Functional Law for the Anticipating Ornstein-Uhlenbeck Process

We prove a functional law of simple logarithm for the Ornstein-Uhlenbeck process with anticipating initial data.      

The role of spillover hydrogen in gas phase catalytic aromatic hydrodechlorination and hydrogenation over nickel/silica

4-Hydroxymethyl-1,3-dioxolan-2-one has been prepared in 70% yield from 1-chloro-2,3-epoxypropane with alkali metal hydrogen carbonates under phase transfer catalysis conditions. Onium halides exhibit higher catalytic activity compared with that of tertiary amines or 18-crown-6. This revised version was published online in June 2006 with corrections to the Cover Date.     

Relative Compactness for Capacities, Measures, Upper Semicontinuous Functions and Closed Sets

We prove an Ascoli theorem for capacities. This theorem which characterizes relatively compact sets of capacities is widely applicable and many Ascoli theorems for particular classes of capacities can immediately be deduced as corollaries. Indeed it is usually necessary only to demonstrate that these classes are closed and then to simplify the characterization when possible. In particular, we show that the proof of the classical Prohorov theorem can be naturally factored into the shorter proof of the Ascoli theorem for capacities and into the somewhat longer proof that the class of probability measures is closed in the class of capacities. We also deduce new and known Ascoli theorems for sup measures, upper semi-continuous functions, the Vietoris hyperspace topology, and various classes of measures.