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We state and prove a version of Sharkovskiȋ's theorem for forced interval maps in which the forcing flow is minimal (Birkhoff recurrent). This setup includes quasiperiodically forced interval maps as a special case. We find that it is natural to substitute the concept of "fixed point" with that of "core strip." Core strips are frequently of almost automorphic type.

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This paper concerns the rotation number for a random family of linear non-autonomous Hamiltonian systems. Several definitions corresponding to its analytic and geometrical approaches are presented, and some of its main properties are studied, as its continuity and its relation with the presence of exponential dichotomy.

This study aimed to evaluate the concentrations of copper, iron, and selenium in elderly people with Alzheimer disease (AD), comparing the same parameters in a paired group of healthy people, in order to verify if the amount of these metals may influence the cognitive impairment progression. Patients' cognitive impairment was evaluated by Clinical Dementia Rating (CDR). The elementary quantification of erythrocytes was performed by inductively coupled plasma mass spectrometry technique. The statistical analyses were carried out by SPSS software 20.0 version, employing Shapiro-Wilk, Wilcoxon, Kruskall-Wallis, and Spearman correlation tests, considering significant results of p < 0.05. The sample was composed of 34% (n = 11) of women and 66% (n = 21) of men in each group. The AD group was characterized by a higher concentration of copper (p < 0.0001) and iron (p < 0.0001); however, there is no significant difference in selenium level. The analyses of the metal levels in different stages of AD were not significant in CDR-1, however in CDR-2 and CDR-3, elevated levels of copper and iron were observed; in CDR-3 patients, the level of selenium was lower (p < 0.008) compared to that of healthy controls. Patients with Alzheimer disease studied present increase in biometal blood levels, especially of copper and iron, and such increase can be different according to the disease stage and can cause more impairment cognitive functions in AD.