Let R be a commutative ring with identity and M be unitary (left) R-module. The principal aim of this paper is to study the relationships between relatively cancellation module and multiplication modules, pure submodules and Noetherian (Artinian) modules.

A transdermal drug delivery system (TDDS) is characterized by the application of medications onto the skin's surface to deliver drugs at a controlled and predefined rate through the skin. Spanlastics, an elastic nanovesicle capable of transporting various pharmacological substances, shows promise as a drug delivery carrier. It offers numerous advantages over traditional vesicular systems applied topically, including enhanced stability, flexibility in penetration, and improved targeting capabilities. This study aims to develop meloxicam (MX)-loaded spanlastics gel as skin delivery carriers and to look into the effects of formulation factors like Tween80, Brij 35, and carbopol concentration on the properties of spanlastics gel, like pH, drug

This study was aimed to evaluate atotal phenolic content, antibacterial activity, and antioxidant activity of M. communis callus extracts were evaluated. Callus induction in general Murashige and Skoog (MS) media is completed by the Benzil adenine's unique knowledge of callus formation. A well diffusion experiment was used to examine antibacterial interest in Staphylococcus aureus, Escherichia coli, Klebsiella pneumonia, and Pseudomonas aeruginosa. The DPPH radical scavenging activity test was used to measure antioxidant activity. FTIR and HPLC have been used to pinpoint the presence of polyphenol compounds in calluses. The total phenol content of plant leaves extract (0.1, 0.5, and 1) mg/ml was 42.12, 94.08, and 189 mg of Gallic ac

The interplay of predation, competition between species and harvesting is one of the most critical aspects of the environment. This paper involves exploring the dynamics of four species' interactions. The system includes two competitive prey and two predators; the first prey is preyed on by the first predator, with the former representing an additional food source for the latter. While the second prey is not exposed to predation but rather is exposed to the harvest. The existence of possible equilibria is found. Conditions of local and global stability for the equilibria are derived. To corroborate our findings, we constructed time series to illustrate the existence and the stability of equilibria numerically by varying the different values