Let R be a commutative ring with nonzero identity and J(R) the Jacobson radical of R. The Jacobson graph of R, denoted by JR, is defined as the graph with vertex set RJ(R) such that two distinct vertices x and y are adjacent if and only if 1 − xy is not a unit of R. The genus of a simple graph G is the smallest nonnegative integer n such that G can be embedded into an orientable surface Sn. In this paper, we investigate the genus number of the compact Riemann surface in which JR can be embedded and explicitly determine all finite commutative rings R (up to isomorphism) such that JR is toroidal., Krishnan Selvakumar, Manoharan Subajini., and Obsahuje seznam literatury
Glyphosate herbicide caused oxidative stress and exhibited negative effects on photosynthesis and gas exchange of peanut [Arachis hypogaea L. cv. Giza (G) 5 and 6] leaves. We demonstrated that glyphosate caused various morphological symptoms, such as chlorosis, yellowing, and appearance of curly edges in leaves treated with high doses of herbicide in both cultivars; however, the G5 cultivar was more sensitive and showed severer symptoms. Glyphosate lowered photosynthesis and reduced contents of pigments and proteins as well as free amino acids in both cultivars. The gas-exchange parameters, such as photosynthetic (P N) and transpiration rate (E), were highly altered by the glyphosate application. For example, P N and E were reduced by 65 and 61%, respectively, in G5 treated with high dose of glyphosate compared with control. Antioxidant enzymes, such as peroxidase, catalase, ascorbate peroxidase, and superoxide dismutase were induced by both low and high concentrations in the glyphosate-treated leaves. Moreover, the level of lipid peroxidation, indicated by a malondialdehyde content, as well as the hydrogen peroxide content increased in the glyphosate-treated leaves. However, an increase in total antioxidant activity was detected in leaves and this reflected changes in the antioxidant status and accumulation of antioxidants as a defense mechanism against glyphosate toxicity in peanut., D. E. M. Radwan , K. A. Fayez., and Obsahuje seznam literatury