Optimization is essentially the art, science and mathematics of choosing the best among a given set of finite or infinite alternatives. Though currently optimization is an interdisciplinary subject cutting through the boundaries of mathematics, economics, engineering, natural sciences, and many other fields of human Endeavour it had its root in antiquity. In modern day language the problem mathematically is as follows - Among all closed curves of a given length find the one that closes maximum area. This is called the Isoperimetric problem. This problem is now mentioned in a regular fashion in any course in the Calculus of Variations. However, most problems of antiquity came from geometry and since there were no general methods to solve suc

This article examines and proposes a dietary chain model with a prey shelter and alternative food sources. It is anticipated that mid-predators' availability is positively correlated with the number of refuges. The solution's existence and exclusivity are examined. It is established that the solution is bounded. It is explored whether all potential equilibrium points exist and are locally stable. The Lyapunov approach is used to investigate the equilibrium points' worldwide stability. Utilizing a Sotomayor theorem application, local bifurcation is studied. Numerical simulation is used to better comprehend the dynamics of the model and define the control set of parameters.

This in vivo study was conducted to investigate the effect of different concentrations of ozonated water on experimentally skin infection with some of bacterial isolates (Pseudomonas aeruginosa and Staphylococcus aureus ) which Showed dermal infection in experimental animals after 48 hours of exposure to these Microorganisms. Results revealed that ozone has the power to accelerated the healing process depending on the perfect concentration of ozonated water used and the severity of infection & nature of causative agent , in which the recovering period was 7 days for the infection caused by P. aeruginosa and 5 day for S.aureus by using the concentration 60 µg/ml . Results also indicated in this study the stimulated effect of O

Background: Radiotherapy, is therapy using ionizing radiation in order to deliver an optimal dose of either particulate or electromagnetic radiation to a particular area of the body with minimal damage to normal tissues. The source of radiation may be outside the body of the patient (external beam irradiation) or it may be an isotope that has been implanted or instilled into abnormal tissue or a body cavity. Called also radiotherapy. The aim of work studies the relationship between the depth dose and the high photon xray energies (6MeV and 10MeV). Patients and methods: in our work, we studied the dose distribution in water phantom given at different depths (zero-18) cm deep at1cm intervals treated with different field size (5×5-,10×1

The study of Lake Hamrin is of enormous importance in understanding changes in water levels and their impact on the local environment. It helps to clarify the role of climatic and human factors in the decline of its water resources from 2013 to 2023 in order to ensure sustainable solutions. Satellite imagery from Landsat 8 is used, and processing is performed using ArcGIS Pro and ENVI. The normalized vegetation index (NDVI) is applied to show the changes in the vegetation cover and reveal the amount of change in the surface water area of the lake. It is noted that the water area changes in one year as it increases in the rainy season and decreases in the summer, and it also varies from one year to another with the difference in the amount o

The aim of this study to evaluate the effects of die holes diameter and speed of die on the performance of machine and feed pellet quality. Machine productivity (Kg.h-1), consumed power (kW), pellet durability (%) and pellet bulk density (g.cm-3) was studied. The study factors consisted of three diameter of die holes (3, 4, and 5 mm), and three speeds die (280, 300, and 320 rpm). Results showed with increasing of die holes diameter from 3 to 4 and to 5 mm give a significant increase in machine productivity, while consumed power, pellet durability and pellet bulk density a significant decreased. By increasing the die speed, from 280 to 300 then to 320 rpm, the machine productivity increased significantly, while consumed power, pellet durabil

Water pollution is one of the global challenges that the society must address in the 21^st century aiming to improve the water quality, reduce human pollutants and ecosystem health impacts. In phytotoxicity test, the plant of Iresine herbstii was exposed to remove nickel from simulated wastewater using two different ratios (mass of plant to the mass of nickel) (,R_p/Ni) for 21 days with sub-surface batch system. During the exposure period, the removal of Ni concentrations (2, 5 and 10 mg/L) for two mass ratio (2,800 and 34,000) were (83.6%, 77.2%, 78.0%) and (86.8%, 97% and 95.6%), respectively. final result of the rate was found that the highest removal occurred, 97%, at a mass ratio of 34,000 and