Roughness in Fuzzy Cayley Graphs

Rough set theory is a worth noticing approach for inexact and uncertain system modelling. When rough set theory accompanies with fuzzy set theory, which both are a complementary generalization of set theory, they will be attended by potency in theoretical discussions. In this paper a definition for fuzzy Cayley subsets is put forward as well as fuzzy Cayley graphs of fuzzy subsets on groups inspired from the definition of Cayley graphs. We introduce rough approximation of a Cayley graph with respect to a fuzzy normal subgroup. We introduce the approximation rough fuzzy Cayley graphs and fuzzy rough fuzzy Cayley graphs. The last approximation is the mixture of the other approximations. Some theorems and properties are investigated and proved

A new bow-shock source with bipolar morphology in the vicinity of Sgr A*

Here we present a new bowshock blue-shifted source in the close vicinity of Sgr A* that we name X8. We use data-sets that are based on SINFONI observations with the Very Large Telescope. We can trace the source between 2006 and 2016 in the blue-shifted line maps and it shows not only positional similarities to X7 but also the same spectral footprint. The symmetry axis of both extended sources points towards Sgr A* and exhibits [Fe III] emission lines that arise due to wind-wind shocks. In particular, the source X8 has a bipolar morphology, which makes it the closest bipolar source in the vicinity of Sgr A*. In addition, we can trace a K-band continuum counterpart of X8. This points towards a stellar counterpart to the line-map emission. Overall, the source X8 can be interpreted as either a Young Stellar Object or a young planetary nebula, which makes this source unique among so-far detected main-sequence OB stars in this region.Comment: Accepted for publication by A&A, 15 pages, 13 figure

The pro-nilpotent group topology on a free group

In this paper, we study the pro-nilpotent group topology on a free group. First we describe the closure of the product of finitely many finitely generated subgroups of a free group in the pro-nilpotent group topology and then present an algorithm to compute it. We deduce that the nil-closure of a rational subset of a free group is an effectively constructible rational subset and hence has decidable membership. We also prove that the G(nil)-kernel of a finite monoid is computable and hence pseudovarieties of the form V (sic) G(nil) have decidable membership problem, for every decidable pseudovariety of monoids V. Finally, we prove that the semidirect product J * G(nil) has a decidable membership problem

First results from a large-scale proper motion study of the Galactic Centre

Proper motion studies of stars in the centre of the Milky Way have been typically limited to the Arches and Quintuplet clusters and to the central parsec. Here, we present the first results of a large-scale proper motion study of stars within several tens of parsecs of Sagittarius A* based on our $0.2''$ angular resolution GALACTICNUCLEUS survey (epoch 2015) combined with NICMOS/HST data from the Paschen-$\alpha$ survey (epoch 2008). This study will be the first extensive proper motion study of the central $\sim 36' \times 16'$ of the Galaxy, which is not covered adequately by any of the existing astronomical surveys such as Gaia because of its extreme interstellar extinction ($A_{V} \gtrsim 30$ mag). Proper motions can help us to disentangle the different stellar populations along the line-of-sight and interpret their properties in combination with multi-wavelength photometry from GALACTICNUCLEUS and other sources. It also allows us to infer the dynamics and interrelationship between the different stellar components of the Galactic Centre (GC). In particular, we use proper motions to detect co-moving groups of stars which can trace low mass or partially dissolved young clusters in the GC that can hardly be discovered by any other means. Our pilot study in this work is on a field in the nuclear bulge associated by HII regions that show the presence of young stars. We detect the first group of co-moving stars coincident with an HII region. Using colour-magnitude diagrams, we infer that the co-moving stars are consistent with being the post-main sequence stars with ages of few Myrs. Simulations show that this group of stars is a real group that can indicate the existence of a dissolving or low to intermediate mass young cluster. A census of these undiscovered clusters will ultimately help us to constrain star formation at the GC in the past few ten Myrs.Comment: Accepted for publication in A&A. 13 pages, 17 figure

Nuclear Activity and the Conditions of Star-formation at the Galactic Center

The Galactic Center is the closest galactic nucleus that can be studied with unprecedented angular resolution and sensitivity. We summarize recent basic observational results on Sagittarius A* and the conditions for star formation in the central stellar cluster. We cover results from the radio, infrared, and X-ray domain and include results from simulation as well. From (sub-)mm and near-infrared variability and near-infrared polarization data we find that the SgrA* system (supermassive black hole spin, a potential temporary accretion disk and/or outflow) is well ordered in its geometrical orientation and in its emission process that we assume to reflect the accretion process onto the supermassive black hole (SMBH).Comment: 11 pages, 4 figures, 1 table; published in PoS-SISSA Proceedings of the: Frontier Research in Astrophysics - II, 23-28 May 2016, Mondello (Palermo), Ital

Experimental Indicators of Accretion Processes in Active Galactic Nuclei

Bright Active Galactic Nuclei are powered by accretion of mass onto the super massive black holes at the centers of the host galaxies. For fainter objects star formation may significantly contribute to the luminosity. We summarize experimental indicators of the accretion processes in Active Galactic Nuclei (AGN), i.e., observable activity indicators that allow us to conclude on the nature of accretion. The Galactic Center is the closest galactic nucleus that can be studied with unprecedented angular resolution and sensitivity. Therefore, here we also include the presentation of recent observational results on Sagittarius A* and the conditions for star formation in the central stellar cluster. We cover results across the electromagnetic spectrum and find that the Sagittarius A* (SgrA*) system is well ordered with respect to its geometrical orientation and its emission processes of which we assume to reflect the accretion process onto the super massive black hole.Comment: 16 pages, 4 figures, conference proceeding: Accretion Processes in Cosmic Sources - APCS2016 - 5-10 September 2016, Saint Petersburg, Russi