On the Jump Number Problem in Hereditary Classes of Bipartite Graphs

We prove a necessary condition for polynomial solvability of the jump number problem in classes of bipartite graphs characterized by a finite set of forbidden induced bipartite subgraphs. For some classes satisfying this condition, we propose polynomial algorithms to solve the jump number problem.     

Time-dependent wavepacket calculations of atom scattering from surfaces with impurities

Exact quantum-mechanical calculations are reported on atom scattering from a crystalline surface with isolated impurities. The calculations are for He scattering from a one-dimensional model of a Cu surface with adsorbed Ar atoms. The difficulties of carrying out calculations on scattering from extended but non-periodic structures are overcome by using a time-dependent wavepacket approach. A recently developed method for solving the time-dependent Schrödinger equation is employed. Scattering intensities are given for several energies and incidence angles. Detailed insight is obtained on impurity effects on surface scattering. The main features are: (1) Broad intensity tails are superimposed on each diffraction spike. The width of the tails decreases with increasing diffraction order; (2) Shallow rainbow peaks arise, due to impurity induced local corrugation; (3) Weak intensity maxima arise due to interference between surface and impurity scattering. The intensities are somewhat sensitive to the position of the impurity within the surface unit cell. Physical interpretation of the effects is provided from exact calculations, and from a simple sudden approximation for the scattering intensities. It is argued that He scattering can be used to determine impurity locations on surfaces.     

Error bounds for the compound poisson approximation

Explicit error bounds in terms of probabilities and stop-loss premiums are given for two kinds of compound Poisson approximations: the first concerns the difference between the individual and the collective model; the second is about the difference of the compound negative binomial and the compound Poisson distribution.     

Neuer Apparat zur Fettbestimmung der Milch

Ohne Zusammenfassung     

Femtosecond pulse shaping by an evolutionary algorithm with feedback

Received: 20 September 1997