Synthesis and subsequent reactivity of 1-amino-2-aza-1,3-butadienes derived from β-amino esters

A high yield preparation of 1-amino-2-aza-1,3-butadienes derived from β-amino esters from N-unsubstituted amidines and acetylenic esters is described. These substrates are efficient starting material for the preparation of dihydrotriazines and 5-amino pyrrolidin-3-ones.     

Study of glasses with grisailles from historic stained glass windows of the cathedral of León (Spain)

This work concerns the study of grisailles of historic glass samples from stained glass windows of the Cathedral of León, which were removed during the restoration carried out in 19th century. Both the glass samples and their coloured grisailles showed very different chemical composition and macroscopic heterogeneity. As a general rule their deterioration degree is rather moderate, maybe due to the pieces removal that preserve them from the high atmospheric pollution occurred in the last century. The present research pointed out the physical characteristics, chemical compositions and deterioration degree of the samples selected from the most important Spanish ensemble of Medieval and Renaissance stained glass windows. Moreover, this work offers sufficient results to be compared with those formerly obtained for other stained glass windows from European cathedrals and churches.     

Viscous-inviscid model for the linear stability of core-annular flow

In this paper the linear stability of two immiscible fluids of widely different kinematic viscosity and equal density flowing through a circular pipe is analysed. A viscous-inviscid model is used which offers a consistent zeroth-order approximation to the stability problem as long as the thickness of the ring flow, where the inviscid fluid is located, is large enough. In this way the laminar sublayer at the pipe wall does not interact with the fluid interface. A closed form expression for the complex dispersion relation due to an arbitrary wavelength perturbation is derived, which determines a stability criterion, and then simplified for large and short wavelength values.     

Stability, resonance and Lyapunov inequalities for periodic conservative systems

This paper is devoted to the study of Lyapunov type inequalities for periodic conservative systems. The main results are derived from a previous analysis which relates the best Lyapunov constants to some especial (constrained or unconstrained) minimization problems. We provide some new results on the existence and uniqueness of solutions of nonlinear resonant and periodic systems. Finally, we present some new conditions which guarantee the stable boundedness of linear periodic conservative systems.     

Boundedness of extremal solutions in dimension 4

In this paper we establish the boundedness of the extremal solution u^∗$u^{\ast }$ in dimension N=4$N=4$ of the semilinear elliptic equation −Δu=λf(u)$-\Delta u=\lambda f\left(u\right)$, in a general smooth bounded domain Ω⊂R^N$\Omega \subset {\mathbb{R}}^N$, with Dirichlet data u_|∂Ω=0$u{|}_{\partial \Omega }=0$, where f$f$ is a C¹$C^1$ positive, nondecreasing and convex function in [0,∞)$[0,\infty )$ such that f(s)/s→∞$f\left(s\right)/s\to \infty$ as s→∞$s\to \infty$.     

Regioselective synthesis of pyrrolin-3-ones and 2,3,4,5-tetrahydro[1,3]-oxazines from N-vinylic amidines

Achiral and optically active N-vinylic amidines are obtained by simple addition of amidines to acetylenic esters. Thermal intramolecular cyclization of these substrates containing a carboxylate group in position 3 gives pyrrolin-3-ones. The enaminone character of these compounds towards propargyl bromide, diethyl azodicarboxylate, diethyl acetylenedicarboxylate, ethyl propiolate and phenyl isocyanate is studied and functionalized pyrrolin-3-one derivatives are obtained. The reaction of the pyrrolinones prepared with diethyl ketomalonate leads to new 1,3-oxazine derivatives.