Embeddings of SL(2,Z) into the Cremona group

Geometric and dynamic properties of embeddings of SL(2,Z) into the Cremona group are studied. Infinitely many non-conjugate embeddings which preserve the type (i.e. which send elliptic, parabolic and hyperbolic elements onto elements of the same type) are provided. The existence of infinitely many non-conjugate elliptic, parabolic and hyperbolic embeddings is also shown. In particular, a group G of automorphisms of a smooth surface S obtained by blowing-up 10 points of the complex projective plane is given. The group G is isomorphic to SL(2,Z), preserves an elliptic curve and all its elements of infinite order are hyperbolic.Comment: to appear in Transformation Group

Suppressed antinodal coherence with a single d-wave superconducting gap leads to two energy scales in underdoped cuprates

Conventional superconductors are characterized by a single energy scale, the superconducting gap, which is proportional to the critical temperature Tc . In hole-doped high-Tc copper oxide superconductors, previous experiments have established the existence of two distinct energy scales for doping levels below the optimal one. The origin and significance of these two scales are largely unexplained, although they have often been viewed as evidence for two gaps, possibly of distinct physical origins. By measuring the temperature dependence of the electronic Raman response of Bi2Sr2CaCu2O8+d (Bi-2212) and HgBa2CuO4+d (Hg-1201) crystals with different doping levels, we establish that these two scales are associated with coherent excitations of the superconducting state which disappears at Tc. Using a simple model, we show that these two scales do not require the existence of two gaps. Rather, a single d-wave superconducting gap with a loss of Bogoliubov quasiparticle spectral weight in the antinodal region is shown to reconcile spectroscopic and transport measurements.Comment: 3 figure

The sound insulation of autoclaved aerated concrete panels lined with gypsum plasterboard

This paper gives the results of 27 laboratory measurements of the sound insulation of 75mm thick tongue and groove autoclaved aerated concrete (AAC) panels with stated nominal dry density of 510kg/m3 (a surface density of 38.2kg/m2).which are lined with 13mm thick gypsum plasterboard. Two configurations that are presently common forms of construction in a region of Australia were tested; 1. Furring channel one side and stud wall the other that maintained an overall wall width of 243mm, and 2. Direct fix one side and stud wall the other. In both cases the gypsum plasterboard is mounted on 64mm steel studs. The gap between the panels and the steel studs is 20, 35 or 48mm. With the exception of one empty cavity, the cavity on this side contains 11kg/m3 glass fibre batts with thickness of 50, 75, 90 or 110mm. On the other side of the panels, the gypsum plasterboard is mounted on furring channels and adjustable clips which are screwed to the panels or in 6 cases directly screwed to the panels. Except for the directly screwed cases, the gap between the panels and the gypsum plasterboard is 30, 43 or 58mm. The cavity is empty or contains 50 or 70mm thick 11kg/m3 glass fibre batts or 25mm thick 24kg/m3 glass fibre batts. The 13mm gypsum plasterboard has nominal surface densities of 7.2, 8.5 or 10.5kg/m2. The aim was to develop a system which has a laboratory measured Rw+Ctr equal to or greater than 50dB which is required by the National Construction Code (NCC) of Australia for walls between separate dwellings. A system with cavities on both sides of the wall is desirable because it allows services to be accommodated without the need for chasing which is not permitted. The undesirable effect is a resultant large Ctr making it difficult to achieve an Rw +Ctr equal to or greater than 50dB

Quantitative genetics of growth traits in the edible snail, Helix aspersa Müller

Genetic parameters of adult weight, age at maturity (adult age), weight after hibernation and relative loss of weight during hibernation were estimated in a population of edible snails (Helix aspersa Müller). Eight thousand four hundred and eighthy three animals were sampled from 143 pairs for adult weight, 4 333 from 87 pairs for adult age and 2 256 from 123 pairs for traits after hibernation. An animal model taking into account all the relationships was used to estimate genetic parameters. Estimates were also computed from the covariances between full-sibs and parent offspring regressions to assess possible non-additive genetic effects. Heritabilities were high except for relative loss of weight during hibernation. Estimates from the animal model were 0.48 ± 0.04 for adult weight, 0.40 ± 0.05 for adult age, 0.40 ± 0.05 for weight after hibernation and 0.12 ± 0.03 for relative loss of weight during hibernation. Adult weight and adult age were neither phenotypically nor genetically correlated (0.05 and 0.003 ± 0.07, respectively). A substantial maternal effect, especially on adult weight was found.Les paramètres génétiques de plusieurs caractères de croissance ont été estimés dans une population d’escargots Petit-Gris (Helix aspersa Müller). Il s’agit du poids adulte, de l’âge à maturité (âge adulte), du poids après hibernation et de la perte relative de poids lors de l’hibernation. Le nombre d’observations collectées se répartit ainsi : 8 483 animaux issus de 143 couples pour le poids adulte, 4 333 issus de 87 couples pour l’âge adulte et 2 256 issus de 123 couples pour les caractères mesurés après hibernation. Afin de tenir compte de toutes les relations de parenté, nous avons utilisé un modèle animal pour estimer les paramètres génétiques. Ils ont également été estimés à partir des covariances entre plein-frères et de la régression parents-descendants. Cela nous a permis de discuter des effets génétiques non additifs. Tous les caractères sauf la perte de poids relative lors de l’hibernation révèlent des héritabilités élevées. Les estimations issues du modèle animal sont de 0,48 ± 0,04 pour le poids adulte, 0,40 ± 0,05 pour l’âge adulte, 0,40 ± 0,05 pour le poids après hibernation et 0, 12 ± 0 03 pour la perte relative de poids lors de l’hibernation. Il n’y a pas de corrélation (ni phénotypique, ni génétique) significative entre le poids et l’âge adultes (0,05 et 0,003 ± 0,07, respectivement). Nous avons également mis en évidence un effet maternel important, en particulier sur le poids adulte

Normal subgroups in the Cremona group (long version)

Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane P^2 over k is not a simple group. The strategy makes use of hyperbolic geometry, geometric group theory, and algebraic geometry to produce elements in the Cremona group that generate non trivial normal subgroups.Comment: With an appendix by Yves de Cornulier. Numerous but minors corrections were made, regarding proofs, references and terminology. This long version contains detailled proofs of several technical lemmas about hyperbolic space

Interrogating Seyferts with NebulaBayes: Spatially probing the narrow-line region radiation fields and chemical abundances

NebulaBayes is a new Bayesian code that implements a general method of comparing observed emission-line fluxes to photoionization model grids. The code enables us to extract robust, spatially resolved measurements of abundances in the extended narrow line regions (ENLRs) produced by Active Galactic Nuclei (AGN). We observe near-constant ionization parameters but steeply radially-declining pressures, which together imply that radiation pressure regulates the ENLR density structure on large scales. Our sample includes four `pure Seyfert' galaxies from the S7 survey that have extensive ENLRs. NGC2992 shows steep metallicity gradients from the nucleus into the ionization cones. An {\it inverse} metallicity gradient is observed in ESO138-G01, which we attribute to a recent gas inflow or minor merger. A uniformly high metallicity and hard ionizing continuum are inferred across the ENLR of Mrk573. Our analysis of IC5063 is likely affected by contamination from shock excitation, which appears to soften the inferred ionizing spectrum. The peak of the ionizing continuum E_peak is determined by the nuclear spectrum and the absorbing column between the nucleus and the ionized nebula. We cannot separate variation in this intrinsic E_peak from the effects of shock or HII region contamination, but E_peak measurements nevertheless give insights into ENLR excitation. We demonstrate the general applicability of NebulaBayes by analyzing a nuclear spectrum from the non-active galaxy NGC4691 using a HII region grid. The NLR and HII region model grids are provided with NebulaBayes for use by the astronomical community.Comment: Accepted for publication in ApJ; 29 pages with 10 figures and 3 table