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

No more nonsense

Discusses the approach of the courts to the quantification of beneficial interests in the family home in the event of a relationship breakdown. Assesses the clarification provided by the Court of Appeal ruling in Fowler v Barron on whether the respondent was the sole beneficial owner of a property purchased with his former partner, by means of a significant cash contribution from him and a mortgage in both their names, focusing on whether he could rebut the presumption that they held the property as joint tenants in equity where it was registered in joint names. [From Legal Journals Index]

Microwave mediated reduction of heterocycle and fluorine containing nitroaromatics with Mo(CO)(6) and DBU

Heterocycle containing nitroaromatics were reduced by Mo(CO)(6) and DBU in EtOH under microwave irradiation within 15 min. Under the same conditions, 4-fluoronitrobenzene was reduced to 4-fluoroaniline, whereas 2-chloro-1-fluoro-4-nitrobenzene afforded a mixture of 3-chloro-4-fluoroaniline and 3-chloro-4-ethoxyaniline. The extent of the competing SNAr/reduction process could be influenced by the nature of the solvent, with t-BuOH the inert solvent of choice. The latter was used as solvent for SNAr/reductions of 2-chloro-1-fluoro-4-nitrobenzene with S-nucleophiles to yield 3-chloro-4-mercaptoanilines. Crown Copyright (c) 2008 Published by Elsevier Ltd. All rights reserved.