Polyhedra with few 3-cuts are hamiltonian

In 1956, Tutte showed that every planar 4-connected graph is hamiltonian. In this article, we will generalize this result and prove that polyhedra with at most three 3-cuts are hamiltonian. In 2002 Jackson and Yu have shown this result for the subclass of triangulations. We also prove that polyhedra with at most four 3-cuts have a hamiltonian path. It is well known that for each $k \ge 6$ non-hamiltonian polyhedra with $k$ 3-cuts exist. We give computational results on lower bounds on the order of a possible non-hamiltonian polyhedron for the remaining open cases of polyhedra with four or five 3-cuts.Comment: 21 pages; changed titl

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

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

SDSS AGNs with X-ray Emission from ROSAT PSPC Pointed Observations

We present a sample of 1744 type 1 active galactic nuclei (AGNs) from the Sloan Digital Sky Survey (SDSS DR4) spectroscopic catalog with X-ray counterparts in the White-Giommi-Angelini Catalog (WGACAT) of ROSAT PSPC pointed observations. Of 1744 X-ray sources, 1410 (80.9%) are new AGN identifications. Of 4574 SDSS DR4 AGNs for which we found radio matches in the catalog of radio sources from the FIRST catalog, 224 turned up in our sample of SDSS X-ray AGNs. The sample objects are given in a catalog that contains optical and X-ray parameters along with radio emission parameters where available. We illustrate the content of our catalog and its potential for AGN science by providing statistical relationships for the catalog data. The potential of the morphological information is emphasized by confronting the statistics of optically resolved and unresolved AGNs. The immediate properties of the catalog objects include significant correlation of X-ray and optical fluxes, which is consistent with expectations. Also expected is the decrease of X-ray flux toward higher redshifts. The X-ray to optical flux ratio for the unresolved AGNs exhibits a decline toward higher redshifts, in agreement with previous results. The resolved AGNs, however, display the opposite trend. At a given optical brightness, X-ray fluxes of radio-quiet AGNs by a factor of 2. We caution, however, that because of the variety of selection effects present in both the WGACAT and the SDSS, the interpretation of any relationships based on our sample of X-ray AGNs requires a careful analysis of these effects.Comment: 34 pages, 18 figure

A digitalized solar ultraviolet spectrum

Digitalized solar ultraviolet spectrum obtained in rocket experiments for use in analysis of upper atmosphere experiment

Temperature and food quantity effects on the harpacticoid copepod Nitocra spinipes : combining in vivo bioassays with population modeling

The harpacticoid copepod Nitocra spinipes has become a popular model species for toxicity testing over the past few decades. However, the combined influence of temperature and food shortage, two climate change-related stressors, has never been assessed in this species. Consequently, effects of three temperatures (15, 20 and 25˚C) and six food regimes (between 0 and 5 × 10^5 algal cells/mL) on the life cycle of N. spinipes were examined in this study. Similarly to other copepod species, development times and brood sizes decreased with rising temperatures. Mortality was lowest in the 20˚C temperature setup, indicating a close-by temperature optimum for this species. Decreasing food concentrations led to increased development times, higher mortality and a reduction in brood size. A sex ratio shift toward more females per male was observed for increasing temperatures, while no significant relationship with food concentration was found. Temperature and food functions for each endpoint were integrated into an existing individual-based population model for N. spinipes which in the future may serve as an extrapolation tool in environmental risk assessment. The model was able to accurately reproduce the experimental data in subsequent verification simulations. We suggest that temperature, food shortage, and potentially other climate change-related stressors should be considered in environmental risk assessment of chemicals to account for non-optimal exposure conditions that may occur in the field. Furthermore, we advocate combining in vivo bioassays with population modeling as a cost effective higher tier approach to assess such considerations

Kinetic simulation of the sheath dynamics in the intermediate radio-frequency regime

The dynamics of temporally modulated plasma boundary sheaths is studied in the intermediate radio frequency regime where the applied radio frequency and the ion plasma frequency are comparable. Two kinetic simulation codes are employed and their results are compared. The first code is a realization of the well-known scheme, Particle-In-Cell with Monte Carlo collisions (PIC/MCC) and simulates the entire discharge, a planar radio frequency capacitively coupled plasma (RF-CCP) with an additional heating source. The second code is based on the recently published scheme Ensemble-in-Spacetime (EST); it resolves only the sheath and requires the time resolved voltage across and the ion flux into the sheath as input. Ion inertia causes a temporal asymmetry (hysteresis) of the sheath charge-voltage relation; also other ion transit time effects are found. The two codes are in good agreement, both with respect to the spatial and temporal dynamics of the sheath and with respect to the ion energy distributions at the electrodes. It is concluded that the EST scheme may serve as an efficient post-processor for fluid or global simulations and for measurements: It can rapidly and accurately calculate ion distribution functions even when no genuine kinetic information is available