Finite Convergence of the Partial Inverse Algorithm

In Refs. 1–2, Lefebvre and Michelot proved the finite convergence of the partial inverse algorithm applied to a polyhedral convex function by means of some suitable tools of convex analysis. They obtained their result under some assumptions on the primal and dual solution sets. The aim of this note is to show that the proof can be extended to remove the nasty assumption on the dual solution set. The result is in conformity with the proof given in Ref. 3, which has been obtained using the concept of folding.     

New Oligomeric Proanthocyanidine from Ziziphus jujuba

Chemical and spectral data establish the structure of an oligomeric proanthocyanidine PZ-5 isolated from Ziziphus jujuba.     

A Filled‐Honeycomb‐Structured Crystal Formed by Self‐Assembly of a Janus Polyoxometalate–Silsesquioxane (POM–POSS) Co‐Cluster

Clusters with diverse structures and functions have been used to create novel cluster‐assembled materials (CAMs). Understanding their self‐assembly process is a prerequisite to optimize their structure and function. Herein, two kinds of unlike organo‐functionalized inorganic clusters are covalently linked by a short organic tether to form a dumbbell‐shaped Janus co‐cluster. In a mixed solvent of acetonitrile and water, it self‐assembles into a crystal with a honeycomb superstructure constructed by hexagonal close‐packed cylinders of the smaller cluster and an orderly arranged framework of the larger cluster. Reconstruction of these structural features via coarse‐grained molecular simulations demonstrates that the cluster crystallization and the nanoscale phase separation between the two incompatible clusters synergistically result in the unique nano‐architecture. Overall, this work opens up new opportunities for generating novel CAMs for advanced future applications.     

Finding Shortest Paths in a Sequence of Triangles in 3D by the Planar Unfolding

We present an efficient algorithm for finding the shortest path joining two points in a sequence of triangles in three-dimensional space using the concept of funnels associated with common edges along the sequence of triangles and the planar unfolding for each funnel. We show that the unfolded image of a funnel is a simple polygon, it thus is non-overlapping. Therefore, such funnels are determined iteratively to their associated common edges by the planar unfolding and the shortest path joining two points is determined by cusps of these funnels.     

活性负离子聚合法制备POSS基七臂星形聚合物及其表征

首先利用高真空活性负离子聚合方法制备聚异戊二烯锂(PI-Li)和(聚苯乙烯-b-聚异戊二烯)锂(PS-PI-Li)活性链,再与单羟基七乙烯基多面体齐聚倍半硅氧烷(VPOSS-OH)发生加成反应,一步法制备2种含羟基的七臂星形聚合物.用分级沉淀法去除低加成产物,即可得到纯的七臂星形聚合物7PI-POSS-OH和7(PS-PI)-POSS-OH,利用凝胶渗透色谱(GPC)、核磁共振波谱(1H-,13C-NMR)、红外光谱(FTIR)和基质辅助激光解吸电离飞行时间质谱(MALDI-TOF MS)表征了聚合物的化学结构、分子量及分子量分布,并通过热失重分析(TGA)测试了聚合物的热分解温度.     

Synthesis and characterization of fillers of controlled structure based on polyhedral oligomeric silsesquioxane cages and their use in reinforcing siloxane elastomers

Four polyhedral oligomeric silsesquioxane (POSS) cages with vinyl groups were linked to a central siloxane core by hydrosilylation. The goal was to obtain filler particles of sizes between those of the POSS cages themselves and the much larger silica particles typically used to reinforce elastomers. The hydrosilylation reaction was monitored with Fourier transform infrared spectroscopy and proton nuclear magnetic resonance, and the resulting structure was confirmed by mass spectrometry. Simply blending these POSS-based fillers into silanol-terminated poly(dimethylsiloxane) (PDMS) had little effect on the mechanical properties, but bonding them to PDMS provided considerable reinforcement. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3314–3323, 2003     

A primal-dual algorithm for the fermat-weber problem involving mixed gauges

We give a new algorithm for solving the Fermat-Weber location problem involving mixed gauges. This algorithm, which is derived from the partial inverse method developed by J.E. Spingarn, simultaneously generates two sequences globally converging to a primal and a dual solution respectively. In addition, the updating formulae are very simple; a stopping rule can be defined though the method is not dual feasible and the entire set of optimal locations can be obtained from the dual solution by making use of optimality conditions. When polyhedral gauges are used, we show that the algorithm terminates in a finite number of steps, provided that the set of optimal locations has nonepty interior and a counterexample to finite termination is given in a case where this property is violated. Finally, numerical results are reported and we discuss possible extensions of these results.     

层流预混气体多棱火焰燃烧现象的分析

在一定条件下,层流预混气体燃烧过程中可清晰地观察到多棱火焰现象。本文从燃料浓度、温度对燃烧速度、气流速度的影响出发,推导出了火焰面变化随空气消耗系数的关系式,并得出了形成多棱火焰现象的条件为:Kx<0。用该式判断的丁烷层流预混气体燃烧的多棱火焰区与实验结果基本吻合。     

Supramolecular inclusion complexation of polyhedral oligomeric silsesquioxane capped poly(ε‐caprolactone) with α‐cyclodextrin

Supramolecular inclusion complexes (ICs) involving polyhedral oligomeric silsesquioxane (POSS) capped poly(?‐caprolactone) (PCL) and α‐cyclodextrin (α‐CD) were investigated. POSS‐terminated PCLs with various molecular weights were prepared via the ring‐opening polymerization of ?‐caprolactone (CL) with 3‐hydroxypropylheptaphenyl POSS as an initiator. Because of the presence of the bulky silsesquioxane terminal group, the inclusion complexation between α‐CD and the POSS‐capped PCL was carried out only with a single end of a PCL chain threading inside the cavity of α‐CD, which allowed the evaluation of the effect of the POSS terminal groups on the efficiency of the inclusion complexation. The X‐ray diffraction results indicated that the organic–inorganic ICs had a channel‐type crystalline structure. The stoichiometry of the organic–inorganic ICs was quite dependent on the molecular weights of the POSS‐capped PCLs. With moderate molecular weights of the POSS‐capped PCLs (e.g., M_n =3860 or 9880), the stoichiometry was 1:1 mol/mol (CL unit/α‐CD), which was close to the literature value based on the inclusion complexation of α‐CD with normal linear PCL chains with comparable molecular weights. When the PCL chains were shorter (e.g., for the POSS‐capped PCL of M_n = 1720 or 2490), the efficiency of the inclusion complexation decreased. The decreased efficiency of the inclusion complexation could be attributed to the lower mobility of the bulky POSS group, which restricted the motion of the PCL chain attached to the silsesquioxane cage. This effect was pronounced with the decreasing length of the PCL chains. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1247–1259, 2007     

Polymeric nanocomposites containing polyhedral oligomeric silsesquioxanes prepared via frontal polymerization

Frontal polymerization (FP) has been successfully applied, for the first time, to obtain polymeric nanocomposites containing polyhedral oligomeric silsesquioxanes (POSS) in an amine‐cured epoxy matrix. Variations of maximum temperature (T_max) and front velocity (V_f) have been studied. A comparison of these products with the corresponding materials, obtained by the classical batch polymerization technique, demonstrated that FP allows a higher degree of conversion than batch polymerization. The products have been characterized in terms of their thermal behavior with DSC analysis. SEM and X‐ray analyses revealed the morphology and the structures of the nanocomposites. The nanocomposites obtained by FP have the same characteristics of those synthesized, in much longer times, by batch polymerization. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4514–4521, 2007