Discretizing dynamic programs

Discretizing certain discrete-time, uncountable-state dynamic programs such that the respective solutions to a sequence of discretized versions converge uniformly to the solution of the original problem is shown. Via a random perturbation device, we apply our general approach to a separable nonconvex program.This paper was completed while the author was Visiting Professor of Management Science at the University of Chicago, Chicago, Illinois.     

Model selection for complex systems involving polynuclear species

1-hydroxyethylidene-1,1-bisphosphonic acid (HEDP) is a phosphonate chelate with several diagnostic and therapeutic applications. Previous studies have indicated that calcium complex aggregation occurs in the basic range of pH; results from this study indicate that complex aggregation occurs throughout the physiological range of pH as well. Calcium complex formation data were used for PQ analyses and plots of the derivative of Z with respect to total diphosphonate at constant free calcium ion concentration were shown to provide valuable information with regard to model selection. A link-addition stepwise complex formation model was shown to be most appropriate; a robust feature of all aggregate formation models examined is a strong pH dependence of polynuclear complex formation in the pH range 5.5–7.0.     

The convexity of the range of three Hermitian forms and of the numerical range of sesquilinear forms

This note contains a demonstration of the convexity of the joint range of three Hermitian forms, and, as an immediate corollary, of the convexity of the numerical range of arbitrary sesquilinear forms.