一类新的极值估计量

提出了一类新的极值指数估计量,证明了该估计量的相合性以及渐近性.

Abstract：

In this paper, a new class of estimator for the extreme value index is proposed, and the consistency and asymptotic property of this estimator are proved.     

离散随机变量序列完备及非完备样本最大值的联合分布

设离散随机变量三角阵列{X_(n,k),K≤n,n≥1}存在数据缺失,对给定的n,M_n=max{X_(n,k),K≤n}为第n行的最大值,(~(M)_n)为该行观测到的随机变量的最大值,研究了离散型随机变量的分布函数某一参数变动时(~(M)_n),M_n)的联合渐近分布.

Abstract：

For triangular array discrete random variables {X_(n,k), k ≤ n,n ≥1},there may exist data missing observation. Denote M_n=max{X_(n,k),k ≤ n}the partial maximum and (~(M)_n) is the maximum of the observed random variables in the nth row.In this paper,the asymptotic joint distributions of (~(M)_n),M_n) of some discrete random variables are obtained as their parameters vary along with sample size.     

相依结构熵及联合熵的分解

把Copula函数引入熵理论,并定义了相依结构熵来度量随机变量之间的相依结构,计论了二维随机向量在单调变换下相依结构熵的不变性并推广到多维的情形.

Abstract：

The copula functions are employed to study the entropy theory and a conception of dependence structure entropy is defined for measuring the dependence structure of random variables.The joint entropy is divided into the dependence structure entropy and the marginal entropy,which is useful of investigating the dependence structure of random variables.In addition,the invariability of dependence structure entro-py of bivariate variables under monotonous transforming is discussed and extended to muhivariable cases.     

具有竞争的Leslie型捕食者-食饵模型的定性分析

考虑了具有竞争的Leslie型模型.证明了解的最终有界性,和系统在一定条件下的一致持续生存性.研究了平衡点的局部稳定性.通过构建适当的Lyapunov函数,获得了正平衡点全局渐进稳定的充分条件.

Abstract：

In this paper, a competitive Leslie model is proposed. It is proved that the system's solution is ultimately bounded and the system is consistent and sustained under appropriate conditions. The local stability of the equilibria is investigated. By constructing a suitable Lyapunov functional, sufficient conditions are derived for the global stability of the positive equilibrium of the model.     

具有两种免疫来源的乙肝病毒模型的全局动力学

研究了免疫反应具有两种来源的乙肝病毒模型.通过对相应特征方程的分析,讨论了感染平衡态和未感染平衡态的局部稳定性,证明了基本再生数>1时疾病的持续性.通过几何方法的应用,得到了感染平衡点全局稳定性的充分条件.

Abstract：

In this paper,an HBV model with activated immune response of two sources is studied.By analyzing the corresponding characteristic equations,the local stability of an infected steady state and an uninfected steady state is discussed.It is proved that if the basic reproductive number is more than one,the disease is persistent.By applying a geometric method,sufficient conditions are obtained for the global stability of the endemic equilibrium.     

一类拟线性椭圆系统的多重解

利用上下解方法和强极大值原理研究了一类拟线性椭圆系统正解的存在性问题.用山路引理研究了该椭圆系统在次临界增长条件下解的多重性问题.

Abstract：

Using upper-lower solution method and strong maximum principle,the existence of positive solutions is considered for a class of quasilinear elliptic systems.By means of mountain pass lemma,the multiplicity of solutions is considered for the related systems with subcritical growth condition.     

伴随积分算子半群及其性质

研究了伴随积分算子半群的性质,给出了经典的Phillips定理的一个简单证明,并明确了伴随算子半群成c0算子半群的最大子空间.

Abstract：

The properties of adjoint integrated semigroups are studied. As an application, the classical Phillips Theorem for adjoint semigroups is proved with a different and somewhat simple way. Furthermore, the maximal subspace to which the restriction of adjoint semigroups is a c0 semigroup is specified.     

两个有限超可解群的积

讨论了有限群G是两个有限群A,B之积时的超可解性的问题.利用半正规和拟正规的概念,在较弱的条件下给出了群G超可解的一些充分条件.

Abstract：

The supersoluability of a finite group G when it is the product G of two finite supersoluable groups A and B is discussed. Some sufficient conditions of the supersoluability of G are obtained under some weaker hypotheses by using the concept of semi-normality and quasi-normality which generalize the known.     

求解线性方程组的一种新的迭代算法

对系数为对称正定矩阵的线性方程组Ax=b,利用系数矩阵A主对角线上元素的和构造了一种新的收敛迭代格式xk+1=(I-2/a11+…+ann A)xk+2/a11+…+ann b,并进一步对这种格式进行了改进.

Abstract：

Using the sum of the elements of the principal diagonal of the coefficient matrix A, a new iterative schine ,i.e.xk+1=(I-2/a11+…+ann A)xk+2/a11+…+ann b,is constructed for the linear equation Ax = b, of which the coefficient is a symmetric positive definite matrix. Further improvement is made of the scheme.     

二阶差分方程边值问题正解的存在性

运用Krasnoselskii不动点定理考察了二阶差分方程边值问题{△2u(k-1)+a(k)f(u(k))=0,k∈[1,T]z/u(0)=0,u(T+1)=αu(τ)1个及2个正解的存在性,其中f:[0,∞)→[0,∞)连续,T∈Z且T≥3,τ∈[2,T-1]z.

Abstract：

In this paper, we use the Krasnoselskii fixed piont theorem to study the existence of one or two positive solutions of second-order boundary value problems for difference equations {△2u(k- 1) +a(k)f(u(k)) = 0, k ∈ [1, T]z/u(0) = 0, u(T + 1) = αu(τ)where of: [0, ∞) → [0, ∞) is continuous, T ∈ Z and T≥ 3, τ∈ [2, T- 1]z.