in this work we develop a new optimal without memory class for approximating a simple root of a nonlinear equation. this class includes three parameters. therefore, we try to derive some with memory methods so that the convergence order increases as high as possible. some numerical examples are also ‎presented.‎‎

A binary matrix is a matrix with entries from the set {0, 1}. We say that a binary matrix A contains a binary matrix S if S can be obtained from A by removal of some rows, some columns, and changing some 1-entries to 0-entries. If A does not contain S, we say that A avoids S. A k-permutation matrix P is a binary k× k matrix with exactly one 1-entry in every row and one 1-entry in every column. ...

This paper studies the vanishing of $Ext$ modules over group rings. Let $R$ be a commutative noetherian ring and $ga$ a group. We provide a criterion under which the vanishing of self extensions of a finitely generated $Rga$-module $M$ forces it to be projective. Using this result, it is shown that $Rga$ satisfies the Auslander-Reiten conjecture, whenever $R$ has finite global dimension and $ga...