Note on a Conjecture of Wegner

The optimal packings of n unit discs in the plane are known for those natural numbers n, which satisfy certain number theoretic conditions. Their geometric realizations are the extremal Groemer packings (or Wegner packings). But an extremal Groemer packing of n unit discs does not exist for all natural numbers n and in this case, the number n is called exceptional. We are interested in number theoretic characterizations of the exceptional numbers. A counterexample is given to a conjecture of Wegner concerning such a characterization. We further give a characterization of the exceptional numbers, whose shape is closely related to that of Wegner's conjecture.Comment: 5 pages; Contributions to Algebra and Geometry, Vol.52 No1 April 201

Effects of impurities on Tamm-like lanthanide-metal surface states

The effects of isolated residual-gas adsorbates on the local electronic structure of the Dy(0001) surface were spatially mapped by scanning tunneling microscopy and spectroscopy at 12 K. Less than 15 A away from an adsorbate, a strong reduction of the intensity and a significant increase of the width of the majority component of the surface state due to impurity scattering were observed, with essentially no change of the minority component; this reflects a high lateral localization of the Tamm-like surface state. Furthermore, an adsorbate-induced state was found that behaves metastable.Comment: 5 pages, 4 figures, accepted as Brief Report for Physical Review

Fundamental Plane Distances to Early-type Field Galaxies in the South Equatorial Strip. I. The Spectroscopic Data

Radial velocities and central velocity dispersions are derived for 238 E/S0 galaxies from medium-resolution spectroscopy. New spectroscopic data have been obtained as part of a study of the Fundamental Plane distances and peculiar motions of early-type galaxies in three selected directions of the South Equatorial Strip, undertaken in order to investigate the reality of large-scale streaming motion; results of this study have been reported in M\"uller $et$ $al.$ (1998). The new APM South Equatorial Strip Catalog ($-17^{\circ}.5 < \delta < +2^{\circ}.5$) was used to select the sample of field galaxies in three directions: (1) 15h10 - 16h10; (2) 20h30 - 21h50; (3) 00h10 - 01h30. The spectra obtained have a median S/N per ${\AA}$ of 23, an instrumental resolution (FWHM) of $\sim$ 4 ${\AA}$, and the spectrograph resolution (dispersion) is $\sim$ 100 km~s$^{-1}$. The Fourier cross-correlation method was used to derive the radial velocities and velocity dispersions. The velocity dispersions have been corrected for the size of the aperture and for the galaxy effective radius. Comparisons of the derived radial velocities with data from the literature show that our values are accurate to 40 km~s$^{-1}$. A comparison with results from J\orgensen et al. (1995) shows that the derived central velocity dispersion have an rms scatter of 0.036 in $\log \sigma$. There is no offset relative to the velocity dispersions of Davies et al. (1987).Comment: accepted for publication in Astronomy & Astrophysics Supplement Serie

Search For Oxygen in Cool DQ White Dwarf Atmospheres

We report new infrared spectroscopic observations of cool DQ white dwarfs by using Coolspec on the 2.7m Harlan-Smith Telescope. DQs have helium-rich atmospheres with traces of molecular carbon thought to be the result of convective dredge-up from their C/O interiors. Recent model calculations predict that oxygen should also be present in DQ atmospheres in detectable amounts. Our synthetic spectra calculations for He-rich white dwarfs with traces of C and O indicate that CO should be easily detected in the cool DQ atmospheres if present in the expected amounts. Determination of the oxygen abundance in the atmosphere will reveal the C/O ratio at the core/envelope boundary, constraining the important and uncertain ^{12}C(alpha,gamma)^{16}O reaction rate.Comment: 2 pages, 2 figures, to appear in proceedings of the 13th European Workshop on White Dwarf