Irreducibility and simplicity in general algebrae and congruences in relatively complemented lattices

Summary Within a framework of general algebra we firstly formulate propositions concerning the connection between irreducibility, id est the absence of certain types of subalgebrae, and simplicity. Then we investigate some uniqueness properties of the congruences of certain types of lattices and we apply the general propositions to algebrae with lattice operations obtaining sufficient conditions for the simplicity of wide classes of such algebrae.

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Riassunto In un contesto di algebra generale noi formuliamo dapprima proposizioni concernenti la connessione tra irriducibilità, cioè l’assenza di certi tipi di sottoalgebre, e semplicità. In seguito investighiamo alcune proprietà di unicità delle conseguenze di certi tipi di reticoli e applichiamo le proposizioni generali ad algebre con operazioni di reticolo ottenendo condizioni sufficienti per la semplicità di ampie classi di tali algebre.

     

Oxidation of tertiary polycycl1c amines by RuO4

The reactions of certain tertiary polycyclic amines such as N-benzyl-9-azabicy-clo- [3,3,1]-nonane, N-benzyl-5, 6-dihydro-11H-dibenz [b,e] azepine, and N-benzyl-1,2,3,4-tetrahydroisoquinoline with ruthenium tetroxide, taking place in both heterogeneous and homogeneous systems, have made it possible to establish the order of reactivity of the various methylene groups adjacent to the nitrogen with respect to this oxidizing agent.     

Heteronuclear decoupling interference during symmetry-based homonuclear recoupling in solid-state NMR

We examine the influence of continuous-wave heteronuclear decoupling on symmetry-based double-quantum homonuclear dipolar recoupling, using experimental measurements, numerical simulations, and average Hamiltonian theory. There are two distinct regimes in which the heteronuclear interference effects are minimized. The first regime utilizes a moderate homonuclear recoupling field and a strong heteronuclear decoupling field; the second regime utilizes a strong homonuclear recoupling field and a weak or absent heteronuclear decoupling field. The second regime is experimentally accessible at moderate or high magic-angle-spinning frequencies and is particularly relevant for many realistic applications of solid-state NMR recoupling experiments to organic or biological materials.     

The Suzuki homocoupling reaction under high-intensity ultrasound

The Pd-catalysed Suzuki homocoupling of boronic acids was successfully carried out in water under high-intensity ultrasound (HIU). Heterogeneous catalysis with Pd/C, facilitating work up and purification, could be used without adding phosphine ligands. Reaction rates and yields were strongly influenced by the oxidant employed; excellent results were obtained using either molecular oxygen or 3-bromo-4-hydroxycoumarin. 3-Arylation of the latter with the Suzuki procedure had failed, exclusively affording the homocoupling products, symmetric biaryls. Besides offering a number of operational advantages, the use of HIU broadens the field of application for the Suzuki reaction.     

Chemical modification of chitosan under high-intensity ultrasound

Chitosan (CTS), a biocompatible, biodegradable, non-toxic polymer, dissolves in water only if pH is lowered under 6.5, when a substantial fraction of the amino groups is protonated. Its range of application has been much extended by partially depolymerising it or converting it to water-soluble derivatives. Working under high-intensity ultrasound at 17.8-18.5 kHz, using either a simple horn or a cup horn, we achieved a controlled depolymerization of CTS, also prepared in high yields several derivatives that can be useful intermediates for further chemical modification, as well as several water-soluble derivatives that lend themselves to a host of industrial applications. Compared to conventional methods, all these reactions went to completion in considerably shorter times at lower temperatures.     

Atomic control of water interaction with biocompatible surfaces: the case of SiC(001)

The interaction of water with Si- and C- terminated beta-SiC(001) surfaces was investigated by means of ab initio molecular dynamics simulations. Irrespective of coverage, varied from 1/4 to 1 monolayer, we found that water dissociates on the Si-terminated surface, substantially modifying the clean surface reconstruction, while the C-terminated surface is nonreactive and hydrophobic. Based on our results, we propose that STM images and photoemission experiments may detect specific changes induced by water on both the structural and electronic properties of SiC(001) surfaces.     

Long Term Stability of Proper Rotations of the Perturbed Euler Rigid Body

We study the long term stability of the proper rotations of the perturbed Euler rigid body, in the framework of Nekhoroshev theory. For simplicity we treat here in detail only the kinetically symmetric case (the potential needs not to be symmetric), but we indicate how to extend the results to the triaxial case. We show that the proper rotations around the symmetry axis are Nekhoroshev stable: more precisely, if the initial datum is sufficiently close to a proper rotation, then for a very long time it remains such, and the tip of the unit vector parallel to the angular momentum precesses, up to a small noise, along the level curves of a regular function on the unit sphere. If the proper rotations are resonant, chaotic motions with positive Lyapunov exponents are possible, but chaos (unlike the case of ordinary motions, that is motions not close to proper rotations) is always localized, and does not affect in an essential way the motion of the angular momentum in space. Preliminary numerical results indicate that the theory is, in many aspects, optimal, although in some points it can still be improved.     

Applications of fractional transforms to object reconstruction from in-line holograms

We propose a method for the digital reconstruction of an object whose diffraction pattern has been recorded on a hologram. The fractional Fourier transform is used for the object reconstruction. To determine the position of the object, the fractional order is scanned. The fractional cosine and fractional Hartley transforms are also employed for object reconstruction. These two transforms are real valued and allow the reconstruction to be done with lower computing complexity. Simulations and experimental results are presented.     

An efficient palladium-catalyzed synthesis of cinnamaldehydes from acrolein diethyl acetal and aryl iodides and bromides

The reaction of aryl iodides and bromides with acrolein diethyl acetal in the presence of Pd(OAc)(2), (n)()Bu(4)NOAc, K(2)CO(3), KCl, and DMF, at 90 degrees C until the disappearance of the acetal followed by the addition of 2 N HCl to the crude reaction mixture, affords cinnamaldehydes in good to high yields. A variety of functional groups are tolerated in the aryl halides, including ether, aldehyde, ketone, ester, dialkylamino, nitrile, and nitro groups. The presence of substituents close to the oxidative addition site does not hamper the reaction.     

Shortest Path Auction Algorithm Without Contractions Using Virtual Source Concept

In this paper, the problem of finding a shortest path tree rooted at a given source node on a directed graph (SPT) is considered. A new efficient algorithm based on a primal-dual approach is presented, which improves both the convergence and the complexity of the best known auction-like algorithm. It uses the virtual source (VS) concept based on the following consideration: when a node i is visited for the first time by any algorithm which preserves verified the dual admissibility conditions, then the shortest path (SP) from the source node to i is found. Therefore, the SP from the source to the remaining nodes may be computed by considering i as a virtual source.We propose a very efficient implementation of an auction-like algorithm that uses this concept and enables us to obtain a computational cost of O(n ²), where n is the number of nodes.Numerical experimentsare reported showing that the new method outdoes previously proposed auction-like algorithms and is highly competitive with other state-of-art SP approaches.