Direct displacement of alkoxy groups of vinylogous esters by Grignard reagents

The direct displacement of alkoxy groups from the β position of aromatic and unsaturated esters and ketones is described. The reaction is chemo- and regioselective, displaying wide substrate scope.     

An implicit preconditioning strategy for large-scale generalized Sylvester equations

Large-scale generalized Sylvester equations appear in several important applications. Although the involved operator is linear, solving them requires specialized techniques. Different numerical methods have been designed to solve them, including direct factorization methods suitable for small size problems, and Krylov-type iterative methods for large-scale problems. For these iterative schemes, preconditioning is always a difficult task that deserves to be addressed. We present and analyze an implicit preconditioning strategy specially designed for solving generalized Sylvester equations that uses a preconditioned residual direction at every iteration. The advantage is that the preconditioned direction is built implicitly, avoiding the explicit knowledge of the given matrices. Only the effect of the matrix-vector product with the given matrices is required. We present encouraging numerical experiments for a set of different problems coming from several applications.     

Generalized thermalization in an integrable lattice system

After a quench, observables in an integrable system may not relax to the standard thermal values, but can relax to the ones predicted by the generalized Gibbs ensemble (GGE) [M. Rigol et al., Phys. Rev. Lett. 98, 050405 (2007)]. The GGE has been shown to accurately describe observables in various one-dimensional integrable systems, but the origin of its success is not fully understood. Here we introduce a microcanonical version of the GGE and provide a justification of the GGE based on a generalized interpretation of the eigenstate thermalization hypothesis, which was previously introduced to explain thermalization of nonintegrable systems. We study relaxation after a quench of one-dimensional hard-core bosons in an optical lattice. Exact numerical calculations for up to 10 particles on 50 lattice sites (≈10(10) eigenstates) validate our approach.     

Synthesis of [60]fullerene derivatives bearing five-membered heterocyclic wings and an investigation of their photophysical kinetic properties

The preparation, characterization and photophysical properties of six new stable [6,6]-closed fullerene cycloadducts bearing five-membered heterocycles are described. The modified [60]fullerenes are obtained by a simple and rapid synthesis via a Bingel-type reaction with tetrazole and oxadiazole malonate derivatives. The photophysical kinetics of these new fullerene derivatives in toluene solution under ultraviolet illumination (375 nm, UVA) are studied by electron paramagnetic resonance and free-radical spin-trapping using α-phenyl-N-tert-butyl nitrone as a spin-trap. The results are compared with pure [60]fullerene and [6,6]-phenyl C₆₁ butyric acid methyl ester (C₆₀-PCBM). It is concluded that for all six new compounds as well as pure [60]fullerene and PCBM both superoxide and singlet oxygen are produced in the first stages of UVA illumination following the type I and II mechanisms, respectively. In all cases singlet oxygen is produced as the primary dominant species; however, the type I mechanism always occurs in parallel with type II. In the end, the superoxide is self-dismuted into hydroxyl radicals, thus yielding PBN-OH spin adducts (g = 2.007 and a_hf (¹⁴N) = 1.54 mT). The kinetic reaction constants and their efficiencies in the production of reactive oxygen species at 375 nm and per mW of absorbed power are determined. The experimental results are consistent with an autocatalytic reaction model in which the system evolutes under UVA illumination, with superoxide catalyzing the conversion of singlet oxygen into more superoxide.     

Carbon materials as electrodes for electrosorption of NaCl in aqueous solutions

Different porous carbons (MWCNT, a carbon aerogel, an activated carbon cloth and a chemically activated carbon) were evaluated as electrode material for the electrosorption of NaCl. The results obtained from the chronoamperometric experiments were correlated to the surface area and the size of the pores present in each carbon. These results indicate that all the surfaces are equivalent for the electrosorption process, demonstrating that both, mesopores and micropores, are equally effective. Nevertheless, the kinetics of the process is influenced by the pore size distribution of the carbon, although it is rather fast for all the carbons studied. The chemically activated carbon seems to be the most suitable carbon material for electrosorption of NaCl due to the combination of a high surface area and an appropriate pore size distribution.     

How Does Aromaticity Rule the Thermodynamic Stability of Hydroporphyrins?

Several measures of aromaticity including energetic, magnetic, and electron density criteria are employed to show how aromatic stabilization can explain the stability sequence of hydroporphyrins, ranging from porphin to octahydroporphin, and their preferred hydrogenation paths. The methods employed involve topological resonance energies and their circuit energy effects, bond resonance energies, multicenter delocalization indices, ring current maps, magnetic susceptibilities, and nuclear-independent chemical shifts. To compare the information obtained by the different methods, the results have been put in the same scale by using recently proposed approaches. It is found that all of them provide essentially the same information and lead to similar conclusions. Also, hydrogenation energies along different hydrogenation paths connecting porphin with octahydroporphin have been calculated with density functional theory. It is shown by using the methods mentioned above that the relative stability of different hydroporphyrin isomers and the observed inaccessibility of octahydroporphin both synthetically and in nature can be perfectly rationalized in terms of aromaticity.     

Heart of Irreducible Morphisms of Bounded Complexes

In [9 Giraldo , H. , Merklen , H. ( 2009 ). Irreducible morphisms of categories of complexes . Journal of Algebra 321 : 2716 – 2736 .[Crossref], [Web of Science ®] , [Google Scholar]] Giraldo and Merklen studied irreducible morphisms in the categories 𝒞(𝒜) and D^?(Λ), where 𝒞(𝒜) is the category of complexes over an abelian Krull–Schmidt category 𝒜 and D^?(Λ) is the derived category of the bounded above complexes of finite generate left modules, over an Artin algebra Λ. In this work, we continue the study of irreducible morphism having one finite irreducible truncation.     

Corrigendum To: “The Odd part of a N-Koszul Algebra”

The paper: The odd part of an N-Koszul algebra, Comm. in Algebra, 33:101–108, 2005, contains some missprints that make it difficult to read. We correct here these mistakes.     

On Moduli Spaces for Abelian Categories

We show that if 𝒜 is an abelian category satisfying certain mild conditions, then one can introduce the concept of a moduli space of (semi)stable objects which has the structure of a projective algebraic variety. This idea is applied to several important abelian categories in representation theory, like highest weight categories.