AN ASTROMETRIC AND PHOTOMETRIC STUDY OF THE INTERMEDIATE-AGE OPEN CLUSTER NGC 2158 AND ITS ECLIPSING BINARY [NBN2015]78

We present a photometric and astrometric analysis of the NGC 2158 cluster using Gaia DR2 and 2MASS data. The cluster age, color excess, intrinsic distance modulus and distance are calculated to be t = 2.240 ± 0.260 Gyr, E(B − V) = 0.420 ± 0.050 mag, (m − M)⨀ = 12.540 ± 0.130 mag and d⨀ = 3224 ± 200 pc respectively. The photometric analysis and light curve modelling of the proposed eclipsing binary member [NBN2015]78 is performed using the latest version of the Wilson-Devinney (W-D) code. The solutions show that the system is an over-contact binary with a secondary component filling its Roche lobe, with a mass ratio q = 0.262. The primary and the secondary components of the system consist of two late spectral types K1 and K2 respectively. The membership of [NBN2015]78 is discussed using two independent methods, and we find that [NBN2015]78 is an interloper and not a member of NGC 2158.

Some new results about the geometry of sets of finite perimeter

We establish that the intrinsic distance dE associated with an indecomposable plane set E of finite perimeter is infinitesimally Euclidean; namely, in E. By this result, we prove through a standard argument that a conservative vector field in a plane set of finite perimeter has a potential. We also provide some applications to complex analysis. Moreover, we present a collection of results that would seem to suggest the possibility of developing a De Rham cohomology theory for integral currents.

Sets of tetrahedra, defined by maxima of distance functions

We study tetrahedra and the space of tetrahedra from the viewpoint of local and global maxima for intrinsic distance functions

APPROXIMATIONS OF SOBOLEV NORMS IN CARNOT GROUPS

This paper deals with a notion of Sobolev space W1, p introduced by Bourgain, Brezis and Mironescu by means of a seminorm involving local averages of finite differences. This seminorm was subsequently used by Ponce to obtain a Poincaré-type inequality. The main results that we present are a generalization of these two works to a non-Euclidean setting, namely that of Carnot groups. We show that the seminorm expressed in terms of the intrinsic distance is equivalent to the Lp-norm of the intrinsic gradient, and provide a Poincaré-type inequality on Carnot groups by means of a constructive approach which relies on one-dimensional estimates. Self-improving properties are also studied for some cases of interest.

W UMa-type systems in globular clusters

W UMa systems can be found everywhere in the Galaxy. They can be used as a distance tracer. Therefore, W UMa systems are very important to investigate the structure of the Galaxy. The distance to W UMa systems in globular clusters (GCs) is determined using a period–color–luminosity relation. It is found that the mean distance (ra) of W UMa systems is consistent with their host cluster distances (rGC) deduced from their intrinsic distance moduli if rGC ≤ 10 kpc. There is a significant difference between ra and rGC for rGC ≥ 10 kpc. We discuss the reasons causing this deviation.