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...

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...

3.1 PRODUCTION OF CLEAN SYNTHESIS GAS......................................................................... 9 3.1.1 Biomass Gasification .............................................................................................. 9 3.1.2 Gas Cleanup.......................................................................................................... 10 3.2 CONVERSION OF SYNTHESIS GAS T...

This paper is intended as a first step in a program for a full algorithmic enumeration of lattice 3-polytopes. The program is based in the following two facts, that we prove: • For each n there is only a finite number of (equivalence classes of) 3polytopes of lattice width larger than one, where n is the number of lattice points. Polytopes of width one are infinitely many, but easy to classify....

INTRODUCTION Adrenocortical activity in various species is sensitive to androgens and estrogens. They may affect adrenal cortex growth and functioning either via central pathways (CRH and ACTH) or directly, via specific receptors expressed in the cortex and/or by interfering with adrenocortical enzymes, among them those involved in steroidogenesis. Only limited data on expression of androgen an...