Optimal control problems with delay, the maximum principle and necessary conditions

In this paper we consider a rather general optimal control problem involving ordinary differential equations with delayed arguments and a set of equality and inequality restrictions on state- and control variables. For this problem a maximum principle is given in pointwise form, using variational techniques. From this maximum principle necessary conditions are derived, as well as a Lagrange-like multiplier rule. Details may be found in ref. [2], together with extensions to the Hamilton-Jacobi equation and free end point problems

Mass Transfer in a closed stirred gas/liquid contactor: Part 1: The mass transfer rate kLS

Liquid phase mass transfer rates kLS for the absorption of oxygen in tap water and in aqueous ionic solutions have been determined in two closed stirred tank contactors for a power input between 3 and 70 W/kg and (impeller diameter)f(tank diameter) ratios DifT of 0.3, 0.35 and 0.4. The contactors had diameters\ud of 0. I9 and 0.6 m. The dispersed phase fraction was 1% by volume in all experiments. The values of kLS were determined using two different techniques:\ud (1) a transient physical absorption method; and (2) the sulphite method

Some Beliefs about Justice

This is the text of The Lindley Lecture for 1961, given by William K. Frankena (1908-1994), an American philosopher