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...

For x real, let {x} be the fractional part of x (i.e. {x} = x − bxc). In this paper we prove the k = 5 case of the following conjecture (the lonely runner conjecture): for any k positive reals v1, . . . , vk there exists a real number t such that 1/(k + 1) ≤ {vit} ≤ k/(k + 1) for i = 1, . . . , k.

We consider the problem whether a permutation of a finite set is uniquely determined by its identification minors. While there exist non-reconstructible permutations of every set with two, three, or four elements, we show that every permutation of a finite set with at least five elements is reconstructible from its identification minors. Moreover, we provide an algorithm for recovering a permut...

Motivated by an old problem known as Ryser’s Conjecture, we prove that for r = 4 and r = 5, there exists > 0 such that every r-partite r-uniform hypergraph H has a cover of size at most (r − )ν(H), where ν(H) denotes the size of a largest matching in H.