An Investigation of the N-Arylsulfonylation of 2-Azetidinones

N-Arylsulfonylation of 2-azetidinones can lead to the diastereoselective formation of oligomerization products. However, a simple increase of arylsulfonyl chloride concentration minimized oligomerization and allowed preparation of 1-arylsulfonyl-2-azetidinones in good yield.     

Spectroscopic Study of Egyptian Blue Mixed with Other Pigments

The Romans used a vast array of colors in their mural paints. The applied pigment mixtures containing Egyptian blue resulting in green, ochre, brown, gray, and white hues were studied. The chromatic characterization of wall paintings by electronic spectroscopy provided an easy and reliable procedure for the grouping of the samples to be studied (see Table). Subsequent use of other spectroscopic techniques such as Fourier‐transform (FT) IR and energy‐dispersive X‐ray spectroscopy (EDS), combined with X‐ray diffraction (XRD), led to convenient identification of the pictorial layer components that define and differentiate each chromatic group. Colors impossible to produce with only one pigment can be obtained by mixing Egyptian blue with other pigments. The dominant wavelength is displaced in such way that the artist obtains new tonalities.     

Spatial energy estimates in dynamical problems for a semi-infinite piezoelectric beam

The behaviour of the total energy for a semi-infinite piezoelectricbeam, with uniform or variable cross-section, in dynamical conditionsis investigated. Precisely, we obtain some estimates in termsof the data for the energy of the portion of the body at distancegreater than z from the base and for its norm in L¹(0,t) (wheret is an arbitrary positive time). We obtain some estimates whichdepend on the initial data if t z/V (where V is a computablepositive material constant); if t > z/V, by using also theKorn inequality, we show that the bounds depend on all the data.Under mild hypotheses on the initial data we derive the asymptoticbehaviour of the energy as z +. All possible combinations ofboundary conditions are examined and the kind of the estimateis formally the same for all the problems whether the beam isa cylinder or not.