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Boundedness in Lebesgue spaces for commutators of multilinear singular integrals and RBMO functions with non-doubling measures

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Science china mathematics 2007年第3期50卷 361-376页

作者： Jing-shi XU department of mathematics, Hunan normal university, Changsha 410081, china department of mathematics Hunan Normal University Changsha 410081 China

The boundedness in Lebesgue spaces for commutators generated by multilinear singular integrals and RMBO(μ) functions of Tolsa with non-doubling measures is obtained, provided that ∥μ∥ = ∞ and multilinear singular... 详细信息

关键词： multilinear singular integral commutator maximal function non-doubling measure RMBO(μ) function Primary 42B20 Secondary 42B25

normal Functions and α-normal Functions

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Acta Mathematica Sinica,English Series 2000年第3期16卷 399-404页

作者： Yan Xu department of mathematics,Nanjing normal university,Nanjing 210097 P.R.china department of mathematics Nanjing Normal University Nanjing 210097 P. R. China

This paper has studied two open questions about normal functions due to Lappan,and obtained two corresponding results for α-normal functions.

关键词： Spherical derivative normal function α-normal function

The Goldbach 3-primes property for polynomial rings over certain infinite fields

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Chinese Science Bulletin 1998年第15期43卷 1256-1260页

作者： WANG Shiqiang department of mathematics, Beijing normal university, Beijing 100875, china department of mathematics Beijing Normal University Beijing China

On the basis of Effinger and Hayes’ theorem about the Goldbach 3_primes property of polynomial rings F over finite fields F , by model_theoretic method it is proved that for each characteristic k (including 0), there... 详细信息

关键词： model theory polynomial 3 primes property.

Linear estimation and distribution of the limit cycles bifurcated from a kind of degenerate polycycles

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Science china mathematics 2007年第3期50卷 334-344页

作者： Li-qin ZHAO department of mathematics, Beijing normal university, Beijing 100875, china department of mathematics Beijing Normal University Beijing 100875 China

In this paper, we investigate the number and the distribution of the limit cycles bifurcated from a kind of degenerate planar polycycles through three singular points: a saddle-node P 0, a fine saddle P 1 with finite order m ∈ N, a contractive (attracting) saddle P 2 with the hyperbolicity ratio q 2(0) ? Q. The connection between P 0 and P 1 is of hh-type and the connection between P 0 and P 2 is of hp-type. It is assumed that the connections between P 0 to P 2 and P 0 to P 1 keep unbroken. We obtain that the cyclicity of this polycycle is not more than 3m + 1, which is linearly dependent on the order of the resonant saddle P 1. We also show that the cyclicity is not more than m + 3 if q 2(0) > m, and that the nearer q 2(0) is close to 1, the more the limit cycles are bifurcated.

关键词： degenerate polycycle cyclicity finitely-smooth normal form transition map 34C05 34C23 58F14

STEADY-STATE SOLUTIONS FOR A ONE-DIMENSIONAL NONISENTROPIC HYDRODYNAMIC MODEL WITH NON-CONSTANT LATTICE TEMPERATURE

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Acta Mathematica Scientia 2008年第3期28卷 479-488页

作者：黎野平 department of mathematics Xianning College

A one-dimensional stationary nonisentropic hydrodynamic model for semiconductor devices with non-constant lattice temperature is studied. This model consists of the equations for the electron density, the electron current density and electron temperature, coupled with the Poisson equation of the electrostatic potential in a bounded interval supplemented with proper boundary conditions. The existence and uniqueness of a strong subsonic steady-state solution with positive particle density and positive temperature is established. The proof is based on the fixed-point arguments, the Stampacchia truncation methods, and the basic energy estimates.

关键词： Steady-state nonisentropic hydrodynamic model semiconductor subsonic

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 1. department of mathematics Shanghai Jiaotong University Shanghai 200240 China 2. department of mathematics Qufu Normal University Qufu 273165 China 3. department of mathematics University of Science and Technology of China Hefei 230026 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

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 321004 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