Optimal birth control of population dynamics

The authors studied optimal birth control policies for an age-structured population of McKendrick type which is a distributed parameter system involving 1st order partial differential equations with nonlocal bilinear boundary control. The functional analytic approach of Dubovitskii and Milyutin is adopted in the investigation. Maximum principles for problems with a free end condition and fixed final horizon are developed, and the time optimal control problems, the problem with target sets, and infinite planning horizon case are investigated.     

A convenient synthesis of a selective gelatinase inhibitor as an antimetastatic agent

Compound 1, 2-(4-phenoxyphenylsulfonylmethyl)thiirane, is a potent and selective inhibitor for human gelatinases (J. Am. Chem. Soc. 2000, 122, 6799-6800), enzymes implicated in a number of diseases, including cancer. This compound is showing excellent promise in animal trials in a number of disease models. Large quantities of this compound were necessary for these studies. A convenient four-step synthetic route for compound 1 is described herein. The synthesis is amenable to scale-up to tens of grams and gives an overall yield of 57% for this important compound.