Similar Sublattices and Coincidence Rotations of the Root Lattice A4 and its Dual

A natural way to describe the Penrose tiling employs the projection method on the basis of the root lattice A4 or its dual. Properties of these lattices are thus related to properties of the Penrose tiling. Moreover, the root lattice A4 appears in various other contexts such as sphere packings, efficient coding schemes and lattice quantizers. Here, the lattice A4 is considered within the icosian ring, whose rich arithmetic structure leads to parametrisations of the similar sublattices and the coincidence rotations of A4 and its dual lattice. These parametrisations, both in terms of a single icosian, imply an index formula for the corresponding sublattices. The results are encapsulated in Dirichlet series generating functions. For every index, they provide the number of distinct similar sublattices as well as the number of coincidence rotations of A4 and its dual.Comment: 8 pages, paper presented at ICQ10 (Zurich, Switzerland

The application of amino acid racemization in the acid soluble fraction of enamel to the estimation of the age of human teeth

Estimation of age-at-death for skeletonised forensic remains is one of the most significant problems in forensic anthropology. The majority of existing morphological and histological techniques are highly inaccurate, and show a bias towards underestimating the age of older individuals. One technique which has been successful in forensic age estimation is amino acid racemization in dentine. However, this method cannot be used on remains where the post-mortem interval is greater than 20 years. An alternative approach is to measure amino acid racemization in dental enamel, which is believed to be more resistant to change post-mortem. The extent of amino acid racemization in the acid soluble fraction of the enamel proteins was determined for modem known age teeth. A strong correlation was observed between the age of the tooth and the extent of racemization. No systematic bias in the direction of age estimation errors was detected. For the majority of teeth analyzed, the presence of dental caries did not affect the results obtained. In a minority of cases, carious teeth showed a higher level of racemization than would be expected given the age of the individual. These results indicate that amino acid racemization in enamel has the potential to be used in age estimation of skeletal remains. (C) 2007 Elsevier Ireland Ltd. All rights reserved

Affine extension of noncrystallographic Coxeter groups and quasicrystals

Unique affine extensions H^{\aff}_2, H^{\aff}_3 and H^{\aff}_4 are determined for the noncrystallographic Coxeter groups $H_2$, $H_3$ and $H_4$. They are used for the construction of new mathematical models for quasicrystal fragments with 10-fold symmetry. The case of H^{\aff}_2 corresponding to planar point sets is discussed in detail. In contrast to the cut-and-project scheme we obtain by construction finite point sets, which grow with a model specific growth parameter.Comment: (27 pages, to appear in J. Phys. A

The ATCA/VLA OH 1612 MHz survey. III. Northern Galactic Plane

We present observations of the region between 5deg < l < 45deg and |b| < 3deg, in the OH 1612 MHz line, taken from 1993 to 1995 with the VLA. These observations are the last part of a larger survey, covering |l| < 45deg and |b| < 3deg, with the ATCA and the VLA. The region was systematically observed on a 30'x30' grid in (l,b) and the resulting coverage was 92%, with 965 pointings. We found 286 OH--masing objects, 161 of which are new detections and 207 have reliable IRAS point-source identifications. The outflow velocity was determined for 276 sources. A total of 766 sources were detected in the combined ATCA/VLA survey, of which 29 were detected in two regions of the survey. The source tables and spectra may be downloaded from http://msowww.anu.edu.au/~msevenst/pubs.html In this article we analyse the data statistically and give identifications with known sources where possible. The efficiency of this VLA survey is 75% of that of the ATCA Bulge survey. This efficiency was determined by comparing the detections in the region where the two surveys overlap. The completeness- and error characteristics are similar, though less homogeneous, except for the much larger errors in the flux densities. The relatively large surface number density found in the northern disk, suggests that we can see the Bar extending to higher longitudes on this side of the galactic Centre.Comment: 9 pages, 9 figs, LaTeX, A&A (accepted), table+spectra on htt

Gaussian cubature arising from hybrid characters of simple Lie groups

Lie groups with two different root lengths allow two mixed sign homomorphisms on their corresponding Weyl groups, which in turn give rise to two families of hybrid Weyl group orbit functions and characters. In this paper we extend the ideas leading to the Gaussian cubature formulas for families of polynomials arising from the characters of irreducible representations of any simple Lie group, to new cubature formulas based on the corresponding hybrid characters. These formulas are new forms of Gaussian cubature in the short root length case and new forms of Radau cubature in the long root case. The nodes for the cubature arise quite naturally from the (computationally efficient) elements of finite order of the Lie group.Comment: 23 pages, 3 figure

The crystal structure of Pneumolysin at 2.0 Å resolution reveals the molecular packing of the pre-pore complex

Pneumolysin is a cholesterol-dependent cytolysin (CDC) and virulence factor of Streptococcus pneumoniae. It kills cells by forming pores assembled from oligomeric rings in cholesterol-containing membranes. Cryo-EM has revealed the structures of the membrane-surface bound pre-pore and inserted-pore oligomers, however the molecular contacts that mediate these oligomers are unknown because high-resolution information is not available. Here we have determined the crystal structure of full-length pneumolysin at 1.98 Å resolution. In the structure, crystal contacts demonstrate the likely interactions that enable polymerisation on the cell membrane and the molecular packing of the pre-pore complex. The hemolytic activity is abrogated in mutants that disrupt these intermolecular contacts, highlighting their importance during pore formation. An additional crystal structure of the membrane-binding domain alone suggests that changes in the conformation of a tryptophan rich-loop at the base of the toxin promote monomer-monomer interactions upon membrane binding by creating new contacts. Notably, residues at the interface are conserved in other members of the CDC family, suggesting a common mechanism for pore and pre-pore assembly

Application of an Energy-Vorticity Turbulence Model to Fully rough Pipe flow

Based on a more direct analogy between turbulent and molecular transport, a foundation was recently presented for an energy-vorticity turbulence model. The new turbulent-energytransport equation contains two closure coefficients; a viscous-dissipation coefficient and a turbulent-transport coefficient. To help evaluate the closure coefficients and provide insight into the energy-vorticity turbulence variables, fully rough pipe flow is considered. For this fully developed flow, excellent agreement with experimental data for velocity profiles and friction factors is attained over a wide range of closure coefficients, provided that a given relation between the coefficients is maintained

Isomorphism classes of Edwards curves over finite fields

Edwards curves are an alternate model for elliptic curves, which have attracted notice in cryptography. We give exact formulas for the number of \Fq-isomorphism classes of Edwards curves and twisted Edwards curves. This answers a question recently asked by R. Farashahi and I. Shparlinski