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2011年 第26卷 第1期    刊出日期：2011-03-30

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凸体诱导的对称函数

黄龙光

2011, 26(1):  1-6. 

摘要 ( 12 )   PDF (276KB) ( 4 )  

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This paper shows some properties of symmetry function induced by a convex body in a normal linear space. Some relationships between symmetry function induced by a convex body and Minkowski functional of the convex body are presented.



关于高阶代数微分方程组亚纯解的计数函数

陈妙玲, 高凌云

2011, 26(1):  7-10. 

摘要 ( 15 )   PDF (237KB) ( 18 )  

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Using Nevanlinna theory and value distribution of meromorphic functions and the other techniques, we investigate the counting functions of meromorphic solutions of systems of higher-order algebraic differential equations and obtain some results.



一个有限维Hamilton系统的Liouville可积性研究

朱云, 尹丽

2011, 26(1):  11-15. 

摘要 ( 20 )   PDF (247KB) ( 24 )  

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Based on a 2 × 2 eigenvalue problem, a set of (1 + 1)-dimensional soliton equations are proposed. Moreover, we obtain a finite dimensional Hamilton system with the help of nonlinearization approach. Then the generating function approach and the way to straighten out of Fm-flow are used to prove the involutivity and the functional independence of conserved integrals for the finite-dimensional Hamilton system, hence, we can verify it is completely integrable in Liouville sense.



一类具有交叉扩散效应的三种群诱饵-捕食系统整体解的存在性

陈志辉, 陈霞

2011, 26(1):  16-20. 

摘要 ( 19 )   PDF (258KB) ( 14 )  

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The prey-predator system of three species with cross-diffusion pressure is known to possess a local solution with the maximal existence time T ≤∞. By obtaining the bounds of W21-norms of the local solution independent of T, it is established the global existence of the solution.



集值映射空间上的自然映射

李祖泉, 王久晶

2011, 26(1):  21-25. 

摘要 ( 22 )   PDF (255KB) ( 14 )  

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In this paper, we discuss the continuities of some natural mappings on point compact continuous set-valued mapping spaces with compact-open topology and obtain the properties of set-valued injective mappings, set-valued diagonal mappings, induced mappings, set-valued evaluation mappings, set-valued topological sum mappings and set-valued topological product mappings.



局部凸空间中集值优化问题的ε-超有效解

王淑玉, 刘万里

2011, 26(1):  26-31. 

摘要 ( 23 )   PDF (288KB) ( 22 )  

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In this paper, the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced. And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps, used new methods, the scalarization theorem and Lagrange multiplier theorem for ε-super effcient solution are established.



多值KM1M2生成器的概率模型

杜宜宾, 黄晓英, 李正朝, 滕吉红

2011, 26(1):  32-38. 

摘要 ( 20 )   PDF (332KB) ( 13 )  

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This paper constructs the probability model of the multi-valued KM1M2 clock controlled generator, and discusses the probability distributing, homogeneous Markov property, ergodic property, strict placidity, numeral character and the property of large numbers of the random variables with this kind of output sequence. It gets the probability formula of the coincidence of the output sequence with the input sequence, and gives important reference to the design and analysis of the multi-valued key stream clock controlled generator in cryptography. 


高阶广义微扰KdV方程的弱解

成军祥, 王艳红

2011, 26(1):  39-45. 

摘要 ( 21 )   PDF (330KB) ( 12 )  

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By using the theory of compensated compactness, we prove that there exists a sequence {u^ε_δ} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturbation terms, namely we prove the existence of the weak solution.



关于非自治Benjiamin-Bona-Mohony方程拉回吸引子的一个注记

秦嘉

2011, 26(1):  46-50. 

摘要 ( 17 )   PDF (277KB) ( 8 )  

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In this paper, we show the existence of pullback attractors for the nonautonomous Benjamin-Bona-Mahony equations by establishing the pullback uniform asymptotically compactness.



随机环境中马氏链的首达分布矩

李守伟, 祝东进

2011, 26(1):  51-55. 

摘要 ( 23 )   PDF (258KB) ( 13 )  

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After defining generating functions, this paper discusses their properties, and then provides a sufficient and necessary condition for a finite property of the moments of first entrance time distributions of Markov chains in random environments by generating functions. Finally, the paper obtains relevant conclusions of the moments of first entrance time distributions.



具无穷时滞退化中立型微分系统的周期解

周桂芳, 张海, 蒋威

2011, 26(1):  56-60. 

摘要 ( 20 )   PDF (273KB) ( 13 )  

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In this paper, we discuss the periodic solutions of the nonlinear singular neutral differential systems with infinite delay. By using matrix measure and Krasnoselskii’s fixed point theorem, we obtained the sufficient conditions of the existence of periodic solutions.



抽象空间中非线性脉冲Volterra积分方程的L^p_loc解的存在性

王儒智

2011, 26(1):  61-68. 

摘要 ( 15 )   PDF (339KB) ( 8 )  

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In this paper, we discuss L^p_loc-solutions of a kind of nonlinear impulsive Volterra integral equation and present an existence theorem of solutions in Banach space.



求解无约束非线性规化问题的一个新的重开始三项共轭梯度算法的收敛性

孙清滢, 桑兆阳, 田凤婷

2011, 26(1):  69-76. 

摘要 ( 19 )   PDF (328KB) ( 19 )  

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In this note, by combining the nice numerical performance of PR and HS methods with the global convergence property of FR method, a class of new restarting three terms conjugate gradient methods is presented. Global convergence properties of the new method with two kinds of common line searches are proved.



具有p-Laplacian算子的二阶微分方程Picard边值问题

刘玉记

2011, 26(1):  77-84. 

摘要 ( 28 )   PDF (353KB) ( 11 )  

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Sufficient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 are established, where [φ(x)] =(|x |p-2x) with p > 1. Our result is new even when [φ(x)] = x in above problem, i.e. p = 2. Examples are presented to illustrate the efficiency of the theorem in this paper.



模余代数的结构定理

王勇, 张良云, 蔡之敏

2011, 26(1):  85-92. 

摘要 ( 19 )   PDF (315KB) ( 12 )  

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This paper, mainly gives the structure theorem for module coalgebras by a kind of new method, and deletes the condition that the antipode S of the Hopf algebra H is bijective.



因子拟适当半群

彭婷婷, 郭小江

2011, 26(1):  93-99. 

摘要 ( 16 )   PDF (303KB) ( 19 )  

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In this paper, we investigate a class of factorisable IC quasi-adequate semigroups, so-called, factorisable IC quasi-adequate semigroups of type-(H,I). Some characterizations of factorisable IC quasi-adequate semigroups of type-(H,I) are obtained. In particular, we prove that any IC quasi-adequate semigroup has a factorisable IC quasi-adequate subsemigroups of type-(H,I) and a band of cancellative monoids.



以幂零李代数Rn为幂零根基的可解李代数

吴明忠

2011, 26(1):  100-107. 

摘要 ( 22 )   PDF (336KB) ( 2 )  

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In this paper we explicitly determine automorphism group of filiform Lie algebra Rn to find the indecomposable solvable Lie algebras with filiform Lie algebra Rn nilradicals. We also prove that the indecomposable solvable Lie algebras with filiform Rn nilradicals is complete.



数值积分的可选择误差界

陆建芳, 封平华

2011, 26(1):  108-113. 

摘要 ( 19 )   PDF (277KB) ( 13 )  

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Similar to having done for the mid-point and trapezoid quadrature rules, we obtain alternative estimations of error bounds for the Simpson’s quadrature rule involving n-time(1 ≤ n ≤ 4) differentiable mappings and then to the estimations of error bounds for the adaptive Simpson’s quadrature rule.



ρ^-_-混合序列部分和最大值的一些不等式和强大数律的收敛速度

谭成良, 吴群英, 何燕梅

2011, 26(1):  114-119. 

摘要 ( 21 )   PDF (293KB) ( 8 )  

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 In this paper, we establish a Rosenthal-type inequality of partial sums for ρ^--mixing random variables. As its applications, we get the complete convergence rates in the strong laws for ρ^--mixing random variables. The result obtained extends the corresponding result.








时间序列中参数变点的检测

金浩, 杨云锋

2011, 26(1):  120-124. 

摘要 ( 30 )   PDF (252KB) ( 12 )  

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The paper considers the problem of testing for a change point in the parameters of AR(p) models. It is shown that the asymptotically limiting distribution of the residual CUSUM of squares test(RCUSQ) is still the sup of a standard Brownian bridge under null hypothesis. We also show via simulations that our asymptotic results provide good approximations in finite samples.





非交换环的基于理想的零因子图

李云慧, 唐高华

2011, 26(1):  125-130. 

摘要 ( 19 )   PDF (272KB) ( 21 )  

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This paper introduces an ideal-boyed zero-divisor graph of non-commutative rings, denoted ΓI(R).ΓI(R) is a directed graph. The properties and possible structures of the graph is studied.





粘弹性波动方程的H¹-Galerkin混合有限元方法误差估计

王金凤, 刘洋, 李宏

2011, 26(1):  131-137. 

摘要 ( 24 )   PDF (324KB) ( 17 )  

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H¹-Galerkin mixed methods are proposed for viscoelasticity wave equation. Depending on the physical quantities of interest, two methods are discussed. The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension. And the methods don’t require the LBB condition.



一类带有三维核的多点边值问题解的存在性

梁菊花, 任立顺, 赵志良

2011, 26(1):  138-143. 

摘要 ( 33 )   PDF (277KB) ( 23 )  

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In this paper, a multi-point boundary value problems for a three order nonlinear deferential equation is considered. With the help of coincidence theorem due to Mawhin, a existence theorem is obtained.



一类Z₂-等变扰动的三次哈密顿系统极限环的个数与分布

周宏宪, 张燕

2011, 26(1):  144-151. 

摘要 ( 18 )   PDF (424KB) ( 10 )  

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This paper is concerned with the number and distributions of limit cycles of a cubic Z₂-symmetry Hamiltonian system under quintic perturbation. By using qualitative analysis of differential equation, bifurcation theory of dynamical systems and the method of detection function, we obtain that this system exists at least 14 limit cycles with the distribution C¹_9...C₁²)].



一类混合型Szàsz-Beta算子的强逆不等式

齐秋兰, 张玉平

2011, 26(1):  152-158. 

摘要 ( 19 )   PDF (335KB) ( 10 )  

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In this paper, a strong converse inequality of type B in terms of a new K-functional K^λ_α(f, t²⁾(0 < α < 2, 0 ≤λ≤ 1) for certain mixed Szász-Beta operators is given. By this inequality, the converse theorem can be obtained for the operators.