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In this paper, we combine the concepts of the fibered Burnside ring and the character ring, viewing them as fibered biset functors, into what we call the global representation fibered ring of a finite group. We compute all ring homomorphisms from this ring to the complex numbers, determine its spectrum and its connected components, and identify the primitive idempotents of this ring tensor with $\mathbb{Q}$ and its conductors.

We have measured the isospin mixing of the I$^\pi$= 1/2$^+$ E$_x$=2.599 MeV state in nearly-doubly-magic $^{47}$Ca with the isobaric analog 1/2$^+$ state of $^{47}$K. Using the TRIUMF atom trap for $\beta$ decay, we have measured a nonzero asymmetry of the progeny $^{47}$Ca with respect to the initial $^{47}$K spin polarization, which together with the $\beta$ asymmetry implies a nonzero ratio of Fermi to Gamow-Teller matrix elements $y$= 0.098$\pm$0.037 for the $1/2^+ \rightarrow 1/2^+$ transition. Interpreting $y$ as mixing between this state and the isobaric analog state implies a Coulomb matrix element magnitude 101 $\pm$ 37 keV. This relatively large matrix element supports a model from the literature of analog-antianalog isospin mixing, which predicts large matrix elements in cases involving excess neutrons over protons occupying more than one major shell. The result supports pursuing a search for time-reversal odd, parity-even, isovector interactions using a correlation in $^{47}$K $\beta$ decay., Comment: 7 (two-column) pages, 7 figures. Reprint of version accepted by Physical Review C Letters May 3, 2024 (proof corrections included, except we retain non-Letter features: section headers; \frac in inline equations; untruncated reference authors)

The Fornax galaxy cluster is the richest nearby (D ~ 20 Mpc) galaxy association in the southern sky. As such, it provides a wealth of oportunities to elucidate on the processes where environment holds a key role in transforming galaxies. Although it has been the focus of many studies, Fornax has never been explored with contiguous homogeneous wide-field imaging in 12 photometric narrow- and broad-bands like those provided by the Southern Photometric Local Universe Survey (S-PLUS). In this paper we present the S-PLUS Fornax Project (S+FP) that aims to comprehensively analyse the galaxy content of the Fornax cluster using S-PLUS. Our data set consists of 106 S-PLUS wide-field frames (FoV ~ 1.4 x 1.4 deg$^2$) observed in five SDSS-like ugriz broad-bands and seven narrow-bands covering specific spectroscopic features like [OII], CaII H+K, H$\delta$, G-band, Mg b triplet, H$\alpha$, and the CaII triplet. Based on S-PLUS specific automated photometry, aimed at correctly detecting Fornax galaxies and globular clusters in S-PLUS images, our dataset provides the community with catalogues containing homogeneous 12-band photometry for ~ 3 x 10$^6$ resolved and unresolved objects within a region extending over ~ 208 deg$^2$ (~ 5 Rvir in RA) around Fornax' central galaxy, NGC 1399. We further explore the EAGLE and IllustrisTNG cosmological simulations to identify 45 Fornax-like clusters and generate mock images on all 12 S-PLUS bands of these structures down to galaxies with M$\star \geq 10^8$ M$\odot$. The S+FP dataset we put forward in this first paper of a series will enable a variety of studies some of which are briefly presented., Comment: 25 pages, 30 figures, accepted for publication in MNRAS

Let A be an abelian group, not necessarily finite. The main objective of this paper is to provide two constructions for a fibered A-biset functor. The first is the lower plus construction, and the other is the upper plus construction. These constructions coincide with the lower plus and upper plus constructions for biset functors (see [2]) when the fiber is the trivial group {.}.

In this article, we describe the lattice of ideals of some Green biset functors. We consider Green biset functors which satisfy that each evaluation is a finite dimensional split semisimple commutative algebra and use the idempotents in these evaluations to characterize any ideal of these Green biset functors. For this we will give the definition of M C-group, this definition generalizes that of a B-group, given for the Burnside functor. Given a Green biset functor A, with the above hypotheses, the set of all M C-groups of A has a structure of a poset and we prove that there exists an isomorphism of lattices between the set of ideals of A and the set of upward closed subsets of the M C-groups of A.

In the context of the S-PLUS Fornax Project (S+FP), we analyze the galaxy population in the direction of the Fornax cluster ($D\approx 20$~Mpc). We have 23 fields of size $1.4^{\circ}\times 1.4^{\circ}$, covering the projected positions of 999 Fornax galaxies reported in the literature. 244 of those galaxies are detected with confident photometry in our fields which were observed simultaneously in 12 photometric bands. Besides those of Fornax galaxies, we obtained confident structural and photometric parameters for $\approx 3\times10^5$ additional galaxies detected in our fields. In this work we present preliminary results on the characterization of the galaxy population of the Fornax cluster with respect to the background galaxy population. Among other goals, we expect that such a characterization provides photometric criteria to identify new candidate members of the cluster., Comment: 3 pages, 3 figures, accepted for Bolet\'in de la Asociaci\'on Argentina de Astronom\'ia

This paper studies community formation in OSS collaboration networks. While most current work examines the emergence of small-scale OSS projects, our approach draws on a large-scale historical dataset of 1.8 million GitHub users and their repository contributions. OSS collaborations are characterized by small groups of users that work closely together, leading to the presence of communities defined by short cycles in the underlying network structure. To understand the impact of this phenomenon, we apply a pre-processing step that accounts for the cyclic network structure by using Renewal-Nonbacktracking Random Walks (RNBRW) and the strength of pairwise collaborations before implementing the Louvain method to identify communities within the network. Equipping Louvain with RNBRW and the contribution strength provides a more assertive approach for detecting small-scale teams and reveals nontrivial differences in community detection such as users tendencies toward preferential attachment to more established collaboration communities. Using this method, we also identify key factors that affect community formation, including the effect of users location and primary programming language, which was determined using a comparative method of contribution activities. Overall, this paper offers several promising methodological insights for both open-source software experts and network scholars interested in studying team formation., Comment: 8 pages

We present a new time-series VI CCD photometry of the globular cluster NGC 6397, from which we obtained and analysed the light curves of 35 variables carefully identified in the cluster field. We assessed the membership of the variables with an astrometric analysis based on \emph{Gaia} DR2 data. The cluster colour-magnitude diagram was differentially dereddened and cleaned of non members, which allowed us to fit isochrones for [Fe/H]$ = -2.0$ dex in the range 13.0--13.5 Gyr, for a mean reddening $E(B-V)=0.19$, and a distance of 2.5 kpc. This distance was confirmed using the period-luminosity relation for the cluster's five SX Phoenicis variables (V10, V11, V15, V21, and V23) present among its blue stragglers, yielding $2.24\pm0.13$ kpc. We also modelled the light curves of four eclipsing binaries (V4, V5, V7, and V8), and gave the parameters of the systems; the contact binaries V7 and V8 have distances consistent with that of the cluster. NGC 6397 appears to harbour no RR Lyrae stars, being its horizontal branch remarkably blue, much like that of its analogous cluster, M10. To match the blue tail of the horizontal branch population, models of 0.64--0.66 $M_\odot$ with mass loss at the RGB are required, indicating rather thin shell masses for the HB stars., Comment: 19 pages, 9 figures

Time-series VI CCD photometry of the globular cluster M10 (NGC 6254) is employed to perform a detailed identification, inspection of their light curves, their classification and their cluster membership, of all the known variables reported up to 2018. The membership analysis is based on the Gaia-DR2 positions and proper motions. The metallicity of the cluster is estimated based on the sole RRc star known in the cluster. The Fourier decomposition of its light curve leads to [Fe/H]ZW=-1:59 $\pm$ 0:23 dex. The mean cluster distance, estimated by several independent methods is 5.0 $\pm$ 0.3 kpc. A multi-approach search in a region of about 10x10 arcmin2 around the cluster revealed three new variables, one SX Phe (V35) and two sinusoidal variables on the red giant branch of unclear classification (V36,V37). Modelling the HB stars is very sensitive to the stellar hydrogen shell mass, which surrounds the 0.50 M$_\odot$ helium core. To match the full stretch of the HB population, a range of total mass of 0.56 to 0.62 M$_\odot$ is required. These models support a distance of 5.35 kpc and an age of about 13 Gyrs, and hints to some individual variation of the mass loss on the uppper RGB, perhaps caused by the presence of closed magnetic field in red giants., Comment: 14 pages, 7 Figures, 6 Tables. Manuscript accepted for publication in MNRAS Sept. 23, 2020

We present an extension of our previous research on the early-type galaxy population of the Antlia cluster (d ~ 35 Mpc), achieving a total coverage of ~ 2.6 deg x deg and performing surface photometry for ~300 galaxies, 130 of which are new uncatalogued ones. Such new galaxies mainly fall in the low surface brightness (LSB) regime, but there are also some lenticulars (S0) which support the existence of unique functions that connect bright and dwarf galaxies in the scaling relations. We analyse the projected spatial distribution of galaxies up to a distance of ~800 kpc from NGC 3268, the adopted centre, as well as the radial velocity distribution and the correlation between galaxy colour and effective radius with the projected spatial distribution. We also obtain the luminosity function of the early-type galaxies and the distribution of stellar masses using the T1-band magnitudes and adopted mass-luminosity ratios. Additionally, we correlate the central galaxy distribution with an X-ray emission map from the literature. Based on the analysis of the radial velocities and galaxy colour distributions, we find that galaxies redder than the colour-magnitude relation (CMR) have a velocity distribution strongly concentrated towards the values of the dominant galaxies and are homogeneously distributed throughout the cluster. Those bluer than the CMR, in turn, have a much more extended radial velocity distribution and are concentrated towards the centre of the cluster. We also identify 12 candidates to ultra diffuse galaxies (UDG), that seem to be split into two families, and speculate about their origins in the context of the cluster structure., Comment: Accepted for publication in MNRAS

Sky surveys produce enormous quantities of data on extensive regions of the sky. The easiest way to access this information is through catalogues of standardised data products. {\em XMM-Newton} has been surveying the sky in the X-ray, ultra-violet, and optical bands for 20 years. The {\em XMM-Newton} Survey Science Centre has been producing standardised data products and catalogues to facilitate access to the serendipitous X-ray sky. Using improved calibration and enhanced software, we re-reduced all of the 14041 {\em XMM-Newton} X-ray observations, of which 11204 observations contained data with at least one detection and with these we created a new, high quality version of the {\em XMM-Newton} serendipitous source catalogue, 4XMM-DR9. 4XMM-DR9 contains 810795 detections down to a detection significance of 3 $\sigma$, of which 550124 are unique sources, which cover 1152 degrees$^{2}$ (2.85\%) of the sky. Filtering 4XMM-DR9 to retain only the cleanest sources with at least a 5 $\sigma$ detection significance leaves 433612 detections. Of these detections, 99.6\% have no pileup. Furthermore, 336 columns of information on each detection are provided, along with images. The quality of the source detection is shown to have improved significantly with respect to previous versions of the catalogues. Spectra and lightcurves are also made available for more than 288000 of the brightest sources (36\% of all detections)., Comment: 14 pages, 11 figures, accepted to be published Astronomy and Astrophysics (A&A)

We present an analysis of $\emph{VI}$ CCD time series photometry of globular cluster NGC 6712. Our main goal is to study the variable star population as indicators of the cluster mean physical parameters. We employed the Fourier decomposition of RR Lyrae light curves to confirm that $[\rm Fe/H]_{UVES} = -1.0 \pm 0.05$ is a solid estimate. We estimated the reddening to the cluster as $E(B-V)$ = 0.35 $\pm$ 0.04 from the RRab stars colour curves. The distance to the cluster was estimated using three independent methods which yielded a weighted mean distance $\big < d \big>$ = 8.1 $\pm$ 0.2 kpc. The distribution of RRab and RRc stars on the HB shows a clear segregation around the first overtone red edge of the instability strip, which seems to be a common feature in OoI-type cluster with a very red horizontal branch. We carried out a membership analysis of 60,447 stars in our FoV using the data from $Gaia$-DR2 and found 1529 likely members; we possess the light curves of 1100 among the member stars. This allowed us to produce a clean colour-magnitude diagram, consistent with an age of 12 Gyrs, and enabled us to discover close unresolved contaminants for several variable stars. From the proper motion analysis we found evidence of non-member stars in the FoV of the cluster being tidally affected by the gravitational pull of the bulge of the Galaxy. We found that the RRab variable V6, shows a previously undetected Blazhko effect. Finally, we report sixteen new variables of the EW-type (9) and SR-type (7)., Comment: 19 pages, 13 figures, 10 tables. MNRAS, Accepted January 20, 2020, Received 2020 January 8; in original form 2019 November 7

Time-series \emph{VI} CCD photometry of the globular cluster NGC 1261 is employed to study its variable star population. A membership analysis of most variables based on Gaia~DR2 proper motions and colours, was performed prior to the estimation of the mean cluster distance and metallicity. For the member RR Lyrae, their light curves were Fourier decomposed to calculate their individual values of distance, [Fe/H], radius and mass. The $I$-band P-L for RR Lyrae stars was also employed. Our best estimates of the metallicity and distance of this Oo I cluster are [Fe/H]$_{\rm ZW}$=$-1.42 \pm 0.05$ dex and $d=17.2 \pm 0.4$ kpc. No mixture of fundamental and first overtone RR Lyrae stars in the either-or or bimodal region is seen in this cluster, as it seems to be the rule for Oo~I clusters with a red horizontal branch. A multi-approach search in a region of about 10$\times$10 arcmin$^2$ around the cluster revealed no new variable stars within the limitations of our CCD photometry., Comment: 16 pages, 8 Figures, 6 tables, one of them electronic

In this work we present a method to identify possible members of globular clusters using data from Gaia DR2. The method consists of two stages: the first one based on a clustering algorithm, and the second one based on the analysis of the projected spatial distribution of stars with different proper motions. In order to confirm that the clusters members extracted by the method correspond to actual globular clusters, the spatial distribution, the vector point diagram of the proper motions and the colour-magnitude diagrams are analysed. We apply the developed method to eight clusters: NGC 1261, NGC 3201, NGC 6139, NGC 6205, NGC 6362, NGC 6397, NGC 6712 and Palomar 13; we show the number of members extracted, the mean proper motions derived from them and finally we compare our results with other authors. In order to analyse the efficiency of the extraction method we perform an estimation of the completeness and the degree of contamination of the extracted members.

We present the results from $VI$ CCD time-series photometry of the globular cluster M13 (NGC 6205). From the Fourier decomposition of the light curves of RRab and RRc stars we found an average metallicity of [Fe/H]zw = -1.58 $\pm$ 0.09. The distance to the cluster was estimated as 7.1 $\pm$ 0.1 kpc from independent methods related to the variable star families RR Lyrae, SX Phe and W Virginis, from the luminosity of the theoretical ZAHB and from the orbit solution of a newly discovered contact binary star. The RR Lyrae pulsation modes are segregated by the red edge of the first overtone instability strip in this OoII type cluster. A membership analysis of 52,800 stars in the field of the cluster is presented based on \textit{Gaia}-DR2 proper motions which enabled the recognition of 23,070 likely cluster members, for 7,630 of which we possess $VI$ photometry. The identification of member stars allowed the construction of a clean CMD and a proper ZAHB and isochrone fitting, consistent with a reddening, age and distance of 0.02 mag, 12.6 Gyrs and 7.1 kpc respectively. We report seven new variables; one RRc, two SX Phe stars, three SR and one contact binary. V31 presents double-mode nature and we confirm V36 as RRd. Fifteen variable star candidates are also reported. The analysis of eighteen stars in the field of the cluster, reported as RR Lyrae from the $Gaia$-DR2 data base reveals that at least seven are not variable. We noted the presence of a high velocity star in the field of the cluster., Comment: 18 pages, 21 figures

New time-series VI CCD photometry of the globular cluster NGC 6362 is studied with the aim of estimating the reddening, mean metallicity and distance of the cluster from its population of RR Lyrae stars. The Fourier decomposition of carefully selected single-mode RR Lyrae light curves, and the use of well-established semi-empirical calibrations and revised zero points, lead to the values of [Fe/H]UVES =1:066 +// 0:126 and -1:08 +/- 0:16 and the distance 7:93 +/- 0:32 and 8:02 +/- 0:15 kpc from the RRab and RRc stars respectively. The distribution of RR Lyrae stars in the horizontal branch shows a neat segregation of pulsating modes about the red edge of the first overtone instability strip, which is not necessarily expected in an OoI type cluster like NGC 6362. Four RRab stars are found likely advanced in their evolution towards the AGB. One new foreground SX Phe star, some 4 kpc in front of the cluster and projected onto the field of our images is reported. We comment on the heavy light contamination, by a very close neighbouring star, of the peculiar double-mode V37 variable, recently postulated as a non-typical RRc variable., Comment: 16 pages, 10 figures, 2 identification charts, 1 electronic table. Accepted March 23, 2018, Astronomische Nachrichten 2018

CCD time-series observations of the central region of the globular cluster NGC~3201 were obtained with the aim of performing the Fourier decomposition of the light curves of the RR~Lyrae stars present in that field. This procedure gave the mean values, for the metallicity, of [Fe/H]$_{ZW}=-1.483 \pm 0.006$ (statistical) $\pm 0.090$ (systematical), and for the distance, $5.000 \pm 0.001$~kpc (statistical) $\pm 0.220$ (systematical). The values found from two RRc stars are consistent with those derived previously. The differential reddening of the cluster was investigated and individual reddenings for the RR Lyrae stars were estimated from their $V-I$ curves. We found an average value of $E(B-V)= 0.23 \pm 0.02$. An investigation of the light curves of stars in the {\it blue stragglers} region led to the discovery of three new SX~Phe stars. The period-luminosity relation of the SX~Phe stars was used for an independent determination of the distance to the cluster and of the individual reddenings. We found a distance of 5.0 kpc, Comment: To appear in Revista Mexicana de Astronom\'ia y Astrof\'isica, Octuber 2014 issue, Vol 50. 17 pages, 10 figures

The formation and evolution of dwarf galaxies in clusters need to be understood, and this requires large aperture telescopes. In this sense, we selected the Antlia cluster to continue our previous work in the Virgo, Fornax, and Hydra clusters and in the Local Volume (LV). Because of the scarce available literature data, we selected a small sample of five blue compact dwarf (BCD) candidates in Antlia for observation. Using the Gemini South and GMOS camera, we acquired the Halpha imaging needed to detect star-forming regions in this sample. With the long-slit spectroscopic data of the brightest seven knots detected in three BCD candidates, we derived their basic chemical properties. Using archival VISTA VHS survey images, we derived K_S magnitudes and surface brightness profile fits for the whole sample to assess basic physical properties. FS90-98, FS90-106, and FS90-147 are confirmed as BCDs and cluster members, based on their morphology, K_S surface photometry, oxygen abundance, and velocity redshift. FS90-155 and FS90-319 did not show any H{\alpha} emission, and they could not be confirmed as dwarf cluster star-forming galaxies. Based on our data, we studied some fundamental relations to compare star forming dwarfs (BCDs and dIs) in the LV and in the Virgo, Fornax, Hydra, and Antlia clusters. Star-forming dwarfs in nearby clusters appear to follow same fundamental relations in the near infrared with similar objects in the LV, specifically the size-luminosity and the metallicity-luminosity, while other more fundamental relations could not be checked in Antlia due to lack of data., Comment: Accepted for publication in A&A (early 2014)