数学季刊

李德明, 刘明菊

2010, 25(2): 159-167.

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The incidence chromatic number of G is the least number of colors such that G has an incidence coloring. It is proved that the incidence chromatic number of C_n^p, the p-th power of the circuit graph, is 2p+1 if and only if n = k(2p+1), for other cases, its incidence chromatic number is at most 2p + r/k + 2, where n = k(p + 1) + r, k is a positive integer. This upper bound is tight for some cases.

一个包含F.Smarandache平方补数的极限问题

刘妙华, 王维琼

2010, 25(2): 168-171.

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The main purpose of this paper is using the elementary method to study a limit problem involving the F. Smarandache square complementary number, and obtain its limit value.

齐型空间上的Herz-Morrey空间的线性交换子的有界性

高文华, 江寅生, 龚小兵

2010, 25(2): 172-181.

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Under certain weak local size conditions, the boundedness of linear commutators on Herz-Morrey spaces on spaces of homogeneous type are studied. In addition, the boundedness of Hardy-Littlewood maximum commutators on Herz-Morrey spaces on spaces of homogeneous type are obtained.

线性离散系统的Lyapunov不等式

周美秀, 王欣阵

2010, 25(2): 182-190.

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In this paper, we study the nonlinear discrete systems and obtain several lyapunov inequalities for them. Then we give the application for lyapunov inequality.

多变量Mahler型函数值的超越性

刘华珂, 郝云霞

2010, 25(2): 191-197.

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We prove the transcendence for the values of Mahler type function with several variables, which satisfies some non-linear functional equation.

p-叶星型性的充分条件

徐能

2010, 25(2): 198-207.

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Let A_n(p)(p,n ∈ N = {1,2,3,...}) denote the class of functions of the form f(z) = z^p+a_p+nz^p+n+... which are analytic in the unit diskE = {z:|z| < 1}. A function f(z) in A(p) is said to be in the class S_p(a,b) if it satisfies zf'(z)...bz for some a and b(-1 ≤ b < a ≤ 1). In this paper, using the method of differential subordinations, we give new criteria for f(z) to be in the classes S_p(a,b)(-1 ≤ b < a ≤ 1), that is, if f(z) ∈ A(p) satisfies f(z) = 0 in 0 < |z| < 1,f'(z) = 0 when μ=1, and zf'(z)..., then f(z) ∈S_p(a,b). Our results improve or extend some results due to Owa, Nunokawa, Padmanabhan, Silverman, Obradovic, Yang and

others^[3-10].

二元向量值多重小波包的双正交性质研究

陈绍东, 黄娜

2010, 25(2): 208-213.

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The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets, which are associated with a quantity dilation matrix, is introduced. The biorthogonality property of the multiple vector-valued wavelet packets in higher dimensions is studied by means of Fourier transform and integral transform biorthogonality formulas concerning these wavelet packets are obtained.

关于整函数的微分多项式分担一个小函数的唯一性

熊维玲

2010, 25(2): 214-219.

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In this paper, we deal with the uniqueness problems on entire functions concerning differential polynomials that share one small function. Moreover ,we improve some former results of M Fang and W Lin.

开口弧上核密度属H*的Cauchy奇异积分的稳定性

林娟, 王传荣

2010, 25(2): 220-227.

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The authors examine the relation between the perturbed Cauchy singular integral with its kernel density belong to H* and unperturbed one and show that the Cauchy singular integral is stable under perturbation of the curve of integration.

一类带有时滞和脉冲接种具有不同传染性SIR传染病模型动力学性质的研究

张秀全, 赵中

2010, 25(2): 228-235.

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Differential susceptibility SIR epidemic models with time delay and pulse vaccination is studied in this paper. We show that there exists an infection-free periodic solution by using the comparison method, which is globally attractive provided that R₁<1, and that R₂>1 implies the disease is permanent, which means that after some period of time the disease will become endemic.

解高维热传导方程的一族高精度显式差分格式

陈贞忠, 马小霞

2010, 25(2): 236-243.

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In this paper, a class of explicit difference schemes with parameters for solving five-dimensional heat-conduction equation are constructed and studied. the truncation error reaches O(τ²+h⁴), and the stability condition is given. Finally, the numerical examples and numerical results are presented to show the advantage of the schemes and the correctness of theoretical analysis.

三正则连通图与圈的并图Cordial性

谢炎涛, 车颍涛, 刘峙山

2010, 25(2): 244-248.

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Diab proved the following graphs are Cordial; P_mK_1,n if and only if (m,n) =(1,2); C_mK_1,n; P_mK_n; C_mK_n for all m and n except m≡2(mod 4). In this paper, we proved the Cordiality on the union of 3-regular connected graph K₃ and cycle C_m. First we have the Lemma 2, if uv∈ E(G), G is Cordial, we add 4 vertices x, y, z, w in sequence to the edge uv, obtain a new graph denoted by G*, then G* is still Cordial, by this lemma, we consider four cases on the union of 3-regular connected graph R₃, and for every case we distinguish four subcases on the cycle C_m.

齐型空间上极大算子的复合

原新凤, 张昊

2010, 25(2): 249-256.

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Let Φ be a Young function and MΦ be the maximal operator associated with Φ in the space of homogeneous type. In this paper, the composition of the maximal operators of type M_Φ is considered, and the result established by Carrozza and Passarelli Di Napoli^[2] is generalized to the space of homogeneous type.

富足半群的拟理想恰当断面

罗敏霞

2010, 25(2): 257-266.

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In this paper, we discuss some properties about an abundant semigroup with a quasi-ideal adequate transversal. Moreover, we show that the product of two quasi-ideal adequate transversals of an abundant semigroup which satisfies some conditions is a quasiideal adequate transversal.

风险的厌恶序在再保险中的应用

张瑞, 臧振春, 苏白云等

2010, 25(2): 267-275.

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The aversion order is a way of ordering of risks. Is there the optimal in aversion order in reinsurance contracts of reinsurance? This paper discusses these objects and gives some optimal reinsurance contracts in certain sets of feasible reinsurance contracts.

Hilbert C*-模H中的伪框架分解

姚喜妍

2010, 25(2): 276-281.

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In the paper, we introduce weak Bessel sequences and weak frames in a Hilbert C*-module H, and give a characterization of weak Bessel sequences, weak frames, normalized tight weak frames, and dual weak frames to each other, respectively. Using A-valued linear bounded operator U:H → l²(A), V*U = I, a coustructing method of dual weak frame {x*_j: j ∈ J} for a given weak frame {x_j: j ∈ J} is obtained. Moreover, pseudo frame decompositions for H is given.

零级数Dirichlet级数的增长性

丁晓庆, 刘薇

2010, 25(2): 282-286.

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This note deals with the growth of entire Dirichlet series of order zero and the coefficient characteristic of the type under a kind of weaker exponent condition, and improves some known results. Moreover, the regular growth of the series is considered under the same exponent condition, and a sufficient condition of the regular growth is given.

超空间上的弱δ-连续对应

陈桂秀

2010, 25(2): 287-292.

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In the paper, we define weakly δ-continuous correspondences on super-space, On the basis of δ-open(closed) sets,θ-open(closed) sets and regular open(closed) sets in topological space, some equivalent conditions of this kind of correspondences are obtained, and some applications of subset nets and convergence nets are given.

子独立空间

毛华, 王刚

2010, 25(2): 293-299.

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Cleverly using the relation of independence spaces and B-matroids, this paper firstly deals with the properties of the closure operator of an independence space, followed by presenting the definitions and solving some relative properties for the sub-independence spaces of an independence space with the help of circuits.

左定Sturm-Liouville问题的特征值不等式

张艳霞, 张学锋

2010, 25(2): 300-307.

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There are well-known inequalities among eigenvalues of right-definite Sturm-Liouville problems. In this paper, we study left-definite regular self-adjoint Sturm-Liouville problems with separated and coupled boundary conditions. For any fixed equation, we establish a sequence of inequalities among the eigenvalues for different boundary conditions, which is both theoretical and computational importance.

一类图的色等价性

张淑敏

2010, 25(2): 308-311.

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A class of new graphs is defined. A sufficient condition for pairs of these graphs to be chromatically equivalent is proven.

一个新的混合函数及其均值

马金萍, 葛键

2010, 25(2): 312-316.

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The main purpose of this paper is using the analytic method to study the mean value properties of the arithmetical functions δ_k((m,n)),δ_k([m,n]/m), and give several interesting asymptotic formulae for them.

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