(4) Let K be a field and M1, M2, M3 be matrices over K. Suppose lenM1 = lenM2 and lenM2 = lenM3 and widthM1 = widthM2 and widthM2 = widthM3 and lenM1 > 0 and M1 + M3 = M2 +M3. Then M1 = M2. (5) For every field K and for all matrices M1, M2 over K such that lenM2 > 0 holds M1 − −M2 = M1 +M2. (6) For every field K and for all matrices M1, M2 over K such that lenM1 = lenM2 and widthM1 = widthM2 an...

in this paper, we introduce a considerable machinery which permits us to characterize a number of special (fuzzy) subsets in ag -groupoids. generalizing the concepts of (,q) -fuzzy bi-ideals (interior ideal), we define ( , ) k q -fuzzy bi-ideals, ( , ) k q -fuzzy left (right)-ideals and ( , ) k q -fuzzy interior ideals in ag -groupoids and discuss some fundamental aspects of these i...

let $r$ be a commutative ring with identity and $mathbb{a}(r)$ be the set   of ideals of $r$ with non-zero annihilators. in this paper, we first introduce and investigate the principal ideal subgraph of the annihilating-ideal graph of $r$, denoted by $mathbb{ag}_p(r)$. it is a (undirected) graph with vertices $mathbb{a}_p(r)=mathbb{a}(r)cap mathbb{p}(r)setminus {(0)}$, where   $mathbb{p}(r)$ is...

objective(s): nanotechnology and nanoparticles are increasingly recognized for their potential applications in aerospace engineering, nanoelectronics, and environmental remediation, medicine and consumer products. more importantly is the potential for the application of silver nanoparticles (ag nps) in the treatment of diseases that require maintenance of circulating drug concentration or targe...

Nanomaterials are widely used in health and biomedical applications, however, only a few studies investigate their toxic effects.  The present report signifies a contribution to the study of the toxic effects of silver nanoparticles on   E. coli cells, which is a model organism of anthropogenic pollution. The toxicity of nanoparticles depends on their chemical and surface properties, shape and ...

Silver nanoparticles (Ag NPs) have been widely used as new potent antimicrobial agents in cosmetic and hygienic products. Present study compares the tissue levels of Ag NPs in different organs of Guiana Pigs quantitatively after dermal application and analysis the morphological changes and pathological abnormalities on the basis of the Ag NPs tissue levels. Before toxicological assessments,the...

In the present study, the extract of the plant of Oenothera biennis was used to green synthesis of silver nanoparticles (Ag NPs) as an environmentally friendly, simple and low cost method. And Additionally, TiO2/SiO2 was prepared via facile sol-gel method using starch as an important, naturally abundant organic polymer as an ideal support. The Ag NPs/TiO2/SiO<su...