Average distance in a hierarchical scale-free network: an exact solution

Various real systems simultaneously exhibit scale-free and hierarchical structure. In this paper, we study analytically average distance in a deterministic scale-free network with hierarchical organization. Using a recursive method based on the network construction, we determine explicitly the average distance, obtaining an exact expression for it, which is confirmed by extensive numerical calculations. The obtained rigorous solution shows that the average distance grows logarithmically with the network order (number of nodes in the network). We exhibit the similarity and dissimilarity in average distance between the network under consideration and some previously studied networks, including random networks and other deterministic networks. On the basis of the comparison, we argue that the logarithmic scaling of average distance with network order could be a generic feature of deterministic scale-free networks.Comment: Definitive version published in Journal of Statistical Mechanic

The Bekenstein-Hawking Entropy of Higher-Dimensional Rotating Black Holes

A black hole can be regarded as a thermodynamic system described by a grand canonical ensemble. In this paper, we study the Bekenstein-Hawking entropy of higher-dimensional rotating black holes using the Euclidean path-integral method of Gibbons and Hawking. We give a general proof demonstrating that ignoring quantum corrections, the Bekenstein-Hawking entropy is equal to one-fourth of its horizon area for general higher-dimensional rotating black holes.Comment: 9 pages, Latex, v2: arxiv-id for the references supplemented, v3: accepted for publication by Progress of Theoretical Physic

Variational separable expansion scheme for two-body Coulomb-scattering problems

We present a separable expansion approximation method for Coulomb-like potentials which is based on Schwinger variational principle and uses Coulomb-Sturmian functions as basis states. The new scheme provides faster convergence with respect to our formerly used non-variational approach.Comment: some typos correcte

Fibre bundle formulation of nonrelativistic quantum mechanics. IV. Mixed states and evolution transport's curvature

We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it a pure state of some quantum system is described by a state section (along paths) of a (Hilbert) fibre bundle. It's evolution is determined through the bundle (analogue of the) Schr\"odinger equation. Now the dynamical variables and the density operator are described via bundle morphisms (along paths). The mentioned quantities are connected by a number of relations derived in this work. The present fourth part of this series is devoted mainly to the fibre bundle description of mixed quantum states. We show that to the conventional density operator there corresponds a unique density morphism (along paths) for which the corresponding equations of motion are derived. It is also investigated the bundle description of mixed quantum states in the different pictures of motion. We calculate the curvature of the evolution transport and prove that it is curvature free iff the values of the Hamiltonian operator at different moments commute.Comment: 14 standard (11pt, A4) LaTeX 2e pages. The packages AMS-LaTeX and amsfonts are required. Minor style changes, a problem with the bibliography is corrected. Continuation of quant-ph/9803083, quant-ph/9803084, quant-ph/9804062 and quant-ph/9806046. For continuation of the series and related papers, view http://www.inrne.bas.bg/mathmod/bozhome