捕食者-被捕者中含有化学计量学的离散型模型

大部分捕食者-被捕者模型是连续的,但是生物的发展未必是连续的,而且环境变化对生物的作用普遍存在时滞性.根据连续系统考虑的捕食者和被捕者的相互作用、Beverton-Holt差分方程以及化学计量学因素对系统的影响,建立了离散的捕食者-被捕者模型.分析表明:新建立的模型,基本上保留了连续系统的基本特征,揭示了能量富足的矛盾.进一步通过对全局的吸引集的构造,对模型的动力学行为有深刻的认识,还指出了生物灭绝和濒临灭绝的差别,这表明新模型比连续系统和直接利用连续解的离散方法得到的离散模型包含更多的生物意义.     

奇异摄动中的鸭解问题

鸭解问题是近年来在奇异摄动方程的研究中发现并开始研究的 ,是一种新的分支现象 .用渐近分析方法、微分方程定性理论及不动点方法对一类二维单参数奇异摄动系统进行了研究 ,给出了鸭解和鸭极限环存在的条件及对应的参数估计 .     

用RAYLEIGH-RITZ法确定细长压杆屈曲后挠度方程

本文用RAYLEIGH-RITZ法解出两种边界条件下细长压杆屈曲后挠度方程,并对一端固定、一端铰支的临界力公式中长度折算系数做了改进。     

Branching generation during the free radical copolymerization of p-vinyl benzene sulfonyl chloride with styrene

The branching generation during the free radical copolymerization of chain transfer monomer p-vinyl benzene sulfonyl chloride (VBSC) with styrene was investigated by a simple mathematic model. Chain transfer constant of VBSC was determined to be around 0.3 by fitting the ¹H-NMR monitored experimental results with a mathematic model. According to the theoretical analysis, the obtained poly(VBSC) and its copolymers were substantiated to have a grafting-like main chain with residual pendent sulfonyl chloride groups after consuming most of the vinyl groups. The copolymerization results of VBSC with styrene at varied feed ratios demonstrated that conversion of sulfonyl chloride groups was lower than that of the monomer, which was in agreement with the theoretical results. The glass transition temperature, number average molecular weight and distribution of those obtained polymers were primarily investigated. Comparing with other chain transfer monomers, VBSC has a chain transfer constant much closer to unity therefore a more branched polymer is expected. Additionally, the branched polystyrene with residual sulfonyl chloride groups is hopefully to be further used as ATRP macroinitiators or reactive intermediates to synthesize functional polymers with complex structure.     

一类单中心二次可积系统的Abel积分零点个数

讨论了首次积分为H(x,y)=x~k(1/2y~2+Ax~2+Bx+C)的Abel积分的代数构造,并研究了k=2时具有一个中心的平面二次可积系统在n次扰动下的Abel积分零点个数上界问题,得到了较小的上界估计,     

有机磺酰氯在自由基聚合中的应用进展

有机磺酰氯存在下的自由基聚合(Radical polymerization,RP)具有反应条件温和、体系组成简单、单体适用范围较广的优点。本文主要概述了有机磺酰氯在自由基聚合中的应用,主要包括原子转移自由基聚合(Atom transfer radical polymerization,ATRP)的引发剂、单电子转移活性自由基聚合(Single-electron transfer living radical polymerization,SET-LRP)的引发剂和普通自由基聚合的链转移剂。并分析了以上三种应用单体的适用范围、有机磺酰氯结构与聚合活性的关系以及有机磺酰氯(多官能团有机磺酰氯引发剂和链转移单体)在聚合物分子设计中的应用。     

测定薄板疲劳裂纹扩展门槛值的升降法

测定疲劳裂纹扩展门槛值传统方法的整个过程只测出裂纹扩展门槛值的一个观测值,而由于材料不均匀等客观因素的限制,传统试验法的结果具有一定的随机性.本文利用升降法的原理,提出一种测定疲劳裂纹扩展门槛值的升降法:预制裂纹并逐级降载使裂纹扩展速率接近门槛值速率,设定应力强度因子的级差,按照设定级差逐级降载,直至裂纹扩展速率低于门槛值速率,然后开始升载,直至裂纹扩展速率高于门槛值速率,再开始降载,如此重复进行即可以在疲劳裂纹扩展门槛值附近测得多对相反的数据点.运用小子样升降法数据处理方法,就可得到疲劳裂纹扩展门槛值的均值和方差.最后通过某型铝合金薄板疲劳裂纹扩展门槛值的测定试验验证了此方法的可行性.     

一类哈密顿系统周期函数的单调性

哈密顿函数H(x,y)=F(x)+G(y)所对应的哈密顿系统.给出了这类系统的周期解的周期为单调函数的几个充分条件,并用所得结果讨论了Volterral-Lotka系统和无阻尼、无强迫Duffing方程周期解周期的单调性.