From preface: This report satisfies the quarterly progress report requirements for PL-1 and PL-2 plant design work for the period ending September 30, 1960 At present time a SL-1 Core 2 is under construction. This is a replacement core for SL-1 (ALPR) and will be identical to a PL-2 core; a PL condenser is under test at the SL-1 facility; final construction plans for PL components and modules which are not site sensitive will be completed in March 1961.

"A finite difference approximation to a non-linear set of parabolic differential equations arising in shallow water theory is given. These difference equations were used to determine the shape and rate of propagation of a hum of fluid down a channel of constant depth. The hump of fluid was found to spread instead of steepen, as is the case in the usual shallow water theory."

"The problems of sequencing jobs through machines are discussed in a linear graph framework. The construction of feasible schedules from given technological orderings is related to the construction of transitive graphs from given component graphs. Methods of constructing transitive graphs are given and bounds on the number of different transitive graphs constructed from given components are determined. A recursive convex function defined on the transitive graphs-the job operation completion time and schedule time-is studied. Bounds on the number of different values that the schedule time can attain is obtained. Examples of multiprogramming, flow shop and machine shop scheduling are studied."