrete abelian groups

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Chinese Science Bulletin 1998年第14期43卷 1175-1179页

作者： XU Qingxiang 1 and CHEN Xiaoman 2 1. department of mathematics, Shanghai normal university, Shanghai 200234, china 2. Laboratory of mathematics for Nonlinear Sciences and Institute of mathematics, Fudan university, Shanghai 200433, china department of mathematics Shanghai Normal University Shanghai China Laboratory of mathematics for Nonlinear Sciences and Institute of mathematics Fudan University Shanghai China

The locally finite below sets are introduced and the Fredholm operators in Toeplitz algebras associated with discrete abelian groups are studied.

关键词： discrete abelian group quasi_ordered group Toeplitz operator Fredholm operator.

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.