数学季刊

王友军, 沈尧天

2011, 26(3): 317-324.

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By using variational method, the multiplicity of solutions for nonlinear biharmonic equation involving critical parameter and critical exponent are established.

一类Hartogs域的Bergman核函数的零点问题

王安, 刘玉兰

2011, 26(3): 325-334.

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We obtain the Bergman kernel for a new type of Hartogs domain. The corresponding LU Qi-Keng’s problem is considered.

关于三个算子的算子不等式

杨长森, 王亚青

2011, 26(3): 335-342.

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As a generalization of grand Furuta inequality, recently Furuta obtain: If A≥ B≥0 with A>0, then for t∈[0,1] and p₁, p₂, p₃, p₄≥1, .... In this paper, we generalize this result for three operators as follow: If A≥B≥C≥0 with B>0, t∈[0,1] and p₁, p₂, ···, p_2n-1, p_2n≥1 for a natural number n. Then the following inequalities hold for r≥t, ..., where q_[2n]≡···.

第一类Cartar-egg域上的极值问题

苏简兵, 李海涛

2011, 26(3): 343-349.

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In this paper, we study the extremal problem on Cartan-egg domain of the first type by using some inequalities. The extremal mapping and extremal value between the first type of Cartan-egg domain and the unit ball when k≤1 and k=2, m=2 are constructed.

IPP+M/M／C排队的遍历性

李晓花, 侯振挺

2011, 26(3): 350-354.

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The IP P+M/M/c queueing system has been extensively used in the modern communication system. The existence and uniqueness of stationary distribution of the queue length L(t)for IP P+M/M/1 queue has been proved in [10]. In this paper, we shall give the suffcient and necessary conditions of l-ergodicity, geometric ergodicity, and prove that they are neither uniformly polynomial ergodicity nor strong ergodicity.

3-正则无爪图的导出匹配覆盖

董丽, 汤京永, 宋新宇

2011, 26(3): 355-359.

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The induced matching cover number of a graph G without isolated vertices, denoted by imc(G), is the minimum integer k such that G has k induced matchings {M₁,M₂,···,M_k} such that, V(M₁)∪V(M₂)∪···∪V(M_k) covers V(G). This paper shows that, if G is a 3-regular claw-free graph, then imc(G)∈{2,3}.

关于亚纯函数分担值集正规族的注记

肖冰, 吴奇峰, 袁文俊

2011, 26(3): 360-365.

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In the paper, we prove the main result: Let k(≥2) be an integer, and a, b and c be three distinct complex numbers. Let F be a family of functions holomorphic in a domain D in complex plane, all of whose zeros have multiplicity at least k. Suppose that for each f∈F, f(z) and f(k)(z) share the set {a,b,c}. Then F is a normal family in D.

带有乘右适当断面的右主投射半群

胡耀华, 郭小江

2011, 26(3): 366-371.

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In this paper, the concept of right adequate transversals of rpp semigroups is introduced. We establish the structure of rpp semigroups with multiplicative right adequate transversals in terms of right normal bands and right adequate semigroups.In particular, some special cases are considered.

具ρ-aplacian算子非齐次辊舍型二阶微分方程多点边值问题

刘兴元

2011, 26(3): 372-377.

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A class of multi-point boundary value problems are studied. Easily verified suffcient conditions to guarantee the existence of at least one solutions of above mentioned BVPs are established. The examples are presented to illustrate the main results.

计算Pascal矩阵加数量矩阵之逆的一种新方法

杨胜良, 马成业

2011, 26(3): 378-382.

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In this paper, using the Jordan canonical form of the Pascal matrix P_n, we present a new approach for inverting the Pascal matrix plus a scalar P_n+aI_n for arbitrary real number a≠1.

坡上矩阵的逆与幂

段俊生, 郭爱平, 云文在

2011, 26(3): 383-387.

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Invertible conditions, indices and periods of matrices over an incline are considered. In all proofs multiplicative commutativity is not used. Some results about invertibility, indices and periods in a commutative incline are proved to be correct also for any incline.

四阶椭圆方程的一个十六参数能量正交四面体元

刘鸣放, 曹济伟, 陈绍春

2011, 26(3): 388-393.

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In this paper, the 16-parameter nonconforming tetrahedral element which has an energy-orthogonal shape function space is presented for the discretization of fourth order elliptic partial differential operators in three spatial dimensions. The newly constructed element is proved to be convergent for a model biharmonic equation.

关于分担多项式的全纯函数的正规族

刘志宏, 李迎春, 黄斌

2011, 26(3): 394-399.

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In this paper, we study normal families of holomorphic function concerning shared a polynomial. Let F be a family of holomorphic functions in a domain D, k(2) be a positive integer, K be a positive number and α(z) be a polynomial of degree p(p>1). For each f∈F and z∈D, if f and f sharedα(z)CM and |f^(k)(z)|<K whenever f(z)-α(z)=0 in D, then F is normal in D.

Bernstein-Durrmeyer算子在L^Ba_M空间中的逼近定理

孙志玲

2011, 26(3): 400-404.

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With the weighted modulus of smoothness as a metric, we prove the direct and the inverse theorems of approximation by Bernstein-Durrmeyer operators in LBa M spaces. Especially an approximation equivalent theorem of the operators is also obtained.

带跳的随机比例微分方程的半隐式Euler数值解法

毛伟, 韩修静, 陈波

2011, 26(3): 405-409.

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In this paper, we present the semi-implicit Euler(SIE) numerical solution for stochastic pantograph equations with jumps and prove that the SIE approximation solution converges to the exact solution in the mean-square sense under the Local Lipschitz condition.

关于复射影空间中具有平行平均曲率向量的全实叶的注记

彭慧春

2011, 26(3): 410-414.

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We discussed a totally real Riemannian foliations with parallel mean curvature on a complex projective space. We carried out the divergence of a vector field on it and obtained a formula of Simons’type.

锥似凸映射下集值优化Henig有效解的高阶最优性条件

张健, 王其林

2011, 26(3): 415-419.

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This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems. By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.

Leibniz割线切线问题在数学无穷之逻辑基础层面上的分析研究

朱梧槚, 宫宁生, 杜国平

2011, 26(3): 420-425.

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Refs 1 and 2 provide the definition of the concepts of ‘potential infinity’(poi) and actual infinity(aci); Ref 3 discusses and verifies that poi and aci are a pair of contradictory opposites without intermediate (p,-p).The second part of this paper, i.e., §2, further discusses the manners in which a variable x approaches infinitely to its limit x0 using the poi and aci methods and concludes that, in any system compatible with both poi and aci, the two approaching manners are also a pair of contradictory opposites without intermediate (A,-A). Finally, on the basis of this conclusion, we reexamine the fundamental question of Leibniz’s Secant and Tangent Lines in calculus and the limit theory and offer our analysis and raise new questions.

一类带有外部扰动的模糊离散非线性系统的有限时间控制问题

张应奇, 慕小武, 刘彩侠

2011, 26(3): 426-433.

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This paper give criterions on finite-time control of fuzzy discrete-time nonlinear system subject to exogenous disturbance. Employing the Lyapunov function theory, several suffcient conditions including relaxed ones are presented for finite-time stability via fuzzy controller laws. An illustrative example is given to demonstrate the effectiveness of the proposed method.

两个m-KdV多维类似方程的N-孤子解

马云苓

2011, 26(3): 434-439.

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Using the Hirota’s bilinear method, some new N-soliton solution are presented for two multidimensional analogues of the m-KdV equation w_t+w_{xxx ...}=0 in view of a different treatment.

F粗积分与它的度量

于秀清, 徐风生, 韩忠月

2011, 26(3): 440-444.

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F-rough integrals is defined on the basis of the dual of function one direction S-rough sets, which has dynamic characteristics. Using F-rough integrals, the concepts of expansion measurement-expansion degree and expansion ratio are given. By expansion degree and expansion ratio the changing extent can be expressed with numbers, and the recognition principle of attribute effect on function equivalences is got.

关于元爪图的一个性质

鲁晓旭, 李静, 吴敏

2011, 26(3): 445-447.

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In this paper we consider a property of claw-free graphs. We show that if d(u)+ d(v)≥ν(G)+2k+3, for every two nonadjacent vertices u and v, then G is 2k-vertex-deletable IM-extendable, where ν(G)=|V(G)|. And the bound is tight.

分担多项式的亚纯函数的进一步结果

仇惠玲

2011, 26(3): 448-452.

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In this paper, we use the theory of value distribution and study the uniqueness of meromorphic functions. We will prove the following result: Let f(z) and g(z) be two transcendental meromorphic functions, p(z) a polynomial of degree k, n≥max{11, k+1} a positive integer. If fⁿ(z)f(z) and gⁿ(z)g(z) share p(z)CM, then either f(z)=c_1e^cp(z)dz, g(z)=c₂e^cp(z)dz ,where c₁, c₂ and c are three constants satisfying (c₁c₂)ⁿ⁺¹c₂₌-1 or f(z)≡tg(z) for a constant t such that tⁿ⁺¹=1.

L拓扑空间的局部S_β-紧性

韩红霞, 孟广武, 张安英

2011, 26(3): 453-456.

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In this paper, the notion of local S_β-compactness of L-topological spaces is introduced. It is proved that the local S_β-compactness is an L-good extension, which is inherited by a closed subspace, multiplicative and invariable under the continuous open surjective L-valued Zadeh function.

代数微分方程组的分量允许解

李国望, 高凌云

2011, 26(3): 457-461.

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Using the Nevanlinna value distribution theory of meromorphic function, we investigate the existence problem of admissible solutions of higher-order algebraic differential equations systems, and obtain a result concerning admissible components of solution.

两个算子不等式之间关系的进一步推广

高福根, 左红亮

2011, 26(3): 462-465.

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In this paper, we give out a further extension of the relations between two famous inequalities (B^r/2A^pB^r/2) ^r/(p+r)≥B^r and A^p≥(A^p/2B^rA^{p/2) p/(p+r)}, which can yield the result of Yamazaki and Yanagida’s.

时标上具有正负系数的中立型时超动力方程的强迫振动

杨军, 吴会宁

2011, 26(3): 466-469.

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In this paper, we consider the forced neutral advanced dynamic equations with positive and negative coeffcients [x(t)-R(t)x(t+r)]+P(t)x(t+τ)△Q(t)x(t+δ)= f(t), t≥t₀ on a time scale T.S everal suffcient conditions are obtained for the oscillation of the dynamic equations. The main result is illustrated by an example.

离子声学模型Zakharov方程组的整体吸引子的存在性

房少梅, 邱华, 郭柏灵

2011, 26(3): 470-474.

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In this paper, we consider the initial-boundary problem for Zakharov equations arising from ion-acoustic modes and obtain the existence of global attractor for the initial-boundary problem for Zakharov equations.

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