Asymptotic and structural properties of special cases of the Wright function arising in probability theory

This analysis paper presents previously unknown properties of some special cases of the Wright function whose consideration is necessitated by our work on probability theory and the theory of stochastic processes. Specifically, we establish new asymptotic properties of the particular Wright function 1Ψ1(ρ, k; ρ, 0; x) = X∞ n=0 Γ(k + ρn) Γ(ρn) x n n! (|x| < ∞) when the parameter ρ ∈ (−1, 0)∪(0, ∞) and the argument x is real. In the probability theory applications, which are focused on studies of the Poisson-Tweedie mixtures, the parameter k is a non-negative integer. Several representations involving well-known special functions are given for certain particular values of ρ. The asymptotics of 1Ψ1(ρ, k; ρ, 0; x) are obtained under numerous assumptions on the behavior of the arguments k and x when the parameter ρ is both positive and negative. We also provide some integral representations and structural properties involving the ‘reduced’ Wright function 0Ψ1(−−; ρ, 0; x) with ρ ∈ (−1, 0) ∪ (0, ∞), which might be useful for the derivation of new properties of members of the power-variance family of distributions. Some of these imply a reflection principle that connects the functions 0Ψ1(−−;±ρ, 0; ·) and certain Bessel functions. Several asymptotic relationships for both particular cases of this function are also given. A few of these follow under additional constraints from probability theory results which, although previously available, were unknown to analysts.

Effect of aerobic interval training and caffeine on blood platelet function

Purpose: Hyperactive platelets contribute to the thrombotic response in humans, and exercise transiently increases platelet function. Caffeine is routinely used by athletes as an ergogenic aid, but the combined effect of exercise and caffeine on platelet function has not been investigated. Methods: Twelve healthy males were randomly assigned to one of four groups and undertook four experimental trials of a high-intensity aerobic interval training (AIT) bout or rest with ingestion of caffeine (3 mg·kg-1) or placebo. AIT was 8 × 5 min at approximately 75% peak power output (approximately 80% V?O2peak) and 1-min recovery (approximately 40% peak power output, approximately 50% V?O2peak) intervals. Blood/urine was collected before, 60, and 90 min after capsule ingestion and analyzed for platelet aggregation/activation. Results: AIT increased platelet reactivity to adenosine diphosphate (placebo 30.3%, caffeine 13.4%, P < 0.05) and collagen (placebo 10.8%, caffeine 5.1%, P < 0.05) compared with rest. Exercise placebo increased adenosine diphosphate-induced aggregation 90 min postingestion compared with baseline (40.5%, P < 0.05), but the increase when exercise was combined with caffeine was small (6.6%). During the resting caffeine protocol, collagen-induced aggregation was reduced (-4.3%, P < 0.05). AIT increased expression of platelet activation marker PAC-1 with exercise placebo (P < 0.05) but not when combined with caffeine. Conclusion: A single bout of AIT increases platelet function, but caffeine ingestion (3 mg·kg) does not exacerbate platelet function at rest or in response to AIT. Our results provide new information showing caffeine at a dose that can elicit ergogenic effects on performance has no detrimental effect on platelet function and may have the potential to attenuate increases in platelet activation and aggregation when undertaking strenuous exercise.

The place and function of the Sunday school in the church,

Mode of access: Internet.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.

Smoothing a Discrete Hazard Function for the Number of Patients Colonized with Methicillin-Resistance Staphylococcus Aureus in an Intensive Care Unit

A new method for estimating the time to colonization of Methicillin-resistant Staphylococcus Aureus (MRSA) patients is developed in this paper. The time to colonization of MRSA is modelled using a Bayesian smoothing approach for the hazard function. There are two prior models discussed in this paper: the first difference prior and the second difference prior. The second difference prior model gives smoother estimates of the hazard functions and, when applied to data from an intensive care unit (ICU), clearly shows increasing hazard up to day 13, then a decreasing hazard. The results clearly demonstrate that the hazard is not constant and provide a useful quantification of the effect of length of stay on the risk of MRSA colonization which provides useful insight.