The Generation of Fullerenes

We describe an efficient new algorithm for the generation of fullerenes. Our implementation of this algorithm is more than 3.5 times faster than the previously fastest generator for fullerenes -- fullgen -- and the first program since fullgen to be useful for more than 100 vertices. We also note a programming error in fullgen that caused problems for 136 or more vertices. We tabulate the numbers of fullerenes and IPR fullerenes up to 400 vertices. We also check up to 316 vertices a conjecture of Barnette that cubic planar graphs with maximum face size 6 are hamiltonian and verify that the smallest counterexample to the spiral conjecture has 380 vertices.Comment: 21 pages; added a not

How Saturated are Absorption Lines in the Broad Absorption Line Quasar PG 1411+442 ?

Recently, convincing evidence was found for extremely large X-ray absorption by column densities $> 10^{23} cm^{-2}$ in broad absorption line quasars. One consequence of this is that any soft X-ray emission from these QSOs would be the scattered light or leaked light from partially covering absorbing material. A detection of the unabsorbed soft X-ray and absorbed hard X-ray compo nent will allow to determine the total column density as well as the effective covering factor of the absorbing material, which can be hardly obtained from the UV absorption lines. Brinkmann et al. (1999) showed that both the unabsorbed and absorbed components are detected in the nearby very bright broad absorption line quasar PG 1411+442. In this letter, we make a further analysis of the broad band X-ray spectrum and the UV spectrum from HST, and demonstrate that broad absorption lines are completely saturated at the bottom of absorption troughs.Comment: 6 pages, 3 postscript figures. to appear in Astrophy. J. Letter

XMM-Newton observations of the eastern jet of SS433

The radio supernova remnant W50 hosts at its center the peculiar galactic X-ray binary SS 433. It shows a central spherical structure with two `ears' which are supposed to be formed by the interaction of the precessing jets of SS 433 with the supernova shell. In two pointings in September/October 2004 for 30 ks each the eastern jet of SS 433 was observed with XMM-Newton to study the outermost parts of the `ear' and the X-ray bright emission region about 35 arcmin from SS 433. The spectra consist of two components: a non-thermal power law with photon index \Gamma ~ 2.17+/-0.02 and a thermal component at a typical temperature of kT ~ 0.3 keV. The X-ray emission seems to fill the whole interior region of the radio remnant W50. The jet terminates in the eastern `ear' in a ring-like terminal shock which indicates a flow with a kind of hollow-cone morphology. The spatial coincidence of X-ray and radio emission suggests physical conditions similar to those found at the outer shocks of ordinary supernova remnants. The bright emission region closer to SS 433 radiates non-thermally in a spatially well confined geometry at higher X-ray energies. At soft X-rays the shape of the region gets blurred, centered on the hard lenticular emission. The shape of this region and the bend in the jet propagation direction might be caused by the interaction of a re-collimated jet with the outer, non homogeneous interstellar matter distribution. The physical conditions leading to the re-collimation of the jet and the peculiar emission morphology are far from being understood and require deeper observations as well as a detailed modeling of the interaction of a jet with its surroundings.Comment: 10 pages, 8 figures, to appear in A&

Contact line stability of ridges and drops

Within the framework of a semi-microscopic interface displacement model we analyze the linear stability of sessile ridges and drops of a non-volatile liquid on a homogeneous, partially wet substrate, for both signs and arbitrary amplitudes of the three-phase contact line tension. Focusing on perturbations which correspond to deformations of the three-phase contact line, we find that drops are generally stable while ridges are subject only to the long-wavelength Rayleigh-Plateau instability leading to a breakup into droplets, in contrast to the predictions of capillary models which take line tension into account. We argue that the short-wavelength instabilities predicted within the framework of the latter macroscopic capillary theory occur outside its range of validity and thus are spurious.Comment: 6 pages, 1 figur

X-ray Spectroscopy of QSOs with Broad Ultraviolet Absorption Lines

For the population of QSOs with broad ultraviolet absorption lines, we are just beginning to accumulate X-ray observations with enough counts for spectral analysis at CCD resolution. From a sample of eight QSOs [including four Broad Absorption Line (BAL) QSOs and three mini-BAL QSOs] with ASCA or Chandra spectra with more than 200 counts, general patterns are emerging. Their power-law X-ray continua are typical of normal QSOs with Gamma~2.0, and the signatures of a significant column density [N_H~(0.1-4)x10^{23} cm^{-2}] of intrinsic, absorbing gas are clear. Correcting the X-ray spectra for intrinsic absorption recovers a normal ultraviolet-to-X-ray flux ratio, indicating that the spectral energy distributions of this population are not inherently anomalous. In addition, a large fraction of our sample shows significant evidence for complexity in the absorption. The subset of BAL QSOs with broad MgII absorption apparently suffers from Compton-thick absorption completely obscuring the direct continuum in the 2-10 keV X-ray band, complicating any measurement of their intrinsic X-ray spectral shapes.Comment: 9 pages, 6 figures, uses AASTeX. Accepted to the Astrophysical Journa

Colourings of cubic graphs inducing isomorphic monochromatic subgraphs

A $k$-bisection of a bridgeless cubic graph $G$ is a $2$-colouring of its vertex set such that the colour classes have the same cardinality and all connected components in the two subgraphs induced by the colour classes (monochromatic components in what follows) have order at most $k$. Ban and Linial conjectured that every bridgeless cubic graph admits a $2$-bisection except for the Petersen graph. A similar problem for the edge set of cubic graphs has been studied: Wormald conjectured that every cubic graph $G$ with $|E(G)| \equiv 0 \pmod 2$ has a $2$-edge colouring such that the two monochromatic subgraphs are isomorphic linear forests (i.e. a forest whose components are paths). Finally, Ando conjectured that every cubic graph admits a bisection such that the two induced monochromatic subgraphs are isomorphic. In this paper, we give a detailed insight into the conjectures of Ban-Linial and Wormald and provide evidence of a strong relation of both of them with Ando's conjecture. Furthermore, we also give computational and theoretical evidence in their support. As a result, we pose some open problems stronger than the above mentioned conjectures. Moreover, we prove Ban-Linial's conjecture for cubic cycle permutation graphs. As a by-product of studying $2$-edge colourings of cubic graphs having linear forests as monochromatic components, we also give a negative answer to a problem posed by Jackson and Wormald about certain decompositions of cubic graphs into linear forests.Comment: 33 pages; submitted for publicatio