Necessary and sufficient conditions for the existence of positive solutions to algebraic Riccati equations with indefinite quadratic term

Necessary and sufficient conditions are established in this paper for the existence of positive- and/or negative-definite solutions to the algebraic Riccati equation with indefinite coefficient. An iterative procedure is also given for computing such a solution.Project supported by the National Science Foundation of China and by the special program of the State Education Commission of China under grant 9033507.     

Improved results on the robustness of stochastic approximation algorithms

This paper is a continuation of the research carried out in [1]–[2], where the robustness analysis for stochastic approximation algorithms is given for two cases: 1. The regression function and the Liapunov function are not zero at the sought-forx ⁰; 2. lim sup _n a131_{n i=1} ⁿ _i+1 is not zero, where { _i } are the measurement errors and {a _n} are the weighting coefficients in the algorithm. Allowing these deviations from zero to occur simultaneously but to remain small, this paper shows that the estimation error is still small even for a class of measurement errors more general than that considered in [2].This project is supported by the National Natural Science Foundation of China.     

Synthesis and antimalarial effects of 2-(3,4-dichloroanilino)-7-[[[(dialkylamino)alkyl]amino]]-5-methyl-s-triazolo[1,5-a]pyrimidines

3,4-Dichlorophenylisothioeyanate ( 10 ) was allowed to react with 2-methy1-2-thiopseudourea to give methyl 4-(3,4-dichlorophenyl)(dithioaltophanimidate ( 11 ) (41%), which upon treatment with hydrazine afforded 3-amino-5-(3,4-dichloroanilino)-s-triazole ( 12 ) (54-91%). Ring-closure with ethyl acetoacetale in acetic acid afforded 2-(3,4-dichloroanilino)-5-methyl-s-triazolo[ 1,5-α ]-pyrimidin-7-ol ( 13 ) (81%). Chlorination with phosphorus oxychloride gave 7-chloro-2-(3,4-dichloroanilino)-5-methyl-s-triazolo[1,5-α ]pyrimidine ( 14 ) (98%), which was condensed with various amines to yield the desired 2-(3,4-diehloroanilino)-7-¶[(dialkylamino)alkyl]arnino¶-5-methyl-s-triazolo[ 1,5-α]pyrimidines ( 6 a-d). The structures of the s-triazolo[ 1,5-α ]pyrimidines were based on nmr spectroscopy and ring stability considerations. Several of the amino-s-triazolo[ 1,5-α ]pyrimidines possessed antimalarial activity against P. berghei in mice.