数学季刊

李俊平, 侯振挺

2009, 24(1): 1-9.

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This paper is devoted to studying the stability of Logistic model with random impulse by using the theory of Markov skeleton processes and a convenient condition for Logistic model with random impulse to be stable is given.

Bloch型空间之间的广义Cesaàro算子

吕小芬

2009, 24(1): 10-19.

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We characterize the symbol for which the induced extended Cesaàro operator T: Bω→ Bμ(respectively, Bω,0 → Bμ,0) is bounded or compact, where is a given holomorphic function on the unit disc D, ω and μ both are normal functions on [0,1).

Halin图在环面上嵌入的灵活性

马登举, 任韩

2009, 24(1): 20-26.

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In this paper we show that the face-width of any embedding of a Halin graph(a type of planar graph) in the torus is one, and give a formula for determining the number of all nonequivalent embeddings of a Halin graph in the torus.

二元非乘积型Baskakov算子加权逼近的等价定理

冯国

2009, 24(1): 27-34.

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In this paper, we study the convergence rate of two-dimensional Baskakov operators with Jacobi-weights and the approximation equivalence theorem is obtained, making use of multivariate decompose skills and results of one-dimensional Baskakov operators.

集值终上鞅的一个收敛定理

李高明

2009, 24(1): 35-39.

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In this paper, the properties of set-valued Eventual Supermartingle are discussed. The main result is that suppose {F_n,n ≥ 1} be set-valued Eventual Supermartingle, if sup_TE(d(0,F_τ)) < ∞, then F_n →F and S_F¹= Φ, here T is the sets of all bounded stopping times.

有关E'-矩阵的若干注记

李建平

2009, 24(1): 40-45.

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The class of E -matrices introduced in [4] is a subclass of Q0-matrices whose proper principal submatrices are Q-matrices. In this paper, we investigate the relation of the class E to other known matrix classes and obtain a series of necessary and sufficient conditions for E -matrices.

色多项式对图的刻画

马海成, 刘慧敏, 张海良

2009, 24(1): 46-52.

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By means of the chromatic polynomials, this paper provided a necessary and sufficient condition for the graph G being a mono-cycle graph(the Theorem 1), a first class bi-cycle graph and a second class bicycle graph(the Theorem 2), respectively.

上连通和超连通的三次Bi-Cayley图

曹玲, 孟吉翔

2009, 24(1): 53-57.

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Let G be a finite group and let S(possibly, contains the identity element) be a subset of G. The Bi-Cayley graph BC(G, S) is a bipartite graph with vertex set G×{ 0,1} and edge set {(g,0) (sg,1) : g ∈ G, s ∈ S}. A graph is said to be super-connected if every minimum vertex cut isolates a vertex. A graph is said to be hyper-connected if every minimum vertex cut creates two components, one of which is an isolated vertex. In this paper, super-connected and/or hyper-connected cubic Bi-Cayley graphs are characterized.

用广义特征矩阵计算若当链

李大林

2009, 24(1): 58-62.

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In this paper, we introduce a method to define generalized characteristic matrices of a defective matrix by the common form of Jordan chains. The generalized characteristic matrices can be obtained by solving a system of linear equations and they can be used to compute Jordan basis.

多圆盘上的交换对偶Toeplitz算子

程国正, 于涛

2009, 24(1): 63-68.

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We completely characterize commutativity of S and Sψ on L_a²(Dⁿ)⊥ for bounded pluriharmonic symbols and ψ on D_n, and prove that SS_ψ = S_ψ if and only if is analytic or ψˉ is analytic.

关于非牛顿流体衰减性的一个注记

殷谷良

2009, 24(1): 69-74.

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In the study of long time asymptotic behaviors of the solutions to a class system of the incompressible non-Newtonian fluid flows in R3, it is proved that the weak solutions decay in L2 norm at (1 + t)-34 and the error of difference between non-Newtonian fluid and linear equation is also investigated. The findings are mainly based on the classic Fourier splitting methods.

微分多项式ff^(k)-α的零点与其相应的正规定则

卢谦, 顾永兴

2009, 24(1): 75-80.

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Suppose that function f(z) is transcendental and meromorphic in the plane. The aim of this work is to investigate the conditions in which differential monomials f(z)f^(k)(z) takes any non-zero finite complex number infinitely times and to consider the normality relation to differential monomials f(z)f^(k)(z).

相关于遗传挠理论的(Inco)投射模

张力宏, 辛大伟

2009, 24(1): 81-86.

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In the paper, we define(inco) project modules of relatively hereditary torsion theory τ by intersection complement of module and study their properties; secondly, we define the(inco) τ-semisimple ring by(inco) τ-projective module and study their properties. When τ is a trivial torsion theory on R-mod, we prove that R is a semisimple ring if and only if R is a(inco) semisimple ring and satisfies(inco) condition.

一类变时滞差分方程的振动性

谭琼华, 陈明

2009, 24(1): 87-93.

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Consider the nonautonomous delay logistic equation △y_n = p_ny_n(1-(y_n-l_n)), n ≥ 0, (1)where {p_n}n≥0 is a sequence of nonnegative real numbers, {l_n}n≥0 is a sequence of positive integers satisfying lim n→∞(n - l_n) = ∞, and k is a positive constant. Only solutions which are positive for n ≥ 0 are considered. We obtain a new sufficient for all positive solutions of (1) to oscillate about k which contains the corresponding result in [2] when i = 1.

拟Grünwald插值算子在Wiener空间下平均误差的估计

刘颖, 许贵桥

2009, 24(1): 94-101.

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We obtain an upper bound for the average error of the quasi-Grünwald interpo-lation based on the zeros of Chebyshev polynomial of the second kind in the Wiener space.

一类具有反馈控制项时滞泛函差分系统的周期正解

郭鹏飞, 朱先阳, 李永昆

2009, 24(1): 102-107.

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By using a fixed point theorem on a cone to investigate the existence of two positive periodic solutions for the following delay difference system with feedback control argument of the form △x(n) = -b(n)x(n) + f(n,x(n - τ1(n)),… ,x(n - τm(n)),u(n - δ(n))), △u(n) = -η(n)u(n) + a(n)x(n - σ(n)), n ∈ Z.

Roper-Suffridge算子上的偏差定理下界估计的简单证明

王建飞, 刘太顺

2009, 24(1): 108-111.

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Liczberski-Starkov first found a lower bound for ||D(f)|| near the origin, where f(z) = (F(z₁), F (z₁)z₂,… , F (z₁)z_n) is the Roper-Suffridge operator on the unit ball Bn in Cn and F is a normalized convex function on the unit disk. Later, Liczberski-Starkov and Hamada-Kohr proved the lower bound holds on the whole unit ball using a complex computation. Here we provide a rather short and easy proof for the lower bound. Similarly, when F is a normalized starlike function on the unit disk, a lower bound of ||D(f)|| is obtained again.

紧超凸度量空间中的一个新的不动点定理及其对截口问题和相交问题的应用

文开庭

2009, 24(1): 112-116.

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In this paper, a new Browder fixed point theorem is established in the noncompact sub-admissible subsets of noncompact hyperconvex metric spaces. As application, a Ky Fan section theorem and an intersection theorem are obtained.

拟线性椭圆方程非零解

饶若峰, 何庆高

2009, 24(1): 117-124.

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In this paper, the author has given an existence theorem for the resonant equation, -△_pu = λ₁|u|^p-2u + f(u) + h(x), without any Landesman-Lazer conditions on h(x).

Lowwner链与复Hilbert空间单位球上推广的Roper-Suffridge算子(Ⅰ)

刘涛, 冯淑霞, 闫春燕

2009, 24(1): 125-131.

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In this paper, we prove that the generalized Roper-Suffridge extension operator can be embeded in Loewner chains on the unit ball in Hibert spaces, and obtain the fact that the operator keeps the properties of almost spirallike mapping of type β and order α, almost starlikeness of order α, spirallikeness of type of β and starlikeness.

单机最优分批排序的结构性质

冯密罗

2009, 24(1): 132-137.

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A batch is a subset of jobs which must be processed jointly in either serial or parallel form. For the single machine, batching, total completion time scheduling problems, the algorithmic aspects have been extensively studied in the literature. This paper presents the optimal batching structures of the problems on the batching ways: all jobs in exactly N(arbitrary fix batch number and 1 < N < n) batches.

非均匀介质GL型热弹性问题解的存在唯一性

张同斌, 万建军

2009, 24(1): 138-144.

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We study a new model named the Green-Lindsay type therm-elastic model for nonhomogeneous media that consists of a system of dynamic thermoelasticity equations of displacement and dynamic heat conduction equation. We construct the model based on the classical GL-model for homogeneous material. This system is coupled dynamic problem and the displacement field and heat field must be solved at the same time. By using Fadeo-Galerkin method, we proved that the problem we proposed exist unique weak solution under some regular assumption.

一般区间上柱Bessel方程本征值问题特征问题根的Matlab算法

赵喜来, 崔群法

2009, 24(1): 145-150.

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Root of characteristic equation for cylindrical Bessel equation eigenvalue prob- lems on general interval is of great real physical importance at engineering and physical. First, the characteristic equation of cylindrical Bessel equation eigenvalue problem on general interval is given, second, by mean of compared method, we obtaining roots of characteristic equation with Matlab program is discussed.

不完备信息下的灰色粗糙集成决策模型

侯亚林, 罗党

2009, 24(1): 151-158.

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In this paper, for multiple attribute decision-making problem in which attribute values are interval grey numbers and some of them are null values, a decision model based on grey rough sets integration with incomplete information is proposed. We put forward incidence degree coefficient formula for grey interval, by information entropy theory and analysis technique, the method and principle is presented to fill up null values. We also establish the method of grey interval incidence cluster. Because grey system theory and Rough set theory are complementary each other, decision table with preference information is obtained by the result of grey incidence cluster. An algorithm for inducing decision rules based on rough set theory and the dominance relationship is presented. In some extent, this algorithm can deal with decision-making problem in which the attribute values are interval grey numbers and some of them are null values. Contrasted with classical model of cluster decision-making, the algorithm has an advantage of flexibility and compatibility to new information. 还原

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