Measuring randomness with periodic media

We show that the sensitivity to disorder of certain physical properties of periodic media depends on whether the disorder is truly random or not. This allows to utilize periodic media for testing sequences of random numbers and to quantify their departure from true randomness via simple transmission and/or reflection data analysis. This physics-based model shows promises for device applications to test random data.     

On a generalization of the Gallai-Roy-Vitaver theorem to the bandwidth coloring problem

We generalize to the bandwidth coloring problem a classical theorem, discovered independently by Gallai, Roy and Vitaver, in the context of the graph coloring problem. Two proofs are given, a simple one and a more complex one that is based on a series of equivalent mathematical programming models.     

Biomimetic carbocationic polymerizations III: Investigation of isoprene polymerization initiated by dimethyl allyl bromide

Natural rubber (poly(1,4‐cis‐isoprene), NR) is a polymer of considerable industrial importance due to its exceptional properties. It is mostly produced from the cultivation of Hevea brasiliensis, and to a limited extent from Parthenium argentatum. Till date none of the synthetic equivalent of NR exists. Recently we suggested that the mechanism of NR biosynthesis is based on carbocationic polymerization, similarly to that of natural oligoisoprenoids forming by enzyme‐catalyzed prenylation. In this article we present proof of concept of a new bio‐inspired synthetic route towards the synthesis of polyisoprenes based on carbocationic polymerization initiated by dimethyl allyl bromide (DMABr)/TiCl₄. It is shown that using this strategy, 1,4‐oligoisoprene carrying a dimethyl allyl head group is produced in both cis and trans configurations, together with cyclized sequences. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 2172–2180, 2009     

The Single Crystal Structures of the Copper Usovites Ba2CaCuV2F14 and Ba2CaCuCr2F14

The results of single crystal X‐ray structure determinations are reported for Ba₂CaCuV₂F₁₄ (a = 1383.6(3), b = 540.89(8), c = 1493.1(3) pm, β = 91.65(3)°) and Ba₂CaCuCr₂F₁₄ (a = 1381.1(5), b = 535.5(1), c = 1481.4(6) pm, β = 91,50(4)°), both isotypic with usovite (space group C2/c, Z = 4). The resulting average distances are V‐F: 193.8 pm, Cr‐F: 190.7 pm, and Cu‐F: 209.2 resp. 207.1 pm for the Jahn‐Teller elongated [CuF₆] octahedra. Within the cross‐linked double chains of octahedra F‐bridged trimers M‐Cu‐M, magnetically studied earlier, are confirmed and discussed.     

On the Identifiability of Minimal VARMA Representations

By studying the geometry of relevant Hilbert spaces, we give a characterization of the identifiable standard representations of multivariate ARMA models in terms of the autocovariance function.     

SOS: A Quantile Estimation Procedure for Dynamic Lot-sizing Problems

This paper reviews some of the current approaches available for computing the demand quantiles required to plan the procurement of items with stochastic non-stationary demands. The paper first describes the stochastic single-item lot-sizing problem considered and then presents a practical solution approach based on a dynamic lot-sizing model. Three methods available to compute demand quantiles are then reviewed and a new procedure based on smoothed order statistics (SOS) is proposed. Finally, the behaviour of these estimation methods, when used to solve single-item lot-sizing problems with non-stationary stochastic demands, is studied by simulation.