跃变参数混沌同步及其应用

建立了跃变参数混沌同步的数学模型，提出并证明了其同步的充分条件，在理论上分析了充分条件的可实现性.提出了跃变参数混沌同步和跃变周期同步的有效算法，借助Chua混沌系统仿真实现了参数跃变混沌同步保密通信.最后，分析了跃变参数混沌保密通信对抗现有混沌窃听方法的性能.仿真结果表明跃变参数混沌同步及其保密通信具有易实现和强保密性等优点.     

具P-Laplacian算子型周期边值问题解的存在性

本文利用拓扑度理论和一些分析技巧讨论了具p—Laplacian算子型周期边值问题(φp(χ’))’+d/dt gradF(χ)+gradG(χ)=e(t),χ(0)=χ(T),χ’(0)=χ’(T)解的存在性,在对阻尼项d/dtgradF(χ)没有任何限制的前提下,给出了解存在的充分条件.     

拟单调问题的讨论

This paper gives the necessary condition and one sufficient condition of the quasi-monotonic function, and proves that the linear fractional function is quasi-monotone.     

非光滑非凸多目标规划解的充分条件

Kuhn-Tucker型条件的充分性一直是最优化理论中引人注意的一个问题.本文对非光滑函数提出了几个非凸概念,然后,讨论了非光滑非凸多目标规划中Kuhn-Tucker型条件和Fritz John型条件的充分性,在很弱的条件下,建立了一系列充分条件.     

On Polynomial Functions over Finite Commutative Rings

Let R be an arbitrary finite commutative local ring. In this paper, we obtain a necessary and sufficient condition for a function over R to be a polynomial function. Before this paper, necessary and sufficient conditions for a function to be a polynomial function over some special finite commutative local rings were obtained.     

Complete study on a bi-center problem for the <Emphasis Type="Italic">Z</Emphasis><Subscript>2</Subscript>-equivariant cubic vector fields

For the planar Z ₂-equivariant cubic systems having two elementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed. The necessary and sufficient conditions for the existence of the bi-center are obtained. All possible first integrals are given. Under small Z ₂-equivariant cubic perturbations, the conclusion that there exist at most 12 small-amplitude limit cycles with the scheme 〈6 ∐ 6〉 is proved.     

时变线性系统特征根判稳的推广

本文研究了二维时变线性系统零解的稳定性，给出了一些允许系数矩阵主对角元变号，系数矩阵特征根变号的判定稳定性的充分条件。     

PERIODIC SOLUTIONS FOR A CLASS OF DELAYED NONLINEAR DIFFERENCE EQUATIONS

With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree,some sufficient conditions are established for the global existence of positive periodic solutions of a class of delayed nonlinear difference equations.     

幂零群的若干充分条件

本文利用Ｃ－正规子群的性质，得到了若干有限群为幂零群的充分条件，推广了一些著名定理，如Ｔｈｏｍｐｓｏｎ定理及Ｉｔ＾ｏ定理。     

拟圆的两个充分条件

拟圆是拟共形映照理论中的重要概念和研究对象，对拟圆的研究有着重要意义，许多著作都专门研究了拟圆，得到了拟圆的许多性质以及判定拟圆的充分条件。本文给出了复平面Ｒ↑－＾２＝Ｒ＾２∪｛∞｝上判定拟圆的两个充分条件，它们分别是Ｆ．Ｗ．Ｇｅｈｒｉｎｇ和Ｏ．Ｍａｒｔｉｏ在文［１，２］中两个必要条件在一定条件下的逆。本文的两个充分条件在应用上较为广泛和实用。