In this paper, we introduce the new notion of strongly J-clean rings associated with polynomial identity g(x) = 0, as a generalization of strongly J-clean rings. We denote strongly J-clean rings associated with polynomial identity g(x) = 0 by strongly g(x)-J-clean rings. Next, we investigate some properties of strongly g(x)-J-clean.

We track multiple human subjects using ultra-wide band (UWB) radar based on their target signatures. To resolve the correspondence problem, the use of CLEAN algorithm is proposed. Walking two human subjects are measured by UWB radar. The feasibility of classification is investigated using the suggested method.

In this paper, we introduce the new notion of n-f-clean rings as a generalization of f-clean rings. Next, we investigate some properties of such rings. We prove that $M_n(R)$ is n-f-clean for any n-f-clean ring R. We also, get a condition under which the denitions of n-cleanness and n-f-cleanness are equivalent.

We prove a relationship between the Cleaning problem and the Balanced Vertex– Ordering problem, namely that the minimum total imbalance of a graph equals twice the brush number of a graph. This equality has consequences for both problems. On one hand, it allows us to prove the NP-completeness of the Cleaning problem, which was conjectured by Messinger et al. [7]. On the other hand, it also enab...

Linear depolarization ratios in clean air ranges were measured with POLIS-6 at 355 and 532 nm. The mean deviation from the theoretical values, including the rotational Raman lines within the filter bandwidths, amounts to 0.0005 at 355 nm and to 0.0012 at 532 nm. The mean uncertainty of the measured linear depolarization ratio of clean air is about 0.0005 at 355 nm and about 0.0006 at 532 nm.

A ring $R$ with identity is called ``clean'' if $~$for every element $ain R$, there exist an idempotent $e$ and a unit $u$ in $R$ such that $a=u+e$. Let $C(R)$ denote the center of a ring $R$ and $g(x)$ be a polynomial in $C(R)[x]$. An element $rin R$ is called ``g(x)-clean'' if $r=u+s$ where $g(s)=0$ and $u$ is a unit of $R$ and, $R$ is $g(x)$-clean if every element is $g(x)$-clean. In this pa...