伍艳春, 吴群英

2011, 26(2): 159-163.

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This paper discusses complete convergence properties of the sums of ρ-mixing random sequences. As a result, we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence to the case of ρ-mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.

Hilbert空间中广义变分不等式和Wiener-Hopf方程

商美娟, 王治国

2011, 26(2): 164-169.

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In this paper, we consider the solvability of generalized variational inequalities involving multi-valued relaxed monotone operators in the framework of Hilbert spaces. Our results mainly improve the corresponding results announced by Verma[R U Verma, Generalized variational inequalities involving multivalued relaxed monotone operators, Appl Math Lett,1997,10:107-109]and many others.

线性过程方差变点的平方累计和SCUSUM估计

赵文芝, 夏志明

2011, 26(2): 170-173.

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This paper considers the estimation problem of a variance change-point in linear process. Consistency of a SCUSUM type change-point estimator is proved and its rate of convergence is established. The mean-unknown case is also considered.

Sasakian空间形式中子流形的全实截面曲率

黄广月, 马冰清

2011, 26(2): 174-178.

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By using the methods introduced by Chen[Chen Bang-yen, A series of Kahlerian invarianrts and their applications to Kahlerian geometry, Beitrage Algebra Geom,2001,42(1):165-178], we establish some inequalities for invariant submanifolds in a Sasakian space form involving totally real sectional curvature and the scalar curvature. Moreover, we consider the case of equalities.

二阶非线性微分方程组边值问题的正解

郑冬梅, 鲁世平

2011, 26(2): 179-184.

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By using fixed-point index theory, we study boundary value problems for systems of nonlinear second-order differential equation, and a result on existence and multiplicity of positive solutions is obtained.

一类算子的凸性条件

鲁大前, 刘金林

2011, 26(2): 185-189.

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In this paper, we find a subclass of starlike functions on the unit disk, which are mapped by a operator, given by F(z)=(1+u)/z^u∫^z₀f(t)t^u-1dt(Reu≥0), onto convex functions. The main results extend some known results.

对于金融资产漂移函数估计的双域组合方法

叶绪国, 杜雪樵

2011, 26(2): 190-195.

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Time-domain state-domain methods are common approaches in modern financial analysis. Economic conditions vary time, drift function depends on time and price level for a given state variable. In this paper, to consistently estimate the bivariate drift function, our purpose a new dynamic integrated estimator by combing time-and state-domain methods for estimating drift function. And we establish its asymptotic properties and illustrates it outperforms some old ones by simulations.

关于复代数微分方程组解的增长级问题

苏先锋, 高凌云

2011, 26(2): 196-199.

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This paper is concerned with the order of the solutions of systems of high-order complex algebraic differential equations. By means of Zalcman Lemma, the systems of equations of [1] is extended to more general form.

李群T(D(V_N, F))的自同构群

程永胜, 车颖涛

2011, 26(2): 200-207.

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In this paper, the authors determine maximal connected automorphism group of the Lie transformation group T(D(V_N, F)), which acting on the normal Siegel domain D(V_N, F) is simple and transitive, and prove that the maximal connected automorphism group of T(D(V_N, F)) is its maximal connected inner automorphism group.

关于变分不等式与不动点问题

陆爱霞, 王庆灵

2011, 26(2): 208-212.

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In this paper, a strong convergence theorem for a finite family of non-expansive mappings and relaxed cocoercive mappings based on an iterative method in the framework of Hilbert spaces is established.

拟主k-投射半模

王秀丽, 周茂袁, 陈志寅

2011, 26(2): 213-216.

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In this paper, we principally introduce the concept of quasiprincipally k-projective semimodules, on the basis of the theories of k-projective semimodules and quasi-principally modules, we get some good properties of quasi-principally k-projective semimodules, therefore generalize some properties of quasi-principally modules of ring and k-projective semimodules of semiring to quasi-principally k-projective semimodules of semiring.

一类四阶奇摄动非线性边值问题

李旭, 王世朋

2011, 26(2): 217-222.

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This paper is devoted to study the following the singularly perturbed fourth-order ordinary differential equation ∈y⁽⁴⁾ =f(t,y’,y’’,y’’’),0<t<1,0<ε<<1 with the nonlinear boundary conditions y(0)=y’(1)=0,p(y’’(0),y’’’(0))=0,q(y’’(1),y’’’(1))=0 where f:[0,1]×R3→R is continuous,p,q:R2→R are continuous. Under certain conditions, by introducing an appropriate stretching transformation and constructing boundary layer corrective terms, an asymptotic expansion for the solution of the problem is obtained. And then the uniformly validity of solution is proved by using the differential inequalities.

Banach空间中一类C^∞函数芽等价的条件

岑燕斌, 刘文武, 岑翼刚

2011, 26(2): 223-228.

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In this paper, we prove the converse of gem is right equivalent is also true in [1] and [2], obtain the necessary and suﬃcient conditions of equivalence of a class gems of C^∞ function on Banach spaces.

具ω增长阶的α次积分余弦算子函数

王梅英, 许飞

2011, 26(2): 229-233.

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For a continuous, increasing function ω: [0,∞)→C of finite exponential type, we establish a Hille-Yosida type theorem for strongly continuous α-times (α>0) integrated cosine operator functions with O(ω). It includes the corresponding results for n-times integrated cosine operator functions that are polynomially bounded and exponentially bounded.

交叉立方体的等价定义

王彦辉, 汪雄良, 吴果林

2011, 26(2): 234-238.

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For the crossed cube, an equivalent definition based on the quadrilateral is given, by which we obtain the main properties of this topological architecture, and propose a procedure to find a shortest path between any two vertices in it.

一类基于进入过程保险风险模型的破产概率

肖鸿民, 唐加山

2011, 26(2): 239-244.

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In this note, one kind of insurance risk models with the policies having multiple validity times are investigated. Explicit expressions for the ruin probabilities are obtained by using the martingale method. As a consequence, the obtained probability serves as an upper bound for the ruin probability of a newly developed entrance processes based risk model.

某个用Carlson-Shaffer算子定义的解析函数子类的性质

李宗涛, 刘名生

2011, 26(2): 245-250.

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Let H_n(p) be the class of functions of the form f(z)=z^p+..., which are analytic in the open unit disk U={z:|z|<1}. In the paper, we introduce a new subclass B_n(μ,a,c,α,p;φ) of H_n(p) and investigate its subordination relations, inclusion relations and distortion theorems. The results obtained include the related results of some authors as their special case.

BurrⅫ模型中基于屏蔽数据的参数估计

侯华蕾, 蒋耀伟, 师义民

2011, 26(2): 251-255.

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We consider a series system of two independent and non-identical components which have different BurrⅫ distributed lifetime. The maximum likelihood and Bayes estimators of the parameters of the system’s components are obtained based on masked system life test data. The conclusion is that the Bayes estimates are better than the maximum likelihood estimates in the sense of having smaller mean squared errors.

一类泛函数微分方程的周期解的存在性

林金泉, 林文贤

2011, 26(2): 256-259.

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In this paper, a kind of high order functional differential equation is considered. By using the theory of concidence degree, a sufficient condition of existence of at least one 2π-period solution is obtained.

具连续分布变元的向量抛物型方程振动性的新准则

李元旦, 罗李平, 俞元洪

2011, 26(2): 260-264.

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The oscillations of a class of vector parabolic partial diﬀerential equations with continuous distribution arguments are studied. By employing the concept of H-oscillation and the method of reducing dimension with inner product, the multi-dimensional oscillation problems are changed into the problems of which one-dimensional functional diﬀerential inequalities have not eventually positive solution. Some new suﬃcient conditions for the Hoscillation of all solutions of the equations are obtained under Dirichlet boundary condition, where H is a unit vector of R^M.

Banach空间中广义的Sturm-Liouville m点边界值问题的正解

杨景保, 韦忠礼

2011, 26(2): 265-269.

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By applying the fixed-point theorem of strict-set-contraction, this paper establishes the existence of one solution or one positive solution to the generalized Sturm-Liouville m-point boundary value problem in Banach spaces.

多元部分线性模型的几个渐近性质

周兴才, 胡舒合

2011, 26(2): 270-274.

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The paper considers a multivariate partially linear model under independent errors, and investigates the asymptotic bias and variance-covariance for parametric component βand nonparametric component F(·) by the GJS estimator and Kernel estimation.

Banach代数中有限序列的多项式谱

杨冲

2011, 26(2): 275-279.

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In this paper, we discuss that the polynomial spectrum, relative spectrum and Spectrum of a Pair of Elements are all compact, so their resolvent sets are all open.

一种新形式的二元混合有理插值

邹乐, 唐烁

2011, 26(2): 280-284.

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Newton’s polynomial interpolation may be the favorite linear interpolation, associated continued fractions interpolation is a new type nonlinear interpolation. We use those two interpolation to construct a new kind of bivariate blending rational interpolants. Characteristic theorem is discussed. We give some new blending interpolation formulae.

广义几何规划的压缩共轭梯度路径非单调信赖域算法

党亚峥, 景书杰, 李煜

2011, 26(2): 285-289.

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In this paper, on the basis of making full use of the characteristics of unconstrained generalized geometric programming(GGP), we establish a nonmonotonic trust region algorithm via the conjugate path for solving unconstrained GGP problem. A new type of condensation problem is presented, then a particular conjugate path is constructed for the problem, along which we get the approximate solution of the problem by nonmonotonic trust region algorithm, and further prove that the algorithm has global convergence and quadratic convergence properties.

基于食饵保护的食饵-捕食捕鱼模型分析

孙军芳, 苟晓侃

2011, 26(2): 290-295.

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In this paper, we consider a prey-predator fishery model with prey dispersal in a two-patch environment, one is assumed to be a free fishing zone and the other is a reserved zone where fishing and other extractive activities are prohibited. The existence of possible steady states of the system is discussed. The local and global stability analysis has been carried out. An optimal harvesting policy is given using Pontryagin's maximum principle.

函数粗集生成的粗积分

于秀清, 徐凤生

2011, 26(2): 296-299.

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The concepts of the lower approximation integral, the upper approximation integral and rough integrals are given on the basis of function rough sets. Based on these concepts, the relation of the lower approximation integrals, the relation of the upper approximation integrals, the relation of rough integrals, and the double median theorem of rough integrals are discussed. Rough integrals have finite contraction characteristic and finite extension characteristic.

基于切比雪夫节点的一类带显式系数的广义高斯求积公式

曹丽华, 赵毅

2011, 26(2): 300-305.

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The goal here is to give a simple approach to a quadrature formula based on the divided diffierences of the integrand at the zeros of the nth Chebyshev polynomial of the first kind, and those of the (n-1)st Chebyshev polynomial of the second kind. Explicit expressions for the corresponding coefficients of the quadrature rule are also found after expansions of the divided diffierences, which was proposed in [14].

两类关于二项式系数倒数的级数

宋海涛

2011, 26(2): 306-310.

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By applying the theory of formal power series, the author obtains the closed forms for two kinds of infinite series involving the reciprocals of binomial coefficients, and the author gets another closed form for the infinite series Σ_r≥mt^n+r/(n+r r).

Anti-de Sitte:空间H³₁中的广义弹性曲线

黄荣培, 廖蔡生, 商东虎

2011, 26(2): 311-316.

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In this paper, the extremals of curvature energy actions on non-null Frenet curves in 3-dimensional Anti-de Sitter space are studied. We completely solve the Euler-Lagrange equation by quadratures. By using the Killing fields, we obtain existence for closed general-ized elastica fully immersed in Anti-de Sitter space H13.

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