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    Correlation inequalities for noninteracting Bose gases

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    For a noninteracting Bose gas with a fixed one-body Hamiltonian H^0 independent of the number of particles we derive the inequalities _N < _{N+1}, _N _N _N for i\neq j, \partial _N/\partial \beta >0 and ^+_N _N. Here N_i is the occupation number of the ith eigenstate of H^0, \beta is the inverse temperature and the superscript + refers to adding an extra level to those of H^0. The results follow from the convexity of the N-particle free energy as a function of N.Comment: a further inequality adde

    Integrated pest management portfolios in UK arable farming: results of a farmer survey.

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    Farmers are faced with a wide range of pest management (PM) options that can be adopted in isolation or alongside complementary or substitute strategies. This paper presents the results of a survey of UK cereal producers, focusing on the character and diversity of PM strategies currently used by, or available to, farmers. In addition, the survey asked various questions pertaining to agricultural policy participation, attitude towards environmental issues, sources of PM advice and information and the important characteristics of PM technologies. The results indicate that many farmers do make use of a suite of PM techniques, and that their choice of integrated PM (IPM) portfolio appears to be jointly dictated by farm characteristics and government policy. Results also indicate that portfolio choice does affect the number of subsequent insecticide applications per crop. These results help to identify the type of IPM portfolios considered to be adoptable by farmers and highlight the importance of substitution in IPM portfolios. As such, these results will help to direct R&D effort towards the realisation of more sustainable PM approaches and aid the identification of potential portfolio adopters. These findings highlight the opportunity that a revised agri-environmental policy design could generate in terms of enhancing coherent IPM portfolio adoption

    Consistent Quantum Counterfactuals

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    An analysis using classical stochastic processes is used to construct a consistent system of quantum counterfactual reasoning. When applied to a counterfactual version of Hardy's paradox, it shows that the probabilistic character of quantum reasoning together with the ``one framework'' rule prevents a logical contradiction, and there is no evidence for any mysterious nonlocal influences. Counterfactual reasoning can support a realistic interpretation of standard quantum theory (measurements reveal what is actually there) under appropriate circumstances.Comment: Minor modifications to make it agree with published version. Latex 8 pages, 2 figure

    Polarization Gradient Study of Interstellar Medium Turbulence Using The Canadian Galactic Plane Survey

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    We have investigated the magneto-ionic turbulence in the interstellar medium through spatial gradients of the complex radio polarization vector in the Canadian Galactic Plane Survey (CGPS). The CGPS data cover 1300 square-degrees, over the range 53∘≀ℓ≀192∘{53^{\circ}}\leq{\ell}\leq{192^{\circ}}, −3∘≀b≀5∘{-3^{\circ}}\leq{b}\leq{5^{\circ}} with an extension to b=17.5∘{b}={17.5^{\circ}} in the range 101∘≀ℓ≀116∘{101^{\circ}}\leq{\ell}\leq{116^{\circ}}, and arcminute resolution at 1420 MHz. Previous studies found a correlation between the skewness and kurtosis of the polarization gradient and the Mach number of the turbulence, or assumed this correlation to deduce the Mach number of an observed turbulent region. We present polarization gradient images of the entire CGPS dataset, and analyze the dependence of these images on angular resolution. The polarization gradients are filamentary, and the length of these filaments is largest towards the Galactic anti-center, and smallest towards the inner Galaxy. This may imply that small-scale turbulence is stronger in the inner Galaxy, or that we observe more distant features at low Galactic longitudes. For every resolution studied, the skewness of the polarization gradient is influenced by the edges of bright polarization gradient regions, which are not related to the turbulence revealed by the polarization gradients. We also find that the skewness of the polarization gradient is sensitive to the size of the box used to calculate the skewness, but insensitive to Galactic longitude, implying that the skewness only probes the number and magnitude of the inhomogeneities within the box. We conclude that the skewness and kurtosis of the polarization gradient are not ideal statistics for probing natural magneto-ionic turbulence.Comment: 21 pages, 15 figures, accepted by Ap

    Report on the 2018 trials of the multistatic NeXtRAD dual band polarimetric radar

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    NeXtRAD is a polarimetric, L and X Band, multistatic (three nodes), pulse Doppler radar, developed by UCT and UCL, as a follow on to the NetRAD sensor. This paper reports on the trials carried out in 2018, mostly in Simon's Bay, South Africa. The sensors (one active, two passive) are connected by WiFi communications link, with a maximum separation of 40 km. Practically, results are reported with 8 km maximum baselines. The focus is on targets in sea clutter and micro-Doppler. We report on the final integration and test of the system command and control system that allows for scheduling of measurement and recording of bursts of pulses, as well as video of the radar field of view. Some innovations have been made in terms of digital hardware, firmware, and high performance computing technology. The system is synchronised with the UCT GPS Disciplined Oscillators (one per node), but we also report on bistatic measurements with White Rabbit, fibre timing system, as well as the consequences of GPS failure (GPS Denied Environment)
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