Self-diffusivity of a large tracer ring polymer, Dr, immersed in a matrix of linear polymers with Nl monomers each shows unusual length dependence. Dr initially increases, and then decreases with increasing Nl. To understand the relationship between the nonmonotonic variation in Dr and threading by matrix chains, we perform equilibrium Monte Carlo simulations of ring-linear blends in which the ...

In this paper, we investigate the recently defined notion of inverse along an element in the context of matrices over a ring. Precisely, we study the inverse of a matrix along a lower triangular matrix, under some conditions.

A ring R is called strongly clean if every element of R is the sum of a unit and an idempotent that commute with each other. A recent result of Borooah, Diesl and Dorsey [3] completely characterized the commutative local rings R for which Mn(R) is strongly clean. For a general local ring R and n > 1, however, it is unknown when the matrix ring Mn(R) is strongly clean. Here we completely determi...

We characterize the pseudo-equivalence of a block lower triangular matrix T = [Tij ] over a regular ring, and its block diagonal matrix D(T ) = [Tii], in terms of suitable Roth consistency conditions. The latter can in turn be expressed in terms of the solvability of certain matrix equations of the form TiiX − Y Tjj = Uij .