Primes in short intervals

Contrary to what would be predicted on the basis of Cram\'er's model concerning the distribution of prime numbers, we develop evidence that the distribution of $\psi(x+H)- \psi(x)$, for $0\le x\le N$, is approximately normal with mean $\sim H$ and variance $\sim H\log N/H$, when $N^\delta \le H \le N^{1-\delta}$.Comment: 29 page

Evidence of epistasis between Interleukin-1 and Selenoprotein-S with susceptibility to rheumatoid arthritis

Objective: Selenoprotein-S (SELS) is involved in the stress response within the endoplasmic reticulum (ER) and inflammation. Recently, promoter variants in the SELS gene were shown to be associated with plasma levels of interleukin (IL)6, IL1β and tumour necrosis factor (TNF). It was hypothesised that these variants could influence rheumatoid arthritis (RA) susceptibility and may interact with functional single nucleotide polymorphisms (SNPs) in the genes for IL1, IL6 and TNF. Methods: Genotyping was performed in 988 unrelated healthy controls and 965 patients with RA. Stratified analysis was used to test for interactions. Single gene effects and evidence of epistasis were investigated using the Mantel–Haenszel (M–H) test and the linkage disequilibrium (LD)-based statistic. Results: No association of SELS −105 genotype and RA susceptibility was detected. Stratification of SELS −105 genotypes by IL1 −511 genotypes showed that the disease risk (comparing AA/GA to GG at the SELS −105 locus) in individuals with the GG/AG genotype at the IL1β −511 locus was significantly lower than that in individuals having the AA genotype at the IL1β −511 locus (odds ratio (OR): 0.9 and 2.3, respectively; p = 0.004 by M–H test). Significant epistasis was also detected using the LD-based statistic (p = <0.001). No interaction was observed between SELS −105 and IL6 or TNF variants. Conclusion: Our results reveal evidence of strong epistasis in two genes in the IL1 production pathway and highlight the potential importance of gene–gene interactions in the pathogenesis of RA

Velocity field distributions due to ideal line vortices

We evaluate numerically the velocity field distributions produced by a bounded, two-dimensional fluid model consisting of a collection of parallel ideal line vortices. We sample at many spatial points inside a rigid circular boundary. We focus on ``nearest neighbor'' contributions that result from vortices that fall (randomly) very close to the spatial points where the velocity is being sampled. We confirm that these events lead to a non-Gaussian high-velocity ``tail'' on an otherwise Gaussian distribution function for the Eulerian velocity field. We also investigate the behavior of distributions that do not have equilibrium mean-field probability distributions that are uniform inside the circle, but instead correspond to both higher and lower mean-field energies than those associated with the uniform vorticity distribution. We find substantial differences between these and the uniform case.Comment: 21 pages, 9 figures. To be published in Physical Review E (http://pre.aps.org/) in May 200

Bearing tester data compilation, analysis and reporting and bearing math modeling, volume 1

Thermal and mechanical models of high speed angular contact ball bearings operating in LOX and LN2 were developed and verified with limited test data in an effort to further understand the parameters that determine or effect the SSME turbopump bearing operational characteristics and service life. The SHABERTH bearing analysis program which was adapted to evaluate shaft bearing systems in cryogenics is not capable of accommodating varying thermal properties and two phase flow. A bearing model with this capability was developed using the SINDA thermal analyzer. Iteration between the SHABERTH and the SINDA models enable the establishment of preliminary bounds for stable operation in LN2. These limits were established in terms of fluid flow, fluid inlet temperature, and axial load for a shaft speed of 30,000 RPM

Use of a simple pain model to evaluate analgesic activity of ibuprofen versus paracetamol

Objective: To evaluate the analgesic activity of ibuprofen against paracetamol using a simple pain model.Design: A double-blind study.Setting: Twenty general practitioners in Harare, Zimbabwe.Patients: Adults with acute sore throat of a maximum of two days’ duration.Interventions: One hundred and thirteen patients with acute pain associated with tonsillopharyngitis randomly received either 400mg ibuprofen or 1000mg paracetamol. The study design included repeated administration up to 48 hours to assess tolerability.Main outcome measures: At hourly intervals for six hours after the first dose of treatment, the patients evaluated pain intensity on swallowing, difficulty in swallowing and global pain relief according to visual analogue scales.Results: Ibuprofen 400mg was significantly more effective than paracetamol 1000mg in all three ratings, at all time-points for pain intensity and difficulty in swallowing, and from two hours onwards for pain relief. There were no serious adverse effects and no statisticallysignificant difference in the incidence of adverse effects in the two treatment groups.Conclusions: Sore throat pain provided a sensitive model to assess the analgesic efficacy of class I analgesics and discriminated between the analgesic efficacy of ibuprofen and paracetamol