The dynamical behavior of an ecological system of  two predators-one prey updated with incorporating prey refuge and Beddington –De Angelis functional response had been studied in this work, The essential mathematical features of the present model have been studied  thoroughly. The system has local and global stability when certain conditions are met.  had been  proved respectively.  Further, the system has no saddle node bifurcation but transcritical bifurcation and Pitchfork bifurcation are satisfied while the Hopf bifurcation does not occur. Numerical illustrations are performed  to validate the model's applicability under consideration. Finally, the results are included in the form of points in agreement with the obt

The aim of this paper is the study of the influence magnetic field on steady state
flows and heat transfer in microchannels between two parallel plates.
It is found that the motion equations are controlled by many dimensionless
parameter, namely magnetic field parameter M Reynolds number Re, physical
quantity at wall W and Knudsen number Kn also found that the energy equations
are controlled by many dimensionless parameter, namely magnetic field parameter
M Reynolds number Re, physical quantity at wall W and Knudsen number Kn ,
Prinkman number Br and Peclet number Pe.
The equations which controlled this type of fluid flow are complicated, so finding
an analytical solution is not easy.
We obtained the velocit

        In this paper, the necessary optimality conditions are studied and derived for a new class of the sum of two Caputo–Katugampola fractional derivatives of orders (α, ρ) and( β,ρ) with fixed the final boundary conditions. In the second study, the approximation of the left Caputo-Katugampola fractional derivative was obtained by using the shifted Chebyshev polynomials. We also use the Clenshaw and Curtis formula to approximate the integral from -1 to 1. Further, we find the critical points using the Rayleigh–Ritz method. The obtained approximation of the left fractional Caputo-Katugampola derivatives was added to the algorithm applied to the illustrative example so that we obtained the approximate results for the stat

The aim of this study is to utilize the behavior of a mathematical model consisting of three-species with Lotka Volterra functional response with incorporating of fear and hunting cooperation factors with both juvenile and adult predators. The existence of equilibrium points of the system was discussed the conditions with variables. The behavior of model referred by local stability in nearness of any an equilibrium point and the conditions for the method of approximating the solution has been studied locally. We define a suitable Lyapunov function that covers every element of the nonlinear system and illustrate that it works. The effect of the death factor was observed in some periods, leading to non-stability. To confirm the theore

Some aspects of population dynamics of both corbicula species inhabiting intertidal zone of
shatt al-Arab are described. These informations are explained in accordance with the possible
occurrence of competition between the two related species.

The purpose of this paper is to study the application of Weyl module’s resolution in the case of two rows which will be specified in the partitions (7, 7) and (7, 7) / (1, 0), using the homological Weyl (i.e. the contracting homotopy and place polarization).

The study focuses on Kamez model and the Claus Meyer model of instructional design, which are models that provide the learner with educational experiences to suit the logical information of the learner and the variety of instructional models. Research Objective: The present research aims to identify Limitations of the study. The current research is determined by ((fourth grade preparatory students, the book of the date of the fourth preparatory course)) Chapter II includes Arabic and foreign studies on the model of Kemp and Claus Mayer in the acquisition of concepts and direction towards the material. Chapter III Experimental Design: The researcher adopted an experimental design with two experimental groups and a control group. The resea

In this work, the effects of solvent properties on the characteristics of absorption and fluorescence for two laser dyes was studied. Dyes used in this work include Coumarin 5400 and DCM, while the solvents include ethanol, methanol, acetone, propanol and chloroform. Coumarin 5400 dye shows sharp fluorescence peaks in the green band of visible region while the DCM dye shows relatively wide band within 590-630 nm. Therefore, the selection of any dye for random gain medium applications should be performed after determining the most appropriate solvent as the optimum fluorescence characteristics are obtained.