Second-order necessary optimality conditions for domain optimization problems of the Neumann type

In this paper, we treat a domain optimization problem in which the boundary-value problem is a Neumann problem. In the case where the domain is in a three-dimensional Euclidean space, the first-order and the second-order necessary conditions which the optimal domain must satisfy are derived under a constraint which is the generalization of the requisite of constant volume.Portions of this paper were presented at the 13th IFIP Conference on System Modelling and Optimization, Tokyo, Japan, 1987.     

Purines. LII. Synthesis and biological evaluation of 8-methylguanine 7-oxide and its 9-arylmethyl derivatives.

The synthesis of 8-methylguanine 7-oxide (3) was accomplished via a "phenacylamine route", which started from condensation of alpha-(4-methoxybenzylamino)propiophenone (6), prepared by coupling of alpha-bromopropiophenone (4) and 4-methoxybenzylamine (5), with 2-amino-6-chloro-5-nitro-4(3H)-pyrimidinone (7) and proceeded through cyclization of the resulting phenacylaminopyrimidinone (8) and removal of the 4-methoxybenzyl group. The N-oxide 3 and its 9-arylmethyl derivatives 9 and 11 showed only very weak antileukemic activity and no antimicrobial activity.