Factoring ideals in Prüfer domains

We show that in certain Prüfer domains, each nonzero ideal I can be factored as , where I^v is the divisorial closure of I and is a product of maximal ideals. This is always possible when the Prüfer domain is h-local, and in this case such factorizations have certain uniqueness properties. This leads to new characterizations of the h-local property in Prüfer domains. We also explore consequences of these factorizations and give illustrative examples.     

Theoretical elastic moduli for disordered packings of interconnected spheres

A theoretical model has been developed which provides analytical expressions for the elastic moduli of disordered isotropic ensembles of spheres interconnected by physical bonds. Young's and shear moduli have been derived assuming an ideal random isotropic network and the radial distribution function for disordered packings of spheres. The interparticle interactions are accounted for in terms of surface forces for the two distinct cases of perfectly rigid spheres and spheres deformable at contact. A theoretical expression is also derived in a similar way for the bulk or compressibility modulus. In this case, an atomistic approach has been followed based on the analogy with noble gas solids and colloidal crystals. Also in this case, disordered spatial distribution of the spheres is described statistically. For the case of colloidal aggregates, a total two-body mean-field interaction potential is used which includes the Born repulsion energy. This latter contribution plays an essential role in determining the compression behavior of systems of particles aggregated in the primary minimum of the potential well and, therefore, must not be neglected. Both the expression of the Young's modulus and that of the compressibility modulus derived in this work are found to be consistent with two distinct sets of experimental data which recently appeared in the literature.     

Interactions at the surface of organophilic-modified laponites: a multinuclear solid-state NMR study

Organically modified clays are largely employed in the preparation of nanostructured materials. The structural and dynamic characterization of the clay surface appears very important in the perspective of understanding the molecular mechanisms determining the improvement of the material properties. To this aim, in this work, a synthetic clay, Laponite, was studied in its untreated hydrophilic Na+-form, after ion exchange with alkylammonium cations and after subsequent grafting reaction with an alkoxysilane. These three samples were characterized by IR, SEM, TGA, and X-ray techniques and were deeply investigated by means of a wide combination of 29Si, 13C, and 1H high- and low-resolution solid-state NMR experiments. The grafting reaction with alkoxysilanes, occurring at the clay platelet edges, resulted in a reduction of the clay inter-platelet distances, and in an increased disorder in both the arrangement of the platelets and the conformational structure of the intercalated organic cation chains, probably due to the relative twisting of adjacent platelets.     

Violation of distribution symmetry in statistical evaluation of absolute enantioselective synthesis

Enantiomeric excesses obtained in absolute enantioselective synthesis by chiral autocatalysis (Soai-reaction) were statistically analyzed. Two sets of parallel experiments, which were performed under chemically different conditions, are available. One group contains 37, while the other contains 84 preparative results. The former group shows some interesting tendencies but does not give conclusive statistical results. The sample of 84 parallel experiments, providing 39 R- and 45 S-excesses have shown that these data represent two distinct, non-symmetric sets with different non-Gaussian distributions. Clear S preference was found.     

Simulation and experimental validation of the dynamic behavior of an electromechanically actuated multiple‐disk clutch

Automated multiple‐disk clutches in automotive drivelines are at present hydraulically or electrohydraulically actuated. The electromechanical clutch actuation represents an alternative. The subject of the investigation is a functional model of an electromechanical clutch actuator which consists of a servo motor, a reduction gear and a mechanism for the realization of the force acting on the disks. For the simulation of the dynamic behavior of the electromechanically actuated multiple‐disk clutch a detailed multibody model is developed which includes models of the electromechanical actuator and the wet multiple‐disk clutch. The multiple‐disk clutch is described by coupled partial models for the rotational and translational dynamics. The coupling parameters are the relative disk distances and the forces between the disks. The results of test bench measurements are compared to simulation results. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)