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We obtain a fixed point theorem for a type of generalized contractions on preordered complete fuzzy quasi-metric spaces which is applied to deduce, among other results, a procedure to show in a direct and easy fashion the existence of solution for the recurrence equations that are typically associated to Quicksort and Divide and Conquer algorithms, respectively.

In this paper we obtain a generalization of Theorem 3 to preordered fuzzy quasi-metric spaces which is applied to deduce, among other results, a procedure to show in a direct and easy way the existence of solution for the recurrence equations that are typically associated to Quicksort and Divide and Conquer algorithms, respectively.

Notes: *The total deduced amino acid numbers are different from the sum of each gene because we presented the consensus deduced amino acid sequences among the species.

The deduced amino acid sequence is conserved among the reported AADs.

The deduced amino acid sequence is conserved among the reported PDIs.

HA gene nucleotide sequences and deduced amino acid (AA) sequence identities among the 35 tested strains ranged from 84.0 to 100.0% and 89.1 to 100.0%, respectively.

The deduced amino acid sequences showed 40.5 % similarity among the three genes.

The deduced amino acid sequence containing a motif (Cys-Gly-Pro-Cys) that is highly conserved among the reported Trxs.

Conserved core region of the K. setae genome predicted by threading major synteny blocks was ∼5 Mb in length ranging from KSE_13770 to KSE_57600, which is ∼1 Mb smaller than the core regions deduced from comparison among Streptomyces genomes.

mtDNA Bayesian inference and parsimony trees showed the same overall topology, which agreed with the among-species relationships deduced from nuclear histone H3 sequences (see Figures 2 and 3 for the mitochondrial Bayesian trees and Figure S1 in Additional file 1: for the combined tree).

Importantly, these predicted cleavages on both sides of the dyad axis are among those deduced by Brogaard et al. from their empirical in vivo data (Brogaard et al., 2012b), and confirmed by cleavage mapping of reconstituted octasomes.

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