Geometric regularity of direct-sum decompositions in some classes of modules

In this paper, we show that modules with semilocal endomorphism rings appear in abundance in applications, that their direct-sum decompositions are described by the so-called Krull monoids, and that this implies a geometric regularity of the direct-sum decompositions of these modules. Their direct-sum decompositions into indecomposables are not necessarily unique in the sense of the Krull-Schmidt theorem. The application of the theory of Krull monoids to the study of direct-sum decompositions of modules has been developed during the last five years. After a quick survey of the results obtained in this direction, we concentrate in particular on the abundance of examples. At present, these examples are scattered in the literature, and we try to collect them in a systematic way. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 3, pp. 231–244, 2004.     

Twist points of planar domains

We establish a potential theoretic approach to the study of twist points in the boundary of simply connected planar domains.

     

A kinetic Monte Carlo method on super-lattices for the study of the defect formation in the growth of close packed structures

A modified Kinetic Lattice Monte Carlo model has been developed to predict growth rate regimes and defect formation in the case of the homo-epitaxial growth of close packed crystalline structures. The model is an improvement over standard Monte Carlo algorithms, which usually retain fixed atom positions and bond partners indicative of perfect crystal lattices. Indeed, we extend the concepts of Monte Carlo growth simulations on super-lattices containing additional sites (defect sites) with respect to those of the reference material. This extension implies a reconsideration of the energetic mapping, which is extensively presented, and allows to describe a complex phenomenology that is out of accessibility of standard stochastic approaches. Results obtained using the Kawasaki and the Bond-Counting rules for the transition probability of the Monte Carlo event are discussed in details. These results demonstrate how the defect types (local or extended), the formation mechanisms and the defect generation regimes can be characterized using our approach.     

Divisible modules and space of divisibility of an integral domain

Sunto Se A è un modulo divisibile su un dominio d'integrità R e Q è il campo delle frazioni di R, sia R_A Q il massimo sopraanello di R tale che A possa essere dotato della struttura di R_A-modulo. La struttura di R_A riflette quella di A. Se A è un modulo divisibile semplice di torsione, cioè è divisibile di torsione e non ha sottomoduli divisibili propri non nulli, R_A è analiticamente irriducibile. Se C e D sono due moduli divisibili semplici, diciamo C equivalente a D se R_C=R_D. Se d-Space (R) è un insieme di rappresentanti delle classi di equivalenza degli R-moduli divisibili semplici, d-Space (R) puó essere dotato di una struttura di spazio di Hausdorff zero-dimensionale; lo spazio topologico d-Space (R) (da noi chiamato lo spazio di divisibilità di R) contiene un sottospazio chiuso omeomorfo alla superficie di Riemann astratta di R dotata della patch topology.

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Lavoro eseguito con il contribute del Ministero délia Pubblica Istruzione     

Absence of symmetry breaking for systems of rotors with random interactions

We prove that Gibbs states for the Hamiltonian , with thes _x varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if withJ _xy i.i.d. bounded random variables with zero average, 1 in one dimension, and 2 in two dimensions.     

The CeCl3·7H2O-NaI system as promoter in the synthesis of functionalized trisubstituted alkenes via Knoevenagel condensation

The arylidene malonates with two different geminal carboxylate functions, a suitable class of substrates of several synthetic and pharmacological studies, are easily available through Knoevenagel condensation of ethyl tert-butyl malonate and different aromatic aldehydes. The results have increased the potentialities of CeCl₃·7H₂O-NaI system as a type of water-tolerant green Lewis acid promoter for carbon-carbon bond forming procedures.