Multigrid methods for Toeplitz linear systems with different size reduction

Starting from the spectral analysis of g-circulant matrices, we study the convergence of a multigrid method for circulant and Toeplitz matrices with various size reductions. We assume that the size n of the coefficient matrix is divisible by g≥2 such that at the lower level the system is reduced to one of size n/g, by employing g-circulant based projectors. We perform a rigorous two-grid convergence analysis in the circulant case and we extend experimentally the results to the Toeplitz setting, by employing structure preserving projectors. The optimality of the two-grid method and of the multigrid method is proved, when the number θ∈ℕ of recursive calls is such that 1<θ<g. The previous analysis is used also to overcome some pathological cases, in which the generating function has zeros located at “mirror points” and the standard two-grid method with g=2 is not optimal. The numerical experiments show the correctness and applicability of the proposed ideas, both for circulant and Toeplitz matrices.     

Interval methods as a simulation tool for the dynamics of biological wastewater treatment processes with parameter uncertainties

This paper presents sophisticated interval algorithms for the simulation of discrete-time dynamical systems with bounded uncertainties of both initial conditions and system parameters. Since naive implementations of interval algorithms might lead to guaranteed enclosures of all system states which are too conservative to be practically useful, we present algorithmic extensions of classical approaches which are applicable to the simulation of non-cooperative systems with time-varying uncertain parameters. Overestimation arising in the interval evaluation of dynamical system models due to the wrapping effect is reduced by an exact pseudo-linear transformation of nonlinear state equations and by new heuristics for the subdivision of interval enclosures which especially prefer splitting of unstable intervals. To highlight the typical procedure for parameterization of interval-based simulation routines and to demonstrate their efficiency, a nonlinear model of biological wastewater treatment processes is discussed. For this application, we consider the maximum specific growth rate of substrate consuming bacteria as a time-varying uncertain parameter. Only worst-case bounds are assumed to be available for the range of this parameter while no information is provided about its actual variation rate.     

M?ssbauer spectroscopic study of iron�Cnickel nitrides thin films prepared by ion beam assisted deposition

An overview is given of the present status of parity violation tests in neutron decay and nuclear beta decay. Prospects for improved and new measurements are discussed as well.     

Evaluation of methoxy polyethylene glycol‐polylactide diblock copolymers as additive in hypromellose film coating

This paper deals with a new application of diblock methoxy polyethylene glycol‐polylactide block copolymers, a class of synthetic biomaterials largely studied in the pharmaceutical and biomedical fields owing to their favorable properties such as biocompatibility, biodegradability, low immunogenicity, and good mechanical properties. In this work, these materials were evaluated as additives for gastro‐soluble pharmaceutical coating aimed to reduce film stiffness and water permeability. Two copolymers with different polylactide chain lengths were synthesized and characterized in term of molecular weight and solid‐state properties. A series of free films with different hypromellose/copolymers ratio were prepared and characterized in terms of appearance, components miscibility, plasticity, and water vapor permeability. The obtained results demonstrate that copolymers effectively influence hypromellose film properties according to their concentration and molecular weight. Specifically, the addition of the copolymer with a molecular weight of 6.5 kDa in a ratio hypromellose:polymer 5:1, allowed to obtain films with good appearance, improved plasticization, and water permeability properties. For higher molecular weight, copolymer or different ratios was not possible to observe the improvement of all the properties at the same time. The results also make possible to define the critical features to improve in order to use block copolymers as additive in hypromellose film coating. The availability of new water‐soluble additives able to work as plasticizer and moisture sealer in polymeric films represents an important progress not only in the field of pharmaceutical coating but also in that of food coatings, as for example in the formulation of edible films. Copyright © 2013 John Wiley & Sons, Ltd.     

Determination of the Chemical Structure of Poly-β (-)-pinene by NMR Spectroscopy

This paper is dedicated to the memory of our friend and colleague Annalaura Segre.

The chemical structure of a series of β (-)-pinene polymers (PBP) obtained by radiation-induced polymerization, free radical initiation, cationic polymerization over a Friedel-Craft catalyst and by coordinative polymerization over a Ziegler-Natta catalyst has been fully elucidated by ¹H and ¹³C-NMR spectroscopy. 2D NMR techniques have been applied in order to assign all the NMR resonances to the structures of the PBP investigated. The NMR spectra show that the most regular PBP structure is obtained by radiation-induced polymerization followed by the free radical initiated polymerization. The most defective structure has been observed in the case of PBP prepared by cationic mechanism over a Friedel-Crafts catalyst. The discussion accounts for different types of defects and cross-links present in the PBPs investigated whose fundamental structure is based on the p-menthene repeating unit.

NMR self-diffusion measurements have been performed to evaluate the molecular weight of all the PBP investigated. The highest molecular weight (2600 Dalton) was found in the case of PBP prepared by Ziegler-Natta catalyst, while the lowest molecular weight was found in the case of PBP prepared by radiation-induced polymerization (about 1000 Dalton).     

Structures and properties of solvated and unsolvated isopropyl functionalised calix[4]arenes

The tetra-isopropyl ethers of calix[4]arene and p-t-butylcalix[4]arene have been isolated in the cone conformation, and structurally characterised as chloroform solvates. Thermogravimetric analysis demonstrated that the parent isopropylcalix[4]arene solvate is significantly more stable than the p-t-butylcalix[4]arene analogue, retaining the solvent up to a temperature of 125°C. It was found that the calix[4]arene ether sublimes at atmospheric pressure, and solvent-free crystals appropriate for structure determination were produced at reduced pressure. The p-t-butylcalix[4]arene ether was also isolated without solvent in the lattice, but in this case the calixarene was crystallised from acetone, as sublimation did not produce crystals of sufficient quality.