Colourants and opacifiers in seventh and eighth century glass investigated by spectroscopic techniques

Glass fragments dating from the seventh and eighth century AD were excavated in the Crypta Balbi in Rome. They were studied to detect agents involved in colour development and opacification. Reflectance spectra recorded on powdered samples revealed the contribution of Fe(II), Fe(III), Mn(III), Cu(II), and Co(II) ions in determining colour hues. The effect of the Mn/Fe atomic ratio on glass colour is discussed. It is apparent that medieval glassmakers in Italy could obtain a wide range of colours by exploiting the presence of iron and manganese as contaminants of sand and flux and controlling the amount of oxygen let into the furnace. X-ray diffraction and scanning electron microscopy coupled with energy-dispersive X-ray analysis were used to study opaque fragments. The presence of calcium antimonate was detected in white, blue, and blue-green fragments, and elemental copper was detected in a red glass.     

Some new almost sure results on the functional increments of the uniform empirical process

Given an observation of the uniform empirical process α_n, its functional increments α_n(u+a_n⋅)−α_n(u) can be viewed as a single random process, when u is distributed under the Lebesgue measure. We investigate the almost sure limit behaviour of the multivariate versions of these processes as n→∞ and a_n↓0. Under mild conditions on a_n, a convergence in distribution and functional limit laws are established. The proofs rely on a new extension of the usual Poissonisation tools for the local empirical process.     

Carbene-mediated transformations of 1-(benzylideneamino)benzimidazoles

Carbene-mediated transformations of N-(3-butylbenzimidazol-3-ium-1-yl)-1-arylmethanimine iodides with carbon disulfide and benzoyl isothiocyanate gave the corresponding NHC·CS(2) betaines in 68-85% and benzoyl-[1-butyl-3-[(E)-(aryl)methyleneamino]benzimidazol-1-ium-2-carbothioyl]azanides, respectively, in 74-85% yields. However, reaction with excess isopropyl isothiocyanate in NaH/THF at room temperature yielded the 1-butyl-1',3'-diisopropyl-3-[(E)-(aryl)methyleneamino]spiro[benzimidazole-2,5'-imidazolidine]-2',4'-dithiones (74-77%).     

The asymptotically sharp Korn interpolation and second inequalities for shells

We consider shells in three-dimensional Euclidean space that have bounded principal curvatures. We prove Korn's interpolation (or the so-called first and a half¹) and the second inequalities on that kind of shells for $\mathit{u}\in W^{1,2}$ vector fields, imposing no boundary or normalization conditions on u. The constants in the estimates are optimal in terms of the asymptotics in the shell thickness h, having the scalings h or $O(1)$. The Korn interpolation inequality reduces the problem of deriving any linear Korn type estimate for shells to simply proving a Poincaré-type estimate with the symmetrized gradient on the right-hand side. In particular, this applies to linear geometric rigidity estimates for shells, i.e. Korn's fist inequality without boundary conditions.     

Diphenyl(dipyrazolyl)methane complexes of Ni: synthesis, structural characterization, and chromotropism of NiBr2 derivatives

The reaction of NiBr2 with the bidentate ligand diphenyl(dipyrazolyl)methane (dpdpm) gives the pentacoordinated complexes [(dpdpm)Ni(mu-Br)Br]2 (1), [(dpdpm)NiBr2(H2O)] (2a), and [(dpdpm)NiBr(H2O)2]Br (2b), or the octahedral complexes [(dpdpm)NiBr(H2O)2(CH3CN)]Br (3), [(dpdpm)2NiBr2] (4), and [(dpdpm)2NiBr(H2O)]Br (5). All of these complexes are paramagnetic, both in the solid state and in solution, and have been characterized by spectroscopic (IR, NMR, and UV-vis-NIR) and X-ray diffraction studies. The unoccupied coordination site in the pentacoordinated compounds allows long-range interactions, in the solid state, between the Ni center and a Ph substituent of the dpdpm ligand. These weak interactions are replaced by Ni-solvent interactions, both in the solid state and in solution, facilitating the interconversion of these compounds under various reaction conditions and leading to interesting solvato-, vapo-, and thermochromic properties. UV-vis-NIR spectroscopy has been used to study these phenomena. Absorption spectra for the room-temperature methanol or acetonitrile solutions of the pentacoordinate or octahedral compounds show three main bands in the region of 350-1000 nm that represent spin-allowed (d-d) transitions from the ground state 3A2g to the excited states 3T2g, 3T1g(3F), and 3T1g(3P). A weak shoulder was also detected on the middle peak in most spectra (700-800 nm), representing the spin-forbidden 3A2g-->1Eg transition. On the other hand, the spectra of high-temperature CH2Cl2 or acetone solutions of all complexes show four main bands at ca. 490, 650-660, 860, and 1000 nm, in addition to a shoulder on the first or second band.