In the present paper, an eco-epidemiological model consisting of diseased prey consumed by a predator with fear cost, and hunting cooperation property is formulated and studied. It is assumed that the predator doesn’t distinguish between the healthy prey and sick prey and hence it consumed both. The solution’s properties such as existence, uniqueness, positivity, and bounded are discussed. The existence and stability conditions of all possible equilibrium points are studied. The persistence requirements of the proposed system are established. The bifurcation analysis near the non-hyperbolic equilibrium points is investigated. Numerically, some simulations are carried out to validate the main findings and obtain the critical values of th

This study has contributed to understanding a delayed prey-predator system involving cannibalism. The system is assumed to use the Holling type II functional response to describe the consuming process and incorporates the predator’s refuge against the cannibalism process. The characteristics of the solution are discussed. All potential equilibrium points have been identified. All equilibrium points’ local stability analyses for all time delay values are investigated. The system exhibits a Hopf bifurcation at the coexistence equilibrium, which is further demonstrated. The center manifold and normal form theorems for functional differential equations are then used to establish the direction of Hopf bifurcation and the stability of the per

     Utilizing the Turbo C programming language, the atmospheric earth model is created from sea level to 86 km. This model has been used to determine atmospheric Earth parameters in this study. Analytical derivations of these parameters are made using the balancing forces theory and the hydrostatic equation. The effects of altitude on density, pressure, temperature, gravitational acceleration, sound speed, scale height, and molecular weight are examined. The mass of the atmosphere is equal to about 50% between sea level and 5.5 km. g is equal to 9.65 m/s2 at 50 km altitude, which is 9% lower than 9.8 m/s2 at sea level. However, at 86 km altitude, g is close to 9.51 m/s2, which is close to 15% smaller than 9.8 m/s2.  These resu

Introduction: Elite football performance hinges on rapid tactical decision-making under physical and cognitive strain. While peripheral fatigue’s effects on motor output are well documented, the neurophysiological markers of mental fatigue and their impact on in-game decision making remain underexplored. Objective: To determine how EEG-derived central fatigue indices—frontal theta power and the theta/alpha ratio—relate to tactical decision accuracy and speed in elite football players. Methodology: Twenty male national-level footballers (age 22.4 ± 2.1 years; ≥ 5 years’ experience) completed the Yo-Yo Intermittent Recovery Test Level 1 while wearing an 8-channel dry-electrode frontal EEG headset. Frontal theta

In this paper, we study the incorporation of the commensalism interaction and harvesting on the Lotka–Volterra food chain model. The system provides one commensal prey, one harvested prey, and two predators. A set of preliminary results in local bifurcation analysis around each equilibrium point for the proposed model is discussed, such as saddle-node, transcritical and pitchfork. Some numerical analysis to confirm the accruing of local bifurcation is illustrated. To back up the conclusions of the mathematical study, a numerical simulation of the model is carried out with the help of the MATLAB program. It can be concluded that the system's coexistence can be achieved as long as the harvesting rate on the second prey population is

In this paper we use Bernstein polynomials for deriving the modified Simpson's 3/8 , and the composite modified Simpson's 3/8 to solve one dimensional linear Volterra integral equations of the second kind , and we find that the solution computed by this procedure is very close to exact solution.

This research aims to develop new spectrophotometric analytical method to determine drug compound Salbutamol by reaction it with ferric chloride in presence potassium ferricyanide in acid median to formation of Prussian blue complex to determine it by uv-vis spectrophotmetric at wavelengths rang(700-750)nm . Study the optimal experimental condition for determination drug and found the follows: 1- Volume of(10M) H2SO4 to determine of drug is 1.5 ml . 2- Volume and concentration of K3Fe(CN)6 is 1.5 ml ,0.2% . 3- Volume and concentration of FeCl3 is 2.5ml , 0.2%. 4- Temperature has been found 80 . 5- Reaction time is 15 minute . 6- Order of addition is (drug + K3Fe(CN)6+ FeCl3 + acid) . Concentration rang (0.025-5 ppm) , limit detecti