The resultant on compact Riemann surfaces

We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the exponential transform of a quadrature domain in the complex plane is expressed in terms of the resultant of two meromorphic functions on the Schottky double of the domain.Comment: 44 page

Palaeoenvironmental control on distribution of crinoids in the Bathonian (Middle Jurassic) of England and France

Bulk sampling of a number of different marine and marginal marine lithofacies in the British Bathonian has allowed us to assess the palaeoenvironmental distribution of crinoids for the first time. Although remains are largely fragmentary, many species have been identified by comparison with articulated specimens from elsewhere, whilst the large and unbiased sample sizes allowed assessment of relative proportions of different taxa. Results indicate that distribution of crinoids well corresponds to particular facies. Ossicles of Chariocrinus and Balanocrinus dominate in deeper-water and lower-energy facies,with the former extending further into shallower-water facies than the latter. Isocrinus dominates in shallower water carbonate facies, accompanied by rarer comatulids, and was also present in the more marine parts of lagoons. Pentacrinites remains are abundant in very high-energy oolite shoal lithofacies. The presence of millericrinids within one, partly allochthonous lithofacies suggests the presence of an otherwise unknown hard substrate from which they have been transported. These results are compared to crinoid assemblages from other Mesozoic localities, and it is evident that the same morphological ad-aptations are present within crinoids from similar lithofacies throughout the Jurassic and Early Cretaceous

Age and nature of eclogites in the Huwan shear zone, and the multi-stage evolution of the Qinling-Dabie-Sulu orogen, central China

In situ LA-ICPMS U-Pb, trace element, and Hf isotope data in zircon demonstrate a Carboniferous age for eclogite-facies metamorphism in Siluro-Devonian protoliths in the Huwan shear zone, Dabie Mountains, Central China. This age contrasts with the more prevailing Triassic age for high- to ultrahigh pressure (HP to UHP) metamorphism in the Qinling-Dabie-Sulu orogen. Metamorphic zircon in two eclogite samples from Sujiahe is characterized by low Th/U ratios, small negative Eu anomalies, flat HREE patterns, and lo