Rationality of quotients by linear actions of affine groups

Let G be the (special) affine group, semidirect product of SL_n and C^n. In this paper we study the representation theory of G and in particular the question of rationality for V/G where V is a generically free G-representation. We show that the answer to this question is positive if the dimension of V is sufficiently large and V is indecomposable. We have a more precise theorem if V is a two-step extension 0 -> S -> V -> Q -> 0 with S, Q completely reducible.Comment: 18 pages; dedicated to Fabrizio Catanese on the occasion of his 60th birthda

Production mechanism of hot nuclei in violent collisions in the Fermi energy domain

A production mechanism of highly excited nuclei formed in violent collisions in the Fermi energy domain is investigated. The collision of two nuclei is decomposed into several stages which are treated separately. Simplified exciton concept is used for the description of pre-equilibrium emission. A modified spectator-participant scenario is used where motion along classical Coulomb trajectories is assumed. The participant and one of the spectator zones undergo incomplete fusion. Excitation energies of both cold and hot fragment are determined. Results of the calculation are compared to recent experimental data in the Fermi energy domain. Data on hot projectile-like, mid-velocity and fusion-like sources are described consistently. Geometric aspects of pre-equilibrium emission are revealed. Explanations to previously unexplained experimental phenomena are given. Energy deposited into non-thermal degrees of freedom is estimated.Comment: To appear in Nuclear Physics A, 27 pages, 19 figures, LaTe

Molecular Mobility and Gas Transport Properties of Mixed Matrix Membranes Based on PIM-1 and a Phosphinine Containing Covalent Organic Framework

Polymers with intrinsic microporosity (PIMs) are gaining attention as gas separation membranes. Nevertheless, they face limitations due to their pronounced physical aging. In this study, a covalent organic framework containing λ5-phosphinine moieties, CPSF-EtO, was incorporated as a nanofiller (concentration range 0–10 wt %) into a PIM-1 matrix forming dense films with a thickness of ca. 100 μm. The aim of the investigation was to investigate possible enhancements of gas transport properties and mitigating effects on physical aging. The incorporation of the nanofiller occurred on an nanoaggregate level with domains up to 100 nm, as observed by T-SEM and confirmed by X-ray scattering. Moreover, the X-ray data show that the structure of the microporous network of the PIM-1 matrix is changed by the nanofiller. As molecular mobility is fundamental for gas transport as well as for physical aging, the study includes dielectric investigations of pure PIM-1 and PIM-1/CPSF-EtO mixed matrix membranes to establish a correlation between the molecular mobility and the gas transport properties. Using the time-lag method, the gas permeability and the permselectivity were determined for N2, O2, CH4, and CO2 for samples with variation in filler content. A significant increase in the permeability of CH4 and CO2 (50% increase compared to pure PIM-1) was observed for a concentration of 5 wt % of the nanofiller. Furthermore, the most pronounced change in the permselectivity was found for the gas pair CO2/N2 at a filler concentration of 7 wt %

Oases in the Sahara Desert–Linking biological and cultural diversity

The diversity of life sensu lato comprises both biological and cultural diversity, described as “biocultural diversity.” Similar to plant and animal species, cultures and languages are threatened by extinction. Since drylands are pivotal systems for nature and people alike, we use oases in the Sahara Desert as model systems for examining spatial patterns and trends of biocultural diversity. We identify both the underlying drivers of biodiversity and the potential proxies that are fundamental for understanding reciprocal linkages between biological and cultural diversity in oases. Using oases in Algeria as an example we test current indices describing and quantifying biocultural diversity and identify their limitations. Finally, we discuss follow-up research questions to better understand the underlying mechanisms that control the coupling and decoupling of biological and cultural diversity in oases

Projected impacts of climate change on functional diversity of frugivorous birds along a tropical elevational gradient

Climate change forces many species to move their ranges to higher latitudes or elevations. Resulting immigration or emigration of species might lead to functional changes, e.g., in the trait distribution and composition of ecological assemblages. Here, we combined approaches from biogeography (species distribution models; SDMs) and community ecology (functional diversity) to investigate potential effects of climate-driven range changes on frugivorous bird assemblages along a 3000 m elevational gradient in the tropical Andes. We used SDMs to model current and projected future occurrence probabilities of frugivorous bird species from the lowlands to the tree line. SDM-derived probabilities of occurrence were combined with traits relevant for seed dispersal of fleshy-fruited plants to calculate functional dispersion (FDis; a measure of functional diversity) for current and future bird assemblages. Comparisons of FDis between current and projected future assemblages showed consistent results across four dispersal scenarios, five climate models and two representative concentration pathways. Projections indicated a decrease of FDis in the lowlands, an increase of FDis at lower mid-elevations and little changes at high elevations. This suggests that functional dispersion responds differently to global warming at different elevational levels, likely modifying avian seed dispersal functions and plant regeneration in forest ecosystems along tropical mountains

Twenty-million-year relationship between mammalian diversity and primary productivity

At global and regional scales, primary productivity strongly correlates with richness patterns of extant animals across space, suggesting that resource availability and climatic conditions drive patterns of diversity. However, the existence and consistency of such diversity–productivity relationships through geological history is unclear. Here we provide a comprehensive quantitative test of the diversity–productivity relationship for terrestrial large mammals through time across broad temporal and spatial scales. We combine >14,000 occurrences for 690 fossil genera through the Neogene (23–1.8 Mya) with regional estimates of primary productivity from fossil plant communities in North America and Europe. We show a significant positive diversity–productivity relationship through the 20-million-year record, providing evidence on unprecedented spatial and temporal scales that this relationship is a general pattern in the ecology and paleo-ecology of our planet. Further, we discover that genus richness today does not match the fossil relationship, suggesting that a combination of human impacts and Pleistocene climate variability has modified the 20-million-year ecological relationship by strongly reducing primary productivity and driving many mammalian species into decline or to extinction