Osmium isotope variations accompanying the eruption of a single lava flow field in the Columbia River Flood Basalt Province

Geochemical interpretations of continental flood basalts usually assume that individual lava flows represent compositionally homogenous and rapidly erupted products of large well-mixed magma reservoirs. However, inflated pāhoehoe lavas may develop over considerable periods of time and preserve chemical variations that can be temporally linked through flow formation to eruption sequence thus providing an understanding of magma evolution over the timescale of a single eruption. This study presents comprehensive major, trace element and Re–Os isotope data for a single eruption that formed the 2660 km3 Sand Hollow flow field in the Columbia River Basalt Province, USA. Major and trace element variations accompanying flow emplacement (e.g. MgO 3.09–4.55 wt%, Ni 17.5–25.6 ppm) are consistent with fractional crystallisation, but other petrogenetic processes or variable sources cannot be distinguished. However, there is a systematic shift in the initial 187Os/188Os isotope composition of the magma (age corrected to 15.27 Ma), from 0.174 (lava core) to 1.444 (lava crust) within a single 35 m thick sheet lobe. Lava crust values are more radiogenic than any known mantle source, consistent with previous data indicating that neither an enriched reservoir nor the sub-continental lithospheric mantle are likely to have sourced these basalts. Rather, these data indicate that lavas emplaced during the earliest stages of eruption have higher degrees of crustal contamination. These results highlight the limitations of applying chemostratigraphic correlation across continental flood basalt provinces, the use of single data points to define melt sources and magmatic processes, and the dangers of using conventional isochron techniques in such basalt sequences for absolute chronology

The nn-dual space of the space of pp-summable sequences

summary:In the theory of normed spaces, we have the concept of bounded linear functionals and dual spaces. Now, given an $n$-normed space, we are interested in bounded multilinear $n$-functionals and $n$-dual spaces. The concept of bounded multilinear $n$-functionals on an $n$-normed space was initially intoduced by White (1969), and studied further by Batkunde et al., and Gozali et al. (2010). In this paper, we revisit the definition of bounded multilinear $n$-functionals, introduce the concept of $n$-dual spaces, and then determine the $n$-dual spaces of $\ell^p$ spaces, when these spaces are not only equipped with the usual norm but also with some $n$-norms