Using a mathematical model to simulate the interaction between prey and predator was suggested and researched. It was believed that the model would entail predator cannibalism and constant refuge in the predator population, while the prey population would experience predation fear and need for a predator-dependent refuge. This study aimed to examine the proposed model's long-term behavior and explore the effects of the model's key parameters. The model's solution was demonstrated to be limited and positive. All potential equilibrium points' existence and stability were tested. When possible, the appropriate Lyapunov function was utilized to demonstrate the equilibrium points' overall stability. The system's persistence requirements were spe

The present paper investigates the role of fear and predator dependent refuge in the prey-predator system. The system describes the interaction between prey and a stage structure of predator that incorporates Holling II functional response. The predator splits into two compartments immature (juvenile) and mature (adult). The mature predators can hunt and reproduce but this capability is not found in the immature predators, the immature depend on their parents. The growth rate of prey decreases due to the existence of mature predators. The existence, uniqueness, and boundedness of the solution of the system are investigated. Three equilibrium points of the system are determined. The local stability of the system is studied. The global stabil

Mesoporous silica (MPS) nanoparticle was prepared as carriers for drug delivery systems by sol–gel method from sodium silicate as inexpensive precursor of silica and Cocamidopropyl betaine (CABP) as template. The silica particles were characterized by SEM, TEM, AFM, XRD, and N2adsorption–desorption isotherms. The results show that the MPS particle in the nanorange (40-80 nm ) with average diameter equal to 62.15 nm has  rods particle morphology, specific surface area is 1096.122 m²/g, pore volume 0.900 cm³/g, with average pore diameter 2.902 nm, which can serve as efficient carriers for drugs. The adsorption kinetic of Ciprofloxacin (CIP) drug was studied and the data were analyzed and found to match well with

The necessary optimality conditions with Lagrange multipliers  are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time  and the final state  are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.

In solar-thermal adsorption/desorption processes, it is not always possible to preserve equal operating times for the adsorption/desorption modes due to the fluctuating supply nature of the source which largely affects the system’s operating conditions. This paper seeks to examine the impact of adopting unequal adsorption/desorption times on the entire cooling performance of solar adsorption systems. A cooling system with silica gel–water as adsorbent-adsorbate pair has been built and tested under the climatic condition of Iraq. A mathematical model has been established to predict the system performance, and the results are successfully validated via the experimental findings. The results show that, the system can be operational

This study aims at identifying the correlation between digital transformation and knowledge building in educational institutions, as well as finding the influence relationship between digital transformation and knowledge building in educational institutions and knowing the dimensions of digital transformation that have the most impact in improving the level of knowledge building, and by adopting the methodological descriptive analysis method in the Ministry of Education. Education and educational institutions in Baghdad. This research deals with digital transformation as an independent variable according to two dimensions (digital adaptability and digital readiness). Knowledge building was adopted as an approved variable using the s