退化时滞微分系统的Hopf分支

本文讨论了一般二雏退化时滞微分系统当r≠0时平衡点稳定性的范围，并以滞量r为分支参数研究系统出现Hopf分支的条件．     

I THE （μ＋ κ）oORBITS OF ESSENTIALLY NORMAL OPERATORS AND THEIR STRONG IRREDUCIBILITY

The authors characterize the (μ +κ)-orblts of a class essmntially normal operators and provethat some essentially normal operators with connected spectrum are strongly irreducible aftera small compact perturbation. This partially answers a question of Domigo A. Herrero.     

求解课程表问题的分支定界算法

本通过对中学排课程表问题的特征分析，给出了基于分支定界法的优化算法，数值试验表明这是解决一般编排中学课程表问题的有效算法。     

康托的集合定义与罗素悖论

集合论是19世纪80年代由康托（Cantor）创立的，现在已发展为独立的数学分支．它的基本概念与方法已渗入到数学的各个领域，成为现代数学的基石．     

Cs-He光学碰撞中的非绝热跃迁

激光激发Cs He碰撞复合物,测量了Cs(62P)精细结构布居数分支比,由此证实了发生在光学碰撞中的非绝热跃迁.激光频率从Cs(6P3/2)红翼30cm-1调至蓝翼30cm-1,在6P3/2的近翼,分支比与矢谐量有很大的关系.同时测量了Cs(6PJ)态的精细结构转移截面,截面值σ21=9.8×10-19cm2.     

非线性三种群空间周期解的存在性

本文考虑以下系统: ,用Darboux方 法彻底解决了该系统空间周期解的存在性问题.     

Bifurcations and Chaos in a Discrete Predator-prey System with Holling Type-IV Functional Response

A discrete predator-prey system with Holling type-IV functional response obtained by the Euler method is first investigated. The conditions of existence for fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using the center manifold theorem and bifurcation theory. Furthermore, we give the condition for the occurrence of codimension-two bifurcation called the Bogdanov-Takens bifurcation for fixed points and present approximate expressions for saddle-node, Hopfand homoclinic bifurcation sets near the Bogdanov-Takens bifurcation point. We also show the existence of degenerated fixed point with codimension three at least. The numerical simulations, including bifurcation diagrams, phase portraits, and computation of maximum Lyapunov exponents, not only show the consistence with the theoretical analysis but also exhibit the rich and complex dynamical behaviors such as the attracting invariant circle, period-doubling bifurcation from period-2,3,4 orbits.interior crisis, intermittency mechanic, and sudden disappearance of chaotic dynamic.     

平面同宿轨的环性数与二次可积系统

给出平面Hamilton系统的同宿轨在扰动下产生2个或3个极限环的一般方法,获得了同宿轨环性数是1或2的条件.作为对二次多项式系统的应用,证明了除一种情形外,可积且非Hamilton的二次系统的同宿轨的环性数是2.