Birkhoff系统约化的Routh方法

研究Birkhoff系统的约化.首先,列出系统的运动微分方程及其循环积分;其次,构造Birkhoff系统的Routh函数组,利用循环积分约化Birkhoff系统的运动微分方程,并使约化后的动力学方程仍保持Birkhoff方程的形式;最后,举例说明结果的应用. 关键词： Birkhoff系统 约化 循环积分     

Mathematical Modeling of Nylon 6/6,6 Copolymerization in Batch Reactor: Investigating Recipes without Water and with Cyclic Dimer

A model is used to simulate batch copolymerization of caprolactam with hexamethylene diamine (HMD) and adipic acid (ADA) to produce nylon 6/6,6. Four different recipes are considered: a recipe containing caprolactam and an aqueous solution of HMD and ADA, a recipe containing caprolactam and dry HMD/ADA salt, and two recipes with a portion of the caprolactam replaced by nylon 6 cyclic dimer (CD). Consuming CD would be advantageous because CD is an undesirable side product from nylon 6 production. Simulation results lead to three important findings: (i) operation using dry salt rather than aqueous salt solution leads to higher degree of polymerization, (ii) substantial quantities of CD can be consumed to produce nylon 6/6,6 copolymer, and (iii) including water in the recipe is beneficial for achieving improved consumption of CD. The results of this study will be helpful in designing experiments aimed at improving industrial nylon 6/6,6 copolymerization processes.     

Synthesis and Electronic Properties of Novel 5,7-Diazapentacene Derivatives

A route to the synthesis of novel 5,7-diazapentacenes and some preliminary studies on their properties is reported. A single crystal X-ray diffraction study of the dihexyl derivative showed it had formed a dimer during the analysis. The materials possess lower lying frontier orbitals than pentacene and may have potential applications in organic electronic devices. This synthetic method may be applicable to the synthesis of other azaacenes.     

Assessment of the in vitro toxicity of calixarenes and a metal-seamed calixarene: a chemical pathway for clinical application

Calixarenes are known to form host–guest complexes and supramolecular nanoassemblies with well-defined architectures. However, the use of these materials in conjunction with drug moieties is still under explored. One reason is the insufficient biocompatibility studies. Our present study represents a systematic in vitro investigation of the cytotoxicity associated with C-methylresorcin[4]arene, C-methylpyrogallol[4]arene, p-phosphonated calix[8]arene and a metal-seamed calixarene–copper(II) complex, using human HEK293 and rat C6G cell lines and two different cell viability assays (MTT and CellTiter-Glo) to avoid species-biased results. All compounds showed low to moderate toxicity. The trend in the CC₅₀ values indicated that the suppression of the coordination ability and the presence of phosphonate groups decrease the overall cytotoxicity of the compounds. The results of this study not only establish calixarenes and their immediate families as potential drug carriers and drug modifiers, but also reveal a pathway for fine-tuning their toxicological behaviour by appropriate chemical modification.     

Parallel Versus Antiparallel β-Sheet Structure in Cyclic Peptide Hybrids Containing γ- or δ-Cyclic Amino Acids

Cyclic peptides with disc-shaped structures have emerged as potent building blocks for the preparation of new biomaterials in fields ranging from biological to material science. In this work, we analyze in depth the self-assembling properties of a new type of cyclic peptides based on the alternation of α-residues and cyclic δ-amino acids (α,δ-CPs). To examine the preferred stacking properties adopted by cyclic peptides bearing this type of amino acids, we carried out a synergistic in vitro/in silico approximation by using simple dimeric models and then extended to nanotubes. Although these new cyclic peptides (α,δ-CPs) can interact either in a parallel or antiparallel fashion, our results confirm that although the parallel β-sheet is more stable, it can be switched to the antiparallel stacking by choosing residues that can establish favorable cross-strand interactions. Moreover, the subsequent comparison by using the same methodology but applied to α,γ-CPs models, up to the moment assumed as antiparallel-like d,l -α-CPs, led to unforeseen conclusions that put into question preliminary conjectures about these systems. Surprisingly, they tend to adopt a parallel β-sheet directed by the skeleton interactions. These results imply a change of paradigm with respect to cyclic peptide designs that should be considered for dimers and nanotubes.     

Cycloaddition Reactions of an Active Cyclic Phosphane/Borane Pair with Alkenes,Alkynes, and Carbon Dioxide

The active six-membered cyclo-FLP 6 undergoes a rapid P/B addition reaction to carbon dioxide. At elevated temperature, the resulting heterobicyclo[2.2.2]octane derived product 7 undergoes ring opening and equilibrates with the cyclotetramer (7)₄ . In the large macrocyclic structure, four monomeric six-membered cyclo-FLP units are connected by four CO₂ molecules to form the supramolecular ring system. The P/B cyclo-FLP 6 undergoes a variety of additional cycloaddition reactions.     

一类混杂动态系统的能控性（I）——基本结果

首次将时滞现象引入到线性切换系统的模型中，研究含有时滞线性切换系统的能控性及其判定条件．全部工作由三部分组成，第I部分首先，提出含时滞的线性切换系统的数学模型，并介绍切换系统的基本概念——切换序列．其次，引入列空间、循环不变子空间和广义循环不变子空间等基本几何概念，给出一些有关概念的基本性质，特别是分离引理．然后以一个基本引理的形式揭式某一积分方程的解集与广义循环不变子空间之间的联系，这个引理将在能控性的判定中起关键作用．这些概念和引理都将作为以后展开能控性分析所必需的研究工具．     

非水体系中哌啶在银电极表面的表面增强喇曼散射

本文测定了哌啶在甲醇溶液中吸附在银电极表面的表面增强喇曼散射(SERS)光谱,及其随电位的变化,同时还测定了电极经不同氧化-还原循环(ORC)预处理时的SERS谱,对所得结果进行了分析比较,并进一步研究了非水体系和水体系SERS谱之间的关系.实验结果表明:哌啶在甲醇体系中比在水体系中SERS谱的增强因子要小,并且它们的SERS谱线随电位的变化也有一定的差别.     

一类无限群中局部幂零性的判定准则

设G是任意群,群G的Frattini子群nat(G)定义为G的所有极大子群的交.类似地,群G的另外两个特征子群nFrat(G)及R(G)分别定义为群G的所有极大正规子群及群G的所有正规的极大子群的交.本文通过对nat(G),nnat(G)及R(G)的相互包含关系的研究,得到CF-群或中心由多重循环群的扩张群中局部幂零性的一个判定准则.同时也讨论了在某些群类中若干种广义幂零性的等价性.