On pairs of free modules over a Dedekind domain

The study of pairs of modules (over a Dedekind domain) arises from two different perspectives, as a starting step in the analysis of tuples of submodules of a given module, or also as a particular case in the analysis of Abelian structures made by two modules and a morphism between them. We discuss how these two perspectives converge to pairs of modules, and we follow the latter one to obtain an alternative approach to the classification of pairs of torsionfree objects. Then we restrict our attention to pairs of free modules. Our main results are that the theory of pairs of free Abelian groups is co-recursively enumerable, and that a few remarkable extensions of this theory are decidable. Work performed under the auspices of GNSAGA-INDAM     

A new microwave dielectric method for studying photoinitiated chain radical polymerization processes

Measurements of both real and imaginary parts of the dielectric constant at a fixed microwave frequency have been performed on n-butyl acrylate/poly(n-butyl acrylate) mixtures. The dielectric constant of the mixtures has been compared with that of neat n-butyl acrylate during UV photoinitiated polymerization. The values of the imaginary part of the dielectric constant thus obtained have allowed determination of the instantaneous monomer concentration and verified the kinetic equation for the photoinitiated polymerization process. The limits of validity of the method as well as its capability of providing detailed kinetic information are also discussed.     

A highly active fungal β-glucosidase

A highly active thermostable β-glucosidase was purified to homogeneity from a strain ofTrichoderma sp. The enzyme was an extracellular glycoprotein and showed hydrolytic activity toward several β-glucosides. Cellobiose was found to be the substrate of choice for this enzyme. This finding could suggest future technological applications of the purified protein.     

The complexity of minimum difference cover

The complexity of searching minimum difference covers, both in Z⁺ and in Z_n, is studied. We prove that these two optimization problems are NP-hard. To obtain this result, we characterize those sets—called extrema—having themselves plus zero as minimum difference cover. Such a combinatorial characterization enables us to show that testing whether sets are not extrema, both in Z⁺ and in Z_n, is NP-complete. However, for these two decision problems we exhibit pseudo-polynomial time algorithms.     

Search of theH particle in antiproton-nuclear interactions

The proposal of hunting theH-particle taking advantage of antiproton annihilation at rest on³He is discussed. The obtained K^* beam should allow one to obtain a flux ofΞ ^? with momentum low enough to optimize the fusion probability (ΞN) to give anH. The experimental apparatus to detectH-events as the only missing mass of the fully reconstructed reaction¯p ³He →KKπ ⁺ H is the OBELIX Spectrometer at LEAR. A detailed Monte Carlo simulation of the overall acceptance of OBELIX for the above reaction is performed. The obtained final rate shows the feasibility of the experiment also in a not dedicated detector like OBELIX.     

The simulation of molecular and organic devices: a critical review and look at future developments

Molecular devices have lately attracted increased attention due to some appealing features such as their low production cost, flexibility in the substrate choice, possibility of large area deployment, and possibly higher integration capabilities. Starting from a series of results obtained from our groups, we critically review the state-of-the-art in the field of simulation of organic and molecular systems, by analyzing and comparing existing approaches, and looking at the open problems and possible solutions and future developments. PACS 72.80.Le     

Ethylene polymerization by novel Ziegler–Natta‐type catalysts obtained in situ by the oxidative addition of 8‐hydroxyquinoline‐based ligands to bis(1,5‐cyclooctadiene)nickel(0) and methylaluminoxane

Novel catalytic systems, prepared in situ by the oxidative addition of 8‐hydroxyquinoline ligands to bis(1,5‐cyclooctadiene)nickel(0) and activated by methylaluminoxane, were studied in ethylene polymerization. When 8‐hydroxyquinoline was employed, only oligomeric products were obtained. On the contrary, 5,7‐dinitro‐8‐hydroxyquinoline gave linear polyethylene (PE), but with a modest activity. For the catalyst based on 5‐nitro‐8‐hydroxyquinoline, the productivity was largely dependent on the content of free trimethylaluminum (TMA) present in the commercial aluminoxane. The progressive optimization of the TMA/oligomeric methylaluminoxane ratio increased the productivity, which reached 700 kg of PE/(mol of Ni × h), by an order of magnitude. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 200–206, 2006     

Are there more than five linearly-independent collision invariants for the Boltzmann equation?

The problem of finding the summational collision invariants for the Boltzmann equation is tackled with the aim of proving that the most general solution of the problem is not different from the standard one even when the equation defining a collision invariant is only satisfied almost everywhere inR ³×R ³×S ². The collision invariant is assumed to be in the Hilbert spaceH of the functions which are square integrable with respect to a Maxwellian weight.     

Crystal and molecular structure of thiamine monochloride

The crystal and molecular structure of thiamine monochloride (C₁₂H₁₇N₄OSCl) was determined by X-ray diffraction and refined to a finalR value of 0.042. The compound crystallizes in the monoclinic system, space groupP2₁/a, with cell constantsa=18.929(4),b=11.663(2),c=6.376(2) Å and=96.72(8)°. The thiamine molecule is anhydrous and unprotonated, and the torsion angles at the methylene carbon show that it possesses anF conformation. The dihedral angle value of 84.16(6)° between thiazolium and pyrimidine rings is in the normal range found for the thiamine withF conformation, protonated or not, hydrated or not. Thiamine therefore has the same conformation notwithstanding protonation or hydration, with the rings similarly oriented in all the crystal structures containing thiamine.