Parabolic and Quasiparabolic Subgroups of Free Partially Commutative Groups

Let S be a finite graph and G be the corresponding free partially commutative group. In this paper we study subgroups generated by vertices of the graph S, which we call canonical parabolic subgroups. A natural extension of the definition leads to canonical quasiparabolic subgroups. It is shown that the centralisers of subsets of G are the conjugates of canonical quasiparabolic centralisers satisfying certain graph theoretic conditions.Comment: 18 pages, 1 figur

Automorphisms of Partially Commutative Groups II: Combinatorial Subgroups

We define several "standard" subgroups of the automorphism group Aut(G) of a partially commutative (right-angled Artin) group and use these standard subgroups to describe decompositions of Aut(G). If C is the commutation graph of G, we show how Aut(G) decomposes in terms of the connected components of C: obtaining a particularly clear decomposition theorem in the special case where C has no isolated vertices. If C has no vertices of a type we call dominated then we give a semi-direct decompostion of Aut(G) into a subgroup of locally conjugating automorphisms by the subgroup stabilising a certain lattice of "admissible subsets" of the vertices of C. We then characterise those graphs for which Aut(G) is a product (not necessarily semi-direct) of two such subgroups.Comment: 7 figures, 63 pages. Notation and definitions clarified and typos corrected. 2 new figures added. Appendix containing details of presentation and proof of a theorem adde

Prospective Analysis Spin- and CP-sensitive Variables in H -> ZZ -> l_1 l_1 l_2 l_2 with Atlas

A possibility to prove spin and CP-eigenvalue of a Standard Model (SM) Higgs boson is presented. We exploit angular correlations in the subsequent decay H -> ZZ -> 4l (muons or electrons) for Higgs masses above 200 GeV. We compare the angular distributions of the leptons originating from the SM Higgs with those resulting from decays of hypothetical particles with differing quantum numbers. We restrict our analysis to the use of the Atlas-detector which is one of two multi-purpose detectors at the upcoming 14 TeV proton-proton-collider (LHC) at CERN. By applying a fast simulation of the Atlas detector it can be shown that these correlations will be measured sufficiently well that consistency with the spin-CP hypothesis 0+ of the Standard Model can be verified and the 0- and 1+- can be ruled out with an integrated luminosity of 100 fb^-1.Comment: 25 pages, 9 figures Version 2: Minor changes made as requested by Atlas referee and Springer editor. Added a chapter where background subtraction is detaile

Convergence of the Optimized Delta Expansion for the Connected Vacuum Amplitude: Zero Dimensions

Recent proofs of the convergence of the linear delta expansion in zero and in one dimensions have been limited to the analogue of the vacuum generating functional in field theory. In zero dimensions it was shown that with an appropriate, $N$-dependent, choice of an optimizing parameter \l, which is an important feature of the method, the sequence of approximants $Z_N$ tends to $Z$ with an error proportional to ${\rm e}^{-cN}$. In the present paper we establish the convergence of the linear delta expansion for the connected vacuum function $W=\ln Z$. We show that with the same choice of \l the corresponding sequence $W_N$ tends to $W$ with an error proportional to ${\rm e}^{-c\sqrt N}$. The rate of convergence of the latter sequence is governed by the positions of the zeros of $Z_N$.Comment: 20 pages, LaTeX, Imperial/TP/92-93/5

Activities of \gamma-ray emitting isotopes in rainwater from Greater Sudbury, Canada following the Fukushima incident

We report the activity measured in rainwater samples collected in the Greater Sudbury area of eastern Canada on 3, 16, 20, and 26 April 2011. The samples were gamma-ray counted in a germanium detector and the isotopes 131I and 137Cs, produced by the fission of 235U, and 134Cs, produced by neutron capture on 133Cs, were observed at elevated levels compared to a reference sample of ice-water. These elevated activities are ascribed to the accident at the Fukushima Dai-ichi nuclear reactor complex in Japan that followed the 11 March earthquake and tsunami. The activity levels observed at no time presented health concerns.Comment: 4 pages, 8 figure

Dependence of the Fundamental Plane Scatter on Galaxy Age

The fundamental plane (FP) has an intrinsic scatter that can not be explained purely by observational errors. Using recently available age estimates for nearby early type galaxies, we show that a galaxy's position relative to the FP depends on its age. In particular, the mean FP corresponds to ellipticals with an age of ~10 Gyr. Younger galaxies are systematically brighter with higher surface brightness relative to the mean relation. Old ellipticals form an `upper envelope' to the FP. For our sample of mostly non-cluster galaxies, age can account for almost half of the scatter in the B band FP. Distance determinations based on the FP may have a systematic bias, if the mean age of the sample varies with redshift. We also show that fundamental plane residuals, B-V colors and Mg_2 line strength are consistent with an ageing central burst superposed on an old stellar population. This reinforces the view that these age estimates are tracing the last major episode of star formation induced by a gaseous merger event. We briefly discuss the empirical `evolutionary tracks' of merger-remnants and young ellipticals in terms of their key observational parameters.Comment: 14 pages, Latex, 2 figures, accepted by ApJ Letter

Periodic Thermonuclear X-ray Bursts from GS 1826-24 and the Fuel Composition as a Function of Accretion Rate

We analyze 24 type I X-ray bursts from GS 1826-24 observed by the Rossi X-ray Timing Explorer between 1997 November and 2002 July. The bursts observed between 1997-98 were consistent with a stable recurrence time of 5.74 +/- 0.13 hr. The persistent intensity of GS 1826-24 increased by 36% between 1997-2000, by which time the burst interval had decreased to 4.10 +/- 0.08 hr. In 2002 July the recurrence time was shorter again, at 3.56 +/- 0.03 hr. The bursts within each epoch had remarkably identical lightcurves over the full approx. 150 s burst duration; both the initial decay timescale from the peak, and the burst fluence, increased slightly with the rise in persistent flux. The decrease in the burst recurrence time was proportional to Mdot^(-1.05+/-0.02) (where Mdot is assumed to be linearly proportional to the X-ray flux), so that the ratio alpha between the integrated persistent and burst fluxes was inversely correlated with Mdot. The average value of alpha was 41.7 +/- 1.6. Both the alpha value, and the long burst durations indicate that the hydrogen is burning during the burst via the rapid-proton (rp) process. The variation in alpha with Mdot implies that hydrogen is burning stably between bursts, requiring solar metallicity (Z ~ 0.02) in the accreted layer. We show that solar metallicity ignition models naturally reproduce the observed burst energies, but do not match the observed variations in recurrence time and burst fluence. Low metallicity models (Z ~ 0.001) reproduce the observed trends in recurrence time and fluence, but are ruled out by the variation in alpha. We discuss possible explanations, including extra heating between bursts, or that the fraction of the neutron star covered by the accreted fuel increases with Mdot.Comment: 9 pages, 6 figures, accepted by ApJ. Minor revisions following the referee's repor

Unquenched QCD with Light Quarks

We present recent results in unquenched lattice QCD with two degenerate light sea quarks using the truncated determinant approximation (TDA). In the TDA the infrared modes contributing to the quark determinant are computed exactly up to some cutoff in quark off-shellness (typically 2$\Lambda_{QCD}$). This approach allows simulations to be performed at much lighter quark masses than possible with conventional hybrid MonteCarlo techniques. Results for the static energy and topological charge distributions are presented using a large ensemble generated on very coarse (6$^4$) but physically large lattices. Preliminary results are also reported for the static energy and meson spectrum on 10$^3$x20 lattices (lattice scale $a^{-1}$=1.15 GeV) at quark masses corresponding to pions of mass $\leq$ 200 MeV. Using multiboson simulation to compute the ultraviolet part of the quark determinant the TDA approach becomes an exact with essentially no increase in computational effort. Some preliminary results using this fully unquenched algorithm are presented.Comment: LateX, 39 pages, 16 eps figures, 1 ps figur