聚{N-[2-(4′-硫代乙酸苄酯基)丙酰基]-对氨基苯乙炔}的合成和热稳定性及有序纳米结构的形成

采用两性离子型的催化剂Rh+[η-C6H5(nbd)B-(C6H5)3]实现了含手征性中心和硫代乙酸酯基的苯乙炔单体的聚合,用红外光谱、核磁共振氢谱和紫外-可见吸收光谱表征了聚合物的结构,证实得到了预期产物.聚合物的重均分子量达到了73200,在氯仿、四氢呋喃、二氯甲烷等有机溶剂中有良好的溶解性能.聚合物热稳定性高,在氮气氛围下热分解温度为336℃,在900℃的高温下有31%的重量残留.用扫描电子显微镜观察发现,在浓度为5.0mg/mL的聚合物氯仿溶液形成的薄膜中有微米长度的棒状有序结构;由浓度为0.5mg/mL的聚合物氯仿稀溶液形成的薄膜表面有晶体析出.用透射电子显微镜观察聚合物在氯仿溶液中缓慢形成的微结构,发现当浓度高于1.0mg/mL时,聚合物在碳膜上形成铺展的薄膜,薄膜由纳米尺寸的丝带状结构取向排列而成;当浓度低于0.5mg/mL时,聚合物形成具有规则几何形态的微晶体.在聚合物热稳定性的显著提高和有序微结构的形成过程中,聚苯乙炔侧链中的手征性中心发挥了关键的作用.     

有序介孔C-Al2O3纳米复合材料的合成及其红外发射率

以嵌段共聚物F127(PEO106PPO70PEO106, MW=12600)为模板剂, 异丙醇铝为铝源, 低分子量的酚醛树脂为碳源, 通过溶胶-凝胶三元共组装法合成了C-Al2O3纳米复合材料. 用X射线衍射(XRD)、透射电子显微镜(TEM)及N2吸脱附法对该复合材料进行结构与性能表征, 结果显示复合材料MC5A5具有较好的有序介孔结构, 其比表面积可达175 m2·g-1, 孔容0.22 cm3·g-1. 又以三元乙丙橡胶(EPDM)为粘结剂, 与介孔纳米复合材料混合制备涂层. 随着复合材料中Al2O3质量分数从30%增加到70%, 该涂层的红外发射率从0.575降至0.456, 表明Al2O3能有效降低复合材料的红外发射率, 预示该复合材料在军事装备隐身需求领域将具有较好的应用前景.     

A note on cones associated to Schauder bases

We study the existence of infima of subsets in Banach spaces ordered by normal cones associated to shrinking Schauder bases. Under these conditions we prove the existence of infima for a class of subsets verifying a weakly compactness property. Moreover we prove that a normal cone associated to a Schauder basis in a reflexive Banach space is strongly minihedral extending the known result for unconditional Schauder bases. Several examples are also discussed. Miguel Sama: The work of this author is partially supported by Ministerio de Educación y Ciencia (Spain), project MTM2006-02629 and Ingenio Mathematica (i-MATH) CSD2006-00032 (ConsoliderIngenio 2010).     

An Asymptotic Independence Theorem for the Number of Matchings in Graphs

Let z(G) be the number of matchings (independent edge subsets) of a graph G. For a set M of edges and/or vertices, the ratio represents the probability that a randomly picked matching of G does not contain an edge or cover a vertex that is an element of M. We provide estimates for the quotient , depending on the sizes of the disjoint sets A and B, their distance and the maximum degree of the underlying graph G. It turns out that this ratio approaches 1 as the distance of A and B tends to ∞, provided that the size of A and B and the maximum degree are bounded, showing asymptotic independence. We also provide an application of this theorem to an asymptotic enumeration problem related to the dimer-monomer model from statistical physics. This material is based upon work supported by the German Research Foundation DFG under grant number 445 SUA-113/25/0-1 and the South African National Research Foundation under grant number 65972.     

三种不同需求分布条件下报童问题期望费用的计算

报童问题是运筹学中典型的随机性存贮模型.目前很多运筹学和管理科学教科书一般只给出报童问题最优订购量应该满足的条件,而没有给出具体的期望费用的表达式,这对于报童问题模型在实际中的应用造成不便.研究了三种不同需求分布条件下报童问题期望费用计算问题,所得出的关于期望费用计算公式具有简洁和便于实际应用的特点.     

L_n×L_2上几类特殊类型格蕴涵代数方程的解法

在格蕴涵代数中提出了加既约元、乘既约元,研究了一类重要的格蕴涵代数L_n×L_2中元素的不可约有限分解, 并将这一理论用于研究L_n×L_2上的几类格蕴涵代数方程,讨论了方程有解的充分必要条件,在此基础上给出了方程的具体解集.     

基于映射理论下的决策评判模型

按照映射理论,通过建立评价指标标准值与评价指标标准值顺序数之间的函数,将非等长度区间映射成长度为1的等长区间,提出了一种求解决策评判的新模型,解决了不同标度下的评价因子、评价类别的决策评判问题,纠正了可拓理论关联函数基本公式的错误,简化了可变模糊集模型中的M矩阵和B矩阵,进而统一了可拓评价和可变模糊集理论在决策评判中的一致性,并实例验证了模型的优越性和正确性,对决策评判问题具有重要的应用拓广参考价值.     

完全分配格上的覆盖粗糙集模型

将集合论中的覆盖概念抽象到完全分配格L上,利用它定义格L上关于覆盖的上(下)近似算子,给出格L上覆盖粗糙集模型.文中先讨论格L上覆盖的相关性质,进而研究了覆盖上(下)近似算子的性质,得到若干结果.     

The Ordered Gradual Covering Location Problem on a Network

In this paper we develop a network location model that combines the characteristics of ordered median and gradual cover models resulting in the Ordered Gradual Covering Location Problem (OGCLP). The Gradual Cover Location Problem (GCLP) was specifically designed to extend the basic cover objective to capture sensitivity with respect to absolute travel distance. The Ordered Median Location problem is a generalization of most of the classical locations problems like p-median or p-center problems. The OGCLP model provides a unifying structure for the standard location models and allows us to develop objectives sensitive to both relative and absolute customer-to-facility distances. We derive Finite Dominating Sets (FDS) for the one facility case of the OGCLP. Moreover, we present efficient algorithms for determining the FDS and also discuss the conditional case where a certain number of facilities is already assumed to exist and one new facility is to be added. For the multi-facility case we are able to identify a finite set of potential facility locations a priori, which essentially converts the network location model into its discrete counterpart. For the multi-facility discrete OGCLP we discuss several Integer Programming formulations and give computational results.     

Euler-Mahonian statistics on ordered set partitions (II)

[E. Steingrímsson, Statistics on ordered partitions of sets, arXiv: math.CO/0605670] introduced several hard statistics on ordered set partitions and conjectured that their generating functions are related to the q-Stirling numbers of the second kind. In a previous paper, half of these conjectures have been proved by Ishikawa, Kasraoui and Zeng using the transfer-matrix method. In this paper, we shall give bijective proofs of all the conjectures of Steingrímsson. Our basic idea is to encode ordered set partitions by a kind of path diagrams and explore the rich combinatorial properties of the latter structure. As a bonus of our approach, we derive two new σ-partition interpretations of the p,q-Stirling numbers of the second kind introduced by Wachs and White. We also discuss the connections with MacMahon's theorem on the equidistribution of the inversion number and major index on words and give a partition version of his result.