聚合物中长程关联能的动力学研究

本文计算采用扩展的SSH哈密顿模型, 加上长程关联哈密顿量,在自然边界条件下,用绝热动力学方法研究了有限长反式聚乙炔链中平均关联能随时间的演化,计算了长程电子关联对极化子动力学的影响并计算了极化子状态下的长程关联能。结果发现,加入一个电子或空穴,平均关联能的大小随着时间呈非周期性阻尼振荡,经过一定时间后,平均关联能趋近一个恒定值,此时得到比较稳定的极化子位形。当格点增加时,长程关联能趋于恒定的时间逐渐缩短。     

解析计算SM中电子混合链图传播下Compton 散射微分截面

采用电弱统一标准模型(SM), 对由参与电弱相互作用的各种混合圈构成的电子重整化链图传播子的构架方式作了详细分析, 并完成了有关解析计算, 进而获得了电子重整化链图传播子的解析计算结果. 作者又将此结果应用到Compton散射, 精确计算了电子混合链图传播下Compton散射微分截面的解析结果 . 此外, 作者还将计算结果与最低阶微分截面 和量子电动力学(QED)中电子链图传播下的Compton散射微分截面 做了具体的数值计算与对比分析, 发现 比 能更加精细的反应辐射修正效应.     

成批到达排队系统的随机比较

本文研究成批到达排队系统中队长过程的随机比较问题．利用随机比较方法我们对成批到达指数服务的多服务台排队系统进行分析,得到了该排队系统中队长过程的随机比较以及队长函数关于时间的凹性和凸性．同时我们也给出了成批到达一般服务的单服务台排队系统队长过程、稳态队长的随机比较以及队长函数关于时间的凹性和凸性．     

Analysis of a time-dependent scheduling problem by signatures of deterioration rate sequences

In the paper a single machine time-dependent scheduling problem is considered. The processing time p_j of each job is described by a function of the starting time t of the job, p_j=1+α_jt, where the job deterioration rate α_j?0 for j=0,1,…,n and t?0. Jobs are nonpreemptable and independent, there are no ready times and no deadlines. The criterion of optimality of a schedule is the total completion time.First, the notion of a signature for a given sequence of job deterioration rates is introduced, two types of the signature are defined and their properties are shown. Next, on the basis of these properties a greedy polynomial-time approximation algorithm for the problem is formulated. This algorithm, starting from an initial sequence, iteratively constructs a new sequence concatenating the previous sequence with new elements, according to the sign of one of the signatures of this sequence.Finally, these results are applied to the problem with job deterioration rates which are consecutive natural numbers, α_j=j for j=0,1,…,n. Arguments supporting the conjecture that in this case the greedy algorithm is optimal are presented.     

非均匀Chemostat中非单食物链模型稳态正解的存在性

研究一类由反应扩散方程组描述的非均匀Chemostat中微生物之间既表现竞争关系又表现捕食被捕食关系的模型．用特征值理论确定了系统正稳态解存在的必要条件，用锥映射不动点指数方法给出了系统正稳态解存在的充分条件．     

树映射的链等价集与拓扑熵

本文讨论了树映射f的链等价集的性质,得到了f具有零拓扑熵的几个等价条件,并证明了:如果 f的一个链等价集是个无限集,那么这个链等价集的任何孤立点都是f的非周期的终于周期点.     

Quasi-compactness and absolutely continuous kernels

We show how the essential spectral radius r _e (Q) of a bounded positive kernel Q, acting on bounded functions, is linked to the lower approximation of Q by certain absolutely continuous kernels. The standart Doeblin’s condition can be interpreted in this context, and, when suitably reformulated, it leads to a formula for r _e (Q). This results may be used to characterize the Markov kernels having a quasi-compact action on a space of measurable functions bounded with respect to some test function, when no irreducibilty and aperiodicity are assumed.      

Selectively reductive cleavage of the protected taxol side chain with sodium borohydride

During the course of our studies on the taxol chemistry,we have ever tried thereductive cleavage of the acotyl group at 20-C in compound 1a~(1,2) with the hydroxylgroup assistance at 4-C by sodium borohydride. However, the major product 2a~2(27%)still had the acetyl group at 20-C and the signal for the 10-C proton at 6.61 ppm(s)was shifted to 6.31 ppm(d, J=3.79 Hz). A new doublet signal at 3.62 ppm(d, J=3.80     

连续时间遗传算法模型及其强收敛性分析

本文在隐马尔可夫链的框架下利用隐马尔可夫链{Xt:t∈[0,∞)}的观测链的概率分布提出一个连续化遗传算法模型，并给出其一个强收敛结果，讨论了其离散骨架的性质。     

具有苯烷基侧链的芳香液晶聚酯的合成及性质

以熔融缩聚方法全盛了具有苯烷基侧链取代的全芳香液晶聚酯，用TG，DSC，热台偏光显微镜研究了聚酯的热性能，并讨论了取代基对聚酯热性能的影响，所有合成的聚酯均为热致型液晶，且具有较低的相转变温度。特别是当聚对苯二甲酸对苯二酚酯的两个苯环上分别取代了叔丁基和苯烷基，或取代了两个苯烷基侧链后，聚酯的熔融温度下降到225℃以下，并可在室温下溶于普通的有机溶剂中。