Correction: de Gonzalo, G. Lipase Catalysed Kinetic Resolution of Racemic 1,2-Diols Containing a Chiral Quaternary Center. Molecules 2018, 23, 1585

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Lipase catalysed kinetic resolution of racemic 1,2-diols containing a chiral quaternary center

Optically active 1,2-diols are valuable buildings blocks in organic synthesis. In the present paper, a set of racemic 1,2-diols with an ester functional group are prepared, starting from -ketoesters in a three-step procedure with moderate yields. The racemic 1,2-diols, containing a chiral quaternary center in their structure, are subjected to selective acylation in order to perform their kinetic resolution catalysed by a set of commercially available lipases. Under optimized reaction conditions, good conversions and enantioselectivities are achieved by using the lipase PSL-C from Pseudomonas cepacia in tert-butyl methyl ether. This biocatalyst could be reused up to five times without losing its properties.Ministerio de Economía y Competitividad (contract RYC-2012-10014 for G.d.G., Grants CTQ2016-76908-C2-1-P and CTQ2016-76908-C2-2-P)European FEDER FundsJunta de Andalucía (Grant 2012/FQM 10787

An economic cross-diffusion mutualistic model for cities emergence

We study an evolution cross-diffusion problem with mutualistic Lotka-Volterra reaction term to modelize the long-term spatial distribution of labor and capital. The mutualistic behavior is deduced from the gradient flow associated to profits maximization. We perform a linear and weakly nonlinear stability analysis and find conditions under which the uniform optimum of profits becomes unstable, leading to pattern formation. The patterns alternate regions of high and low concentrations of both labor and capital, which may be interpreted as cities. Finally, numerical simulations based on the weakly nonlinear analysis, as well as in a finite element approximation, are provided.Comment: Keywords: Cross-diffusion, mutualism, Turing instability, weakly nonlinear analysis, labor, capital, cit