In the paper we report on the parallel enumeration of the degree sequences (their number is denoted by G(n)) and zerofree degree sequences (their number is denoted by (Gz(n)) of simple graphs on n = 30 and n = 31 vertices. Among others we obtained that the number of zerofree degree sequences of graphs on n = 30 vertices is Gz(30) = 5 876 236 938 019 300 and on n = 31 vertices is Gz(31) = 22 974 847 474 172 374. Due to Corollary 21 in [52] these results give the number of degree sequences of simple graphs on 30 and 31 vertices.
Indoor navigation is an important research topic nowadays. The complexity of larger buildings, supermarkets, museums, etc. makes it necessary to use applications which can facilitate the orientation. While for outdoor navigation already exist tried and tested solutions, but few reliable ones are available for indoor navigation. In this paper we investigate the possible technologies for indoor navigation. Then, we present a general, cost effective system as a solution. This system uses the advantages of semantic web to store data and to compute the possible paths as well. Furthermore it uses Augmented Reality techniques and map view to provide interaction with the users. We made a prototype based on client-server architecture. The server runs in a cloud and provides the appropriate data to the client, which can be a smartphone or a tablet with Android operation system.
Shubnikov-de Haas oscillations corresponding to the spin-resolved Landau levels of the two-dimensional electron gas at an In 0.53 Ga 0.47 As-InP heterointerface were studied in wide ranges of magnetic fields (up to 22 T) and tilt angles. Dependences of the spin splitting s on the parallel component of magnetic field were investigated for half-filled Landau levels 0↑, 1↓, 1↑, 2↓ and 2↑. The exchange interaction was shown to be strongly dependent on the broadening and overlapping of adjacent Landau levels. On the basis of this model, the experimental magnetic field dependences of s were described. As a result, the absolute value of bare g-factor g 0 = 2.9, exchange energy E x = 30 meV and Landau level broadening = 7-11 meV were obtained.
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