Differential forms on free and almost free divisors

We introduce a variant of the usual Kähler forms on singular free divisors, and show that it enjoys the same depth properties as Kähler forms on isolated hypersurface singularities. Using these forms it is possible to describe analytically the vanishing cohomology, and the Gauss–Manin connection, in families of free divisors, in precise analogy with the classical description for the Milnor fibration of an isolated complete intersection singularity, due to Brieskorn and Greuel. This applies in particular to the family Formula of discriminants of a versal deformation Formula of a singularity of a mapping

Predicting sonic pulse shapes of underwater spark discharges

Measurements of the acoustic pressure of spark discharges were made at a shallow depth (10 feet) for various voltages, stored energies, inductances and capacitances of the system, and electrode areas. The voltages ranged from 1500 V to 11 KV, and the energy storing capacitances from 8 to 800 ufd. In this range the peak pressure observed was proportional to peak current and the decay constant of the pressure-time curve was essentially the same as the electrical discharge decay constant.Office of Naval Research under Contract Nonr 1 367(00) NR 261-10