Period two implies chaos for a class of ODEs

We extend a result of J. Andres and K. Pastor concerning scalar time-periodic first order ordinary differential equations without uniqueness, by proving that the existence of just one subharmonic implies the existence of large sets of subharmonics of all given orders. Since these periodic solutions must coexist with complicated dynamics, we might paraphrase T. Y. Li and J. A. Yorke by loosely saying that in this setting even period two implies chaos. Similar results are obtained for a class of differential inclusions.

     

全空间中带时滞的反应扩散方程组

文应用上下解的方法以及单调迭代序列的积分表达式,证明了在半空间R~n中耦合的时滞反应扩散方程组全局解的存在唯一性,并且用它解决了一类特殊的、Volterra-Lotka模型的解的存在性问题．     

节点失效下全端可靠性的上界

推广了A bdu llah K onak and A lice E.Sm ith提出的方法,在链路和节点均不可靠的条件下,给出了全端可靠性上界的估算公式,利用该公式估算上界简洁方便,精度高.具有实用价值.     

Equality conditions for the singular values of 3 × 3 matrices with one-point spectrum

Let Γ_a be an upper triangular 3 × 3 matrix with diagonal entries equal to a complex scalar a. Necessary and su.cient conditions are found for two of the singular values of Γ_a to be equal. These conditions are much simpler than the equality discr ? = 0, where the expression in the left-hand side is the discriminant of the characteristic polynomial ? of the matrix _Ga = Γ_aΓ_a. Understanding the behavior of singular values of Γ_a is important in the problem of finding a matrix with a triple zero eigenvalue that is closest to a given normal matrix A.     

THE STRUCTURE OF RAPIDLY DECAYING SOLUTIONS OF △u f(u) = 0 in R~n

1IntroductionInthispaper,westudythesingularpositivesolutionsofinR"(n>2),wheref(u)islocallyLipschtizcontinuouson[0, co)andf(u)20.Byasingularpositivesolutionof(1.1)-(1.2)wemeanthesolutionwhichsatisfies(1.1)-(l.2)inR"\{0}andtendsto coattheorigin.Bytheresults…     

System of Generalized Vector Quasi-Equilibrium Problems with Applications to Fixed Point Theorems for a Family of Nonexpansive Multivalued Mappings

In this paper, we establish the existence theorems of the generalized vector quasi-equilibrium problems. From some existence theorem, we establish fixed point theorems for a family of lower semicontinuous or nonexpansive multivalued mappings. We also obtain the existence theorems of system of mixed generalized vector variational-like inequalities and existence theorems of the Debreu vector equilibrium problems and the Nash vector equilibrium problems.     

集值映射的广义对称向量拟平衡问题

本文提出了一类集值映射的广义对称向量拟平衡问题．利用非线性标量化函数,分别在局部凸Hausdorff拓扑向量空间和一般的Hausdorff拓扑向量空间中,证明了广义对称向量拟平衡问题解的存在性定理．     

Existence of Solutions to Implicit Vector Variational Inequalities

In this paper, we study a class of implicit vector variational inequalities which contain implicit variational inequalities and generalized quasivariational inequalities as special cases. By employing the Fan–Kakutani fixed-point theorem and the Oettli scalarization procedure, respectively, we establish several existence results for implicit vector variational inequalities.     

Geometric analysis on H ‐type groups related to division algebras

The present article applies the method of Geometric Analysis to the study H ‐type groups satisfying the J² condition and finishes the series of works describing the Heisenberg group and the quaternion H ‐type group. The latter class of H ‐type groups satisfying the J² condition is related to the octonions. The relations between the group structure and the boundary of the corresponding Siegel upper half space are given. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

附有选择性服务与无等待能力的M/G/1排队系统的系统主算子的性质

研究了附有选择性服务与无等待能力的M/G/1排队系统.运用C_0半群理论,通过服务率均值的观念,对系统主算子的谱上界进行了估值,并得到谱上界即为各服务率均值的最小者的相反数.然后运用了共尾的概念及相关的理论,得到了系统主算子的谱上界与系统主算子产生的半群的增长界相等,从而得到其增长界也是各服务率均值的最小者的相反数.