Stokes’ phenomenon and the absolutely continuous spectrum of one-dimensional Schrödinger operators

AbstractIt is well known that the Airy functions, Ai(−x−μ) and Bi(−x−μ), form a fundamental set of solutions for the differential equationLu(x)≔−u″(x)−xu(x)=μu(x),0⩽x<∞,μ∈R,and that the spectrum of the associated selfadjoint operator consists of the whole real axis and is purely absolutely continuous for any choice of boundary condition at x=0. Also widely known is the fact that the semi-axis [−μ,∞) is an anti-Stokes’ line for solutions of the differential equation Lu(z)=μu(z),z∈C, for each fixed value of the spectral parameter μ. In this paper, we show that this connection between the existence of anti-Stokes’ lines on the real axis and points of the absolutely continuous spectrum holds under much more general circumstances. Further correlations, relating the Stokes’ phenomenon to subordinacy properties of solutions of Lu=μu at infinity and to the boundary behaviour of the Titchmarsh–Weyl m-function on the real axis, are also deduced

Radar studies of the vertical distribution of insects migrating over southern Britain: the influence of temperature inversions on nocturnal layer concentrations

Insects migrating over two sites in southern UK (Malvern in Worcestershire, and Harpenden in Hertfordshire) have been monitored continuously with nutating vertical-looking radars (VLRs) equipped with powerful control and analysis software. These observations make possible, for the first time, a systematic investigation of the vertical distribution of insect aerial density in the atmosphere, over temporal scales ranging from the short (instantaneous vertical profiles updated every 15 min) to the very long (profiles aggregated over whole seasons or even years). In the present paper, an outline is given of some general features of insect stratification as revealed by the radars, followed by a description of occasions during warm nights in the summer months when intense insect layers developed. Some of these nocturnal layers were due to the insects flying preferentially at the top of strong surface temperature inversions, and in other cases, layering was associated with higher-altitude temperature maxima, such as those due to subsidence inversions. The layers were formed from insects of a great variety of sizes, but peaks in the mass distributions pointed to a preponderance of medium-sized noctuid moths on certain occasions

Floodplain sediment from a 100-year-recurrence flood in 2005 of the Ping River in northern Thailand

Hydrology and Earth System Sciences124959-97

Linking routinely collected social work, education and health data to enable monitoring of the health and health care of school-aged children in state care (‘looked after children’) in Scotland: a national demonstration project

Background and objectives: Children in state care (‘looked after children’) have poorer health than children who are not looked after. Recent developments in Scotland and elsewhere have aimed to improve services and outcomes for looked after children. Routine monitoring of the health outcomes of looked after children compared to those of their non-looked after peers is currently lacking. Developing capacity for comparative monitoring of population based outcomes based on linkage of routinely collected administrative data has been identified as a priority. To our knowledge there are no existing population based data linkage studies providing data on the health of looked after and non-looked after children at national level. Smaller scale studies that are available generally provide very limited information on linkage methods and hence do not allow scrutiny of bias that may be introduced through the linkage process. Study design and methods: National demonstration project testing the feasibility of linking routinely collected looked after children, education, and health data. Participants: All children in publicly funded school in Scotland in 2011/12. Results: Linkage between looked after children data and the national pupil census classified 10,009 (1.5%) and 1,757 (0.3%) of 670,952 children as, respectively, currently and previously looked after. Recording of the unique pupil identifier (Scottish Candidate Number, SCN) on looked after children returns is incomplete, with 66% of looked after records for 2011/12 for children of possible school age containing a valid SCN. This will have resulted in some under-ascertainment of currently and, particularly, previously looked after children within the general pupil population. Further linkage of the pupil census to the NHS Scotland master patient index demonstrated that a safe link to the child’s unique health service (Community Health Index, CHI) number could be obtained for a very high proportion of children in each group (94%, 95%, and 95% of children classified as currently, previously, and non-looked after respectively). In general linkage rates were higher for older children and those living in more affluent areas. Within the looked after group, linkage rates were highest for children with the fewest placements and for those in permanent fostering. Conclusions: This novel data linkage demonstrates the feasibility of monitoring population based health outcomes of school aged looked after and non-looked after children using linked routine administrative data. Improved recording of the unique pupil identifier number on looked after data returns would be beneficial. Extending the range of personal identifiers on looked after children returns would enable linkage to health data for looked after children who are not in publicly funded schooling (i.e. those who are pre- or post-school, home schooled, or in independent schooling)

Charge transfer efficiency in a p-channel CCD irradiated cryogenically and the impact of room temperature annealing

It is important to understand the impact of the space radiation environment on detector performance, thereby ensuring that the optimal operating conditions are selected for use in flight. The best way to achieve this is by irradiating the device using appropriate mission operating conditions, i.e. holding the device at mission operating temperature with the device powered and clocking. This paper describes the Charge Transfer Efficiency (CTE) measurements made using an e2v technologies p-channel CCD204 irradiated using protons to the 10 MeV equivalent fluence of 1.24×109 protons.cm-2 at 153 K. The device was held at 153 K for a period of 7 days after the irradiation before being allowed up to room temperature where it was held at rest, i.e. unbiased, for twenty six hours to anneal before being cooled back to 153 K for further testing, this was followed by a further one week and three weeks of room temperature annealing each separated by further testing. A comparison to results from a previous room temperature irradiation of an n-channel CCD204 is made using assumptions of a factor of two worse CTE when irradiated under cryogenic conditions which indicate that p-channel CCDs offer improved tolerance to radiation damage when irradiated under cryogenic conditions

The small-scale manufacture of compound animal feed (ODNRI Bulletin No. 9)

This bulletin supersedes TDRI report G67 The small-scale manufacture of compound animal feed, which was first published in 1971. lt retains a similar format to G67, but the text has been extensively revised and expanded in the light of numerous enquiries dealt with by ODNRI on all aspects of feed production in the intervening years. lt is hoped that it will act as a technical and investment guide for those interested in initiating the production of compound animal feeds, as well as acting as a useful reference report for those already actively operating in this field. Chapter 1 describes the economic background to the industry; theoretical aspects of animal nutrition are dealt with in Chapter 2; these are related to the properties of the various raw materials used in feed production in Chapter 3. Chapter 4 describes the manufacturing process and examines the physical requirements for setting up plants at various scales of output, and Chapter 5 develops cost and return models for the plants described

Carbon nanotubes : from molecular to macroscopic sensors

The components that contribute to Raman spectral shifts of single-wall carbon nanotubes (SWNT’s) embedded in polymer systems have been identified. The temperature dependence of the Raman shift can be separated into the temperature dependence of the nanotubes, the cohesive energy density of the polymer, and the buildup of thermal strain. Discounting all components apart from the thermal strain from the Raman shift-temperature data, it is shown that the mechanical response of single-wall carbon nanotubes in tension and compression are identical. The stress-strain response of SWNT’s can explain recent experimental data for carbon nanotube-composite systems

Influence of kNN-Based Load Forecasting Errors on Optimal Energy Production

This paper presents a study of the influence of the accuracy of hourly load forecasting on the energy planning and operation of electric generation utilities. First, a k Nearest Neighbours (kNN) classification technique is proposed for hourly load forecasting. Then, obtained prediction errors are compared with those obtained results by using a M5’. Second, the obtained kNN-based load forecast is used to compute the optimal on/off status and generation scheduling of the units. Finally, the influence of forecasting errors on both the status and generation level of the units over the scheduling period is studied

Dynamical model of sequential spatial memory: winnerless competition of patterns

We introduce a new biologically-motivated model of sequential spatial memory which is based on the principle of winnerless competition (WLC). We implement this mechanism in a two-layer neural network structure and present the learning dynamics which leads to the formation of a WLC network. After learning, the system is capable of associative retrieval of pre-recorded sequences of spatial patterns.Comment: 4 pages, submitted to PR