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.     

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.     

Probability of ionization of sputtered particles as a function of their energy: Part I: Negative Si ions

In this study we have investigated how the probability of ionization of sputtered Si atoms to form negative ions depends on the energy of the atoms. We have determined the ionization probability from experimental SIMS energy distributions using a special experimental technique, which included de-convolution of the energy distribution with an instrumental transmission function, found by separate measurements.We found that the ionization probability increases as a power law ∼E^0.677 for particles sputtered with energies of 0-10 eV, then becomes a constant value (within the limits of experimental error) for particles sputtered with energies of 30-100 eV. The energy distributions of Si⁻ ions, measured under argon and cesium ion sputtering, confirmed this radical difference between the yields from low and high-energy ions.To explain these results we have considered ionization mechanisms that are different for the low energy atoms (<10 eV) and for the atoms emitted with higher energy (>30 eV).     

Critical distance for secondary ion formation: Experimental SIMS measurements

We have performed direct experimental measurements of the critical distance for the secondary ion formation process. To this end, we compared the experimentally measured energy distribution of secondary Si⁻ ions with the theoretical energy distribution (Sigmund-Thompson relation) of secondary Si atoms. Our model states that the maxima positions of these two energy distributions differ by the Coulomb interaction potential between the outgoing ion (Si⁻ in our case) and a charge with the opposite polarity formed at the surface after electron transition between the outgoing Si atom and the surface. Quite a reasonable value was obtained for the critical distance, but with a large scatter in experimental data. The conclusion has been made that the experimental technique should be improved to get more precise values of the critical distance, which is of high importance for practical purposes.     

Lyapunov-type Inequalities for Differential Equations

Let us consider the linear boundary value problem

A representation of recursively enumerable sets through Horn formulas in higher recursion theory

We prove the existence of graphs with empty intersection of their longest paths or cycles as subgraphs of lattices on the torus and the Möbius strip.