Moon [J. Combin. Inform. System Sci. 19 (1994), 207–214] showed that every strong tournament contains a Hamiltonian cycle through at least three pancyclic arcs. In this paper, we extend the result of Moon and prove that if D is a strong c-partite tournament with c ≥ 3, then D contains a cycle C containing vertices from exactly c partite sets such that C contains at least three arcs, each of whi...

We report the discovery of 4 new strong lensing systems by visual inspection of the Sloan Digital Sky Survey images of galaxy clusters in Data Release 6 (SDSS DR6). Two of them show Einstein rings, and the others show tangential giant arcs. These arcs or rings have large angle separations of > 8 from the bright central galaxies and show blue color compared to the red cluster galaxies. In additi...

The origin of the arc-shaped stellar complexes in the LMC4 region is still unknown. These perfect arcs could not have been formed by O-stars and SNe in their centers; the strong arguments exist also against the possibility of their formation from infalling gas clouds. The origin from microquasars/GRB jets is not excluded, because there is the strong concentration of X-ray binaries in the same r...

We perform ray-tracing simulations evaluating the effect of a cD galaxy on the strong lensing properties of five galaxy cluster halos obtained from N-body simulations. The cD galaxy is modelled using both axially symmetric and elliptical models and assuming several masses for its dark matter halo. The effect of the cD orientation with respect to the mass distribution of the host galaxy cluster ...

Aims. We present a detailed mass reconstruction of the cluster RCS0224-0002 at z = 0.773 from the strong lensing features observed with HST/WFPC2. Methods. The mass profile is reconstructed using a parametric approach. We introduce a novel method to fit extended multiple images based on the Modified Hausdorff Distance between observed arcs and the arcs reproduced by the model. We perform the de...

Naive Bayes is a simple Bayesian classifier with strong independence assumptions among the attributes. This classifier, despite its strong independence assumptions, often performs well in practice. It is believed that relaxing the independence assumptions of a naive Bayes classifier may improve the classification accuracy of the resulting structure. While finding an optimal unconstrained Bayesi...

In a random n-vertex digraph, each arc is present with probability p, independently of the presence or absence of other arcs. We investigate the structure of the strong components of a random digraph and present an algorithm for the construction of the transitive closure of a random digraph. We show that, when n is large and np is equal to a constant c greater than 1, it is very likely that all...

A strong oriented k-coloring of an oriented graph G is a homomorphism φ from G to H having k vertices labelled by the k elements of an abelian additive group M , such that for any pairs of arcs −→ uv and −→ zt of G, we have φ(v)−φ(u) 6= −(φ(t)−φ(z)). The strong oriented chromatic number χs(G) is the smallest k such that G admits a strong oriented k-coloring. In this paper, we consider the follo...

We present the results of a CCD imaging survey for gravitational lensing in a sample of 38 Xray-selected clusters of galaxies. Our sample consists of the most X-ray luminous (Lx ≥ 2 × 10 erg s−1) clusters selected from the Einstein Observatory Extended Medium Sensitivity Survey (EMSS) that are observable from Mauna Kea (δ > −40o). The sample spans a redshift range of 0.15≤ z ≤0.823 and includes...