Improved bounds for the crossing numbers of K_m,n and K_n

It has been long--conjectured that the crossing number cr(K_m,n) of the complete bipartite graph K_m,n equals the Zarankiewicz Number Z(m,n):= floor((m-1)/2) floor(m/2) floor((n-1)/2) floor(n/2). Another long--standing conjecture states that the crossing number cr(K_n) of the complete graph K_n equals Z(n):= floor(n/2) floor((n-1)/2) floor((n-2)/2) floor((n-3)/2)/4. In this paper we show the following improved bounds on the asymptotic ratios of these crossing numbers and their conjectured values: (i) for each fixed m >= 9, lim_{n->infty} cr(K_m,n)/Z(m,n) >= 0.83m/(m-1); (ii) lim_{n->infty} cr(K_n,n)/Z(n,n) >= 0.83; and (iii) lim_{n->infty} cr(K_n)/Z(n) >= 0.83. The previous best known lower bounds were 0.8m/(m-1), 0.8, and 0.8, respectively. These improved bounds are obtained as a consequence of the new bound cr(K_{7,n}) >= 2.1796n^2 - 4.5n. To obtain this improved lower bound for cr(K_{7,n}), we use some elementary topological facts on drawings of K_{2,7} to set up a quadratic program on 6! variables whose minimum p satisfies cr(K_{7,n}) >= (p/2)n^2 - 4.5n, and then use state--of--the--art quadratic optimization techniques combined with a bit of invariant theory of permutation groups to show that p >= 4.3593.Comment: LaTeX, 18 pages, 2 figure

Supersolidity, entropy and frustration

We study the properties of t-t'-V model of hard-core bosons on the triangular lattice that can be realized in optical lattices. By mapping to the spin-1/2 XXZ model in a field, we determine the phase diagram of the t-V model where the supersolid characterized by the ordering pattern (x,x,-2x') ("ferrimagnetic" or SS A) is a ground state for chemical potential \mu >3V. By turning on either temperature or t' at half-filling \mu =3V, we find a first order transition from SS A to the elusive supersolid characterized by the (x,-x,0) ordering pattern ("antiferromagnetic" or SS C). In addition, we find a large region where a superfluid phase becomes a solid upon raising temperature at fixed chemical potential. This is an analog of the Pomeranchuk effect driven by the large entropic effects associated with geometric frustration on the triangular lattice.Comment: 4 pages, igures, LaTe

Bellucia grossularioides (L.) Triana and B. dichotoma Cogn. (Melastomataceae): two important elements of flora in secondary forest succession of the central Amazon.

The aim of the comparative studies in autoecology of common secondary forest species carried out at the EMBRAPA/SHIFT experimental site near Manaus, Amazonas is to acquire a better understanding of the mechanisms responsible for the successional pathways in Terra Firme secondary forests

Isotopic composition (238U/235U) of some commonly used uranium reference materials

We have determined 238U/235U ratios for a suite of commonly used natural (CRM 112a, SRM 950a, and HU-1) and synthetic (IRMM 184 and CRM U500) uranium reference materials by thermal ionisation mass-spectrometry (TIMS) using the IRMM 3636 233U-236U double spike to accurately correct for mass fractionation. Total uncertainty on the 238U/235U determinations is estimated to be < 0.02% (2σ). These natural 238U/235U values are different from the widely used ‘consensus’ value (137.88), with each standard having lower 238U/235U values by up to 0.08%. The 238U/235U ratio determined for CRM U500 and IRMM 184 are within error of their certified values; however, the total uncertainty for CRM U500 is substantially reduced (from 0.1% to 0.02%). These reference materials are commonly used to assess mass spectrometer performance and accuracy, calibrate isotope tracers employed in U, U-Th and U-Pb isotopic studies, and as a reference for terrestrial and meteoritic 238U/235U variations. These new 238U/235U values will thus provide greater accuracy and reduced uncertainty for a wide variety of isotopic determinations

Revealing the Archetype: The Journey of a Trecento Madonna and Child at the National Museum of Scotland

The National Museums Scotland Madonna and Child project sought to uncover and document the history of a fine polychrome wood carving attributed to The Master of the Gualino St Catherine and to prepare it for display. A new body of knowledge has been assembled by the interdisciplinary team. The conservation treatment was informed by this work and led to further discoveries: the removal of overpaint exposing a previously hidden underdrawing. The ethics of the treatment decisions, including the removal of the Christ Child’s 1960s’ fingers required team dialogue and was opened up for the public to respond to in a series of blogs. The discovery of a rich polychromy including gold and glazed tin has led to further plans to produce a 3-D colour reconstruction. The collaborations developed during this project will facilitate future joint ventures for polychrome sculpture in Scottish collections

GHRS and ORFEUS-II Observations of the Highly Ionized Interstellar Medium Toward ESO141-055

We present Goddard High Resolution Spectrograph and ORFEUS-II measurements of Si IV, CIV, N V, and O VI absorption in the interstellar medium of the Galactic disk and halo toward the nucleus of the Seyfert galaxy ESO141-055. The high ionization absorption is strong, with line strengths consistent with the spectral signature expected for hot (log T = 5-6) collisionally ionized gas in either a ``Galactic fountain'' or an inhomogeneous medium containing a mixture of conductive interfaces and turbulent mixing layers. The total O VI column density of log N ~ 15 suggests that the scale height of O VI is large (>3 kpc) in this direction. Comparison of the high ion column densities with measurements for other sight lines indicates that the highly ionized gas distribution is patchy. The amount of O VI perpendicular to the Galactic plane varies by at least a factor of ~4 among the complete halo sight lines thus far studied. In addition to the high ion absorption, lines of low ionization species are also present in the spectra. With the possible exception of Ar I, which may have a lower than expected abundance resulting from partial photoionization of gas along the sight line, the absorption strengths are typical of those expected for the warm, neutral interstellar medium. The sight line intercepts a cold molecular cloud with log N(H2) ~ 19. The cloud has an identifiable counterpart in IRAS 100-micron emission maps of this region of the sky. We detect a Ly-alpha absorber associated with ESO141-055 at z = 0.03492. This study presents an enticing glimpse into the interstellar and intergalactic absorption patterns that will be observed at high spectral resolution by the Far Ultraviolet Spectroscopic Explorer.Comment: 24 pages + 8 figures, uses aaspp4.sty. Accepted for publication in Ap

Simultaneous quantization of edge and bulk Hall conductivity

The edge Hall conductivity is shown to be an integer multiple of $e^2/h$ which is almost surely independent of the choice of the disordered configuration. Its equality to the bulk Hall conductivity given by the Kubo-Chern formula follows from K-theoretic arguments. This leads to quantization of the Hall conductance for any redistribution of the current in the sample. It is argued that in experiments at most a few percent of the total current can be carried by edge states.Comment: 6 pages Latex, 1 figur

Universal quantum signature of mixed dynamics in antidot lattices

We investigate phase coherent ballistic transport through antidot lattices in the generic case where the classical phase space has both regular and chaotic components. It is shown that the conductivity fluctuations have a non-Gaussian distribution, and that their moments have a power-law dependence on a semiclassical parameter, with fractional exponents. These exponents are obtained from bifurcating periodic orbits in the semiclassical approximation. They are universal in situations where sufficiently long orbits contribute.Comment: 7 page

Probing The Multiphase Interstellar Medium Of The Dwarf Starburst Galaxy NGC 625 With FUSE Spectroscopy

We present new FUSE spectroscopy of the dwarf starburst galaxy NGC 625. These observations probe multiple phases of the interstellar medium, including the coronal, ionized, neutral and molecular gas. This nearby (D = 3.9 +/- 0.2 Mpc) system shows a clear detection of outflowing coronal gas as traced by OVI 1032 Angstrom absorption. The centroid of the OVI profile is blueshifted with respect to the galaxy systemic velocity by ~ 30 km/sec, suggesting a low-velocity outflow. The implied OVI velocity extent is found to be 100 +/- 20 km/sec, which is fully consistent with the detected HI outflow velocity found in radio synthesis observations. We detect multiple lines of diffuse H2 absorption from the ISM of NGC 625; this is one of only a few extragalactic systems with FUSE detections of H2 lines in the Lyman and Werner bands. We find a potential abundance offset between the neutral and nebular gas that exceeds the errors on the derived column densities. Since such an offset has been found in multiple dwarf galaxies, we discuss the implications of a lower-metallicity halo surrounding the central star forming regions of dwarf galaxies. The apparent offset may be due to saturation of the observed OI line, and higher S/N observations are required to resolve this issue.Comment: ApJ, in press; full-resolution version may be obtained at http://www.astro.umn.edu/~cannon/n625.fuse.p