Within conventional superconductivity, BCS theory represents a well defined weakcoupling limit. The central result are the Universal Ratios which do not depend on physical parameters of the particular superconductor under study. Several attempts have been made to introduce the van Hove Scenario within BCS theory but in none of them the Universal Ratios of conventional superconductivity appear to be a number independent of parameters.This fact prevents the precise definition of a deviation from the BCS value for a particular superconductor. This concept is at the basis of several applications of BCS theory in characterizing conventional superconductors. We define a system that constitutes a weak coupling limit that retains the essential features of the high-Tc oxides and which does not differ in any essential way from other models widely used in generalizations of BCS theory to high-Tc superconductors. The difference is that we found a natural way of dealing with the mathematics of the problem so as to get Universal Ratios in the same sense as in conventional superconductivity. This formulation could play an analogous role as the original BCS theory played in conventional superconductivity. A central result of this theory are the Universal Ratios (UR). These relate thermodynamic quantities among themselves in a universal way, i. e. they are equal to the same number for every possible superconductor.When compared to experiment, BCS turns out not to be an exact theory of CS. Deviations from it are frequent in all but some of the weak coupling CSr as Al, In, and Sn.Since it is a precisely established limit, the deviations from it do have a well defined physical meaning. This theory is useful as a point of reference and as a tool to study different, more complicated physical situations in a transparent and easy way from which trends can be established. It is important to recall that, in the spirit of the theoretical treatment of CS, the deviations from BCS theory characterize the particular superconductor, not the theory. The validity of BCS theory itself is based on its approximate description of the most important experimental trends and on its characterization as a well-defined weak coupling limit. This is a very important point for this letter. The precise many-body theory of the electron-phonon (e-ph) CS is described through the so called Eliashberg gap Equations [2]

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PbS thin films with thickness between 100 and 150 nm were grown for the first time by microwave-assisted chemical bath deposition in a commercial automated system with deposition times not exceeding 5 min. X-ray diffraction analysis shows that the thin films have cubic rock salt type structure with good crystallinity. The grain size increased from 18 to 20 nm, as the deposition time increased. Energy dispersive X-ray results confirm that the films are stoichiometric. Optical measurements show that thin films have relatively high absorption coefficients between 104 and 105 cm-1 in the visible range. In addition, the films exhibit a direct gap, within the energy range from 1.0 to 1.35 eV. The electrical properties, such as conductivity, the Seebeck coefficient, carrier concentration, and carrier mobility, are discussed.

Dynamic Bayesian networks usually make the assumption that the underlying process they model is first-order Markovian, that is, that the future state is independent of the past given the present. However, there are situations in which this assumption has to be relaxed. When this order increases, the size of the search space grows greatly, not all structure learning algorithms may be suited to learn higher-order networks, and a new appropriate order has to be found. To address the computational issues of huge networks, we propose a structure learning method that uses particle swarm optimization to search in the space of possible structures. To avoid the additional costs of increasing the Markovian order, we provide an order-invariant encoding that represents the networks as vectors of natural numbers whose length remains constant. Due to this encoding, we only need to set a maximum desired order rather than the exact one. Our experimental results show that this method is efficient in high orders and performs better than similar algorithms in both execution time and quality of the obtained networks.

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