Change of variable formulas for non-anticipative functionals on path space

We derive a change of variable formula for non-anticipative functionals defined on the space of Rd-valued right-continuous paths with left limits. The functionals are only required to possess certain directional derivatives, which may be computed pathwise. Our results lead to functional extensions of the Itô formula for a large class of stochastic processes, including semimartingales and Dirichlet processes. In particular, we show the stability of the class of semimartingales under certain functional transformations.     

Colour symmetry double point groups

Thirty four distinct composition series arising out of the 32 crystallographic double point groups are employed to re-derive in a simple and elegant fashion all the 169 distinct colour symmetry groups generated by the 32 double point groups, exploiting the idea of colour generators. The advantage of the method employed and some possible applications of these colour groups are discussed. The resulting colour groups are tabulated.     

Heat transfer and pressure drop studies in a circular tube fitted with straight full twist

Experimental investigation of heat transfer characteristics of circular tube fitted with straight full twist insert has been presented. The heat transfer coefficient increases with Reynolds number and decreasing spacer distance with maximum being 2 in. spacer distance for both the type of twist inserts. Also, there is no appreciable increase in heat transfer enhancement in straight full twist insert with 2 in. spacer distance. Experiments were carried out in turbulent flow using straight full twist insert with 4 in. spacer and similar trend of increasing Nusselt number with Reynolds number was observed. Performance evaluation analysis was made and the maximum performance ratio was obtained for each twist insert corresponding to the Reynolds number of 2550.     

Kinetics of the reaction of methyl 4‐nitrobenzenesul‐fonate + Br− in ethanol amine based surfactants

The kinetics of the reaction of methyl 4‐nitrobenzenesulfonate + Br^? ions has been studied in ethanol amine based (alkyldimethylethanolammonium bromide and alkyldiethylethanolammonium bromide) surfactant solutions. The observed first‐order rate constants increase monotonically with surfactant concentration, with hydrophobic chain length and with head group bulk in a manner similar to other quaternary ammonium surfactants. The results were analyzed using the pseudophase model of micellar rate effects in conjunction with a Langmuir form to describe micellar binding of bromide ion. An attempt to estimate activation parameters of the reaction from temperature variance of micellar pseudophase rate constants has also been made. © 2006 Wiley Periodicals, Inc. Int J Chem Kinet 38: 303–308, 2006