Rearrangement of N-Aryl-2-Vinylaziridines to Benzoazepines and Dihydropyrroles: A Synthetic and Theoretical Study

Herein we report the one-pot synthesis of several N-heterocyclic compounds by rearrangement reactions of N-aryl-2-vinylaziridines. The optimization of the synthetic methodology employed allowed us to obtain differently substituted 2,5-dihydro-1H-benzo[b]azepines in good yields and purities. The relationship between the nature of the starting N-aryl-2-vinylaziridine and the obtained N-heterocycle was also investigated. Finally, to rationalize all the experimental results reported in this paper a theoretical study was performed that casts light on the reaction mechanism.     

A molecular modelling approach to rationalize the stereochemical outcome of the Burkholderia cepacia lipase-catalyzed transesterification of aromatic primary alcohols with vinyl esters with different chain lengths in chloroform

The Burkholderia cepacia lipase-catalyzed transesterification of 2-methyl-3-phenyl-1-propanol with vinyl esters proceeds with high enantioselectivity independently of the acyl chain length and the low enantioselectivity of the same reaction with 2-phenyl-1-propanol is not affected by chain length of the vinyl esters. A molecular modelling approach has been developed in order to rationalize the enzymatic results.     

Enantioselective synthesis,chiroptical properties and absolute configuration of 3-aminosubstituted isothiazole S-oxides

Herein we report a mild and efficient method to synthesize chiral 3-aminosubstituted isothiazole sulfoxides taking advantage of (+)- and (?)-((8,8-dichlorocamphoryl)sulfonyl)oxaziridine under microwave irradiation. The determination of the absolute configuration of the chiral sulfoxide was achieved by theoretical calculation of the CD spectra. The reason for the observed stereoselectivity was enlightened by means of analysis of our data using DFT calculations.     

On a class of nonconvex and nonlinear optimal control problems

We propose two relaxation approaches for the existence of solutions of a nonconvex optimal control problem with a nonlinear dynamics and two fixed endpoints. The first approach adds to the functional a term depending on the final state; the second one introduces a new scalar control into both the functional and the dynamics. Our results generalize those obtained in the linear case. We assume that the integrand be concave w.r.t. the state variable, and provide an example showing that a strict concavity condition, in the nonlinear case, is essential. Finally, a result without relaxation is presented.     

Finite vertex algebras and nilpotence

I show that simple finite vertex algebras are commutative, and that the Lie conformal algebra structure underlying a reduced (= without nilpotent elements) finite vertex algebra is nilpotent.     

Stability of incompressible current-vortex sheets

We revisit the study in [Y. Trakhinin, On the existence of incompressible current-vortex sheets: study of a linearized free boundary value problem, Math. Methods Appl. Sci. 28 (2005) 917–945] where an energy a priori estimate for the linearized free boundary value problem for planar current-vortex sheets in ideal incompressible magnetohydrodynamics was proved for a part of the whole stability domain found a long time ago in [S.I. Syrovatskij, The stability of tangential discontinuities in a magnetohydrodynamic medium, Zh. Eksper. Teor. Fiz. 24 (1953) 622–629 (in Russian); W.I. Axford, Note on a problem of magnetohydrodynamic stability, Canad. J. Phys. 40 (1962) 654–655]. In this paper we derive an a priori estimate in the whole stability domain. The crucial point in deriving this estimate is the construction of a symbolic symmetrizer for a nonstandard elliptic problem for the small perturbation of total pressure. This symmetrizer is an analogue of Kreiss' type symmetrizers. As in hyperbolic theory, the failure of the uniform Lopatinski condition, i.e., the fact that current-vortex sheets are only weakly (neutrally) stable yields loss of derivatives in the energy estimate. The result of this paper is a necessary step to prove the local-in-time existence of stable nonplanar incompressible current-vortex sheets by a suitable Nash–Moser type iteration scheme.     

Oxidation of alkanes by Ph4PHSO5 catalyzed by manganese(III) porphyrins. A study of the factors determining alcohol and ketone formation

As reported in previous papers, the oxidation of ethylbenzene with Ph₄PHSO₅ catalyzed by Mn(TMP)Cl in the presence of nitrogen bases in 1,2-dichloroethane homogeneous solution affords fair yields (up to 80%) of oxygenated products. Acetophenone is the major product together with minor amounts of 1-phenylethanol ([ketone]/[alcohol]6). In this paper we report further observations concerning this system. In particular we find that a similar products distribution is observed when soluble Co(II) or Fe(II) species, i.e. acetylacetonate derivatives, are used instead of the manganese porphyrin. On the other hand for these compounds, which are catalysts of radical reactions, the product distribution is determined by a remarkably larger reactivity of the alcohol initially formed compared with that of the alkane (k_R–OH/k_R–H200). The product distribution for the Mn(TMP)Cl catalysis cannot be rationalized on the same basis. Direct experiments show that the reactivity of the two substrates is similar (k_R–OH/k_R–H2–6) thus suggesting that a mechanism different from the simple radical hydrogen atom abstraction is taking place. The dependence of the chemioselectivity of hydrocarbon oxidation on the nature of the manganese porphyrin employed and of a number of additives indicates that the product distribution is mainly determined by the relevance of the association of the alcohol intermediate to the catalyst prior to the second oxidation step leading to ketone. Two different rho Hammett's values are obtained for ethylbenzenes oxidation depending on the method employed for the measurement of reaction rates, i.e. by separate or by competitive experiments thus providing further mechanistic information on the association of the substrates to the oxo-species.     

Lower Bounds for the Nodal Length of Eigenfunctions of the Laplacian

We prove lower bounds for the length of the zero set of aneigenfunction of the Laplace operator on a Riemann surface; inparticular, in non-negative curvature, or when the associated eigenvalueis large, we give a lower bound which involves only the square root ofthe eigenvalue and the area of the manifold (modulo a numericalconstant, this lower bound is sharp).