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In the context of nonextensive Tsallis statistics, sensible examples are employed in order to compare the variational method proposed in Phys. Rev. Lett. 80 (1998) 218 with the one in J. Phys. A 26 (1993) L893. These examples are such that they can be solved exactly. Thus, a comparison of the exact result with the approximated ones is possible. The analysis of these examples indicates that the calculation related to the first variational method is easier to work with than the other method. In particular, when one is trying to apply the last variational method, the calculation of the approximated case can be more cumbersome than solving the exact one. [Copyright &y& Elsevier]

In a comparative study, the q-exponential and Weibull distributions are employed to investigate frequency distributions of basketball baskets, cyclone victims, brand-name drugs by retail sales, and highway length. In order to analyze the intermediate cases, a distribution, the q-Weibull one, which interpolates the q-exponential and Weibull ones, is introduced. It is verified that the basketball baskets distribution is well described by a q-exponential, whereas the cyclone victims and brand-name drugs by retail sales ones are better adjusted by a Weibull distribution. On the other hand, for highway length the q-exponential and Weibull distributions do not give satisfactory adjustment, being necessary to employ the q-Weibull distribution. Furthermore, the introduction of this interpolating distribution gives an illumination from the point of view of the stretched exponential against inverse power law (q-exponential with q>1) controversy. [Copyright &y& Elsevier]

We report on the time dependent solutions of the q -generalized Schrödinger equation proposed by Nobre et al. (2011). Here we investigate the case of two free particles and also the case where two particles were subjected to a Moshinsky-like potential with time dependent coefficients. We work out analytical and numerical solutions for different values of the parameter q and also show that the usual Schrödinger equation is recovered in the limit of q → 1 . An intriguing behavior was observed for q = 2 , where the wave function displays a ring-like shape, indicating a bind behavior of the particles. Differently from the results previously reported for the case of one particle, frozen states appear only for special combinations of the wave function parameters in case of q = 3 . [ABSTRACT FROM AUTHOR]

Abstract: In this work, we address modal parameter fluctuations in statistical distributions describing charge-to-breakdown and/or time-to-breakdown during the dielectric breakdown regime of ultra-thin oxides, which are of high interest for the advancement of electronic technology. We reobtain a generalized Weibull distribution (q-Weibull), which properly describes data when oxide thickness fluctuations are present, in order to improve reliability assessment of ultra-thin oxides by time-to-breakdown extrapolation and area scaling. The incorporation of fluctuations allows a physical interpretation of the q-Weibull distribution in connection with the Tsallis statistics. In support to our results, we analyze data of -based MOS devices obtained experimentally and theoretically through a percolation model, demonstrating an advantageous description of the dielectric breakdown by the q-Weibull distribution. [Copyright &y& Elsevier]