Hodge–de Rham numbers of almost complex 4-manifolds

We introduce and study Hodge–de Rham numbers for compact almost complex 4-manifolds, generalizing the Hodge numbers of a complex surface. The main properties of these numbers in the case of complex surfaces are extended to this more general setting, and it is shown that all Hodge–de Rham numbers for compact almost complex 4-manifolds are determined by the topology, except for one (the irregularity). Finally, these numbers are shown to prohibit the existence of complex structures on certain manifolds, without reference to the classification of surfaces.     

On stability of strong and weak reflected shocks

A time-realistic adaptive unstructured Euler code is used to demonstrate the numerical existence and investigate the stability of both weak and strong reflected shocks in regular reflection. For supersonic parallel flow in a channel, impinging on two symmetrical opposing wedges, the weak reflected configuration is insensitive to downstream pressure disturbances and therefore stable. The strong reflected shock configuration is unstable to positive perturbations in back-pressure and neutrally stable to negative perturbations. A unique -shock structure provides the transition mechanism between weak and strong reflected shock configurations. Received 6 September 1999 / Accepted 10 August 2000     

Micellar and associated thermodynamic properties of binary mixtures of alkyl triphenyl phosphonium bromides in ethylene glycol and water mixtures

Micellar properties of binary combinations of a family of cationic alkyl triphenyl phosphonium bromides with varying chain length (C₁₀–C₁₆) were investigated in aqueous and aqueous ethylene glycol mixtures employing conductometric technique. The results of the mixed systems were analyzed in the light of the Regular Solution Theory and the Gibbs–Duhem equation to evaluate the composition of the mixed micelle, the activity coefficients, and the interaction parameter (β). The excess free energy and the other related thermodynamic parameters of mixing were calculated and discussed in terms of the stability of the mixed micelles in the presence of an ethylene glycol additive. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users.     

On impulsive processes

Consider impulsive processes that consists of between two impulses non-autonomous, non-linear continuous processes subjected to time-varying impulsive constraints. By extending compact processes defined by Dafermos for non-autonomous systems without impulses, a class of regular impulsive processes is provided and its applications are stressed by selected examples. A weak invariance principle and an invariance principle are established for the regular impulsive processes. The paper thus lays ground work for geometric theory of general impulsive processes.