The food web is a crucial conceptual tool for understanding the dynamics of energy transfer in an ecosystem, as well as the feeding relationships among species within a community. It also reveals species interactions and community structure. As a result, an ecological food web system with two predators competing for prey while experiencing fear was developed and studied. The properties of the solution of the system were determined, and all potential equilibrium points were identified. The dynamic behavior in their immediate surroundings was examined both locally and globally. The system’s persistence demands were calculated, and all conceivable forms of local bifurcations were investigated. With the aid of MATLAB, a numerical simu

 In this study, we derived the estimation for Reliability of the Exponential distribution based on the Bayesian approach. In the Bayesian approach, the parameter of the Exponential distribution is assumed to be random variable .We  derived  posterior distribution the parameter of the Exponential distribution under four types priors distributions for the scale parameter of the Exponential distribution is: Inverse Chi-square distribution, Inverted Gamma distribution, improper distribution, Non-informative distribution. And the estimators for Reliability is obtained using the two proposed loss function in this study which is based on the natural logarithm for Reliability function .We used simulation technique, to compare the

A mathematical eco-epidemiological model consisting of harvested prey–predator system involving fear and disease in the prey population is formulated and studied. The prey population is supposed to be separated into two groups: susceptible and infected. The susceptible prey grows logistically, whereas the infected prey cannot reproduce and instead competes for the environment’s carrying capacity. Furthermore, the disease is transferred through contact from infected to susceptible individuals, and there is no inherited transmission. The existence, positivity, and boundedness of the model’s solution are discussed. The local stability analysis is carried out. The persistence requirements are established. The global behavior of th

      In this work, a weighted H lder function that approximates a Jacobi polynomial which solves the second order singular Sturm-Liouville equation is discussed. This is generally equivalent to the Jacobean translations and the moduli of smoothness. This paper aims to focus on improving methods of approximation and finding the upper and lower estimates for the degree of approximation in weighted H lder spaces by modifying the modulus of continuity and smoothness. Moreover, some properties for the moduli of smoothness with direct and inverse results are considered.

            This paper is interested in certain  subclasses of univalent and bi-univalent functions concerning  to shell- like curves connected with k-Fibonacci numbers involving modified Sigmoid activation function θ(t)=2/(1+e^(-t) ) ,t ≥0 in unit disk |z|<1 . For estimating of the initial coefficients |c_2 | , |c_3 |, Fekete-Szego ̈ inequality and the  second Hankel determinant have been investigated for the functions in our classes. 

In this study, a factorial experiment was conducted using a Randomized Complete Block Design (RCBD) with three replicates to investigate the effects of silicon at four concentrations: 0, 2, 4, and 6 ml/L, designated as S0, S1, S2, and S3, respectively and a calcium-boron combination at three concentrations: 0, (0.5 g/L Ca-EDTA, + 10 mg/L B), and (1 g/L Ca-EDTA, + 20 mg/L B), designated as C0, C1, and C2, respectively. on the activity of antioxidant enzymes and some qualitative traits of fruits. The results indicated that the studied traits were significantly influenced by the factors. Silicon application notably increased enzyme activity, treatment S3 showed the highest activity levels for peroxidase (POD) and superoxide dismutase (SOD) rea

Geographical, economic, historical, environmental and security factors play a role in strengthening the drive towards union, as well as addressing the need to express regional and federal identity. This is a clear example of this tendency. One legal or one political system with the parts of this united personality retaining their privacy and identity, and there is a delegation to the central entity of the union with some of the common powers while retaining some powers for these parts or states, which means the availability of autonomy for the constituent states of the union and this is the most important characteristic of the federal states or federations It is the autonomy of each state or country participating in the union. Accordingly,