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

Four New BL Lac Surveys: Sampling New Populations

The advent of large area deep radio and X-ray surveys is leading to the creation of many new BL Lac samples. In particular, the ROSAT All-Sky, Green Bank and FIRST surveys are proving to be rich sources of new BL Lacs. We will discuss the methods used in four independent BL Lac searches based on these surveys. Comparison of the broadband spectral energy distributions of these BL Lacs with those of previously known objects clearly points to the existence of a large previously unrecognized population of objects with characteristics intermediate between those exhibited by Low and High energy peaked BL Lacs.Comment: 4 pages, 3 postscript figures, To be published in the Proceedings of the conference "BL Lac Phenomenon" held in Turku, Finland, June 22-26, 199

The size distribution of galaxies in the Sloan Digital Sky Survey

abridged: We use a complete sample of about 140,000 galaxies from the Sloan Digital Sky Survey (SDSS) to study the size distribution of galaxies and its dependence on their luminosity, stellar mass, and morphological type. The large SDSS database provides statistics of unprecedented accuracy. For each type of galaxy, the size distribution at given luminosity (or stellar mass) is well described by a log-normal function, characterized by its median $\bar{R}$ and dispersion $\sigma_{\ln R}$. For late-type galaxies, there is a characteristic luminosity at $M_{r,0}\sim -20.5$ (assuming $h=0.7$) corresponding to a stellar mass M_0\sim 10^{10.6}\Msun. Galaxies more massive than $M_0$ have $\bar{R}\propto M^{0.4}$ and $\sigma_{\ln R}\sim 0.3$, while less massive galaxies have $\bar{R}\propto M^{0.15}$ and $\sigma_{\ln R}\sim 0.5$. For early-type galaxies, the $\bar{R}$ - $M$ relation is significantly steeper, $\bar{R}\propto M^{0.55}$, but the $\sigma_{\ln R}$ - $M$ relation is similar to that of late-type galaxies. Faint red galaxies have sizes quite independent of their luminosities.Comment: 42 pages, 18 figures, 2 tables; replaced with the version accepted by MNRA

S-Duality and Exact Type IIB Superstring Backgrounds

A geometrical approach in the non-symmetric connection framework is employed to examine the issue of higher order $\alpha'$ corrections to D=10 type IIB superstring backgrounds with a covariantly constant null Killing isometry and non-zero Ramond-Ramond field content. These describe generalized supersymmetric string waves and were obtained recently by us through the S-duality transformation of purely NS-NS plane wave backgrounds. We find that the backgrounds are exact subject to the existence of certain field redefinitions and provided certain restrictive conditions are satisfied.Comment: 21 Pages, LATEX fil

HST Observations of the Serendipitous X-ray Companion to Mrk 273: Cluster at z=0.46?

We have used HST I-band images to identify Mrk 273X, the very unusual high-redshift X-ray-luminous Seyfert 2 galaxy found by ROSAT in the same field-of-view as Mrk 273. We have measured the photometric properties of Mrk 273X and have also analyzed the luminosity distribution of the faint galaxy population seen in the HST image. The luminosity of the galaxy and the properties of the surrounding environment suggest that Mrk 273X is the brightest galaxy in a relatively poor cluster at a redshift near 0.46. Its off-center location in the cluster and the presence of other galaxy groupings in the HST image may indicate that this is a dynamically young cluster on the verge of merging with its neighboring clusters. We find that Mrk 273X is a bright featureless elliptical galaxy with no evidence for a disk. It follows the de Vaucouleurs (r^{1/4}) surface brightness law very well over a range of 8 magnitudes. Though the surface brightness profile does not appear to be dominated by the AGN, the galaxy has very blue colors that do appear to be produced by the AGN. Mrk 273X is most similar to the IC 5063 class of active galaxies --- a hybrid Sy 2 / powerful radio galaxy.Comment: Accepted for publication in the Astrophysical Journal. 8 pages, including 4 postscript figures. Uses emulateapj.sty and psfig.sty. Higher quality version of Figure 1 is available at http://rings.gsfc.nasa.gov/~borne/fig1-markgals.gi

Temperature Dependence of the Cu(2) NQR Line Width in YBa2_2Cu3_3O7−y_{7-y}

Systematic measurements of the $^{63}$Cu(2) NQR line width were performed in underdoped YBa$_2$Cu$_3$O$_{7-y}$ samples over the temperature range 4.2 K $<T<300$ K. It was shown that the copper NQR line width monotonically increases upon lowering temperature in the below-critical region, resembling temperature behavior of the superconducting gap. The observed dependence is explained by the fact that the energy of a condensate of sliding charge-current states of the charge-density-wave type depends on the phase of order parameter. Calculations show that this dependence appears only at $T<T_c$. Quantitative estimates of the line broadening at $T<T_c$ agree with the measurement results.Comment: 4 pages, 2 figure

Beam Based Alignment of Interaction Region Magnets

In conventional beam based alignment (BBA) procedures, the relative alignment of a quadrupole to a nearby beam position monitor is determined by finding a beam position in the quadrupole at which the closed orbit does not change when the quadrupole field is varied. The final focus magnets of the interaction regions (IR) of circular colliders often have some specialized properties that make it difficult to perform conventional beam based alignment procedures. At the HERA interaction points, for example, these properties are: (a) The quadrupoles are quite strong and long. Therefore a thin lens approximation is quite imprecise. (b) The effects of angular magnet offsets become significant. (c) The possibilities to steer the beam are limited as long as the alignment is not within specifications. (d) The beam orbit has design offsets and design angles with respect to the axis of the low-beta quadrupoles. (e) Often quadrupoles do not have a beam position monitor in their vicinity. Here we present a beam based alignment procedure that determines the relative offset of the closed orbit from a quadrupole center without requiring large orbit changes or monitors next to the quadrupole. Taking into account the alignment angle allows us to reduce the sensitivity to optical errors by one to two orders of magnitude. We also show how the BBA measurements of all IR quadrupoles can be used to determine the global position of the magnets. The sensitivity to errors of this method is evaluated and its applicability to HERA is shown

Contact Representations of Graphs in 3D

We study contact representations of graphs in which vertices are represented by axis-aligned polyhedra in 3D and edges are realized by non-zero area common boundaries between corresponding polyhedra. We show that for every 3-connected planar graph, there exists a simultaneous representation of the graph and its dual with 3D boxes. We give a linear-time algorithm for constructing such a representation. This result extends the existing primal-dual contact representations of planar graphs in 2D using circles and triangles. While contact graphs in 2D directly correspond to planar graphs, we next study representations of non-planar graphs in 3D. In particular we consider representations of optimal 1-planar graphs. A graph is 1-planar if there exists a drawing in the plane where each edge is crossed at most once, and an optimal n-vertex 1-planar graph has the maximum (4n - 8) number of edges. We describe a linear-time algorithm for representing optimal 1-planar graphs without separating 4-cycles with 3D boxes. However, not every optimal 1-planar graph admits a representation with boxes. Hence, we consider contact representations with the next simplest axis-aligned 3D object, L-shaped polyhedra. We provide a quadratic-time algorithm for representing optimal 1-planar graph with L-shaped polyhedra