Boltzmann equation for a dissociating gas

The incorporation of three-body collisions for dissociation/recombination into the Boltzmann equation is discussed. Conditions are assumed such that collisions are completed in the sense of scattering theory, so the collision operator is determined by scattering and reaction cross sections. The resulting equation has anH-theorem, and the equilibrium solution requires the law of mass action in addition to the Maxwellian dependence on momentum. A brief discussion is given of the normal solution and the transport coefficients.This paper is dedicated to Prof. E. G. D. Cohen on the occasion of his 65th birthday.     

Consistent conditional systems in noncooperative game theory

A space ofconsistent conditional systems is obtained by combining concepts introduced by Kreps and Wilson (1982) and Myerson (1986). The sequential equilibrium concept is displayed as the set of fixed points of a best response correspondence from this space to itself. A thorough exploration of the space shows that the best response correspondence satisfies the hypotheses of the Eilenberg-Montgomery (1946) fixed point theorem, and this allows notions of stability analogous to those introduced by Kohlberg and Mertens (1986) to be defined.     

Asymmetric Isothiourea‐Catalysed Formal [3+2] Cycloadditions of Ammonium Enolates with Oxaziridines

A highly enantioselective Lewis base‐catalysed formal [3+2] cycloaddition of ammonium enolates and oxaziridines to give stereodefined oxazolidin‐4‐ones in high yield is described. Employing an enantioenriched oxaziridine in this process leads to a matched/mis‐matched effect with the isothiourea catalyst and allowed the synthesis of either syn‐ or anti‐stereodefined oxazolidin‐4‐ones in high d.r., yield and ee. Additionally, the oxazolidin‐4‐one products have been derivatised to afford functionalised enantioenriched building blocks.