even though, to date, a lot of studies have been conducted on the subject of politeness theory, there are very few studies regarding the applicability of this theory to translation between english and persian which shows the reason behind conducting the present study. this study was carried out with the aim of highlighting whether there is any difference between english and persian methods of u...

Doubly stochastic matrices play a fundamental role in the theory of majorization. Birkhoff's theorem explains the relation between $ntimes n$ doubly stochastic matrices and permutations. In this paper, we first introduce double-null  operators and we will find some important properties of them. Then with the help of double-null operators, we investigate Birkhoff's theorem for descreate $l^p$ sp...