In this paper we introduce an extension of the well known Rural Postman Problem, which combines arc routing with profits and facility location. Profitable arcs must be selected and facilities must be located at both end-points of the selected arcs, and a tour must be identified that maximizes the difference between the profit collected along the arcs and the cost of traversing the arcs and inst...

A digraph obtained by replacing each edge of a complete multipartite graph by an arc or a pair of mutually opposite arcs with the same end vertices is called a semicomplete multipartite digraph. L. Volkmann conjectured that l ≤ 2c− 1, where l (c, respectively) is the number of vertices in a longest path (longest cycle) of a strong semicomplete multipartite digraph. The bound on l is sharp. We s...

Fuel minimum range cruise of aircraft with high aerodynamic ef-ciency is considered as an optimal periodic control problem. Optimality conditions for trajectories with singular arcs and state variable constraints are derived. Computation of periodic optimal trajectories in the case addressed presents strong requirements on the numerical algorithm. Computational diiculties become larger when aer...

The already published first part of this paper1 described arc phenomena and gasdynamic effects produced by interaction of shock-heated plasma flow with a magnetic field perpendicular to the flow direction. Currents of density j flowed through electrodes flush mounted on the inside of the shock tube and connected on the outside. The plasma wras therefore subjected to retarding j X B forces direc...

The incidence of giant arcs due to strong-lensing clusters of galaxies is known to be discrepant with current theoretical expectations. This result derives from a comparison of several cluster samples to predictions in the framework of the currently favored ΛCDM cosmology, and one possible explanation for the discrepancy is that this cosmological model is not correct. In this paper we discuss t...

karun river with a length of about 890 km is considered as a main river in the country. in this paper, types of karun’s screws regarding to the geometric factors of radius of curvature and chord length were identified by fitting circles with the arcs of the river’s axis. river’s arcs were classified into simple and compound screws. then, by formation of the database consist of topographic...