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.

     

Characterization of hydrogen bonds in the interactions between the hydroperoxyl radical and organic acids

The hydrogen bonds formed between the hydroperoxyl radical and formic, acetic, and trifluoroacetic acids were characterized using geometric, energetic, and electronic parameters through calculations done with the UB3LYP/6-311++G (3df,3pd) and UB3LYP/EPR-III methods. The wave functions were analyzed through the natural bond orbital, natural steric analysis, natural resonance theory, and atoms in molecules methods. The energy decomposition method proposed by Xantheas was used. The vibrational frequencies and the intensity of the O-H stretching bands, as well as the spin densities, were compared with experimental evidence. The results allowed the characterization of the hydrogen bonds formed in the complexation of the acids with the hydroperoxyl radical. Complexation led to significant alterations in the equilibrium geometry of the monomers. Energetic analysis proved that the studied complexes are stable and allowed the understanding of the effect of the electron-donating and electron-withdrawing groups in their stabilization. The alterations in the electronic structure of the monomers after complexation led to an increase in the resonance of the carboxyl group, which can be partially attributed to the hydrogen bond.     

Collisionless relaxation in non-neutral plasmas

A theoretical framework is presented which allows us to quantitatively predict the final stationary state achieved by a non-neutral plasma during a process of collisionless relaxation. As a specific application, the theory is used to study relaxation of charged-particle beams. It is shown that a fully matched beam relaxes to the Lynden-Bell distribution. However, when a mismatch is present and the beam oscillates, parametric resonances lead to a core-halo phase separation. The approach developed accounts for both the density and the velocity distributions in the final stationary state.     

Immobilization of Eversa® Transform via CLEA Technology Converts It in a Suitable Biocatalyst for Biolubricant Production Using Waste Cooking Oil

The performance of the previously optimized magnetic cross-linked enzyme aggregate of Eversa (Eversa-mCLEA) in the enzymatic synthesis of biolubricants by transesterification of waste cooking oil (WCO) with different alcohols has been evaluated. Eversa-mCLEA showed good activities using these alcohols, reaching a transesterification activity with isoamyl alcohol around 10-fold higher than with methanol. Yields of isoamyl fatty acid ester synthesis were similar using WCO or refined oil, confirming that this biocatalyst could be utilized to transform this residue into a valuable product. The effects of WCO/isoamyl alcohol molar ratio and enzyme load on the synthesis of biolubricant were also investigated. A maximum yield of around 90 wt.% was reached after 72 h of reaction using an enzyme load of 12 esterification units/g oil and a WCO/alcohol molar ratio of 1:6 in a solvent-free system. At the same conditions, the liquid Eversa yielded a maximum ester yield of only 34%. This study demonstrated the great changes in the enzyme properties that can be derived from a proper immobilization system. Moreover, it also shows the potential of WCO as a feedstock for the production of isoamyl fatty acid esters, which are potential candidates as biolubricants.     

Synthesis and cation binding properties of fluorescent calix[4]arene derivatives bearing tryptophan units at the lower rim

The fluorescent peptidocalixarenes, 5,11,17,23-tetra-tert-butyl-25,26,27,28-tetrakis(O-methyl-l-tryptophanylcarbonylmethoxy)calix[4]arene (1) and 5,11,17,23-tetra-tert-butyl-25,27-di(O-methyl)-26,28-bis(O-methyl-l-tryptophanylcarbonylmethoxy)calix[4]arene (2), were prepared by introducing tryptophan subunits at a lower calixarene rim. Coordination abilities of 1 and 2 towards Eu(III) and alkali metal cations were studied by spectrophotometric, spectrofluorimetric, conductometric and potentiometric titrations in acetonitrile at 25°C. Rather strong complexation was observed for smaller alkali metal cations Li⁺ and Na⁺ (log K _Li1 >6, log K _Li2 >6, log K _Na1  = 8.25, log K _Na2  = 6.94), and moderate for K⁺ (log K _K1  = 5.09, log K _K2  = 4.09). Larger Rb⁺ and Cs⁺ cations did not fit in the ion binding site of 1 so no complexation was detected, whereas the more flexible ligand 2 accommodated Rb⁺ cation (log K _Rb2  = 3.44). The fluorescence of 1 (λ_ex = 280 nm, λ_em = 340 nm) was remarkably quenched by Eu(III). Stability constant of 1:1 (Eu³⁺:1) complex determined spectrofluorimetrically amounted to log K _Eu1  = 6.16.     

Formation of catalytic silver nanoparticles supported on branched polyethyleneimine derivatives

A new and straightforward method for screening highly catalytically active silver nanoparticle-polymer composites derived from branched polyethyleneimine (PEI) is reported. The one-step systematic derivatization of the PEI scaffold with alkyl (butyl or octyl) and ethanolic groups led to a structural diversity correlated to the stabilization of silver nanoparticles and catalysis. Analysis of PEI derivative libraries identified a silver nanoparticle-polymer composite that was able to efficiently catalyze the p-nitrophenol reduction by NaBH(4) in water with a rate constant normalized to the surface area of the nanoparticles per unit volume (k(1)) of 0.57 s(-1) m(-2) L. Carried out in the presence of excess NaBH(4), the catalytic reaction was observed to follow pseudo-first-order kinetics and the apparent rate constant was linearly dependent on the total surface area of the silver nanoparticles (Ag-NPs), indicating that catalysis takes place on the surface of the nanoparticles. All reaction kinetics presented induction periods, which were dependent on the concentration of substrates, the total surface of the nanoparticles, and the polymer composition. All data indicated that this induction time is related to the resistance to substrate diffusion through the polymer support. Hydrophobic effects are also assumed to play an important role in the catalysis, through an increase in the local substrate concentration.