Whittaker-Hill equation and semifinite-gap Schroedinger operators

A periodic one-dimensional Schroedinger operator is called semifinite-gap if every second gap in its spectrum is eventually closed. We construct explicit examples of semifinite-gap Schroedinger operators in trigonometric functions by applying Darboux transformations to the Whittaker-Hill equation. We give a criterion of the regularity of the corresponding potentials and investigate the spectral properties of the new operators.Comment: Revised versio

The opportunities and challenges to co-designing policy options for tree health with policy makers, researchers and land managers

\ua9 2023. We describe experiences between 2018 and 2021 co-designing tree health policy options linked with the UK\u27s evolving land use policy post EU-Exit within the Future Farming and Countryside Programme. Policy makers, researchers and more than 250 land managers took part in a series of co-design engagements in a three-phase iterative co-design process that culminated in a new Tree Health Pilot. After defining the components of co-design, we describe how relationships between policy makers, researchers and land managers were built, the methods researchers introduced into the process to build capability and support participation, and the outcomes in terms of the key opportunities and challenges for policy co-design. We conclude that it is possible to move policy design beyond user focused research and into co-design. However, this relies on adequate time and resources required to build trust and fully engage all parties in a meaningful way, including the development of tools and techniques that include experimentation, different knowledge types, and moving from research and evidence collection into design. Having policy makers with participatory mindsets in the same space as land managers was important to facilitating active learning between all of those involved in the collective. Researchers played a critical role in the co-design, balancing the views and understandings of the policy community with those of the land manager community, facilitating learning, and selecting tools and techniques to make design options explicit. We conclude that policy co-design in the land-based and environmental sector is a real opportunity at an early stage of realisation, but the effectiveness and range of positive and negative outcomes and impacts will need to be evaluated in the future

Patterns of benthic mega-invertebrate habitat associations in the Pacific Northwest continental shelf waters

As human impacts and demands for ocean space increase (fisheries, aquaculture, marine reserves, renewable energy), identification of marine habitats hosting sensitive biological assemblages has become a priority. Epifaunal invertebrates, especially the structure-forming species, are an increasing conservation concern as many traditional (bottom-contact fishing) and novel (marine renewable energy) ocean uses have the potential to displace or otherwise impact these slow-growing organisms. The differences in mega-invertebrate species assemblages between high-relief rocks and low-relief sediments are well documented and likely hold for most marine environments. In anticipation of potential development of marine renewable energy faculties off Oregon and Washington (USA), a survey of the benthic invertebrate assemblages and habitats was conducted on the continental shelf of the Pacific Northwest, using video footage collected by ROV, to more finely characterize these assemblage-habitat associations. Four main associations were found: pure mud/sand dominated by sea whips and burrowing brittle stars; mixed mud-rock (which may be further divided based on size of mixed-in rocks) characterized by various taxa at small densities; consolidated rocks characterized by high diversity and density of sessile or motile mega-invertebrates; and rubble rocks showing less diversity and density than the consolidated rocks, possibly due to the disturbance generated by movement of the unconsolidated rocks. The results of this study will help classify and map the seafloor in a way that represents benthic habitats reflective of biological species assemblage distributions, rather than solely geological features, and support conservation and management planning.Keywords: Soft sediment, Benthic assemblage, Rocky reef, Epifauna, Underwater vide

On Darboux-Treibich-Verdier potentials

It is shown that the four-parameter family of elliptic functions $$u_D(z)=m_0(m_0+1)\wp(z)+\sum_{i=1}^3 m_i(m_i+1)\wp(z-\omega_i)$$ introduced by Darboux and rediscovered a hundred years later by Treibich and Verdier, is the most general meromorphic family containing infinitely many finite-gap potentials.Comment: 8 page

Human Impacts on Forest Biodiversity in Protected Walnut-Fruit Forests in Kyrgyzstan

We used a spatially explicit model of forest dynamics, supported by empirical field data and socioeconomic data, to examine the impacts of human disturbances on a protected forest landscape in Kyrgyzstan. Local use of 27 fruit and nut species was recorded and modeled. Results indicated that in the presence of fuelwood cutting with or without grazing, species of high socioeconomic impor- tance such as Juglans regia, Malus spp., and Armeniaca vulgaris were largely eliminated from the landscape after 50–150 yr. In the absence of disturbance or in the presence of grazing only, decline of these species occurred at a much lower rate, owing to competi- tive interactions between tree species. This suggests that the current intensity of fuelwood harvesting is not sustainable. Conversely, cur- rent grazing intensities were found to have relatively little impact on forest structure and composition, and could potentially play a positive role in supporting regeneration of tree species. These results indicate that both positive and negative impacts on biodiversity can arise from human populations living within a protected area. Potentially, these could be reconciled through the development of participatory approaches to conservation management within this reserve, to ensure the maintenance of its high conservation value while meeting human needs

The macro- and megabenthic fauna on the continental shelf of the eastern Amundsen Sea, Antarctica

In 2008 the BIOPEARL II expedition on board of RRS James Clark Ross sailed to the eastern Amundsen Sea Embayment and Pine Island Bay, one of the least studied Antarctic continental shelf regions due to its remoteness and ice cover. A total of 37 Agassiz trawls were deployed at depth transects along the continental and trough slopes. A total of 5,469 specimens, belonging to 32 higher taxonomic groups and more than 270 species, were collected. Species richness per station varied from 1–55. The benthic assemblages were dominated by echinoderms and clearly different to those in the Ross, Scotia and Weddell seas. Here we present the macro- and megafaunal assemblage structure, its species richness and the presence of several undescribed species

Comparison of the bifurcation scenarios predicted by the single-mode and multimode semiconductor laser rate equations

We present a detailed comparison of the bifurcation scenarios predicted by single-mode and multimode semiconductor laser rate equation models under large amplitude injection current modulation. The influence of the gain model on the predicted dynamics is investigated. Calculations of the dependence of the time averaged longitudinal mode intensities on modulation frequency are compared with experiments performed on an AlxGa1-xAs Fabry-Pérot semiconductor laser.K. A. Corbett and M. W. Hamilto