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2010年 第25卷 第1期    刊出日期：2010-03-30

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Yamabe方程在完备流形上的一个推广

武三星

2010, 25(1):  1-7. 

摘要 ( 17 )   PDF (314KB) ( 15 )  

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This paper considers a semilinear elliptic equation on a n-dimensional complete noncompact Riemannian manifold, which is a generalization of the well known Yamabe equation. An existence result is proved.


平面弹性问题及Stokes问题的一个矩形有限元方法

陈绍春, 张步英

2010, 25(1):  8-15. 

摘要 ( 12 )   PDF (333KB) ( 9 )  

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In this paper, a locking-free nonconforming rectangular finite element scheme is presented for the planar elasticity problem with pure displacement boundary condition. Meanwhile, we prove that this element is also convergent for stationary Stokes problem.



广义Bernoulli和Euler多项式之间关系的一些注记

雒秋明, 葛淑梅

2010, 25(1):  16-22. 

摘要 ( 23 )   PDF (292KB) ( 16 )  

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In this paper, we prove the Srivastava-Pinter's addition theorems(see Applied Mathematic Lett.17(2004),375-380) by applying the another methods. We also provide some analoges of these addition theorems and deduce the corresponding special cases.


关于一类微分多项式的值分布

徐俊峰, 张占亮

2010, 25(1):  23-29. 

摘要 ( 21 )   PDF (326KB) ( 7 )  

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Let f(z) be a transcendental meromorphic function in the complex plane and a = 0 be a constant, for any positive integer m,n,k, satisfy m ≥ nk+n+2, ψ = f^m+a(f^(k))ⁿ has infinitely many zeros. The corresponding normal criterion also is proved.



SL(3,C)中两类可解子群及其对复数域上微分方程的应用

张绍飞, 李慧珍

2010, 25(1):  30-36. 

摘要 ( 13 )   PDF (327KB) ( 26 )  

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Structures of two classes of solvable subgroups in SL(3,C) are given in this paper, and the integrability of the 3-order Fuchsian equation which is integrable in the sense that its monodromy group is solvable is discussed.


一类具有阶段结构、种群内部捕食和脉冲干扰的三种群模型研究

师向云, 崔学英

2010, 25(1):  37-44. 

摘要 ( 17 )   PDF (354KB) ( 12 )  

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This paper considers a stage-structured three species model with intra-guild predation and disturbing pulse. Sufficient conditions which guarantee the global attractivity of boundary periodic solution and permanence of the system are obtained. Our results show that the pulse and time delay bring great effect on the dynamical behaviors of the model.



具有离散时滞的HIV-I免疫反应模型的数学分析

王战伟, 王稳地

2010, 25(1):  45-51. 

摘要 ( 16 )   PDF (317KB) ( 6 )  

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This paper considers a model of cell-to-cell spread of HIV-I with CTL immune response. By using a discrete delay to model the intracellular delay, it is shown that the uninfected equilibrium is globally asymptotical stable in some conditions and the sufficient condition to ensure the stability of the infected equilibrium does not change would be enlarged by Sturm sequence. Numerical simulations are presented to illustrate the results.





解一类运输生产问题修正的松驰型分枝定界算法

杜廷松, 费浦生, 蹇继贵

2010, 25(1):  52-59. 

摘要 ( 19 )   PDF (328KB) ( 22 )  

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In this paper, a new algorithm relaxation-strategy-based modification branch-and-bound algorithm is developed for a type of solving the minimum cost transportation production problem with concave production costs. The major improvement of the proposed new method is that modification algorithm reinforces the bounding operation using a Lagrangian relaxation, which is a concave minimization but obtains a tighter bound than the usual linear programming relaxation. Some computational results are included. Computation results indicate that the algorithm can solve fairly large scale problems. 



一类递归序列的两类和

庞进丽, 叶晓丽

2010, 25(1):  60-64. 

摘要 ( 16 )   PDF (273KB) ( 7 )  

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A conjecture posed by Melham for U_n^2k+U_n+1^2k in [2] is considered in this article. Several positive results on V_n+s^2k +...U_n+s^{2k ar}e achieved which generalize existed results on V_n+1²-...U_n+1².





Sⁿ上子流形的Moebius数量曲率的上界

钟定兴, 孙弘安, 慕晓凯

2010, 25(1):  65-73. 

摘要 ( 21 )   PDF (386KB) ( 50 )  

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The most important Moebius invariants in the Moebius differential geometry of submanifolds in S^n+p are the Moebius metric g, the Moebius second fundamental form B, the Moebius form Φ and the Blaschke tensor A. In this paper, we obtain the upper bound of the Moebius scalar curvature of submanifolds with parallel Moebius form in S^n+p.



一类时滞Liénard型方程周期解的存在与唯一性

汪娜

2010, 25(1):  74-80. 

摘要 ( 15 )   PDF (318KB) ( 12 )  

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By means of Mawhin’s continuation theorem, we study a kind of lienard functional differential equations: x"(t)+f(x(t))x’(t)+g(t,x(t-τ(t)))=e(t). Some new results on the existence and uniqueness of periodic solutions are obtained.



格子方程的Backlund变换及其显式解

吴勇旗

2010, 25(1):  81-85. 

摘要 ( 21 )   PDF (232KB) ( 16 )  

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The Backlund transformation and the generalized Miura transformation for the Volterra lattice equation are constructed by using point symmetry method. As an application, the explicit solution to the lattice equation is obtained.



从B⁰到Q_K和Q_K,0空间的复合算子

郭健, 刘永民

2010, 25(1):  86-91. 

摘要 ( 15 )   PDF (299KB) ( 18 )  

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When φ is an analytic map of the unit disk D into itself, and X is a Banach space of analytic functions on D, define the composition operator Cφ by Cφ(f) = f ο φ, for f ∈ X. In this paper, we study the boundedness and compactness of composition operators from the space B⁰ to Q_K and Q_K,0.



高阶微分方程解的零点的分布

陈裕先, 吴昭君

2010, 25(1):  92-97. 

摘要 ( 17 )   PDF (291KB) ( 33 )  

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In this paper, by using the Nevanlinna Theory on angular domain, we establish a theorem which concerns the growth of entire function and his zero. As an application, we survey the location of zero of higher order differential equation, which can be regarded as an alternating but precise version of Wu^[6] and Yi^[7].



连通控制数与2-连通控制数相等的一类图

陈宏宇, 朱柘琍

2010, 25(1):  98-103. 

摘要 ( 14 )   PDF (268KB) ( 11 )  

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A subset S of V is called a k-connected dominating set if S is a dominating set and the induced subgraph S has at most k components. The k-connected domination number γ_c^k(G) of G is the minimum cardinality taken over all minimal k-connected dominating sets of G. In this paper, we characterize trees and unicyclic graphs with equal connected domination and 2-connected domination numbers.


集值映射向量优化的ε-强有效解

王其林

2010, 25(1):  104-109. 

摘要 ( 19 )   PDF (277KB) ( 27 )  

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In locally convex Hausdorff topological vector spaces, ε-strongly efficient solutions for vector optimization with set-valued maps are discussed. Firstly, ε-strongly efficient point of set is introduced. Secondly, under the nearly cone-subconvex like set-valued maps, the theorem of scalarization for vector optimization is obtained. Finally, optimality conditions of ε-strongly efficient solutions for vector optimization with generalized inequality constraints and equality constraints are obtained.


具广义周期边界条件之含第一类界参数抽象动力方程边值问题的积分算子求解法

喻德坚

2010, 25(1):  110-117. 

摘要 ( 14 )   PDF (370KB) ( 10 )  

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In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter λ = 0 and generalized periodic boundary conditions are introduced in a Lebesgue space which consists of functions with vector valued in a general Banach space, and then describe the solution of these abstract boundary value problem by the abstract linear integral operator of Volterra type. We call this process the integral operator solving process.


多元极值分布的偏序关系及其极值

董永权, 徐付霞

2010, 25(1):  118-123. 

摘要 ( 17 )   PDF (281KB) ( 8 )  

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This paper studies the dependence order among multivariate extreme value distributions with a fixed marginal distribution. Making use of copulas to prove that the set organized by multivariate extreme value distributions and the dependence order defined in it is a partial order set. Finally, the maximum and minimum values of the set is discussed.


具扇形非线性时滞神经网络全局同步

黄优良

2010, 25(1):  124-131. 

摘要 ( 16 )   PDF (398KB) ( 18 )  

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In this paper, global synchronization is discussed for a general class of delayed neural networks with time-varying and distributed delays. Furthermore, the activation functions in the neural networks can be different type. Based on the drive-response concept and the Lyapunov stability theorem, some sufficient criteria are obtained to guarantee the global synchronization of the considered models even when input sector nonlinearity caused by physical limitations is presented in response systems. Finally, a typical example is also given to illustrate the effectiveness of the proposed synchronization scheme. 

Hausdorff拓扑向量空间中锥拟凸多目标规划锥有效解集的连通性

周轩伟

2010, 25(1):  132-139. 

摘要 ( 18 )   PDF (323KB) ( 15 )  

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This paper deals with the connectedness of the cone-efficient solution set for vector optimization in locally convex Hausdorff topological vector spaces. The connectedness of the cone-efficient solution set is proved for multiobjective programming defined by a continuous one-to-one cone-quasiconvex mapping on a compact convex set of alternatives. During the proof, the generalized saddle theorem plays a key role.


一个Hermite-型矩形元的V-cycle多重网格法

赵艳敏, 石东洋

2010, 25(1):  140-145. 

摘要 ( 17 )   PDF (306KB) ( 8 )  

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In this paper, a V-cycle multigrid method is presented for a Hermite rectangular element. By defining proper mesh-dependent inner product and transfer operator, we obtain its convergence property and the uniform convergence rate independent of mesh size and level are established.


单群的一个性质

王慧群, 姬小龙

2010, 25(1):  146-150. 

摘要 ( 19 )   PDF (275KB) ( 13 )  

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In this note, we use an elementary method to prove the fact: if G is a nonabelian simple group, then 2∈/cd_p(G),where p is a prime and p > 2.



超线性奇异半正二阶m点边值问题正解的存在性

张兴秋

2010, 25(1):  151-158. 

摘要 ( 20 )   PDF (354KB) ( 7 )  

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By applying fixed point theorem, the existence of positive solution is considered for superlinear semipositone singular m-point boundary value problem -(Lφ)(x) = ···, f ∈ C[(0,1) × R⁺,R⁺], f(x,φ) may be singular at x = 0 and x = 1, g(x):(0,1) → R is Lebesgue measurable, g may tend to negative infinity and have finitely many singularities.