An example employing convexity in functional fixed point arguments

This paper illustrates a convexity technique to be employed with functional fixed point theorems in proving the existence of solutions to boundary value problems

An Extension of the Compression-Expansion Fixed Point Theorem of Functional Type

In this article we use an interval of functional type as the underlying set in our compression-expansion fixed point theorem argument which can be used to exploit properties of the operator to improve conditions that will guarantee the existence of a fixed point in applications. An example is provided to demonstrate how intervals of functional type can improve conditions in applications to boundary value problems. We also show how one can use suitable k-contractive conditions to prove that a fixed point in a functionaltype interval is unique

Alternative iterative technique

The standard methods of applying iterative techniques do not apply when the nonlinear term is neither monotonic (corresponding to an increasing or decreasing operator) nor Lipschitz (corresponding to a condensing operator). However, by applying the Layered Compression–Expansion Theorem in conjunction with an alternative inversion technique, we show how one can apply monotonicity techniques to a right focal boundary value problem

Water incident related hospital activity across England between 1997/8 and 2003/4: a retrospective descriptive study

Every year in the United Kingdom, 10,000 people will die from accidental injury and the treatment of these injuries will cost the NHS £2 billion and the consequences of injuries received at home cost society a further £25 billion [1]. Non-fatal injuries result in 720,000 people being admitted to hospital a year and more than six million visits to accident and emergency departments each year [2]. Drowning is the second leading cause of unintentional injury mortality globally behind road traffic injuries. It is estimated that a total of 409, 272 people drown each year [3]. This equates to a global incident rate of 7.4 deaths per 100, 000 people worldwide and relates to a further 1.3 million Disability Adjusted Life Years (DALYs) which are lost as a result of premature death or disability [4]. 'Death' represents only the tip of the injury "iceberg" [5]. For every life lost from an injury, many more people are admitted to hospital, attend accident and emergency departments or general practitioners, are rescued by search and rescue organisations or resolve the situation themselves. It is estimated that 1.3 million people are injured as a result of near drowning episodes globally and that many more hundreds of thousands of people are affected through incidents and near misses but there are no accurate data [4]. The United Kingdom has reported a variable drowning fatality rate, the injury chart book reports a rate of 1.0 – 1.5 per 100,000 [6] and other studies suggest a rate as low as 0.5 per 100, 000 population [7] for accidental drowning and submersion, based on the International Classification of Disease 10 code W65 – 74, however, the problem is even greater and these Global Burden of Disease (GDB) figures are an underestimate of all drowning deaths, since they exclude drownings due to cataclysms (floods), water related transport accidents, assaults and suicide [3]. A recent study in Scotland highlighted this underestimation in drowning fatality data and found that the overall death rate due to drownings in Scotland 3.26 per 100,000 [8]. Even though drowning fatality rates in the United Kingdom vary, little is known about the people who are admitted to hospital after an incident either in or on water. This paper seeks to address this gap in our knowledge through the investigation of the data available on those admitted to NHS hospitals in England

The Relationship Between Fractures and DXA Measures of BMD in the Distal Femur of Children and Adolescents With Cerebral Palsy or Muscular Dystrophy

Children with limited or no ability to ambulate frequently sustain fragility fractures. Joint contractures, scoliosis, hip dysplasia, and metallic implants often prevent reliable measures of bone mineral density (BMD) in the proximal femur and lumbar spine, where BMD is commonly measured. Further, the relevance of lumbar spine BMD to fracture risk in this population is questionable. In an effort to obtain bone density measures that are both technically feasible and clinically relevant, a technique was developed involving dual-energy X-ray absorptiometry (DXA) measures of the distal femur projected in the lateral plane. The purpose of this study is to test the hypothesis that these new measures of BMD correlate with fractures in children with limited or no ability to ambulate. The relationship between distal femur BMD Z-scores and fracture history was assessed in a cross-sectional study of 619 children aged 6 to 18 years with muscular dystrophy or moderate to severe cerebral palsy compiled from eight centers. There was a strong correlation between fracture history and BMD Z-scores in the distal femur; 35% to 42% of those with BMD Z-scores less than −5 had fractured compared with 13% to 15% of those with BMD Z-scores greater than −1. Risk ratios were 1.06 to 1.15 (95% confidence interval 1.04–1.22), meaning a 6% to 15% increased risk of fracture with each 1.0 decrease in BMD Z-score. In clinical practice, DXA measure of BMD in the distal femur is the technique of choice for the assessment of children with impaired mobility. © 2010 American Society for Bone and Mineral Researc

Measuring Disease-Free Survival and Cancer Relapse Using Medicare Claims From CALGB Breast Cancer Trial Participants (Companion to 9344)

To determine the accuracy with which Medicare claims data measure disease-free survival in elderly Medicare beneficiaries with cancer, we performed a criterion validation study. We merged gold-standard clinical trial data of 45 elderly patients with node-positive breast cancer who were treated on the Cancer and Leukemia Group B (CAL-GB) adjuvant breast trial 9344 with Centers for Medicare and Medicaid Services (CMS) data files and compared the results of a CMS-based algorithm with the CALGB disease-free survival information to determine sensitivity and specificity. For 5-year disease-free survival, the sensitivity of the CMS-based algorithm was 100% (95% confidence interval [CI] = 81% to 100%), the specificity was 97% (95% CI = 83% to 100%), and the area under the receiver operator curve was 97% (95% CI = 90% to 100%). For 2-year disease-free survival, the test characteristics were less favorable: sensitivity was 83% (95% CI = 36% to 100%), specificity was 95% (95% CI = 83% to 100%), and area under the receiver operator curve was 84% (95% CI = 66% to 100%)

Hydroclimate Variability and Change in the Prairie Pothole Region, the “Duck Factory” of North America

The Prairie Pothole Region (PPR) of the northern Great Plains is a vital ecosystem responsible each year for producing 50%–80% of new recruits to the North American duck population. Climate variability and change can impact the hydrology and ecology of the region with implications for waterfowl populations. The historical relationship between PPR wetlands, duck populations, and seasonal hydroclimate are explored. Model experiments from phase 5 of the Coupled Model Intercomparison Project are used to determine whether a recent wetting trend is due to natural variability or changing climate and how PPR hydroclimate will change into the future. Year-to-year variations in May duck populations, pond numbers, and the Palmer drought severity index are well correlated over past decades. Pond and duck numbers tend to increase in spring following La Niña events, but the correlation is not strong. Model simulations suggest that the strengthening of the precipitation gradient across the PPR over the past century is predominantly due to natural variability and therefore could reverse. Model projections of future climate indicate precipitation will increase across the PPR in all seasons except summer, but this gain for surface moisture is largely offset by increased evapotranspiration because of higher temperatures and increased atmospheric evaporative demand. In summer, the combined effects of warming and precipitation changes indicate seasonal surface drying in the future. The presented hydroclimate analyses produce potential inputs to ecological and hydrological simulations of PPR wetlands to inform risk analysis of how this North American waterfowl habitat will evolve in the future, providing guidance to land managers facing conservation decisions

Assessment and correction of skinfold thickness equations in estimating body fat in children with cerebral palsy

To assess the accuracy of skinfold equations in estimating percentage body fat in children with cerebral palsy (CP), compared with assessment of body fat from dual energy X-ray absorptiometry (DXA)