Cylindrical Algebraic Sub-Decompositions

Cylindrical algebraic decompositions (CADs) are a key tool in real algebraic geometry, used primarily for eliminating quantifiers over the reals and studying semi-algebraic sets. In this paper we introduce cylindrical algebraic sub-decompositions (sub-CADs), which are subsets of CADs containing all the information needed to specify a solution for a given problem. We define two new types of sub-CAD: variety sub-CADs which are those cells in a CAD lying on a designated variety; and layered sub-CADs which have only those cells of dimension higher than a specified value. We present algorithms to produce these and describe how the two approaches may be combined with each other and the recent theory of truth-table invariant CAD. We give a complexity analysis showing that these techniques can offer substantial theoretical savings, which is supported by experimentation using an implementation in Maple.Comment: 26 page

Changing an Unfavorable Employment Reputation: A Longitudinal Examination

Although a favorable employment reputation plays an important role in generating a large and qualified pool of job applicants for an organization (Rynes & Cable, 2003), little research has investigated whether organizations can improve applicants’ existing unfavorable employment reputation perceptions. Results from a four-week longitudinal experiment using 222 student job seekers revealed that participants’ employment reputation perceptions improved after exposure to recruitment practices and followed diminishing returns trajectories over time. High information recruitment practices (e.g., personal communication from a recruiter) from both single and multiple sources were more effective for changing unfavorable employment reputation perceptions than repeated mere exposure to the organization (i.e., exposure to only the company logo), and high information practices from multiple sources were the most effective overall. Finally, participants reporting less familiarity with the organization experienced greater reputation change across the four weeks, but only for participants in the mere exposure condition

Radial distribution of gas and dust in spiral galaxies: The case of M 99 (NGC 4254) and M 100 (NGC 4321)

By combining Herschel-SPIRE data with archival Spitzer, H i , and CO maps, we investigate the spatial distribution of gas and dust in the two famous grand-design spirals M 99 and M 100 in the Virgo cluster. Thanks to the unique resolution and sensitivity of the Herschel-SPIRE photometer, we are for the first time able to measure the distribution and extent of cool, submillimetre (submm)-emitting dust inside and beyond the optical radius. We compare this with the radial variation in both the gas mass and the metallicity. Although we adopt a model-independent, phenomenological approach, our analysis provides important insights. We find the dust extending to at least the optical radius of the galaxy and showing breaks in its radial profiles at similar positions as the stellar distribution. The colour indices f350/f500 and f250/f350 decrease radially consistent with the temperature decreasing with radius. We also find evidence of an increasing gas to dust ratio with radius in the outer regions of both galaxies

The central region of spiral galaxies as seen by Herschel: M 81, M 99, and M 100

With appropriate spatial resolution, images of spiral galaxies in thermal infrared (~10 μm and beyond) often reveal a bright central component, distinct from the stellar bulge, superimposed on a disk with prominent spiral arms. ISO and Spitzer studies have shown that much of the scatter in the mid-infrared colors of spiral galaxies is related to changes in the relative importance of these two components, rather than to other modifications, such as the morphological type or star formation rate, that affect the properties of the galaxy as a whole. With the Herschel imaging capability from 70 to 500 μm, we revisit this two-component approach at longer wavelengths, to see if it still provides a working description of the brightness distribution of galaxies, and to determine its implications on the interpretation of global far-infrared properties of galaxies. We quantify the luminosity of the central component by both a decomposition of the radial surface brightness profile and a direct extraction in 2D. We find the central component contribution is variable within the three galaxies in our sample, possibly connected more directly to the presence of a bar than to the morphological type. The central component’s relative contribution is at its maximum in the mid-infrared range and drops around 160 μm to reach a constant value beyond 200 μm. The central component contains a greater fraction of hot dust than the disk component, and while the colors of the central components are scattered, colors of the disk components are more homogenous from one galaxy to the next

Mapping the interstellar medium in galaxies with Herschel/SPIRE

The standard method of mapping the interstellar medium in a galaxy, by observing the molecular gas in the CO 1-0 line and the atomic gas in the 21-cm line, is largely limited with current telescopes to galaxies in the nearby universe. In this letter, we use SPIRE observations of the galaxies M99 and M100 to explore the alternative approach of mapping the interstellar medium using the continuum emission from the dust. We have compared the methods by measuring the relationship between the star-formation rate and the surface density of gas in the galaxies using both methods. We find the two methods give relationships with a similar dispersion, confirming that observing the continuum emission from the dust is a promising method of mapping the interstellar medium in galaxies

Using geophysical surveys to test tracer-based storage estimates in headwater catchments

Acknowledgements The authors are grateful to Stian Bradford, Chris Gabrielli, and Julie Timms for practical and logistical assistance. The provision of transport by Iain Malcolm and Ross Glover of Marine Scotland Science was greatly appreciated. We also thank the European Research Council ERC (project GA 335910 VEWA) for funding through the VeWa project and the Leverhulme Trust for funding through PLATO (RPG-2014-016).Peer reviewedPostprin

The Herschel Space Observatory view of dust in M81

We use Herschel Space Observatory data to place observational constraints on the peak and Rayleigh-Jeans slope of dust emission observed at 70−500 μm in the nearby spiral galaxy M81. We find that the ratios of wave bands between 160 and 500 μm are primarily dependent on radius but that the ratio of 70 to 160 μm emission shows no clear dependence on surface brightness or radius. These results along with analyses of the spectral energy distributions imply that the 160−500 μm emission traces 15−30 K dust heated by evolved stars in the bulge and disc whereas the 70 μm emission includes dust heated by the active galactic nucleus and young stars in star forming regions

SPIRE imaging of M 82: Cool dust in the wind and tidal streams

M 82 is a unique representative of a whole class of galaxies, starbursts with superwinds, in the Very Nearby Galaxy Survey with Herschel. In addition, its interaction with the M 81 group has stripped a significant portion of its interstellar medium from its disk. SPIRE maps now afford better characterization of the far-infrared emission from cool dust outside the disk, and sketch a far more complete picture of its mass distribution and energetics than previously possible. They show emission coincident in projection with the starburst wind and in a large halo, much more extended than the PAH band emission seen with Spitzer. Some complex substructures coincide with the brightest PAH filaments, and others with tidal streams seen in atomic hydrogen. We subtract the far-infrared emission of the starburst and underlying disk from the maps, and derive spatially-resolved far-infrared colors for the wind and halo. We interpret the results in terms of dust mass, dust temperature, and global physical conditions. In particular, we examine variations in the dust physical properties as a function of distance from the center and the wind polar axis, and conclude that more than two thirds of the extraplanar dust has been removed by tidal interaction, and not entrained by the starburst wind

Herschel photometric observations of the low metallicity dwarf galaxy NGC 1705

We present Herschel SPIRE and PACS photometeric observations of the low metallicity (Z ~ 0.35 Z_☉) nearby dwarf galaxy, NGC 1705, in six wavelength bands as part of the Dwarf Galaxy Survey guaranteed time Herschel key program. We confirm the presence of two dominant circumnuclear IR-bright regions surrounding the central super star cluster that had been previously noted at mid-IR wavelengths and in the sub-mm by LABOCA. On constructing a global spectral energy distribution using the SPIRE and PACS photometry, in conjunction with archival IR measurements, we note the presence of an excess at sub-mm wavelengths. This excess suggests the presence of a significant cold dust component within NGC 1705 and was modeled as an additional cold component in the SED. Although alternative explanations for the sub-mm excess beyond 350 μm, such as changes to the dust emissivity cannot be ruled out, the most likely explanation for the observed submillimetre excess is that of an additional cold dust component

Observation of H_2O in a strongly lensed Herschel-ATLAS source at z = 2.3

The Herschel survey, H-ATLAS, with its large areal coverage, has recently discovered a number of bright, strongly lensed high-z submillimeter galaxies. The strong magnification makes it possible to study molecular species other than CO, which are otherwise difficult to observe in high-z galaxies. Among the lensed galaxies already identified by H-ATLAS, the source J090302.9-014127B (SDP.17b) at z = 2.305 is remarkable because of its excitation conditions and a tentative detection of the H_2O 2_(02)-1_(11) emission line (Lupu et al. 2010, ApJ, submitted). We report observations of this line in SDP.17b using the IRAM interferometer equipped with its new 277–371 GHz receivers. The H_2O line is detected at a redshift of z = 2.3049 ± 0.0006, with a flux of 7.8 ± 0.5 Jy km s^(-1) and a FWHM of 250 ± 60   km   s^(-1). The new flux is 2.4 times weaker than the previous tentative detection, although both remain marginally consistent within 1.6σ. The intrinsic line luminosity and ratio of H_2O(2_(02) − 1_(11))/CO(8 − 7) are comparable with those of the nearby starburst/enshrouded-AGN Mrk 231, and the ratio I(H_2O)/L_(FIR) is even higher, suggesting that SDP.17b could also host a luminous AGN. The detection of a strong H_2O 2_(02) − 1_(11) line in SDP.17b implies an efficient excitation mechanism of the water levels that must occur in very dense and warm interstellar gas probably similar to Mrk 231