r is called commuting regular ring (resp. semigroup) if for each x,y $in$ r thereexists a $in$ r such that xy = yxayx. in this paper, we introduce the concept of commuting$pi$-regular rings (resp. semigroups) and study various properties of them.

Abstract We present some accelerated variants of fixed point iterations for computing the minimal non-negative solution unilateral matrix equation associated with an M/G/1-type Markov chain. These derive from certain staircase regular splittings block Hessenberg M-matrix By exploiting profile, we introduce a two-step iteration. The iteration can be further by weighted average between approximat...

We introduce a family of local inhomogeneous mark-weighted summary statistics, order two and higher, for general marked point processes. Depending on how the involved weight function is specified, these statistics capture different kinds dependence structures. first derive some basic properties show new statistical tools can be used to construct most existing (marked) then propose test random l...