Boutet de Monvel`s calculus and groupoids I

Can Boutet de Monvel`s algebra on a compact manifold with boundary be obtained as the algebra Psi(0)(G) of pseudodifferential operators on some Lie groupoid G? If it could, the kernel G of the principal symbol homomorphism would be isomorphic to the groupoid C*-algebra C*(G). While the answer to the above question remains open, we exhibit in this paper a groupoid G such that C*(G) possesses an ideal I isomorphic to G. In fact, we prove first that G similar or equal to Psi circle times K with the C*-algebra Psi generated by the zero order pseudodifferential operators on the boundary and the algebra K of compact operators. As both Psi circle times K and I are extensions of C(S*Y) circle times K by K (S*Y is the co-sphere bundle over the boundary) we infer from a theorem by Voiculescu that both are isomorphic.

Estimated lifetimes of road pavements in Sweden using time-to-event analysis

Maintenance planning of road pavement requires reliable estimates of roads’ lifetimes. In determining the lifetime of a road, this study combines maintenance activities and road condition measurements. The scope of the paper is to estimate lifetimes of road pavements in Sweden with time to event analysis. The model used includes effects of pavement type, road type, bearing capacity, road width, speed limit, stone size and climate zone, where the model is stratified according to traffic load. Among the nine analyzed pavement types, stone mastic had the longest expected lifetime, 32 percent longer than asphalt concrete. Among road types, ordinary roads with cable barriers had 30 percent shorter lifetime than ordinary roads. Increased speed lowered the lifetime, while increased stone size (up to 20 mm) and increased road width lengthened the lifetime. The results are of importance for life cycle cost analysis and road management.