Banach空间的无穷维子空间结构的若干问题

本文论述了关于Ｂａｎａｃｈ空间的无穷维子空间结构的两分枝问题，三分枝问题和无条件基序列的存在性等五个问题，这些是当前Ｂａｎａｃｈ空间理论中尚未解决的几个基本问题，同时介绍了试图解决这几个问题的有关概念和方法如Ｂａｎａｃｈ空间的稳定性，扭曲范数和空间的饱合性等。     

Effects of Hard Limits on Bifurcation, Chaos and Stability

An SMIB model in the power systems,especially that concering the effects of hard limits onbifurcations,chaos and stability is studied.Parameter conditions for bifurcations and chaos in the absence ofhard limits are compared with those in the presence of hard limits.It has been proved that hard limits can affectsystem stability.We find that (1) hard limits can change unstable equilibrium into stable one;(2) hard limits canchange stability of limit cycles induced by Hopf bifurcation;(3) persistence of hard limits can stabilize divergenttrajectory to a stable equilibrium or limit cycle;(4) Hopf bifurcation occurs before SN bifurcation,so the systemcollapse can be controlled before Hopf bifurcation occurs.We also find that suitable limiting values of hard limitscan enlarge the feasibility region.These results are based on theoretical analysis and numerical simulations,such as condition for SNB and Hopf bifurcation,bifurcation diagram,trajectories,Lyapunov exponent,Floquetmultipliers,dimension of attractor and so on.     

超分枝多元醇的合成及其在紫外光固化体系中的应用

合成超分枝聚酯多元醇，并进一步与一柔顺剂作用，得到柔顺的超分枝聚酯多元醇，用于阳离子紫外光固化体系中作为链转移剂和交联剂。经测试，超分枝聚酯多元醇对阳离子紫外光固化膜的柔韧性、抗冲击和耐溶剂性等性能均有明显提高。     

线性调控分枝过程

本文提出了线性调控分枝过程和在零点停止的线性调控分枝过程的数学模型,并讨论了它们的均值、方差函数和灭绝概率,从而推广了[1]、[3]和[4]有关结果。     

变化环境中的分枝过程

设｛犣狀｝为变化环境中的上临界的分枝过程，犠为非负鞅｛犣狀／犈犣狀｝的极限，在一致上临界以及控制后代分布尾行为的假设条件下，给出了犠非退化的必要条件，且证明了｛犣狀／犈犣狀｝的犔１ 收敛性质成立．     

随机环境中的分枝游动

本文研究了一类随机环境中的分枝游动模型,应用大偏差的有关结果证明了该模型大范围内平均质点密度是以指数速度增长的,且明确地给出了其增长指数。     

On total progeny of multitype Galton-Watson process and the first passage time of random walk on lattice

In this paper,we form a method to calculate the probability generating function of the total progeny of multitype branching process.As examples,we calculate probability generating function of the total progeny of the multitype branching processes within random walk which could stay at its position and(2-1) random walk.Consequently,we could give the probability generating functions and the distributions of the first passage time of corresponding random walks.Especially,for recurrent random walk which could stay at its position with probability 0 r 1,we show that the tail probability of the first passage time decays as 2/(π(1-r)~(1/2)) n~(1/1)= when n →∞.     

随机环境中受控两性分枝过程的概率性质

本文介绍了一类配对依赖人口数的随机环境中受控两性分枝过程,研究了它的马氏性,对偶律及其概率母函数的性质.     

随机环境中分枝随机游动的极限定理

在随机环境中分枝随机游动模型中,粒子的繁衍机制是随机环境中分枝过程,各代粒子在直线上的位置由依赖随机环境的点过程给定,讨论了各代点过程的Laplace变换由其条件期望规范化后的极限性质.