Lower bound for energies of harmonic tangent unit-vector fields on convex polyhedra

We derive a lower bound for energies of harmonic maps of convex polyhedra in $\R^3$ to the unit sphere $S^2,$ with tangent boundary conditions on the faces. We also establish that $C^\infty$ maps, satisfying tangent boundary conditions, are dense with respect to the Sobolev norm, in the space of continuous tangent maps of finite energy.Comment: Acknowledgment added, typos removed, minor correction

Ongoing, but slowing, habitat loss in a rural landscape over 85 years

© 2019, The Author(s). Context: Studies evaluating biodiversity loss and altered ecosystem services have tended to examine changes over the last few decades, despite the fact that land use change and its negative impacts have been occurring over a much longer period. Examining past land use change, particularly over the long-term and multiple time periods, is essential for understanding how rates and drivers of change have varied historically. Objectives: To quantify and assess patterns of change in semi-natural habitats across a rural landscape at five time points between 1930 and 2015. Methods: We determined the habitat cover at over 3700 sites across the county of Dorset, southern England in 1930, 1950, 1980, 1990 and 2015, using historical vegetation surveys, re-surveys, historical maps and other contemporary spatial data. Results: Considerable declines in semi-natural habitats occurred across the Dorset landscape between 1930 and 2015. This trend was non-linear for the majority of semi-natural habitats, with the greatest losses occurring between 1950 and 1980. This period coincides with the largest gains to arable and improved grassland, reflecting agricultural expansion after the Second World War. Although the loss of semi-natural habitats declined after this period, largely because there were very few sites left to convert, there were still a number of habitats lost within the last 25 years. Conclusions: The findings illustrate a long history of habitat loss in the UK, and are important for planning landscape management and ameliorative actions, such as restoration. Our analysis also highlights the role of statutory protection in retaining semi-natural habitats, suggesting the need for continued protection of important habitats

Forest landscape restoration in the drylands of Latin America

Forest Landscape Restoration (FLR) involves the ecological restoration of degraded forest landscapes, with the aim of benefiting both biodiversity and human well-being. We first identify four fundamental principles of FLR, based on previous definitions. We then critically evaluate the application of these principles in practice, based on the experience gained during an international, collaborative research project conducted in six dry forest landscapes of Latin America. Research highlighted the potential for FLR; tree species of high socioeconomic value were identified in all study areas, and strong dependence of local communities on forest resources was widely encountered, particularly for fuelwood. We demonstrated that FLR can be achieved through both passive and active restoration approaches, and can be cost-effective if the increased provision of ecosystem services is taken into account. These results therefore highlight the potential for FLR, and the positive contribution that it could make to sustainable development. However, we also encountered a number of challenges to FLR implementation, including the difficulty of achieving strong engagement in FLR activities among local stakeholders, lack of capacity for community-led initiatives, and the lack of an appropriate institutional and regulatory environment to support restoration activities. Successful implementation of FLR will require new collaborative alliances among stakeholders, empowerment and capacity building of local communities to enable them to fully engage with restoration activities, and an enabling public policy context to enable local people to be active participants in the decision making process. © 2012 by the author(s). Published here under license by the Resilience Alliance

Effect of Lowered Light Quality (R:FR Ratio) at Targeted Organs on Branching of Trifolium Repens

This report examined results from four similarly conducted experiments using Trifolium repens in which the R:FR ratio but not the photosynthetically active radiation (PAR) of incident light was altered at specific organ(s) of several successive phytomers or just at a single phytomer. Results indicate the local response to lowered R:FR light treatment was similar irrespective of the number of phytomers treated. This response pattern provides the means whereby plants can initiate strong localised responses to a heterogeneous light environment

Inconsistent detection of extinction debts using different methods

© 2020 The Authors. Ecography published by John Wiley & Sons Ltd on behalf of Nordic Society Oikos The extinction debt, delayed species extinctions following landscape degradation, is a widely discussed concept. But a consensus about the prevalence of extinctions debts is hindered by a multiplicity of methods and a lack of comparisons among habitats. We applied three contrasting species–area relationship methods to test for plant community extinction debts in three habitats which had different degradation histories over the last century: calcareous grassland, heathland and woodland. These methods differ in their data requirements, with the first two using information on past and current habitat area alongside current species richness, whilst the last method also requires data on past species richness. The most data-intensive, and hence arguably most reliable method, identified extinction debts across all habitats for specialist species, whilst the other methods did not. All methods detected an extinction debt in calcareous grassland, which had undergone the most severe degradation. We conclude that some methods failed to detect an extinction debt, particularly in habitats that have undergone moderate degradation. Data on past species numbers are required for the most reliable method; as such data are rare, extinction debts may be under-reported

Local states of free bose fields

These notes contain an extended version of lectures given at the ``Summer School on Large Coulomb Systems'' in Nordfjordeid, Norway, in august 2003. They furnish a short introduction to the theory of quantum harmonic systems, or free bose fields. The main issue addressed is the one of local states. I will adopt the definition of Knight of ``strictly local excitation of the vacuum'' and will then state and prove a generalization of Knight's Theorem which asserts that finite particle states cannot be perfectly localized. It will furthermore be explained how Knight's a priori counterintuitive result can be readily understood if one remembers the analogy between finite and infinite dimensional harmonic systems alluded to above. I will also discuss the link between the above result and the so-called Newton-Wigner position operator thereby illuminating, I believe, the difficulties associated with the latter. I will in particular argue that those difficulties do not find their origin in special relativity or in any form of causality violation, as is usually claimed

Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities

We examine in detail the relative equilibria in the four-vortex problem where two pairs of vortices have equal strength, that is, \Gamma_1 = \Gamma_2 = 1 and \Gamma_3 = \Gamma_4 = m where m is a nonzero real parameter. One main result is that for m > 0, the convex configurations all contain a line of symmetry, forming a rhombus or an isosceles trapezoid. The rhombus solutions exist for all m but the isosceles trapezoid case exists only when m is positive. In fact, there exist asymmetric convex configurations when m < 0. In contrast to the Newtonian four-body problem with two equal pairs of masses, where the symmetry of all convex central configurations is unproven, the equations in the vortex case are easier to handle, allowing for a complete classification of all solutions. Precise counts on the number and type of solutions (equivalence classes) for different values of m, as well as a description of some of the bifurcations that occur, are provided. Our techniques involve a combination of analysis and modern and computational algebraic geometry

Measurement of O17(p,γ)F18 between the narrow resonances at Erlab=193 and 519keV

The O17(p,γ)F18 reaction sensitively influences hydrogen burning nucleosynthesis in a number of stellar sites, including classical novae. These thermonuclear explosions, taking place in close binary star systems, produce peak temperatures in the range of T=100-400 MK. Recent results indicate that the thermonuclear rates for this reaction in this particular temperature range are dominated by the direct capture process. We report on the measurement of the O17(p,γ)F18 cross section between the narrow resonances at Erlab=193 and 519keV, where the S factor is expected to vary smoothly with energy. We extract the direct capture contribution from the total cross section and demonstrate that earlier data are inconsistent with our results

The Young Planetary System K2-25: Constraints on Companions and Starspots

The abundance of planets with orbital periods of a few to tens of days suggests that exoplanets experience complex dynamical histories. Planets in young stellar clusters or associations have well-constrained ages and therefore provide an opportunity to explore the dynamical evolution of exoplanets. K2-25b is a Neptune-sized planet in an eccentric, 3.48 day orbit around an M4.5 dwarf star in the Hyades cluster (650 Myr). In order to investigate its non-zero eccentricity and tight orbit, we analyze transit timing variations (TTVs) which could reveal clues to the migration processes that may have acted on the planet. We obtain 12 nonconsecutive transits using the MEarth observatories and long-term photometric monitoring, which we combine with 10 transits from the Spitzer Space Telescope and 20 transits from K2. Tables of MEarth photometry accompany this work. We fit each transit lightcurve independently. We first investigate whether inhomogeneities on the stellar surface (such as spots or plages) are differentially affecting our transit observations. The measured transit depth does not vary significantly between transits, though we see some deviations from the fiducial transit model. We then looked for TTVs as evidence of a nontransiting perturber in the system. We find no evidence for >1 M ? mass companions within a 2:1 period ratio, or for >5 M ? mass planets within a 7:2 period ratio

Bethe Ansatz solutions for highest states in N=4{\cal N}=4 SYM and AdS/CFT duality

We consider the operators with highest anomalous dimension $\Delta$ in the compact rank-one sectors $\mathfrak{su}(1|1)$ and $\mathfrak{su}(2)$ of ${\cal N}=4$ super Yang-Mills. We study the flow of $\Delta$ from weak to strong 't Hooft coupling $\lambda$ by solving (i) the all-loop gauge Bethe Ansatz, (ii) the quantum string Bethe Ansatz. The two calculations are carefully compared in the strong coupling limit and exhibit different exponents $\nu$ in the leading order expansion $\Delta\sim \lambda^{\nu}$. We find $\nu = 1/2$ and $\nu = 1/4$ for the gauge or string solution. This strong coupling discrepancy is not unexpected, and it provides an explicit example where the gauge Bethe Ansatz solution cannot be trusted at large $\lambda$. Instead, the string solution perfectly reproduces the Gubser-Klebanov-Polyakov law $\Delta = 2\sqrt{n} \lambda^{1/4}$. In particular, we provide an analytic expression for the integer level $n$ as a function of the U(1) charge in both sectors.Comment: 42 pages, JHEP style LaTe