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It is well known that there exist statistical and structural differences between the stock markets of developed and emerging countries. In this work, we present an analysis of the variations and autocorrelations of the Mexican Stock Market index (IPC) for different periods of its historical daily data, showing evidence that the Mexican Stock Market has been increasing its efficiency in recent times. We have analyzed the returns autocorrelation function (ACF) and used detrended fluctuation analysis (DFA) methods. We also analyze the volatility of the IPC and the Dow Jones Industrial Average (DJIA) and compare their evolution. The data samples analyzed here, correspond to daily values of the IPC and DJIA for the period 10/30/1978 to 02/28/2006.

The transmission coefficient for one dimensional systems is given in terms of Chebyshev polynomials using the tight binding model. This result is applied to a system composed of two impurities located between N sites of a host lattice. It is found that the system has extended states for several values of the energy. Analytical expressions are given for the impurity site energy in terms of the electron's energy. The number of resonant states grow like the number of host sites between the impurities. This property makes the system interesting since it is a simple task to design a configuration with resonant energy very close to the Fermi level EF .

Complex networks are used to describe interactions in many real world systems, including economic, biological and social systems. An analysis was done of inter-student friendship, enmity and kinship relationships at three elementary schools by building social networks of these relationships and studying their properties. Friendship network measurements were similar between schools and produced a Poisson topology with a high clustering index. Enmity network measurements were also similar between schools and produced a power law topology. Spatial confinement and the sense of belonging to a social group played vital roles in shaping these networks. Two models were developed which generate complex friendship and enmity networks that reproduce the properties observed at the three studied elementary schools.