Budget Imbalance Criteria for Auctions: A Formalized Theorem

We present an original theorem in auction theory: it specifies general conditions under which the sum of the payments of all bidders is necessarily not identically zero, and more generally not constant. Moreover, it explicitly supplies a construction for a finite minimal set of possible bids on which such a sum is not constant. In particular, this theorem applies to the important case of a second-price Vickrey auction, where it reduces to a basic result of which a novel proof is given. To enhance the confidence in this new theorem, it has been formalized in Isabelle/HOL: the main results and definitions of the formal proof are re- produced here in common mathematical language, and are accompanied by an informal discussion about the underlying ideas.Comment: 6th Podlasie Conference on Mathematics 2014, 11 page

Probing the LMC age gap at intermediate cluster masses

The LMC has a rich star cluster system spanning a wide range of ages and masses. One striking feature of the LMC cluster system is the existence of an age gap between 3-10 Gyrs. But this feature is not as clearly seen among field stars. Three LMC fields containing relatively poor and sparse clusters whose integrated colours are consistent with those of intermediate age simple stellar populations have been imaged in BVI with the Optical Imager (SOI) at the Southern Telescope for Astrophysical Research (SOAR). A total of 6 clusters, 5 of them with estimated initial masses M < 10^4M_sun, were studied in these fields. Photometry was performed and Colour-Magnitude Diagrams (CMD) were built using standard point spread function fitting methods. The faintest stars measured reach V ~ 23. The CMD was cleaned from field contamination by making use of the three-dimensional colour and magnitude space available in order to select stars in excess relative to the field. A statistical CMD comparison method was developed for this purpose. The subtraction method has proven to be successful, yielding cleaned CMDs consistent with a simple stellar population. The intermediate age candidates were found to be the oldest in our sample, with ages between 1-2 Gyrs. The remaining clusters found in the SOAR/SOI have ages ranging from 100 to 200 Myrs. Our analysis has conclusively shown that none of the relatively low-mass clusters studied by us belongs to the LMC age-gap.Comment: 9 pages, 8 figures. Accepted to MNRA

Bridge over troubled gas: clusters and associations under the SMC and LMC tidal stresses

We obtained SOAR telescope B and V photometry of 14 star clusters and 2 associations in the Bridge tidal structure connecting the LMC and SMC. These objects are used to study the formation and evolution of star clusters and associations under tidal stresses from the Clouds. Typical star clusters in the Bridge are not richly populated and have in general relatively large diameters (~30-35 pc), being larger than Galactic counterparts of similar age. Ages and other fundamental parameters are determined with field-star decontaminated photometry. A self-consistent approach is used to derive parameters for the most-populated sample cluster NGC 796 and two young CMD templates built with the remaining Bridge clusters. We find that the clusters are not coeval in the Bridge. They range from approximately a few Myr (still related to optical HII regions and WISE and Spitzer dust emission measurements) to about 100-200 Myr. The derived distance moduli for the Bridge objects suggests that the Bridge is a structure connecting the LMC far-side in the East to the foreground of the SMC to the West. Most of the present clusters are part of the tidal dwarf candidate D 1, which is associated with an H I overdensity. We find further evidence that the studied part of the Bridge is evolving into a tidal dwarf galaxy, decoupling from the Bridge.Comment: 15 pages, 15 figures, MNRAS, Accepted 2015 July 2

Mass segregation in rich LMC clusters from modelling of deep HST colour-magnitude diagrams

We used the deep colour-magnitude diagrams (CMDs) of five rich LMC clusters (NGC1805, 1818, 1831, 1868, and Hodge14) observed with HST/WFPC2 to derive their present day mass function (PDMF) and its variation with position within the cluster. The PDMF was parameterized as a power law in the available main-sequence mass range of each cluster, typically 0.9 <~ m/M_sun <~ 2.5; its slope was determined at different positions spanning from the very centre out to several core radii. The CMDs in the central regions of the clusters were carefully studied earlier, resulting in accurate age, metallicity, distance modulus, and reddening values. The slope alpha (where Salpeter is 2.35) was determined in annuli by following two distinct methods: 1) a power law fit to the PDMF obtained from the systemic luminosity function (LF); 2) a statistical comparison between observed and model CMDs. In all clusters, significant mass segregation is found from the positional dependence of the PDMF slope: alpha <~ 1.8 for R <= 1.0 R_core and alpha ~ Salpeter inside R=2~3 R_core (except for Hodge 14, where alpha ~ Salpeter for R ~ 4 R_core). The results are robust in the sense that they hold true for both methods used. The CMD method reveals that unresolved binaries flatten the PDMF obtained form the systemic LF, but this effect is smaller than the uncertainties in the alpha determination. For each cluster we estimated dynamical ages inside the core and for the entire system. In both cases we found a trend in the sense that older clusters have flatter PDMF, consistent with a dynamical mass segregation and stellar evaporation

Self-adjoint symmetry operators connected with the magnetic Heisenberg ring

We consider symmetry operators a from the group ring C[S_N] which act on the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We investigate such symmetry operators a which are self-adjoint (in a sence defined in the paper) and which yield consequently observables of the Heisenberg model. We prove the following results: (i) One can construct a self-adjoint idempotent symmetry operator from every irreducible character of every subgroup of S_N. This leads to a big manifold of observables. In particular every commutation symmetry yields such an idempotent. (ii) The set of all generating idempotents of a minimal right ideal R of C[S_N] contains one and only one idempotent which ist self-adjoint. (iii) Every self-adjoint idempotent e can be decomposed into primitive idempotents e = f_1 + ... + f_k which are also self-adjoint and pairwise orthogonal. We give a computer algorithm for the calculation of such decompositions. Furthermore we present 3 additional algorithms which are helpful for the calculation of self-adjoint operators by means of discrete Fourier transforms of S_N. In our investigations we use computer calculations by means of our Mathematica packages PERMS and HRing.Comment: 13 page

The sub-millimetre evolution of V4334 Sgr (Sakurai's Object)

We report the results of monitoring of V4334 Sgr (Sakurai's Object) at 450 microns and 850 microns with SCUBA on the James Clerk Maxwell Telescope. The flux density at both wavelengths has increased dramatically since 2001, and is consistent with continued cooling of the dust shell in which Sakurai's Object is still enshrouded, and which still dominates the near-infrared emission. Assuming that the dust shell is optically thin at sub-millimetre wavelengths and optically thick in the near-infrared, the sub-millimetre data imply a mass-loss rate during 2003 of ~3.4(+/0.2)E-5 for a gas-to-dust ratio of 75. This is consistent with the evidence from 1-5micron observations that the mass-loss is steadily increasing.Comment: 5 pages, 4 eps figures, accepted for publication in MNRA

A low-absorption disk zone at low Galactic latitude in Centaurus

We investigate the properties of two stellar concentrations in a low-absorption disk zone in Centaurus, located respectively at $\ell=306.47^{\circ}$, $b=-0.61 ^{\circ}$, and $\ell=307.01^{\circ}$, $b=-0.74 ^{\circ}$. The present analysis is based mostly on 2MASS photometry, as well as optical photometry. Based on colour-magnitude diagrams and stellar radial density profiles, we show that these concentrations are not open star clusters. Instead, they appear to be field stars seen through a differentially-reddened window. We estimate that the bulk of the stars in both stellar concentrations is located at $\sim1.5$ kpc from the Sun, a distance consistent with that of the Sgr-Car arm in that direction. This low-absorption window allows one to probe into distant parts of the disk besides the Sgr-Car arm, probably the tangent part of the Sct-Cru arm, and/or the far side of the Sgr-Car arm in that direction. The main sequence associated to the Sgr-Car arm is reddened by \ebv\sim0.5, so that this window through the disk is comparable in reddening to Baade's window to the bulge. We also investigate the nature of the open cluster candidate Ru 166. The presently available data do not allow us to conclude whether Ru 166 is an actual open cluster or field stars seen through a small-scale low-absorption window

Mothers of Soldiers in Wartime: A National News Narrative

National news media represent mothers of US combat soldiers in the Iraq War as archetypal good mothers, that is, mothers who continue their maternal work even after their children are deployed. However, not all mothers are depicted as the archetypal patriotic mother, i.e., a good mother who is also stoic and silent about the war and her child\u27s role in it. Mothers of soldiers are portrayed as good mothers who sometimes also voice their attitudes about the war effort. The maternal attitudes ranged from complete support for the war to opposition to the war but support for the soldiers. The findings suggest a picture of wartime motherhood that is more nuanced than the historical image of the patriotic mother suggests

Analysis of colour-magnitude diagrams of rich LMC clusters: NGC 1831

We present the analysis of a deep colour-magnitude diagram (CMD) of NGC 1831, a rich star cluster in the LMC. The data were obtained with HST/WFPC2 in the F555W (~V) and F814W (~I) filters, reaching m_555 ~ 25. We discuss and apply a method of correcting the CMD for sampling incompleteness and field star contamination. Efficient use of the CMD data was made by means of direct comparisons of the observed to model CMDs. The model CMDs are built by an algorithm that generates artificial stars from a single stellar population, characterized by an age, a metallicity, a distance, a reddening value, a present day mass function and a fraction of unresolved binaries. Photometric uncertainties are empirically determined from the data and incorporated into the models as well. Statistical techniques are presented and applied as an objective method to assess the compatibility between the model and data CMDs. By modelling the CMD of the central region in NGC 1831 we infer a metallicity Z = 0.012, 8.75 < log(tau) < 8.80, 18.54 < (m-M)_0 < 18.68 and 0.00 < E(B-V) < 0.03. For the position dependent PDMF slope (alpha = -dlog(Phi(M))/dlog(M)), we clearly observe the effect of mass segregation in the system: for projected distances R < 30 arcsec, alpha ~ 1.7, whereas 2.2 < alpha < 2.5 in the outer regions of NGC 1831.Comment: 12 pages, 14 figure