Subexponential solutions of scalar linear integro-differential equations with delay

This paper considers the asymptotic behaviour of solutions of the scalar linear convolution integro-differential equation with delay x0(t) = − n Xi=1 aix(t − i) + Z t 0 k(t − s)x(s) ds, t > 0, x(t) = (t), − t 0, where = max1in i. In this problem, k is a non-negative function in L1(0,1)\C[0,1), i 0, ai > 0 and is a continuous function on [−, 0]. The kernel k is subexponential in the sense that limt!1 k(t)(t)−1 > 0 where is a positive subexponential function. A consequence of this is that k(t)et ! 1 as t ! 1 for every > 0

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

Effects of water quality in Bassenthwaite Lake on anglers' catches of salmon and sea-trout in the River Derwent

This is the report on the Effects of Water Quality in the Bassenthwaite Lake on Anglers Catches of Salmon and Sea-trout in the River Derwent April 1993 by the Institute of Freshwater Ecology. An analysis of the catch statistics for salmon and sea-trout in the Rivers Derwent and Cocker was undertaken in relation to available information on the algal water quality in Bassenthwaite Lake to test the hypothesis that poor catch returns were associated with a deterioration of water quality within the lake. Analysis of the catch statistics failed to reveal any correlation between water quality and catch returns for either species of fish and it is concluded that any water deterioration in Bassenthwaite Lake has not caused any major damage to the salmon and sea trout fisheries of the Derwent/Cocker system. This conclusion is supported by the analysis of the Windermere/Leven and Crake system, where no correlation could be found between lake water quality and downstream catches of migratory salmonid fish. However, the possibility still exists and such an effect might be detected by further field work on the macroinvertebrates and on the composition of potential salmonid spawning in the area

Low-intensity repetitive magnetic stimulation lowers action potential threshold and increases spike firing in layer 5 pyramidal neurons in vitro

Repetitive transcranial magnetic stimulation (rTMS) has become a popular method of modulating neural plasticity in humans. Clinically, rTMS is delivered at high intensities to modulate neuronal excitability. While the high-intensity magnetic field can be targeted to stimulate specific cortical regions, areas adjacent to the targeted area receive stimulation at a lower intensity and may contribute to the overall plasticity induced by rTMS. We have previously shown that low-intensity rTMS induces molecular and structural plasticity in vivo, but the effects on membrane properties and neural excitability have not been investigated. Here we investigated the acute effect of low-intensity repetitive magnetic stimulation (LI-rMS) on neuronal excitability and potential changes on the passive and active electrophysiological properties of layer 5 pyramidal neurons in vitro. Whole-cell current clamp recordings were made at baseline prior to subthreshold LI-rMS (600 pulses of iTBS, n = 9 cells from 7 animals) or sham (n = 10 cells from 9 animals), immediately after stimulation, as well as 10 and 20 min post-stimulation. Our results show that LI-rMS does not alter passive membrane properties (resting membrane potential and input resistance) but hyperpolarises action potential threshold and increases evoked spike-firing frequency. Increases in spike firing frequency were present throughout the 20 min post-stimulation whereas action potential (AP) threshold hyperpolarization was present immediately after stimulation and at 20 min post-stimulation. These results provide evidence that LI-rMS alters neuronal excitability of excitatory neurons. We suggest that regions outside the targeted region of high-intensity rTMS are susceptible to neuromodulation and may contribute to rTMS-induced plasticity

Modelling the effect of L/S ratio and granule moisture content on the compaction properties in continuous manufacturing

The pharmaceutical field is currently moving towards continuous manufacturing pursuing reduced waste, consistency, and automation. During continuous manufacturing, it is important to understand how both operating conditions and material properties throughout the process affect the final properties of the product to optimise and control production. In this study of a continuous wet granulation line, the liquid to solid ratio (L/S) and drying times were varied to investigate the effect of the final granule moisture content and the liquid to solid ratio on the properties of the granules during tabletting and the final tensile strength of the tablets. Both variables (L/S and granule moisture) affected the tablet tensile strength with the moisture content having a larger impact. Further analysis using a compaction model, showed that the compactability of the granules was largely unaffected by both L/S and moisture content while the compressibility was influenced by these variables, leading to a difference in the final tablet strength and porosity. The granule porosity was linked to the L/S ratio and used instead for the model fitting. The effect of moisture content and granule porosity was added to the model using a 3d plane relationship between the compressibility constant, the moisture content and porosity of the granules. The tablet tensile strength model, considering the effect of moisture and granule porosity, performed well averaging a root mean squared error across the different conditions of 0.17 MPa

Transparent predictive modelling of the twin screw granulation process using a compensated interval type-2 fuzzy system

In this research, a new systematic modelling framework which uses machine learning for describing the granulation process is presented. First, an interval type-2 fuzzy model is elicited in order to predict the properties of the granules produced by twin screw granulation (TSG) in the pharmaceutical industry. Second, a Gaussian mixture model (GMM) is integrated in the framework in order to characterize the error residuals emanating from the fuzzy model. This is done to refine the model by taking into account uncertainties and/or any other unmodelled behaviour, stochastic or otherwise. All proposed modelling algorithms were validated via a series of Laboratory-scale experiments. The size of the granules produced by TSG was successfully predicted, where most of the predictions fit within a 95% confidence interval

A terminal assessment of stages theory : introducing a dynamic states approach to entrepreneurship

Stages of Growth models were the most frequent theoretical approach to understanding entrepreneurial business growth from 1962 to 2006; they built on the growth imperative and developmental models of that time. An analysis of the universe of such models (N=104) published in the management literature shows no consensus on basic constructs of the approach, nor is there any empirical confirmations of stages theory. However, by changing two propositions of the stages models, a new dynamic states approach is derived. The dynamic states approach has far greater explanatory power than its precursor, and is compatible with leading edge research in entrepreneurship

The First VERITAS Telescope

The first atmospheric Cherenkov telescope of VERITAS (the Very Energetic Radiation Imaging Telescope Array System) has been in operation since February 2005. We present here a technical description of the instrument and a summary of its performance. The calibration methods are described, along with the results of Monte Carlo simulations of the telescope and comparisons between real and simulated data. The analysis of TeV $\gamma$-ray observations of the Crab Nebula, including the reconstructed energy spectrum, is shown to give results consistent with earlier measurements. The telescope is operating as expected and has met or exceeded all design specifications.Comment: Accepted by Astroparticle Physic