On the solvability of a class of second kind integral equations on unbounded domains

We consider integral equations of the form ψ(x) = φ(x) + ∫Ωk(x, y)z(y)ψ(y) dy(in operator form ψ = φ + Kzψ), where Ω is some subset ofRn(n ≥ 1). The functionsk,z, and φ are assumed known, withz ∈ L∞(Ω) and φ ∈ Y, the space of bounded continuous functions on Ω. The function ψ ∈ Yis to be determined. The class of domains Ω and kernelskconsidered includes the case Ω = Rnandk(x, y) = κ(x − y) with κ ∈ L1(Rn), in which case, ifzis the characteristic function of some setG, the integral equation is one of Wiener–Hopf type. The main theorems, proved using arguments derived from collectively compact operator theory, are conditions on a setW ⊂ L∞(Ω) which ensure that ifI − Kzis injective for allz ∈ WthenI − Kzis also surjective and, moreover, the inverse operators (I − Kz)−1onYare bounded uniformly inz. These general theorems are used to recover classical results on Wiener–Hopf integral operators of21and19, and generalisations of these results, and are applied to analyse the Lippmann–Schwinger integral equation.

Some uniform stability and convergence results for integral equations on the real line and projection methods for their solution

The paper considers second kind equations of the form (abbreviated x=y + K2x) in which and the factor z is bounded but otherwise arbitrary so that equations of Wiener-Hopf type are included as a special case. Conditions on a set are obtained such that a generalized Fredholm alternative is valid: if W satisfies these conditions and I − Kz, is injective for each z ε W then I − Kz is invertible for each z ε W and the operators (I − Kz)−1 are uniformly bounded. As a special case some classical results relating to Wiener-Hopf operators are reproduced. A finite section version of the above equation (with the range of integration reduced to [−a, a]) is considered, as are projection and iterated projection methods for its solution. The operators (where denotes the finite section version of Kz) are shown uniformly bounded (in z and a) for all a sufficiently large. Uniform stability and convergence results, for the projection and iterated projection methods, are obtained. The argument generalizes an idea in collectively compact operator theory. Some new results in this theory are obtained and applied to the analysis of projection methods for the above equation when z is compactly supported and k(s − t) replaced by the general kernel k(s,t). A boundary integral equation of the above type, which models outdoor sound propagation over inhomogeneous level terrain, illustrates the application of the theoretical results developed.

On the nature of ULF wave power during nightside auroral activations and substorms: 2. temporal evolution

We present a statistical analysis of the time evolution of ground magnetic fluctuations in three (12–48 s, 24–96 s and 48–192 s) period bands during nightside auroral activations. We use an independently derived auroral activation list composed of both substorms and pseudo-breakups to provide an estimate of the activation times of nightside aurora during periods with comprehensive ground magnetometer coverage. One hundred eighty-one events in total are studied to demonstrate the statistical nature of the time evolution of magnetic wave power during the ∼30 min surrounding auroral activations. We find that the magnetic wave power is approximately constant before an auroral activation, starts to grow up to 90 s prior to the optical onset time, maximizes a few minutes after the auroral activation, then decays slightly to a new, and higher, constant level. Importantly, magnetic ULF wave power always remains elevated after an auroral activation, whether it is a substorm or a pseudo-breakup. We subsequently divide the auroral activation list into events that formed part of ongoing auroral activity and events that had little preceding geomagnetic activity. We find that the evolution of wave power in the ∼10–200 s period band essentially behaves in the same manner through auroral onset, regardless of event type. The absolute power across ULF wave bands, however, displays a power law-like dependency throughout a 30 min period centered on auroral onset time. We also find evidence of a secondary maximum in wave power at high latitudes ∼10 min following isolated substorm activations. Most significantly, we demonstrate that magnetic wave power levels persist after auroral activations for ∼10 min, which is consistent with recent findings of wave-driven auroral precipitation during substorms. This suggests that magnetic wave power and auroral particle precipitation are intimately linked and key components of the substorm onset process.

On the effect of power amplifier nonlinearity on MIMO transmit diversity systems

Nonlinearity of high-power amplifier (HPA) plays a crucial role in the performance of multiple-input multiple-output (MIMO) systems. In this paper, we investigate the performance of MIMO orthogonal space-time block coding (STBC) systems in the presence of nonlinear HPA. Specifically, we assess the impact of HPA nonlinearity on the average symbol error probability (SEP), total degradation (TD), and system capacity of orthogonal STBC in uncorrelated Nakagami-m fading channels. Numerical results are provided and show the effects of several system parameters, such as the output back-off (OBO) of nonlinear HPA, numbers of transmit and receive antennas, and modulation order of quadrature amplitude modulation (QAM), on performance.

Influence of dietary protein intake and glycemic index on the association between TCF7L2 HapA and weight gain

BACKGROUND: Genetic polymorphisms of transcription factor 7-like 2 (TCF7L2) have been associated with type 2 diabetes and BMI. OBJECTIVE: The objective was to investigate whether TCF7L2 HapA is associated with weight development and whether such an association is modulated by protein intake or by the glycemic index (GI). DESIGN: The investigation was based on prospective data from 5 cohort studies nested within the European Prospective Investigation into Cancer and Nutrition. Weight change was followed up for a mean (±SD) of 6.8 ± 2.5 y. TCF7L2 rs7903146 and rs10885406 were successfully genotyped in 11,069 individuals and used to derive HapA. Multiple logistic and linear regression analysis was applied to test for the main effect of HapA and its interaction with dietary protein or GI. Analyses from the cohorts were combined by random-effects meta-analysis. RESULTS: HapA was associated neither with baseline BMI (0.03 ± 0.07 BMI units per allele; P = 0.6) nor with annual weight change (8.8 ± 11.7 g/y per allele; P = 0.5). However, a previously shown positive association between intake of protein, particularly of animal origin, and subsequent weight change in this population proved to be attenuated by TCF7L2 HapA (P-interaction = 0.01). We showed that weight gain becomes independent of protein intake with an increasing number of HapA alleles. Substitution of protein with either fat or carbohydrates showed the same effects. No interaction with GI was observed. CONCLUSION: TCF7L2 HapA attenuates the positive association between animal protein intake and long-term body weight change in middle-aged Europeans but does not interact with the GI of the diet.

Non-orthogonal version of the arbitrary polygonal C-grid and a new diamond grid

Quasi-uniform grids of the sphere have become popular recently since they avoid parallel scaling bottle- necks associated with the poles of latitude–longitude grids. However quasi-uniform grids of the sphere are often non- orthogonal. A version of the C-grid for arbitrary non- orthogonal grids is presented which gives some of the mimetic properties of the orthogonal C-grid. Exact energy conservation is sacrificed for improved accuracy and the re- sulting scheme numerically conserves energy and potential enstrophy well. The non-orthogonal nature means that the scheme can be used on a cubed sphere. The advantage of the cubed sphere is that it does not admit the computa- tional modes of the hexagonal or triangular C-grids. On var- ious shallow-water test cases, the non-orthogonal scheme on a cubed sphere has accuracy less than or equal to the orthog- onal scheme on an orthogonal hexagonal icosahedron. A new diamond grid is presented consisting of quasi- uniform quadrilaterals which is more nearly orthogonal than the equal-angle cubed sphere but with otherwise similar properties. It performs better than the cubed sphere in ev- ery way and should be used instead in codes which allow a flexible grid structure.

The impact of eBusiness on the City of London office market

The City of London is a major financial centre where the property market is heavily dependent on the space requirements of office occupiers. Technological change, however, is changing the way in which organisations conduct their business and is challenging the continued locational pull of the City. This research presents findings from a major survey of City occupiers carried out by The College research team during 2002. The research examines how the shape and form of the office property market in the City will be affected by process change in eBusiness and related technology over the next 5 years. The report, which includes an extensive literature review, examines the implications of increased homeworking and other trends for future office supply in the City. The research was funded by the Worshipful Company of Chartered Surveyors Trust (Toby Sutton Research Award), and part of the literature review by the Small Business Support Research Unit of DTI. It is essential reading for surveyors, planners, facilities managers and all those interested in the technology and property interface.

A trading strategy based on the lead–lag relationship between the spot index and futures contract for the FTSE 100

This paper examines the lead–lag relationship between the FTSE 100 index and index futures price employing a number of time series models. Using 10-min observations from June 1996–1997, it is found that lagged changes in the futures price can help to predict changes in the spot price. The best forecasting model is of the error correction type, allowing for the theoretical difference between spot and futures prices according to the cost of carry relationship. This predictive ability is in turn utilised to derive a trading strategy which is tested under real-world conditions to search for systematic profitable trading opportunities. It is revealed that although the model forecasts produce significantly higher returns than a passive benchmark, the model was unable to outperform the benchmark after allowing for transaction costs.

On the application of optimal wavelet filter banks for ECG signal classification

This paper discusses ECG signal classification after parametrizing the ECG waveforms in the wavelet domain. Signal decomposition using perfect reconstruction quadrature mirror filter banks can provide a very parsimonious representation of ECG signals. In the current work, the filter parameters are adjusted by a numerical optimization algorithm in order to minimize a cost function associated to the filter cut-off sharpness. The goal consists of achieving a better compromise between frequency selectivity and time resolution at each decomposition level than standard orthogonal filter banks such as those of the Daubechies and Coiflet families. Our aim is to optimally decompose the signals in the wavelet domain so that they can be subsequently used as inputs for training to a neural network classifier.

Effect of milk type and processing on iodine concentration of organic and conventional winter milk at retail: implications for nutrition

Milk is the largest source of iodine in UK diets and an earlier study showed that organic summer milk had significantly lower iodine concentration than conventional milk. There are no comparable studies with winter milk or the effect of milk fat class or heat processing method. Two retail studies with winter milk are reported. Study 1 showed no effect of fat class but organic milk was 32.2% lower in iodine than conventional milk (404 vs. 595 μg/L; P < 0.001). Study 2 found no difference between conventional and Channel Island milk but organic milk contained 35.5% less iodine than conventional milk (474 vs. 306 μg/L; P < 0.001). UHT and branded organic milk also had lower iodine concentrations than conventional milk (331 μg/L; P < 0.001 and 268 μg/L: P < 0.0001 respectively). The results indicate that replacement of conventional milk by organic or UHT milk will increase the risk of sub-optimal iodine status especially for pregnant/lactating women.

Missing steps in a staircase: a qualitative study of the perspectives of key stakeholders on the use of adaptive designs in confirmatory trials

Background Despite the promising benefits of adaptive designs (ADs), their routine use, especially in confirmatory trials, is lagging behind the prominence given to them in the statistical literature. Much of the previous research to understand barriers and potential facilitators to the use of ADs has been driven from a pharmaceutical drug development perspective, with little focus on trials in the public sector. In this paper, we explore key stakeholders’ experiences, perceptions and views on barriers and facilitators to the use of ADs in publicly funded confirmatory trials. Methods Semi-structured, in-depth interviews of key stakeholders in clinical trials research (CTU directors, funding board and panel members, statisticians, regulators, chief investigators, data monitoring committee members and health economists) were conducted through telephone or face-to-face sessions, predominantly in the UK. We purposively selected participants sequentially to optimise maximum variation in views and experiences. We employed the framework approach to analyse the qualitative data. Results We interviewed 27 participants. We found some of the perceived barriers to be: lack of knowledge and experience coupled with paucity of case studies, lack of applied training, degree of reluctance to use ADs, lack of bridge funding and time to support design work, lack of statistical expertise, some anxiety about the impact of early trial stopping on researchers’ employment contracts, lack of understanding of acceptable scope of ADs and when ADs are appropriate, and statistical and practical complexities. Reluctance to use ADs seemed to be influenced by: therapeutic area, unfamiliarity, concerns about their robustness in decision-making and acceptability of findings to change practice, perceived complexities and proposed type of AD, among others. Conclusions There are still considerable multifaceted, individual and organisational obstacles to be addressed to improve uptake, and successful implementation of ADs when appropriate. Nevertheless, inferred positive change in attitudes and receptiveness towards the appropriate use of ADs by public funders are supportive and are a stepping stone for the future utilisation of ADs by researchers.

Heathland restoration on former agricultural land: effects of artificial acidification on the availability and uptake of toxic metal cations

Lowland heath is an internationally important habitat type that has greatly declined in abundance throughout Western Europe. In recent years this has led to a growing interest in the restoration of heathland on agricultural land. This generally requires the use of chemical treatments to return soil chemical conditions to those appropriate for the support of heathland ecosystems. However, the potential for negative impacts on the environment due to the potential of these treatments to increase the availability of trace metals via raised soil acidity requires investigation. A large-scale field study investigated the effect of two chemical treatments used in heathland restoration, elemental sulphur and ferrous sulphate, on soil acidity and whether it is possible to predict the effect of the treatments on availability of two potentially toxic cations (Al and Cd) in the soil along with their subsequent accumulation in the shoots of the grass Agrostis capillaris. Results showed that both treatments decreased soil pH, but that only elemental sulphur produced a pH similar to heathland soil. The availability of Al, measured by extraction with 1 M ammonium nitrate, could not be predicted by soil pH, depth in the soil and total Al concentration in the soil. By contrast, availability of Cd could be predicted from these three variables. Concentrations of both Al and Cd in the shoots of A. capillaris showed no significant relationship with the extractable concentration in the soil. Results are discussed in light of the possible environmental impacts of the chemical restoration techniques.

Stereochemistry and thermal stability of tartaric acid on the intrinsically chiral Cu{531} surface

Intrinsically chiral metal surfaces provide enantiospecific reaction environments without the need of coadsorbed modifiers. Amongst the intrinsically chiral copper surfaces, Cu{531} has the smallest unit cell and the highest density of chiral sites. XPS, NEXAFS and TPD were employed to investigate the adsorption and decomposition behaviour of the two chiral enantiomers of tartaric acid on this surface. The results obtained from XPS and NEXAFS show that at saturation coverage both enantiomers of tartaric acid adsorb in a μ4 configuration through the two carboxylic groups,which are rotatedwith respect to each other by 90°±≈15°within the surface plane. At intermediate coverage the R,R enantiomer adopts a similar configuration, but the S,S enantiomer is different and shows a high degree of dissociation. Growth of multilayers is observed at high exposures when the sample is kept at below 370 K. TPD experiments show that multilayers desorb between 390 K and 470 K and decomposition of the chemisorbed layer occurs between 470 K and 600 K. The desorption spectra support a two-step decomposition mechanism with a O_C_C_O or HO–HC_CH–OH intermediate that leads to production of CO2 and CO. Enantiomeric differences are observed in the desorption features related to the decomposition of the chemisorbed layer.

On the importance of Vaisala RS92 radiosonde humidity corrections for a better agreement between measured and modeled satellite radiances

A study has been carried out to assess the importance of radiosonde corrections in improving the agreement between satellite and radiosonde measurements of upper-tropospheric humidity. Infrared [High Resolution Infrared Radiation Sounder (HIRS)-12] and microwave [Advanced Microwave Sounding Unit (AMSU)-18] measurements from the NOAA-17 satellite were used for this purpose. The agreement was assessed by comparing the satellite measurements against simulated measurements using collocated radiosonde profiles of the Atmospheric Radiation Measurement (ARM) Program undertaken at tropical and midlatitude sites. The Atmospheric Radiative Transfer Simulator (ARTS) was used to simulate the satellite radiances. The comparisons have been done under clear-sky conditions, separately for daytime and nighttime soundings. Only Vaisala RS92 radiosonde sensors were used and an empirical correction (EC) was applied to the radiosonde measurements. The EC includes correction for mean calibration bias and for solar radiation error, and it removes radiosonde bias relative to three instruments of known accuracy. For the nighttime dataset, the EC significantly reduces the bias from 0.63 to 20.10 K in AMSU-18 and from 1.26 to 0.35 K in HIRS-12. The EC has an even greater impact on the daytime dataset with a bias reduction from 2.38 to 0.28 K in AMSU-18 and from 2.51 to 0.59 K in HIRS-12. The present study promises a more accurate approach in future radiosonde-based studies in the upper troposphere.

Variation on the effects of the 2003 CAP reform and regional differences in the Italian olive oil sector

This paper analyses the impacts of the 2003 CAP reform on the production of Italian olive oil controlling for the regional differences in olive oil production as well as for the differences between years. Italian olive oil production time series data from the Farm Accountancy Data Network for the 2000-2010 period at regional level is used to examine the effect of the 2003 Fischler reform on the production of olive oil. Production costs and payments received by farmers to support their income are considered. The data were collected at micro level based on a sample of farms representative of the production systems in the country. In order to consider the differences in production among the regions, eight representative regions in terms of surveyed farms are considered: Liguria, Toscana, Umbria, Lazio, Campania, Calabria, Puglia and Sicilia. We found that the most important factors affecting the production of olive oil are the area under olive groves and labour productivity. Results also show no evidence that the level of payments have an impact to the level of production, however, the type of payments has. Future work should explore the impact of the 2003 reform into the technical and production efficiency of the Italian olive oil farmers. It would be interesting to link the measures introduced by the cross compliance and the management practices of the different farms to have a more complete picture of the various parameters influencing the production of olive oil.