Exact solutions for Belousov-Zhabotinskii reaction-diffusion system

Abstract. We consider the following simplified model for the Belousou-Zhabotinskii(B-Z)reaction:     

The occupation time of Brownian motion in a ball

LetW be a Wiener process of dimensiond3, starting from 0, and letX(t) be the total time spent byW in the ball centered at 0 with radiust. We give an affirmative answer to a conjecture of Taylor and Tricot⁽¹⁶⁾ on the tail distribution ofX(t). Lévy's lower functions ofX(t) are characterized by an integral test.     

Synthesis and reactions of 2-(alkylthio)-4,4-dimenthyl-1,3-thiazole-5(4H)-thiones

Six 2-(alkylthio)-substituted 4,4-dimethyl-1,3-thiazole-5(4H)-thiones were synthesized according to a new method. The reactions of these compounds with allyl- and benzyllithium reagents, 1,3-dipoles, and dimethyl acetylenedicarboxylate proceeded in a similar manner to 2-alkyl-substituted analogues, while methyllithium reacted in a different way yielding trithio-orthoester derivatives.