Singular solutions of fully nonlinear elliptic equations and applications

We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in each cone of $\mathbb{R}^n$, and the solutions are unique in an appropriate sense. We introduce a new method for analyzing the behavior of solutions near certain Lipschitz boundary points, which permits us to classify isolated boundary singularities of solutions which are bounded from either above or below. We also obtain a sharp Phragm\'en-Lindel\"of result as well as a principle of positive singularities in certain Lipschitz domains.Comment: 41 pages, 2 figure

The environmental effectiveness of the Higher Level Stewardship scheme; resurveying the baseline agreement monitoring sample to quantify change between 2009 and 2016. Full technical final report

Agri-environment schemes (AES) are one of the most significant mechanism for delivering environmental policy within England, both in terms of expenditure and coverage of land. AES are multi-objective, primarily addressing conservation of wildlife, landscapes and the historic environment and providing public access as well as addressing broader environmental issues such as climate change and flood management. This project contributes to evaluation of the Higher Level Stewardship (HLS) AES, which was designed to achieve the highest standards of environmental management and target features of the greatest conservation value, including Sites of Special Scientific Interest (SSSIs). Monitoring is a key element of scheme delivery in order to assess the efficacy of AES, and determine which factors contribute to successful AES outcomes. Here, we resurveyed a sample of HLS agreements (surveyed 6-7 years previously), to assess environmental outcomes and in particular change in plant communities over time in relation to AES management. The assessment of change over time allowed the effects of AES management to be quantified against defined objectives, as opposed to drawing conclusions from a single assessment where the conservation value of land entered into an AES can be confounded with AES management effects

Designing a survey to monitor multi-scale impacts of agri-environment schemes on mobile taxa

Agri-environment schemes (AES) are key mechanisms to deliver conservation policy, and include management to provide resources for target taxa. Mobile species may move to areas where resources are increased, without this necessarily having an effect across the wider countryside or on populations over time. Most assessments of AES efficacy have been at small spatial scales, over short timescales, and shown varying results. We developed a survey design based on orthogonal gradients of AES management at local and landscape scales, which will enable the response of several taxa to be monitored. An evidence review of management effects on butterflies, birds and pollinating insects provided data to score AES options. Predicted gradients were calculated using AES uptake, weighted by the evidence scores. Predicted AES gradients for each taxon correlated strongly, and with the average gradient across taxa, supporting the co-location of surveys across different taxa. Nine 1 × 1 km survey squares were selected in each of four regional blocks with broadly homogenous background habitat characteristics. Squares in each block covered orthogonal contrasts across the range of AES gradients at local and landscape scales. This allows the effects of AES on species at each scale, and the interaction between scales, to be tested. AES options and broad habitats were mapped in field surveys, to verify predicted gradients which were based on AES option uptake data. The verified AES gradient had a strong positive relationship with the predicted gradient. AES gradients were broadly independent of background habitat within each block, likely allowing AES effects to be distinguished from potential effects of other habitat variables. Surveys of several mobile taxa are ongoing. This design will allow mobile taxa responses to AES to be tested in the surrounding countryside, as well as on land under AES management, and potentially in terms of population change over time. The design developed here provides a novel, pseudo-experimental approach for assessing the response of mobile species to gradients of management at two spatial scales. A similar design process could be applied in other regions that require a standardized approach to monitoring the impacts of management interventions on target taxa at landscape scales, if equivalent spatial data are available

Energetic particle influence on the Earth's atmosphere

This manuscript gives an up-to-date and comprehensive overview of the effects of energetic particle precipitation (EPP) onto the whole atmosphere, from the lower thermosphere/mesosphere through the stratosphere and troposphere, to the surface. The paper summarizes the different sources and energies of particles, principally galactic cosmic rays (GCRs), solar energetic particles (SEPs) and energetic electron precipitation (EEP). All the proposed mechanisms by which EPP can affect the atmosphere are discussed, including chemical changes in the upper atmosphere and lower thermosphere, chemistry-dynamics feedbacks, the global electric circuit and cloud formation. The role of energetic particles in Earth’s atmosphere is a multi-disciplinary problem that requires expertise from a range of scientific backgrounds. To assist with this synergy, summary tables are provided, which are intended to evaluate the level of current knowledge of the effects of energetic particles on processes in the entire atmosphere

Measurement of the cross section for isolated-photon plus jet production in pp collisions at √s=13 TeV using the ATLAS detector

The dynamics of isolated-photon production in association with a jet in proton–proton collisions at a centre-of-mass energy of 13 TeV are studied with the ATLAS detector at the LHC using a dataset with an integrated luminosity of 3.2 fb−1. Photons are required to have transverse energies above 125 GeV. Jets are identified using the anti- algorithm with radius parameter and required to have transverse momenta above 100 GeV. Measurements of isolated-photon plus jet cross sections are presented as functions of the leading-photon transverse energy, the leading-jet transverse momentum, the azimuthal angular separation between the photon and the jet, the photon–jet invariant mass and the scattering angle in the photon–jet centre-of-mass system. Tree-level plus parton-shower predictions from Sherpa and Pythia as well as next-to-leading-order QCD predictions from Jetphox and Sherpa are compared to the measurements