Moment decay rates of solutions of stochastic differential equations

The objective of this paper is to investigate the p-ίh moment asymptotic stability decay rates for certain finite-dimensional Itό stochastic differential equations. Motivated by some practical examples, the point of our analysis is a special consideration of general decay speeds, which contain as a special case the usual exponential or polynomial type one, to meet various situations. Sufficient conditions for stochastic differential equations (with variable delays or not) are obtained to ensure their asymptotic properties. Several examples are studied to illustrate our theory.

Predicting HCl concentrations in fire enclosures using an HCl decay model coupled to a CFD-based fire field model

The amount of atmospheric hydrogen chloride (HCl) within fire enclosures produced from the combustion of chloride-based materials tends to decay as the fire effluent is transported through the enclosure due to mixing with fresh air and absorption by solids. This paper describes an HCl decay model, typically used in zone models, which has been modified and applied to a computational fluid dynamics (CFD)-based fire field model. While the modified model still makes use of some empirical formulations to represent the deposition mechanisms, these have been reduced from the original three to two through the use of the CFD framework. Furthermore, the effect of HCl flow to the wall surfaces on the time to reach equilibrium between HCl in the boundary layer and on wall surfaces is addressed by the modified model. Simulation results using the modified HCl decay model are compared with data from three experiments. The model is found to be able to reproduce the experimental trends and the predicted HCl levels are in good agreement with measured values

Salivary antimicrobial peptides (LL-37 and alpha-defensins HNP1-3), antimicrobial and IgA responses to prolonged exercise

There are many factors in mucosal secretions that contribute to innate immunity and the 'first line of defence' at mucosal surfaces. Few studies, however, have investigated the effects of exercise on many of these 'defence' factors. The aim of the present study was to determine the acute effects of prolonged exercise on salivary levels of selected antimicrobial peptides (AMP) that have not yet been studied in response to exercise (HNP1-3 and LL-37) in addition to immunoglobulin A (IgA). A secondary objective was to assess the effects of exercise on saliva antibacterial capacity. Twelve active men exercised on a cycle ergometer for 2.5 h at approximately 60% of maximal oxygen uptake. Unstimulated whole saliva samples were obtained before and after exercise. There was a significant decrease (P < 0.05) in salivary IgA:osmolality ratio, following exercise, but IgA concentration and secretion rate were unaltered. Salivary HNP1-3 and LL-37 concentrations (P < 0.01 and P < 0.05, respectively), concentration:osmolality ratios (P < 0.01) and secretion rates (P < 0.01) all increased following exercise. Salivary antibacterial capacity (against E. coli) did not change. The increased concentration of AMPs in saliva may confer some benefit to the 'first line of defence' and could result from synergistic compensation within the mucosal immune system and/or airway inflammation and epithelial damage. Further study is required to determine the significance of such changes on the overall 'defence' capacity of saliva and how this influences the overall risk for infection.

Effect of caffeine ingestion during prolonged exhaustive exercise on salivary immunoglobulin A, alpha-amylase and cortisol

Exercise can have deleterious effects on the secretion of salivary immunoglobulin A (s-IgA), which appears to be related to perturbations in sympatheticoadrenal activation (Teeuw et al., 2004). Caffeine, commonly used for its ergogenic properties is associated with increased sympathetic nervous system activity, and it has been previously shown that caffeine ingestion before intensive cycling enhances s-IgA responses during exercise (Bishop et al., 2006). Therefore, the aim of the present study was to examine the effect of a performance cereal bar, containing caffeine, before and during prolonged exhaustive cycling on exercise performance and the salivary secretion of IgA, alpha-amylase activity and cortisol. Using a randomised cross-over design and following a 10 – 12 hour overnight fast, 12 trained cyclists, mean (SEM) age: 21(1) yr; height: 179(2) cm; body mass: 73.6(2.5) kg; maximal oxygen uptake, VO2max: 57.9(1.2) completed 2.5 h of cycling at 60%VO2max (with regular water ingestion) on a stationary ergometer, which was followed by a ride to exhaustion at 75% VO2max. Immediately before exercise, and after 55 min and 115 min of exercise participants ingested a 0.9 MJ cereal bar containing 45 g carbohydrate, 5 g protein, 3 g fat and 100 mg of caffeine (CAF) or an isocaloric noncaffeine bar (PLA). Unstimulated timed saliva samples were collected immediately before exercise, after 70 min and 130 min of exercise, and immediately after the exhaustive exercise bout. Saliva was analysed for s-IgA, alpha-amylase activity and cortisol concentration. Saliva flow rates were determined to calculate the s-IgA secretion rate. Data were analysed using a 2-way repeated measures ANOVA and post-hoc t-tests with Holm Bonferroni adjustments applied where appropriate. Time to exhaustion was 35% longer in CAF compared with PLA ((2177 (0.2) vs 1615 (0.16) s; P < 0.05)). Saliva flow rate did not change significantly during the exercise protocol. Exercise was associated with elevations in s-IgA concentration (9% increase), s-IgA secretion rate (24% increase) and alpha-amylase activity (224% increase) post-exhaustion (P < 0.01), but there was no effect of CAF on these responses. Salivary cortisol concentration increased by 64% post-exhaustion in the CAF trial only (P < 0.05), indicating an increase in adrenal activity following caffeine ingestion. Values were 35.7 (5.5) and 19.6 (3.4) nmol/L post-exhaustion for CAF and PLA, respectively. These findings show that ingestion of a caffeine containing cereal bar during prolonged exhaustive cycling enhances endurance performance, increases salivary cortisol secretion post-exhaustion, but does not affect the exercise-induced increases in s-IgA or alpha-amylase activity.