New Families of Third-Order Iterative Methods for Finding Multiple Roots

Two families of third-order iterative methods for finding multiple roots of nonlinear equations are developed in this paper. Mild conditions are given to assure the cubic convergence of two iteration schemes (I) and (II). The presented families include many third-order methods for finding multiple roots, such as the known Dong's methods and Neta's method. Some new concrete iterative methods are provided. Each member of the two families requires two evaluations of the function and one of its first derivative per iteration. All these methods require the knowledge of the multiplicity. The obtained methods are also compared in their performance with various other iteration methods via numerical examples, and it is observed that these have better performance than the modified Newton method, and demonstrate at least equal performance to iterative methods of the same order

Novel Colicin F-Y of Yersinia frederiksenii Inhibits Pathogenic Yersinia Strains via YiuR-Mediated Reception, TonB Import, and Cell Membrane Pore Formation

A novel colicin type, designated colicin F-Y, was found to be encoded and produced by the strain Yersinia frederiksenii Y27601. Colicin F-Y was active against both pathogenic and nonpathogenic strains of the genus Yersinia. Plasmid YF27601 (5,574 bp) of Y. frederiksenii Y27601 was completely sequenced. The colicin F-Y activity gene (cfyA) and the colicin F-Y immunity gene (cfyI) were identified. The deduced amino acid sequence of colicin F-Y was very similar in its C-terminal pore-forming domain to colicin Ib (69% identity in the last 178 amino acid residues), indicating pore forming as its lethal mode of action. Transposon mutagenesis of the colicin F-Y-susceptible strain Yersinia kristensenii Y276 revealed the yiuR gene (ykris001_4440), which encodes the YiuR outer membrane protein with unknown function, as the colicin F-Y receptor molecule. Introduction of the yiuR gene into the colicin F-Y-resistant strain Y. kristensenii Y104 restored its susceptibility to colicin F-Y. In contrast, the colicin F-Y-resistant strain Escherichia coli TOP10F' acquired susceptibility to colicin F-Y only when both the yiuR and tonB genes from Y. kristensenii Y276 were introduced. Similarities between colicins F-Y and Ib, similarities between the Cir and YiuR receptors, and the detected partial cross-immunity of colicin F-Y and colicin Ib producers suggest a common evolutionary origin of the colicin F-Y-YiuR and colicin Ib-Cir systems