Automaton semigroup constructions

The aim of this paper is to investigate whether the class of automaton semigroups is closed under certain semigroup constructions. We prove that the free product of two automaton semigroups that contain left identities is again an automaton semigroup. We also show that the class of automaton semigroups is closed under the combined operation of 'free product followed by adjoining an identity'. We present an example of a free product of finite semigroups that we conjecture is not an automaton semigroup. Turning to wreath products, we consider two slight generalizations of the concept of an automaton semigroup, and show that a wreath product of an automaton monoid and a finite monoid arises as a generalized automaton semigroup in both senses. We also suggest a potential counterexample that would show that a wreath product of an automaton monoid and a finite monoid is not a necessarily an automaton monoid in the usual sense.Comment: 13 pages; 2 figure

Automaton semigroups: new construction results and examples of non-automaton semigroups

This paper studies the class of automaton semigroups from two perspectives: closure under constructions, and examples of semigroups that are not automaton semigroups. We prove that (semigroup) free products of finite semigroups always arise as automaton semigroups, and that the class of automaton monoids is closed under forming wreath products with finite monoids. We also consider closure under certain kinds of Rees matrix constructions, strong semilattices, and small extensions. Finally, we prove that no subsemigroup of $(\mathbb{N}, +)$ arises as an automaton semigroup. (Previously, $(\mathbb{N},+)$ itself was the unique example of a finitely generated residually finite semigroup that was known not to arise as an automaton semigroup.)Comment: 27 pages, 6 figures; substantially revise

Spatial kinematics of Brightest Cluster Galaxies and their close companions from Integral Field Unit spectroscopy

We present Integral Field Unit (IFU) spectroscopy of four brightest cluster galaxies (BCGs) at z~0.1. Three of the BCGs have close companions within a projected radius of 20 kpc and one has no companion within that radius. We calculate the dynamical masses of the BCGs and their companions to be 1.4x10^11<M_dyn (M_solar)<1.5x10^12. We estimate the probability that the companions of the BCGs are bound using the observed masses and velocity offsets. We show that the lowest mass companion (1:4) is not bound while the two nearly equal mass (1:1.45 and 1:1.25) companions are likely to merge with their host BCGs in 0.35 Gyr in major, dry mergers. We conclude that some BCGs continue to grow from major merging even at z~0. We analyse the stellar kinematics of these systems using the \lambda_R parameter developed by the SAURON team. This offers a new and unique means to measure the stellar angular momentum of BCGs and make a direct comparison to other early-type galaxies. The BCGs and their companions have similar ellipticities to those of other early-type galaxies but are more massive. We find that not all these massive galaxies have low \lambda_R_e as one might expect. One of the four BCGs and the two massive companions are found to be fast-rotating galaxies with high angular momentum, thereby providing a new test for models of galaxy evolution and the formation of Intra-Cluster Light.Comment: 5 pages. Accepted for publication in MNRAS Letter

The Properties of Brightest Cluster Galaxies in X-Ray Selected Clusters

We present the K-band Hubble diagram for 162 brightest cluster galaxies (BCGs) in X-ray selected clusters, 0.01<z<0.83. The sample incorporates that of Burke, Collins, & Mann (2000) and includes additional infrared data from the 2MASS extended source catalogue. We show that below z=0.1 the BCGs show no correlation with their environment, however, above z=0.1 BCGs in more X-ray luminous clusters are more uniform in their photometric properties. This suggests that there may be two populations of BCGs which have different evolutionary histories.Comment: 2 pages, to appear in the proceedings of the Sesto 2001 conference on tracing cosmic evolution with galaxy cluster

Context-free word problem semigroups

fellowship SFRH/BPD/121469/2016. The second author was supported by the ‘Investigador FCT’ fellowship IF/ 01622/2013/CP1161/CT0001. For the first and second authors, this work was partially supported by FCT projects UID/MAT/00297/2019. PTDC/MHC-FIL/2583/2014 and PTDC/MAT-PUR/31174/2017. This work was started during a visit by the third author to the Universidade Nova de Lisboa, which was supported by the exploratory project IF/01622/2013/ CP1161/CT0001 attached to the second author’s research fellowship.This paper studies the classes of semigoups and monoids with context-free and deterministic context-free word problem. First, some examples are exhibited to clarify the relationship between these classes and their connection with the notions of word-hyperbolicity and automaticity. Second, a study is made of whether these classes are closed under applying certain semigroup constructions, including direct products and free products, or under regressing from the results of such constructions to the original semigroup(s) or monoid(s).authorsversionpublishe

Galaxy And Mass Assembly (GAMA): end of survey report and data release 2

The Galaxy And Mass Assembly (GAMA) survey is one of the largest contemporary spectroscopic surveys of low redshift galaxies. Covering an area of ˜286 deg2 (split among five survey regions) down to a limiting magnitude of r < 19.8 mag, we have collected spectra and reliable redshifts for 238 000 objects using the AAOmega spectrograph on the Anglo-Australian Telescope. In addition, we have assembled imaging data from a number of independent surveys in order to generate photometry spanning the wavelength range 1 nm-1 m. Here, we report on the recently completed spectroscopic survey and present a series of diagnostics to assess its final state and the quality of the redshift data. We also describe a number of survey aspects and procedures, or updates thereof, including changes to the input catalogue, redshifting and re-redshifting, and the derivation of ultraviolet, optical and near-infrared photometry. Finally, we present the second public release of GAMA data. In this release, we provide input catalogue and targeting information, spectra, redshifts, ultraviolet, optical and near-infrared photometry, single-component Sérsic fits, stellar masses, Hα-derived star formation rates, environment information, and group properties for all galaxies with r < 19.0 mag in two of our survey regions, and for all galaxies with r < 19.4 mag in a third region (72 225 objects in total). The data base serving these data is available at http://www.gama-survey.org/

How young people from culturally and linguistically diverse backgrounds experience mental health: some insights for mental health nurses

This article reports on a part of a study which looked at the mental health of culturally and linguistically diverse (CALD) young people. The research sought to learn from CALD young people, carers, and service providers experiences relevant to the mental health of this group of young people. The ultimate goal was to gain insights that would inform government policy, service providers, ethnic communities and most importantly the young people themselves. To this end, qualitative interviews were undertaken with 123 CALD young people, 41 carers and 14 mental health service providers in Queensland, Western Australia and South Australia. Only one aspect of the study will be dealt with here, namely the views of the young CALD participants, which included risk factors, coping strategies and recommendations about how they could be supported in their struggle to maintain mental health. One of the most important findings of the study relates to the resilience of these young people and an insight into the strategies that they used to cope. The efforts of these young people to assist us in our attempts to understand their situation deserve to be rewarded by improvements in the care that we provide. To this end this article sets out to inform mental health nurses of the results of the study so that they will be in a position to better understand the needs and strengths of their CALD clients and be in a better position to work effectively with them

The SAMI Galaxy Survey: Satellite galaxies undergo little structural change during their quenching phase

At fixed stellar mass, satellite galaxies show higher passive fractions than centrals, suggesting that environment is directly quenching their star formation. Here, we investigate whether satellite quenching is accompanied by changes in stellar spin (quantified by the ratio of the rotational to dispersion velocity V/$\sigma$) for a sample of massive ($M_{*}>$10$^{10}$ M$_{\odot}$) satellite galaxies extracted from the SAMI Galaxy Survey. These systems are carefully matched to a control sample of main sequence, high $V/\sigma$ central galaxies. As expected, at fixed stellar mass and ellipticity, satellites have lower star formation rate (SFR) and spin than the control centrals. However, most of the difference is in SFR, whereas the spin decreases significantly only for satellites that have already reached the red sequence. We perform a similar analysis for galaxies in the EAGLE hydro-dynamical simulation and recover differences in both SFR and spin similar to those observed in SAMI. However, when EAGLE satellites are matched to their `true' central progenitors, the change in spin is further reduced and galaxies mainly show a decrease in SFR during their satellite phase. The difference in spin observed between satellites and centrals at $z\sim$0 is primarily due to the fact that satellites do not grow their angular momentum as fast as centrals after accreting into bigger halos, not to a reduction of $V/\sigma$ due to environmental effects. Our findings highlight the effect of progenitor bias in our understanding of galaxy transformation and they suggest that satellites undergo little structural change before and during their quenching phase.Comment: 11 pages, 7 figures. Accepted for publication in MNRA