In this study, we set up and analyze a cancer growth model that integrates a chemotherapy drug with the impact of vitamins in boosting and strengthening the immune system. The aim of this study is to determine the minimal amount of treatment required to eliminate cancer, which will help to reduce harm to patients. It is assumed that vitamins come from organic foods and beverages. The chemotherapy drug is added to delay and eliminate tumor cell growth and division. To that end, we suggest the tumor-immune model, composed of the interaction of tumor and immune cells, which is composed of two ordinary differential equations. The model’s fundamental mathematical properties, such as positivity, boundedness, and equilibrium existence, are exami

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

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.

The goal of this investigation is to prepare zinc oxide (ZnO) nano-thin films by pulsed laser deposition (PLD) technique through Q-switching double frequency Nd:YAG laser (532 nm) wavelength, pulse frequency 6 Hz, and 300 mJ energy under vacuum conditions (10-3 torr) at room temperature. (ZnO) nano-thin films were deposited on glass substrates with different thickness of 300, 600 and 900 nm. ZnO films, were then annealed in air at a temperature of 500 °C for one hour. The results were compared with the researchers' previous theoretical study. The XRD analysis of ZnO nano-thin films indicated a hexagonal multi-crystalline wurtzite structure with preferential growth lines (100), (002), (101) for ZnO nano-thin films with different thi

Optimum perforation location selection is an important study to improve well production and hence in the reservoir development process, especially for unconventional high-pressure formations such as the formations under study. Reservoir geomechanics is one of the key factors to find optimal perforation location. This study aims to detect optimum perforation location by investigating the changes in geomechanical properties and wellbore stress for high-pressure formations and studying the difference in different stress type behaviors between normal and abnormal formations. The calculations are achieved by building one-dimensional mechanical earth model using the data of four deep abnormal wells located in Southern Iraqi oil fields. The magni