Bernoullian,Terminal, Penultimate or Third Order Markov Statistics?

Summary: A series of 7 homogeneous ethylene‐propylene copolymers is modeled by a Bernoullian, a terminal, a penultimate and a third order Markov model and it is found that the penultimate model describes this series best. The Bernoullian and terminal model prove to be insufficient and the third order Markov model is statistically not justified. Based on these results, a criterion to select the optimal Markovian order of homogeneous, single site catalyst produced copolymers is developed.

Schematic of the [(3‐MePh)(4‐MePh)C(2,7‐di‐tert‐BuFlu)(Cp)]ZrCl₂ metallocene copolymerizing ethene and propene.     

A Computational Study on Bounding the Makespan Distribution in Stochastic Project Networks

Due to the practical importance of stochastic project networks (PERT-networks), many methods have been developed over the past decades in order to obtain information about the random project completion time. Of particular interest are methods that provide (lower and upper) bounds for its distribution, since these aim at balancing efficiency of calculation with accuracy of the obtained information.We provide a thorough computational evaluation of the most promising of these bounding algorithms with the aim to test their suitability for practical applications both in terms of efficiency and quality. To this end, we have implemented these algorithms and compare their behavior on a basis of nearly 2000 instances with up to 1200 activities of different test-sets. These implementations are based on a suitable numerical representation of distributions which is the basis for excellent computational results. Particularly a distribution-free heuristic based on the Central Limit Theorem provides an excellent tool to evaluate stochastic project networks.     

Functional,hyperbranched polyesters via baylis–hillman polymerization

Hyperbranched polyesters are among the most common hyperbranched polymers. One of the interesting features of hyperbranched polyesters is that they contain unreacted hydroxyl and carboxylic acid groups at the linear and terminal structural units, which can be postmodified to adjust thermal, solubility, or mechanical properties, or to prepare core–shell type architectures. This article reports on the synthesis of a novel class of hyperbranched polyesters via an A₂ + B₃ type Baylis–Hillman polymerization of 2,6‐pyridinedicarboxaldehyde and trimethylolpropane triacrylate. Baylis–Hillman polymerization generates highly functional polyesters that contain not only unreacted aldehyde and/or acrylate groups at the linear and terminal structural units but also chemically orthogonal vinyl and hydroxyl groups along the polymer backbone. Using 3‐hydroxyquinuclidine as the catalyst, hyperbranched polymers with number‐average molecular weights up to 7500 g/mol and degrees of branching up to 0.81 were obtained. To demonstrate the versatility of these hyperbranched polyesters to act as platforms for further derivatization, the orthogonal postpolymerization modification of the hydroxyl, vinyl, and pyridine functional moieties with phenyl isocyanate, methyl‐3‐mercaptopropionate, and methyl iodide is presented. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012.