We prove a large deviation result for return times of the orbits of a dynamical system in a r-neighbourhood of an initial point x. Our result may be seen as a differentiable version of the work by Jain and Bansal who considered the return time of a stationary and ergodic process defined in a space of infinite sequences.
We investigate the length of the longest common substring for encoded sequences and its asymptotic behaviour. The main result is a strong law of large numbers for a re-scaled version of this quantity, which presents an explicit relation with the Rényi entropy of the source. We apply this result to the zero-inflated contamination model and the stochastic scrabble. In the case of dynamical systems, this problem is equivalent to the shortest distance between two observed orbits and its limiting relationship with the correlation dimension of the pushforward measure. An extension to the shortest distance between orbits for random dynamical systems is also provided.keywords: string matching, Rényi entropy, shortest distance, correlation dimension, random dynamical systems, coding MSC: 60F15, 60Axx, 60C05, 37A50, 37A25, 37Hxx, 37C45, 94A17, 68P30
Nanocrystalline hydroxyapatite was prepared by a precipitation method with add of ultrasonic
irradiation. In this work the effect of H3PO4 addition rate during synthesis and the influence of
the magnesium incorporation into apatite were studded. The results revealed that the morphology
and cristalinity of synthesized nanopowders are significantly affected by ultrasonic irradiation. Monophase
hydroxyapatite was obtained when magnesium was added into HA lattice during the synthesis
with ultrasonic irradiation.
A busca por melhores propriedades mecânicas e maior confiabilidade de cerâmicas à base de Si3N4 faz com que seus compósitos sejam desenvolvidos e intensivamente estudados. A maioria das pesquisas realizadas foca as interações e propriedades mecânicas obtidas, mas interações químicas entre as fases foram pouco estudadas. O objetivo deste trabalho é estudar as interações químicas que ocorrem durante a sinterização do compósito Si3N4-20%vol. TiC. A cinética de sinterização foi estudada por dilatometria, com patamar a 1750 °C/1 h em atmosfera dinâmica de N2. Os resultados de dilatometria indicam alterações na cinética de sinterização, quando comparado ao Si3N4 monolítico. Para avaliar as fases que se formam em temperaturas intermediárias, os compósitos foram tratados termicamente entre 1400 °C e 1850 °C. As amostras foram caracterizadas por difração de raios X. Foi observada a formação da solução sólida TiCN e da fase SiC.
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