In this work, we study two species of predator with two species of prey model, where the two species of prey live in two diverse habitats and have the ability to group-defense. Only one of the two predators tends to switch between the habitats. The mathematical model has at most 13 possible equilibrium points, one of which is the point of origin, two are axial, tow are interior points and the others are boundary points. The model with , where n is the switching index, is discussed regarding the boundedness of its solutions and the local stability of its equilibrium points. In addition, a basin of attraction was created for the interior point. Finally, three numerical examples were given to support the theoretical results.

This study presents an adaptive control scheme based on synergetic control theory for suppressing the vibration of building structures due to earthquake. The control key for the proposed controller is based on a magneto-rheological (MR) damper, which supports the building. According to Lyapunov-based stability analysis, an adaptive synergetic control (ASC) strategy was established under variation of the stiffness and viscosity coefficients in the vibrated building. The control and adaptive laws of the ASC were developed to ensure the stability of the controlled structure. The proposed controller addresses the suppression problem of a single-degree-of-freedom (SDOF) building model, and an earthquake control scenario was conducted and simulat

Baghdad Metro is a vital project to fulfill the rapidly increased traffic volume requirements. The proposed metro will connect both sides of Baghdad City, passing under the Tigris River. This study is employed finite elements software (PLAXIS 3D) to evaluate the seepage force developed around the sub-river segment during different construction stages and for other water levels of Tigris. The study found that when the water level changes from maximum to minimum, the developed seepage force decreases by (8 to 13%) and (22 to 27%) respectively. The seepage forces were found to be maximum during the excavation stage. The concrete lining process led to a noticeable reduction in seepage forces at all locations. The study also

In this research an Artificial Neural Network (ANN) technique was applied for the prediction of Ryznar Index (RI) of the flowing water from WTPs in Al-Karakh side (left side) in Baghdad city for year 2013. Three models (ANN1, ANN2 and ANN3) have been developed and tested using data from Baghdad Mayoralty (Amanat Baghdad) including drinking water quality for the period 2004 to 2013. The results indicate that it is quite possible to use an artificial neural networks in predicting the stability index (RI) with a good degree of accuracy. Where ANN 2 model could be used to predict RI for the effluents from Al-Karakh, Al-Qadisiya and Al-Karama WTPs as the highest correlation coefficient were obtained 92.4, 82.9 and 79.1% respe

This work is concerned with the study of the effect of cement types, particularly OPC and SRPC, which are the main cement types manufactured in Iraq. In addition, study the effect of mineral admixtures, which are HRM and SF on the resistance of high performance concrete (HPC) to internal sulphate attack. The HRM is used at (10%) and SF is used at (8 and 10)% as a partial replacement by weight of cement for both types. The percentages of sulphate investigated are (1,2 and 3)% by adding natural gypsum as a partial replacement by weight of fine aggregate. The tests carried out in this work are: compressive strength, flexural strength, ultrasonic pulse velocity, and density at the age of 7, 28, 90 and 120 days.

The r

    A theoretical calculation of the binding and excitation energies have been used at low – lying energies based on shell model and quantum theory. In this model, we evaluated the energies under assume Ni 28 56 30 as inert core with two nucleon extra, nucleons in the  2P3/2 ,  1f 5/2  and 2P1/2  configuration. Modified Surface Delta Interaction (MSDI) and Reid's Potential (RP) theory for two body matrix elements are evaluated by using a Matlab program to calculate the energies of experimental and Reid single particle energies. Our results of the theoretical calculation have been compared with the experimental results, which show no good agreement with the experiment but have a good agreement wit

  In this paper, we introduce and discuss an algorithm for the numerical solution of two- dimensional fractional dispersion equation.  The algorithm for the numerical solution of this equation is based on explicit finite difference approximation. Consistency, conditional stability, and convergence of this numerical method are described. Finally, numerical example is presented to show the dispersion behavior according to the order of the fractional derivative and we demonstrate that our explicit finite difference approximation is a computationally efficient method for solving two-dimensional fractional dispersion equation

In this paper a stage structure prey-predator model with Hollimg type IV functional response is proposed and analyzed. The local stability analysis of the system is carried out. The occurrence of a simple Hopf bifurcation and local bifurcation are investigated. The global dynamics of the system is investigated with the help of the Lyapunov function. Finally, the analytical obtained results are supported with numerical simulation and the effects of parameters system are discussed. It is observed that, the system has either stable point or periodic dynamics.

This paper is concerned with finding the approximation solution (APPS) of a certain type of nonlinear hyperbolic boundary value problem (NOLHYBVP).  The given BVP is written in its discrete (DI) weak form (WEF), and is proved that  it has a unique APPS, which is obtained via the mixed Galerkin finite element method (GFE) with implicit method (MGFEIM) that reduces the problem to solve the Galerkin nonlinear algebraic system  (GNAS).  In this part, the predictor and the corrector technique (PT and CT) are proved convergent and are used to transform the obtained GNAS to  linear (GLAS ), then the GLAS is solved using the Cholesky method (ChMe). The stability and the convergence of the method are studied. The results