A modified Leslie-Gower predator-prey model with a Beddington-DeAngelis functional response is proposed and studied. The purpose is to examine the effects of fear and quadratic fixed effort harvesting on the system's dynamic behavior. The model's qualitative properties, such as local equilibria stability, permanence, and global stability, are examined. The analysis of local bifurcation has been studied. It is discovered that the system experiences a saddle-node bifurcation at the survival equilibrium point whereas a transcritical bifurcation occurs at the boundary equilibrium point. Additionally established are the prerequisites for Hopf bifurcation existence. Finally, using MATLAB, a numerical investigation is conducted to verify t

A modified Leslie-Gower predator-prey model with a Beddington-DeAngelis functional response is proposed and studied. The purpose is to examine the effects of fear and quadratic fixed effort harvesting on the system's dynamic behavior. The model's qualitative properties, such as local equilibria stability, permanence, and global stability, are examined. The analysis of local bifurcation has been studied. It is discovered that the system experiences a saddle-node bifurcation at the survival equilibrium point whereas a transcritical bifurcation occurs at the boundary equilibrium point. Additionally established are the prerequisites for Hopf bifurcation existence. Finally, using MATLAB, a numerical investigation is conducted to verify the va

In a connected graph , the distance function between each pair of two vertices from a set vertex  is the shortest distance between them and the vertex degree  denoted by  is the number of edges which are incident to the vertex  The Schultz and modified Schultz polynomials of  are have defined as:

 respectively, where the summations are taken over all unordered pairs of distinct vertices in  and  is the distance between  and  in  The general forms of Schultz and modified Schultz polynomials shall be found and indices of the edge – identification chain and ring – square graphs in the present work.

      The main problem when dealing with fuzzy data variables is that it cannot be formed by a model that represents the data through the method of Fuzzy Least Squares Estimator (FLSE) which gives false estimates of the invalidity of the method in the case of the existence of the problem of multicollinearity. To overcome this problem, the Fuzzy Bridge Regression Estimator (FBRE) Method was relied upon to estimate a fuzzy linear regression model by triangular fuzzy numbers. Moreover, the detection of the problem of multicollinearity in the fuzzy data can be done by using Variance Inflation Factor when the inputs variable of the model crisp, output variable, and parameters are fuzzed. The results were compared usin

Epoxy (EP) – Silica (SiO2) composites are well known composites used in microelectronic industry . So it is important to study their dielectric behavior under different conditions such as
the presence carbon black (UV absorber) and immersion in the water for 30 days .
Dielectric properties were calculated over the frequency range 102 – 106 Hz for epoxy composites with different weight % of micrometer 1.5μm SiO2 particles (60%, 65% and 70wt%) modified with 0.5wt% silane coupling agent to improve adhesion between EP and SiO2 phases .

   This study includes Estimating scale parameter, location parameter  and reliability function  for Extreme Value (EXV) distribution by two methods, namely: -
- Maximum Likelihood Method (MLE).
- Probability Weighted Moments Method (PWM).

 Used simulations to generate the required samples to estimate the parameters and reliability function of different sizes(n=10,25,50,100) , and give real values for the parameters are and , replicate the simulation experiments (R_P=1000)