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The aim of this paper is to construct left-invariant Einstein pseudo-Riemannian Sasaki metrics on solvable Lie groups. We consider the class of $\mathfrak z$-standard Sasaki solvable Lie algebras of dimension $2n+3$, which are in one-to-one correspondence with pseudo-K\"ahler nilpotent Lie algebras of dimension $2n$ endowed with a compatible derivation, in a suitable sense. We characterize the pseudo-K\"ahler structures and derivations giving rise to Sasaki-Einstein metrics. We classify $\mathfrak z$-standard Sasaki solvable Lie algebras of dimension $\leq 7$ and those whose pseudo-K\"ahler reduction is an abelian Lie algebra. The Einstein metrics we obtain are standard, but not of pseudo-Iwasawa type., Comment: 26 pages, 2 figures; v2: corrected Proposition 4.3 and Theorem 4.4 to account for the sign ambiguity; v3: improved notation and presentation; introduction and Section 1 expanded to illustrate the geometric meaning of the construction; Examples 3.9 and 4.6 expanded; title changed for clarity; added Example 2.6 and two figures

Relevant information on the technology employed in the production of concotto and coarse pottery was derived mainly by 57Fe Mossbauer spectroscopy. The concotto and the coarse pottery are two types of fired clay mixtures unearthed from the protohistoric settlement site of Concordia Sagittaria. The concotto pottery was produced by firing clay mixtures under oxidizing conditions at high temperatures in kilns, or at lower temperatures in open air. The firing of these clay mixtures, containing partially ground pieces of waste pottery, resulted in hard, impermeable and coloured construction materials, particularly suitable for humid environments. In turn, the coarse pottery was produced by firing clay mixtures less heterogeneous than those of the concotto. The firing was performed under reducing conditions at high temperature with a final exposition to air by opening the still hot kiln. This firing technique yielded light and agreeable coarse pottery with a red-coloured surface covering the grey–black core. Both the ancient firing techniques were substantially reconstructed by comparing the Mossbauer patterns of the artefacts with those of the replica samples produced from local clay fired in the laboratory.

Neutron-scattering and magnetization experiments on ${R}_{x}{\mathrm{Sc}}_{1\ensuremath{-}x}$ ($R=\mathrm{G}\mathrm{d},\phantom{\rule{0ex}{0ex}}\mathrm{T}\mathrm{b},\phantom{\rule{0ex}{0ex}}\mathrm{H}\mathrm{o},\phantom{\rule{0ex}{0ex}}\mathrm{a}\mathrm{n}\mathrm{d}\phantom{\rule{0ex}{0ex}}\mathrm{E}\mathrm{r}$) alloys have given anomalous results for the concentration dependence of the magnetic-ordering temperature. In contrast to conventional theoretical arguments and to data on other rare-earth alloys, these systems require large rare-earth concentrations ($15%l~xl~39%$) for the onset of long-range magnetic order to occur. The work which we report here deals with the investigation of the ${\mathrm{Dy}}_{x}{\mathrm{Sc}}_{1\ensuremath{-}x}$ system in the concentration range $0.02l~xl~0.75$. The M\"ossbauer effect was used to examine the magnetic hyperfine interaction at the $^{161}\mathrm{Dy}$ nuclei both as a function of temperature and concentration. Neutron scattering on the samples containing 35-at.% Dy indicated no long-range magnetic order at $T=4.2$ K. However, each of the alloys investigated, including the 2-at.% Dy alloy which was the lowest concentration measured, exhibits a well-defined magnetic hyperfine splitting at this temperature. The magnitude of this splitting is 45 \ifmmode\pm\else\textpm\fi{} 0.5 cm/sec and corresponds to a field approximately equal to that found in pure Dy metal, and is independent of the Dy concentration contained in the alloy. The observed magnetic hyperfine lines for the alloys in the lower Dy concentration region (\ensuremath{\le}25%) are relaxation broadened with increasing temperature, while the overall splitting remains essentially independent of temperature. These spectra are analyzed in terms of an electronic-spin-relaxation model for an effective spin-\textonehalf{} system.

TbxSc1−x and CdxSc1−x alloys have been shown to exhibit no long‐range magnetic order for x