A construction of a robust family of exponential attractors

Given a dissipative strongly continuous semigroup depending on some parameters, we construct a family of exponential attractors which is robust, in the sense of the symmetric Hausdorff distance, with respect to (even singular) perturbations.

     

α-(3,7-Dioxa-r-1-azabicyclo[3.3.0]oct-c-5-ylmethoxy)-diazines. Part 1: Synthesis and stereochemistry. Extension to s-triazine series

The general and efficient synthesis of the title compounds, consisting of the (selective) replacement of chlorine in commercial α-chlorodiazines and cyanuryl chloride by the 3,7-dioxa-r-1-azabicyclo[3.3.0]oct-c-5-ylmethoxy group (Williamson method) is described. The stereochemistry of this new series of derivatives is analysed in terms of different conformational chirality exhibited in solution (¹H NMR) versus solid state (X-ray diffractometry), meso against chiral forms, respectively. In solid state, the inclusion capacity of some chiral networks as well as their supramolecular aggregation is pointed out. A good correlation between rotameric behaviour of the c-5-di(s-tri)diazinyloxymethyl group in the two states is found.     

Efficient one pot preparation of variously substituted thieno [2,3‐b] thiophene

An efficient one pot access to variously substituted thieno[2,3‐b]thiophene is described. The title compounds were obtained from 1,3‐dicarbonyl or equivalent compounds, carbon disulfide and halomethyl derivatives in good to high yields and fully characterized.     

Cycloaddition reactions of carbohydrate derivatives. Part V. A hetero Diels-Alder approach to swainsonine analogs

Diastereoselective hetero Diels-Alder reactions of sugar derived azomethines 4a–4g have been used for the construction of chiral piperidones 6 and 7. Configuration of the major products was 6,1′-threo in every case. The enone system of 6 and 7 was reduced diastereoselectively and subsequently swainsonine-analog hydroxyindolizidines 28–32 were prepared by an intramolecular reductive amination.     

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.