The inhibitory behavior of L-Cysteine (Cys) and its derivatives towards iron corrosion through density functional theory (DFT) was investigated. The current research study undertakes a rigorous evaluation of global as well as local reactivity descriptors of the Cys in protonated as well as neutral forms and the changes in reactivity after the combination of Cys into di- and tripeptides. The inhibitory effect of di- and tri-peptides increases since, in the molecular structure, the number of reaction centers increase. We computed the adsorption energies (Eads) and low energy complexes with most stability for the adsorption of small peptides and Cys amino acids onto the surfaces of Fe (1 1 1). We found that the adsorption of tri-peptides onto

In this work, we study several features of the non-zero divisor graphs (ℵZD- graph) for the ring Zn of integer modulo n. For instance, the clique number, radius, girth, domination number, and the local clustering coefficient are determined. Furthermore, we present an algorithm that calculates the clique number and draws the non-zero divisor for the ring Zn.

Premature degradation is the problem of maxillofacial silicones, significantly affected by ultraviolet exposure, contributing to silicones photodegradation. Degradation necessitates frequent replacement of prostheses that increase the total cost of rehabilitation.

Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.