数学季刊

王丽丽, 徐瑞

2011, 26(4): 475-487.

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In this paper, a Lotka-Volterra type predator-prey model with time delays due to gestation of the predator and dispersal for both the prey and the predator is investigated. We first establish two different results on the permanence of the system. Using coincidence degree theory, sufficient conditions are derived for the existence of positive periodic solutions, and by constructing an appropriate Lyapunov functional, we further discuss their uniqueness and global stability. Numerical simulations are carried out to illustrate the main results.

函数P-集合与未知信息规律的挖掘-发现定理

赵文菊, 李东亚

2011, 26(4): 488-493.

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Function P-sets are a set pair which are composed of function internal packetsets S^F and function outer packet sets S^F or (S^F, S^F) are function P-sets. Function P-sets have dynamic characteristics and law characteristics. Based on function P-sets, P-information law discovery theorems which has attribute supplementing-deleting are given. Mining-discovery and mining-discovery theorems of unknown information law are proposed. Function P-sets are a new theory and new method to research dynamic information laws for information systems.

P-集合与它的依赖特性

周玉华, 赵文菊, 张冠宇

2011, 26(4): 494-498.

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P-sets is a set pair, it is composed of internal P-set and outer P-set, it has dynamic characteristic. By using structure of P-sets, dependence theorem and identification theorem are proposed in this paper.

关于ρ^--混合随机变量序列部分最大和范数的矩条件

谭成良, 吴群英, 何燕梅

2011, 26(4): 499-504.

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In this paper, we obtain the moment conditions for the supermun of normed sums of ρ--mixing random variables by using the Rosenthal-type inequality for Maximum partial sums of ρ--mixing random variables. The result obtained generalize the results of Chen(2008) and extend those to negatively associated sequences and ρ--mixing random variables.

内部锥类凸集值优化问题的严有效性

余丽

2011, 26(4): 505-510.

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An important property of ic-cone-convexlike set-valued functions is obtained in this paper. Under the assumption of ic-cone-convexlikeness, the scalarization theorem and the Lagrange multiplier theorem for strict efficient solution are derived, respectively.

抽象算子与高阶线性偏微分方程#br#

毕光庆, 毕越凯

2011, 26(4): 511-515.

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We summarize several relevant principles for the application of abstract operators in partial differential equations, and combine abstract operators with the Laplace transform. Thus we have developed the theory of partial differential equations of abstract operators and obtained the explicit solutions of initial value problems for a class of higher-order linear partial differential equations.

具有可变时滞的二阶非线性差分方程的有界振动性

杨甲山, 孙文兵

2011, 26(4): 516-520.

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In this paper, a class of second order nonlinear neutral difference equations with variable delays are studied. The criteria for existence of bounded eventually positive solution is obtained by using Banach contraction mapping principle and some necessary techniques. Moreover, some sufficient conditions for oscillation of the equations are given. Some results available in documents are extended in this paper. Illustrative examples are given.

逆wpp半群

胡志斌, 郭小江

2011, 26(4): 521-525.

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It is dedicated to the study of inverse wrpp semigroup, we obtain some charac-terizations of inverse wpp semigroup. In particular, we establish some charactizations for C-wrpp semigroup.

超空间C_k(X)的可缩性

曹金文, 李焱, 贾永进

2011, 26(4): 526-529.

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This paper proves the following results: let X be a continuum, let k, m ∈ N, and let B ∈ C_m(X), consider the continuous surjection f_k: C_k(X) → C_k(X). We define the mapping B : C_k(X) → C_k+m(X): by B (A) = f_k(A) B. Then following assertions are equivalent: (1) The hyperspace C_k(X) is g-contractible; (2) For each m ∈ N and for each B ∈ C_m(X) the mapping B is a W-deformation in C_k+m(X); (3) For each m ∈ N there exists B ∈C_m(X) such that the mapping B is a W-deformation in C_k+m(X); (4) There exists m ∈ N such that for each B ∈ C_m(X) the mapping B is a W-deformation in C_k+m(X); (5) There exist m ∈ N and B ∈ C_m(X) such that the mapping B is a W-deformation in C_k+m(X).

一类Calderón-Zygmund算子在Besov空间上的连续性

杨占英

2011, 26(4): 530-534.

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In this paper, we introduce a class of non-convolution-type Calderón-Zygmund operators, whose kernels are certain sums involving the products of the Daubechies wavelets and their convolutions. And we obtain the continuity on the Besov spaces B^0,q_p(1 ≤ p, q ≤∞), which is mainly dependent on the properties of the Daubechies wavelets and Lemari’s T1 theorem for Besov spaces.

渐近跟踪性及其应用

黎日松

2011, 26(4): 535-542.

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Let (X, d) be a bounded metric space and f : X → X be a uniformly continuous surjection. For a given dynamical system (X, f) which may not be compact, we investigate the relation between the asymptotic average shadowing property (AASP), transitivity and mixing. If f has the AASP, then the following statements hold: (1) f n is chain transitive for every positive integer n; (2) If X is compact and f is an expansive homeomorphism, then f is topologically weakly mixing; (3) If f is equicontinuous, then f is topologically weakly mixing; (4) If X is compact and f is equicontinuous, then f ×f is a minimal homeomorphism. We also show that the one-sided shift map has the AASP and the identity map 1 X does not have the AASP. Furthermore, as its applications, some examples are given.

赋范BCI-代数

彭家寅

2011, 26(4): 543-548.

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The notions of norm and distance in BCI-algebras are introduced, and some basic properties in normed BCI-algebras are given. It is obtained that the isomorphic(homomorphic) image and inverse image of a normed BCI-algebra are still normed BCI-algebras. The relations of normaled properties between BCI-algebra and Cartesian product of BCIalgebras are investigated. The limit notion of sequence of points in normed BCI-algebras is introduced, and its related properties are investigated.

p-Laplacian System方程组正解的存在性

杨国英, 祁瑞改

2011, 26(4): 549-555.

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Using the fibering method introduced by Pohozaev, we prove existence of positive solution for a Diriclhlet problem with a quasilinear system involving p-Laplacian operator.

多维热传导方程的紧交替方向差分格式

王晓峰, 袁合才

2011, 26(4): 556-562.

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A compact alternating direction implicit(ADI) method has been developed for solving multi-dimensional heat equations by introducing the differential operators and the truncation error is O(τ²+h⁴). It is shown by the discrete Fourier analysis that this new ADI scheme is unconditionally stable and the truncation error O(τ³+h⁶) is gained with once Richardson’s extrapolation. Some numerical examples are presented to demonstrate the efficiency and accuracy of the new scheme.

五阶图与星图的笛卡尔积交叉数

何小年

2011, 26(4): 563-567.

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The crossing number of cartesian products of paths and cycles with 5-vertex graphs mostly are known, but only few cartesian products of 5-vertex graphs with star K_1,n are known. In this paper, we will extent those results, and determine the crossing numbers of cartesian products of two 5-vertex graphs with star K_1,n .

具有反馈控制和时滞的非自治的Nicholson’s Blowfies模型的持久性

赖尾英

2011, 26(4): 568-572.

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A nonautonomous Nicholson’s Blowflies model with feedback control and delay is investigated in this paper. We show that for this system, feedback control variable has no influence on the persistent property of the system.

抽象空间二阶常微分方程组边值问题解的存在唯一性

武力兵, 孙涛, 何希勤

2011, 26(4): 573-577.

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In this paper, it is discussed by using cone and upper and lower solutions mono- tone iterative theory of mixed monotone operator that the bounary value problem is more generalized style to system of equations in the form of -u... v(0) = v(1) = 0 in abstract space. Moreover, it is obtained unique solutions for system of equations and error estimations between approximation iteration sequence and exact solution under more simpler conditions. Therefore, some new results which extend and improve the related known works in the literatures are obtained.

关于修正Ishikawa型迭代的强收敛和一定的控制条件

王学武

2011, 26(4): 578-584.

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In this paper, we establish the strong convergent theorems of an iterative algorithm for asymptotically nonexpansive mappings in Banach spaces and nonexpansive mappings in uniformly smooth Banach spaces, respectively. The results presented in this paper not only give an affirmative partial answer to Reich’s open question, but also generalize and improve the corresponding results of Chang, Lee and Chan [7] and Kim and Xu [10].

矩条件下任意随机序列的一些收敛结果

王学军, 胡舒合, 杨文志

2011, 26(4): 585-589.

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Let {X_n, n ≥ 1} be an arbitrary sequence of random variables. Some convergence results for the partial sums of arbitrary sequence of random variables are obtained, which generalize the known results for independent sequences, NA sequences, ρ-mixing sequences and φ-mixing sequences, and so on.

非线性泛函微分方程的有界非振动解

王小炎, 李明军, 邓继勤

2011, 26(4): 590-595.

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In this paper, we obtain some nonoscillatory theories of the functional differential equation (r(t)ψ(x(t))x (t)) + f(t, x(t), x(σ(t))) = 0, t ≥ t₀, where r ∈ C¹([t₀, ∞); (0, ∞)), ψ∈ C¹(R, R) and f ∈ C([t₀, ∞) × R × R, R).

量子Yang-Baxter方程的1/2旋子的奇异上三角型解(Ⅰ)

王轲, 王欣, 李娴

2011, 26(4): 596-607.

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In these two papers (I) and (II), the singular upper triangle type solutions with spin 1/2 of quantum Yang-Baxter equation are given. In the Paper (I), we give the Yang-Baxter equation and give the general solutions of some function equations for the next paper.

强伪不变凸性和强伪不变单调性的等价性

赵克全, 陈哲, 杨新民

2011, 26(4): 608-612.

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In this paper, the equivalence is established about strongly pseudoinvexity of function and invariant pseudomonotonicity of corresponding gradient map under some suitable conditions.

广义双积定理

吴文海, 章月娥, 马天水

2011, 26(4): 613-620.

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We develop the Radford’s biproduct theorem which plays an important role in giving a negative answer to a conjecture of I Kaplansky. Let B, H be two Hopf algebras with H acting weakly on B and α, β : B → H be two linear maps verifying suitable conditions. We consider in this paper a twisted Hopf crossed coproduct B^#_×βαH and derive a necessary and sufficient condition for B^#_×βαH with a Hopf smash product structure to be a bialgebra which generalizes in [14, Theorem 1.1] and the well-known Radford biproduct theorem [10, Theorem 1].

直积的零因子图

李云慧, 唐高华

2011, 26(4): 621-627.

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In [1], Joe Warfel investigated the diameter of a zero-divisor graph for a direct product R₁×R₂ with respect to the diameter of the zero-divisor graph of R₁and R₂. But the author only considered those graphs whose diameters ≥ 1 and discussed six cases. This paper further discusses the other nine cases and also gives a complete characterization for the possible diameters for left Artin rings.

涉及两个单形及其内点的几个不等式

周永国

2011, 26(4): 628-632.

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This article establishes several new geometric inequalities, which refer to the lengthes of the edges of a simplex and interior point, height, lateral area, and the circumradius of another simplex.

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