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.

Asia and Middle East represent one of the most dynamic regions in the world which has experienced fast economic and technological growth. Access to clean and affordable water is essential for building resilience and maintaining human’s well-being and livelihood development in this region. Likewise, various energy resources are fundamental to support stable economic and social progress for bette...

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...

Renewable energy can help to tackle energy poverty issues of the availability of modern energy services and the sustainability of energy supply. Based on the concept of the Energy Development Index, published by International Energy Agency, this paper builds the clean energy development index and applies the Grey incidence decision method to analyze regional energy poverty issues in China. A mo...

I begin with the proposition that eating is an agricultural act. Eating ends the annual drama of the food economy that begins with planting and birth. Most eaters, however, are no longer aware that this is true. They think of food as an agricultural product, perhaps, but they do not think of themselves as participants in agriculture. They think of themselves as “consumers.” If they think beyond...

A study is presented of a possible future measurement of the longitudinal structure function FL(x,Q ) with different proton beam energies at HERA. To appear in the proceedings of the workshop “Future Physics at HERA”, DESY, Hamburg, 1996. Future Measurement of the Longitudinal Proton Structure Function at HERA L.A.T. Bauerdick, A. Glazov, M. Klein a DESY, Notkestraße 85, D-22607 Hamburg, German...