BASIC DEFINITIONS: crossing pair of curves and common interior point between two arcs. crossing number cr(G) minimum number of crossings in a drawing of G l-grid is a pair two disjoint edge subset E1, E2 ⊂ E of a drawing of a graph G = (V, E), such that |E1| = |E2| = l and every edge in E1 crosses every edge in E2 bi-clique complete bipartite graph where vertex classes differ in size by at most...

In the minimal model of electroweak interactions we carefully investigate the spectrum of the massive euclidean Dirac operator in three, four and five dimensions (D) in the presence of topologically nontrivial external fields. More specifically we study the cases of the instanton (D = 4), sphaleron (D = 3) as well as that of the (D = 5) Dirac operator that pertains to the existence of the globa...

This study examines the relationship between train traffic and the accident risk for road users at level crossings. The marginal effect of train traffic on the accident risk can be used to derive the marginal cost per train passage that is due to level crossing accidents. Based on Swedish data from 2000 to 2012 on level crossing accidents, train volume and crossing characteristics, the marginal...

The fermion energy spectrum along paths which connect topologically distinct vacua in the Einstein-Yang-Mills theory passing through the gravitational sphaleron equilibrium solutions is investigated. On leave from Physical-Technical Institute of the Academy of Sciences of Russia, Kazan 420029, Russia