Approximate roots of a valuation and the Pierce-Birkhoff Conjecture

This paper is a step in our program for proving the Piece-Birkhoff Conjecture for regular rings of any dimension (this would contain, in particular, the classical Pierce-Birkhoff conjecture which deals with polynomial rings over a real closed field). We first recall the Connectedness and the Definable Connectedness conjectures, both of which imply the Pierce - Birkhoff conjecture. Then we introduce the notion of a system of approximate roots of a valuation v on a ring A (that is, a collection Q of elements of A such that every v-ideal is generated by products of elements of Q). We use approximate roots to give explicit formulae for sets in the real spectrum of A which we strongly believe to satisfy the conclusion of the Definable Connectedness conjecture. We prove this claim in the special case of dimension 2. This proves the Pierce-Birkhoff conjecture for arbitrary regular 2-dimensional rings

A new view on the ISM of galaxies: far-infrared and submillimetre spectroscopy with Herschel

The FIR/submm window is amongst the least explored spectral regions of the electromagnetic spectrum. It is, however, a key to study the general properties of the interstellar medium of galaxies, as it contains important spectral line diagnostics from the neutral, ionized and molecular ISM. The Herschel Space Observatory, successfully launched on 14 May 2009, is the first observatory to cover the entire FIR/submm range between 57 and 672 mum. We discuss the main results from the ISO era on FIR spectroscopy of galaxies and the enormous science potential of the Herschel mission through a presentation of its spectroscopic extragalactic key programs.Comment: 10 pages, 4 figures, accepted for publication in New Astronomy Review

Changes in body composition in women using long-acting reversible contraception

OBJECTIVE: Users of hormonal long-acting reversible contraception (LARC) report weight gain as a side effect, but few studies have assessed body composition change among LARC users. We evaluated weight and body composition of healthy women using the levonorgestrel intrauterine system (LNG-IUS), copper intrauterine device (copper IUD) or etonogestrel implant (ENG implant). We hypothesized that weight gain and body composition over 12 months would not differ between copper IUD, LNG-IUS and ENG implant users. STUDY DESIGN: We performed a prospective cohort study of a subgroup of women enrolled in the Contraceptive CHOICE Project who initiated the LNG-IUS, copper IUD or ENG implant. Inclusion criteria included lack of metabolic and eating disorders or change in body weight of more than 5% in the 6 months before enrollment. We measured changes in weight and body composition (body fat percentage, total body fat mass, total lean mass and total body mass) in women who continued their method for 12 months. RESULTS: We analyzed data from 149 participants: 85 LNG-IUS users, 31 copper IUD users and 33 ENG implant users. The mean age was 25.9 years, 56.4% were White, 82.5% had some college education and 67.6% were nulliparous. Although lean body mass increased over 12 months in LNG-IUS and copper IUD users but not in ENG implant users, changes in body weight and body composition did not differ between the groups. In the adjusted model, Black race was associated with change in total body mass (p<.05). CONCLUSIONS: Among those who continued the method for 12 months, changes in body weight and composition did not differ between copper IUD, LNG-IUS and ENG implant users. IMPLICATIONS STATEMENT: Changes in body weight and composition over 12 months did not differ between copper IUD users and LNG-IUS and ENG implant users among those with 12 months of continuous use

The bolometric and UV attenuation in normal spiral galaxies of the Herschel Reference Survey

The dust in nearby galaxies absorbs a fraction of the UV-optical-near-infrared radiation produced by stars. This energy is consequently re-emitted in the infrared. We investigate the portion of the stellar radiation absorbed by spiral galaxies from the HRS by modelling their UV-to-submillimetre spectral energy distributions. Our models provide an attenuated and intrinsic SED from which we find that on average 32 % of all starlight is absorbed by dust. We define the UV heating fraction as the percentage of dust luminosity that comes from absorbed UV photons and find that this is 56 %, on average. This percentage varies with morphological type, with later types having significantly higher UV heating fractions. We find a strong correlation between the UV heating fraction and specific star formation rate and provide a power-law fit. Our models allow us to revisit the IRX-AFUV relations, and derive these quantities directly within a self-consistent framework. We calibrate this relation for different bins of NUV-r colour and provide simple relations to relate these parameters. We investigated the robustness of our method and we conclude that the derived parameters are reliable within the uncertainties which are inherent to the adopted SED model. This calls for a deeper investigation on how well extinction and attenuation can be determined through panchromatic SED modelling.Comment: 14 pages, 7 figures. Accepted for publication in Astronomy & Astrophysic

Star-forming dwarf galaxies in the Virgo cluster: the link between molecular gas, atomic gas, and dust

We present $^{12}$CO(1-0) and $^{12}$CO(2-1) observations of a sample of 20 star-forming dwarfs selected from the Herschel Virgo Cluster Survey, with oxygen abundances ranging from 12 + log(O/H) ~ 8.1 to 8.8. CO emission is observed in ten galaxies and marginally detected in another one. CO fluxes correlate with the FIR 250 $\mu$m emission, and the dwarfs follow the same linear relation that holds for more massive spiral galaxies extended to a wider dynamical range. We compare different methods to estimate H2 molecular masses, namely a metallicity-dependent CO-to-H2 conversion factor and one dependent on H-band luminosity. The molecular-to-stellar mass ratio remains nearly constant at stellar masses <~ 10$^9$ M$_{\odot}$, contrary to the atomic hydrogen fraction, M$_{HI}$/M$_*$, which increases inversely with M$_*$. The flattening of the M$_{H_2}$/M$_*$ ratio at low stellar masses does not seem to be related to the effects of the cluster environment because it occurs for both HI-deficient and HI-normal dwarfs. The molecular-to-atomic ratio is more tightly correlated with stellar surface density than metallicity, confirming that the interstellar gas pressure plays a key role in determining the balance between the two gaseous components of the interstellar medium. Virgo dwarfs follow the same linear trend between molecular gas mass and star formation rate as more massive spirals, but gas depletion timescales, $\tau_{dep}$, are not constant and range between 100 Myr and 6 Gyr. The interaction with the Virgo cluster environment is removing the atomic gas and dust components of the dwarfs, but the molecular gas appears to be less affected at the current stage of evolution within the cluster. However, the correlation between HI deficiency and the molecular gas depletion time suggests that the lack of gas replenishment from the outer regions of the disc is lowering the star formation activity.Comment: 19 pages, 11 figures, accepted for publication in Astronomy & Astrophysic

The effects of star formation on the low-metallicity ISM: NGC4214 mapped with Herschel/PACS spectroscopy

We present Herschel/PACS spectroscopic maps of the dwarf galaxy NC4214 observed in 6 far infrared fine-structure lines: [C II] 158mu, [O III] 88mu, [O I] 63mu, [O I] 146mu, [N II] 122mu, and [N II] 205mu. The maps are sampled to the full telescope spatial resolution and reveal unprecedented detail on ~ 150 pc size scales. We detect [C II] emission over the whole mapped area, [O III] being the most luminous FIR line. The ratio of [O III]/[C II] peaks at about 2 toward the sites of massive star formation, higher than ratios seen in dusty starburst galaxies. The [C II]/CO ratios are 20 000 to 70 000 toward the 2 massive clusters, which are at least an order of magnitude larger than spiral or dusty starbursts, and cannot be reconciled with single-slab PDR models. Toward the 2 massive star-forming regions, we find that L[CII] is 0.5 to 0.8% of the LTIR . All of the lines together contribute up to 2% of LTIR . These extreme findings are a consequence of the lower metallicity and young, massive-star formation commonly found in dwarf galaxies. These conditions promote large-scale photodissociation into the molecular reservoir, which is evident in the FIR line ratios. This illustrates the necessity to move to multiphase models applicable to star-forming clusters or galaxies as a whole.Comment: Accepted for publication in the A&A Herschel Special Issu

Process plant safety information repository and support for safety applications

The consideration of safety of processing plants from design to operation involves many tasks. Different techniques and tools have been developed to assist in carry out those tasks. With the advances in computing technologies, both in hardware and software, there is the opportunity to bring together the vast amount of engineering, hazard and risk data and handle them in an efficient way to manage and improve safety throughout the life time of a plant. This paper proposes keeping such data in a process plant safety information repository which can be easily accessed by different safety-related tools to enhance the efficiency of safety identification and analysis tasks

The first maps of κd - the dust mass absorption coefficient - in nearby galaxies, with DustPedia

The dust mass absorption coefficient, κd is the conversion function used to infer physical dust masses from observations of dust emission. However, it is notoriously poorly constrained, and it is highly uncertain how it varies, either between or within galaxies. Here we present the results of a proof-of-concept study, using the DustPedia data for two nearby face-on spiral galaxies M 74 (NGC 628) and M 83 (NGC 5236), to create the first ever maps of κd in galaxies. We determine κd using an empirical method that exploits the fact that the dust-to-metals ratio of the interstellar medium is constrained by direct measurements of the depletion of gas-phase metals. We apply this method pixel-by-pixel within M 74 and M 83, to create maps of κd. We also demonstrate a novel method of producing metallicity maps for galaxies with irregularly sampled measurements, using the machine learning technique of Gaussian process regression. We find strong evidence for significant variation in κd. We find values of κd at 500 μm spanning the range 0.11-0.25 m^{2 kg^{-1}} in M 74, and 0.15-0.80 m^{2 kg^{-1}} in M 83. Surprisingly, we find that κd shows a distinct inverse correlation with the local density of the interstellar medium. This inverse correlation is the opposite of what is predicted by standard dust models. However, we find this relationship to be robust against a large range of changes to our method - only the adoption of unphysical or highly unusual assumptions would be able to suppress it

Enhanced [CII] emission in a z=4.76 submillimetre galaxy

We present the detection of bright [CII] emission in the z=4.76 submillimetre galaxy LESS J033229.4-275619 using the Atacama Pathfinder EXperiment. This represents the highest redshift [CII] detection in a submm selected, star-formation dominated system. The AGN contributions to the [CII] and far-infrared (FIR) luminosities are small. We find an atomic mass derived from [CII] comparable to the molecular mass derived from CO. The ratio of the [CII], CO and FIR luminosities imply a radiation field strength G_0~10^3 and a density ~10^4 cm^-3 in a kpc-scale starburst, as seen in local and high redshift starbursts. The high L_[CII]/L_FIR=2.4x10^-3 and the very high L_[CII]/L_CO(1-0) ~ 10^4 are reminiscent of low metallicity dwarf galaxies, suggesting that the highest redshift star-forming galaxies may also be characterised by lower metallicities. We discuss the implications of a reduced metallicity on studies of the gas reservoirs, and conclude that especially at very high redshift, [CII] may be a more powerful and reliable tracer of the interstellar matter than CO.Comment: 5 pages, 2 figures; accepted for publication in Astronomy & Astrophysics Letter