We investigate the occurrence of critical energies—where the Lyapunov exponent vanishes—in random Schrödinger operators when the potentials have some local order, which we call random palindrome models. We give necessary and sufficient conditions for the presence of such critical energies: the commutativity of finite word elliptic transfer matrices. Finally, we perform some numerical calculations of the Lyapunov exponents showing their behavior near the critical energies and the respective time evolution of an initially localized wave packet, obtaining the exponent ruling the algebraic growth of the second momentum. We also consider special random palindrome models with one-letter bounded gap property; the transport effects of such long range order are showed numerically.

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This study evaluated the quantity of total aerobic bacteria, total coliform and Escherichia coli in samples of the Nile tilapia fillet (Oreochromis niloticus) and in water samples at different stages of a tilapia production chain in Brazil. Furthermore, the effect of temperature on the number of such bacterial groups in the fillet and water samples, and the impact of the type of tank, net cages or ponds, during the fattening stage of tilapia on bacterial quantification was ascertained. A generalized linear model with negative binomial distribution was used, aiming to assess the influence of predictor variables like climate season and type of tank, with interaction term, on bacterial counts. Analysis of the results showed that, for water samples, the highest scores of all bacterial groups evaluated were obtained at debugging stage. Additionally, the increase in temperature positively influenced the counting of bacteria, both in water and in fillet samples. Moreover, microbial quantification in fillet samples did not only result from the bacteria present in the animal growth water sites, but also from intrinsic factors involved in the slaughter and filleting processes. In relation to the type of tank, EC and AB counts were significantly lower in net cages than in ponds. In conclusion, the results of this study indicate the need for deployment of additional care, especially at debugging stage, aiming to obtain safer fillets for consumption. Furthermore, in the event of increased temperature, greater attention should be given to the slaughter and filleting processes.

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