Path-based distance functions in n-dimensional generalizations of the face- and body-centered cubic grids

Path-based distance functions are defined on n-dimensional generalizations of the face-centered cubic and body-centered cubic grids. The distance functions use both weights and neighborhood sequences. These distances share many properties with traditional path-based distance functions, such as the city-block distance, but are less rotational dependent. For the three-dimensional case, we introduce four different error functions which are used to find the optimal weights and neighborhood sequences that can be used to define the distance functions with low rotational dependency.     

The power of programmed grammars with graphs from various classes

Programmed grammars, one of the most important and well investigated classes of grammars with context-free rules and a mechanism controlling the application of the rules, can be described by graphs. We investigate whether or not the restriction to special classes of graphs restricts the generative power of programmed grammars with erasing rules and without appearance checking, too. We obtain that Eulerian, Hamiltonian, planar and bipartite graphs and regular graphs of degree at least three are pr-universal in that sense that any language which can be generated by programmed grammars (with erasing rules and without appearance checking) can be obtained by programmed grammars where the underlying graph belongs to the given special class of graphs, whereas complete graphs, regular graphs of degree 2 and backbone graphs lead to proper subfamilies of the family of programmed languages.     

Mode-selected electron-phonon coupling in superconducting Pb nanofilms determined from He atom scattering

The electron-phonon coupling (EPC) strength for each phonon mode in superconducting Pb films is measured by inelastic helium atom scattering (IHAS). This surprising ability of IHAS relies on two facts: (a) In ultrathin metal films, the EPC range exceeds the film thickness, thus enabling IHAS to detect most film phonons, even 1 nm below the surface; (b) IHAS scattering amplitudes from single phonons are shown, by first-principle arguments, to be proportional to the respective EPC strengths. Thus IHAS is the first experiment providing mode-selected EPC strengths (mode-lambda spectroscopy).     

t1/3 Superdiffusivi ty of Fini te-Range Asymme tric Exclusion Processes on $${\ma thbb{Z}}$$

We consider finite-range asymmetric exclusion processes on with non-zero drift. The diffusivity D(t) is expected to be of . We prove that D(t) ≥ Ct ^1/3 in the weak (Tauberian) sense that as . The proof employs the resolvent method to make a direct comparison with the totally asymmetric simple exclusion process, for which the result is a consequence of the scaling limit for the two-point function recently obtained by Ferrari and Spohn. In the nearest neighbor case, we show further that tD(t) is monotone, and hence we can conclude that D(t) ≥ Ct ^1/3(log t)^−7/3 in the usual sense. Supported by the Natural Sciences and Engineering Research Council of Canada. Partially supported by the Hungarian Scientific Research Fund grants T37685 and K60708.