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[en] We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple dynamical construction procedures that produce equilibrium uncorrelated random graphs with an arbitrary degree distribution. In particular, we show that in equilibrium uncorrelated networks, fat-tailed degree distributions may exist only starting from some critical average number of connections of a vertex, in a phase with a condensate of edges
[en] A summary of the pressure-temperature phase diagrams of the elements is presented, with graphs of the experimentally determined solid-solid phase boundaries and melting curves. Comments, including theoretical discussion, are provided for each diagram. The crystal structure of each solid phase is identified and discussed. This work is aimed at encouraging further experimental and theoretical research on phase transitions in the elements
[en] Entropy and Carnot theorem occupy central place in the typical Thermodynamics courses at the university level. In this work, we suggest a new simple approach for introducing the concept of entropy. Using simple procedure in TV plane, we proved that for reversible processes ∫dQ/T=0 and it is sufficient to define entropy. And also, using reversible processes in TS plane, we give an alternative simple proof for Carnot theorem
[en] A modular application of the integration by fractional expansion method for evaluating Feynman diagrams is extended to diagrams that contain loop triangle subdiagrams in their geometry. The technique is based in the replacement of this module or subdiagram by its corresponding multiregion expansion (MRE), which in turn is obtained from Schwinger's parametric representation of the diagram. The result is a topological reduction, transforming the triangular loop into an equivalent vertex, which simplifies the search for the MRE of the complete diagram. This procedure has important advantages with respect to considering the parametric representation of the whole diagram: the obtained MRE is reduced, and the resulting hypergeometric series tends to have smaller multiplicity.
[en] Resonance-enhanced degenerate four wave mixing is analyzed for two-level and three-level systems in both stedy-state and transient cases by means of a time-ordered Feynman-type diagrammatic representation. Particularly in the steady-state case, we introduce the atomic motional effects and field-polarization dependence into our diagrammatic analyses. Furthermore we present quantum-mechnical interpretations of the holographic analogy for the one-photon resonant case and the phenomenon of probe-beam amplification for any resonant case. (Author)