Let R be an associative ring with identity, C(R) denote the center of R, and g(x) be a polynomial in the polynomial ring C(R)[x]. R is called strongly g(x)-clean if every element r ∈ R can be written as r = s+u with g(s) = 0, u a unit of R, and su = us. The relation between strongly g(x)-clean rings and strongly clean rings is determined, some general properties of strongly g(x)-clean rings are...

It is well known that every uniquely clean ring is strongly clean. In this paper, we investigate the question of when this result holds element-wise. We first construct an example showing that uniquely clean elements need not be strongly clean. However, in case every corner ring is clean the uniquely clean elements are strongly clean. Further, we classify the set of uniquely clean elements for ...

it is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. in this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.

We presented a simple and direct way to construct unipotent unit clean but not nil-clean element in ring. New examples of unipotent/unit-regular elements that are given. also study the product two idempotents/unit-regulars which unit-regular. The studies exemplified subrings M_2 (Z).

In this paper, a method for through-wall human detection based on the singular values decomposition of the measurement matrices is presented. After demonstrating the sparsity of the matrices using CLEAN algorithm, an SVD algorithm based on Lanczos process is applied to compute their singular values. We also analyze the singular values of matrices constructed by difference square techniques for ...