Zircon M127 - A Homogeneous Reference Material for SIMS U-Pb Geochronology Combined with Hafnium, Oxygen and, Potentially, Lithium Isotope Analysis

In this article, we document a detailed analytical characterisation of zircon M127, a homogeneous 12.7 carat gemstone from Ratnapura, Sri Lanka. Zircon M127 has TIMS-determined mean U-Pb radiogenic isotopic ratios of 0.084743 ± 0.000027 for 206Pb/238U and 0.67676 ± 0.00023 for 207Pb/235U (weighted means, 2s uncertainties). Its 206Pb/238U age of 524.36 ± 0.16 Ma (95% confidence uncertainty) is concordant within the uncertainties of decay constants. The d18O value (determined by laser fluorination) is 8.26 ± 0.06‰ VSMOW (2s), and the mean 176Hf/177Hf ratio (determined by solution ICP-MS) is 0.282396 ± 0.000004 (2s). The SIMS-determined d7Li value is -0.6 ± 0.9‰ (2s), with a mean mass fraction of 1.0 ± 0.1 µg g-1 Li (2s). Zircon M127 contains ~ 923 µg g-1 U. The moderate degree of radiation damage corresponds well with the time-integrated self-irradiation dose of 1.82 × 1018 alpha events per gram. This observation, and the (U-Th)/He age of 426 ± 7 Ma (2s), which is typical of unheated Sri Lankan zircon, enable us to exclude any thermal treatment. Zircon M127 is proposed as a reference material for the determination of zircon U-Pb ages by means of SIMS in combination with hafnium and stable isotope (oxygen and potentially also lithium) determination

Regular elements and Green's relations in Generalised Linear Transformation Semigroups

If V and W are vector spaces over the same field, we let P(V,W) denote the set of all partial linear transformations from V into W (that is, all linear mappings whose domain and range are subspaces of V and W, respectively). If $\theta\in P(W,V)$, then P(V,W) is a so-called `generalised semigroup' of linear transformations under the `sandwich operation': $\alpha *\beta=\alpha\circ\theta\circ\beta$, for each $\alpha,\beta\in P(V,W)$. We denote this semigroup by $P(V,W,\theta)$ and, in this paper, we characterise Green's relations on it: that is, we study equivalence relations which determine when principal left (or right, or 2-sided) ideals in $P(V,W,\theta)$ are equal. This is related to a problem raised by Magill and Subbiah in 1975. We also discuss the same idea for important subsemigroups of $P(V,W,\theta)$ and characterise when these semigroups satisfy certain regularity conditions.Fundação para a Ciência e a Tecnologia (FCT