In this paper, a discrete- time ratio-dependent prey- predator model is proposed and analyzed. All possible fixed points have been obtained. The local stability conditions for these fixed points have been established. The global stability of the proposed system is investigated numerically. Bifurcation diagrams as a function of growth rate of the prey species are drawn. It is observed that the proposed system has rich dynamics including chaos.

The rheological and fusion behavior of polyvinyl chloride (PVC) compounds plays a dominant role in
the processing operations and in the development of physical properties in the processed material. A
comprehensive study was made in this work to evaluate the effect of shear and thermal history on stability, mechanical and rheological properties of rigid PVC compounds. Different samples of Rigid Poly vinyl chloride including dry blend powder, granules, and bottles molded from both were examined. A study was also made on recycled RPVC where 25% of reclaimed material was continuously blended with fresh dry blend and processed for 15 cycles. Results showed that compaction of the PVC material took place in the brabender plastograph at co

In this paper, a numerical approximation for a time fractional one-dimensional bioheat equation (transfer paradigm) of temperature distribution in tissues is introduced. It deals with the Caputo fractional derivative with order for time fractional derivative and new mixed nonpolynomial spline for second order of space derivative. We also analyzed the convergence and stability by employing Von Neumann method for the present scheme.

The estimation of recharge to ground water is the important basics to improve the use of ground water with other available resources, and to save ground water resource from depletion, especially when using large quantity of ground water during a long time such as for agricultural purposes. Al-Wand River Basin in Iraq suffers from water shortage of its requirement of Blajo–Al-Wand Project, and to cover this shortage, the ground water plays a good role to overcome this problem. In this study, three methods were used to estimate the recharge and ground water storage for Al-Wand Basin, these methods are: Water Table Fluctuation (WTF), Water Balance of Climatic for Basin, and Water Table Balance for Basin. The results showe

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% respectively. For

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

Background : To assess the actual practice of breast self-examination (BSE), as an early detection tool for breast cancer, among a sample of patients affected with breast cancer in Iraq.Methods: A random sample of 200 female patients with breast cancer was analyzed to evaluate the extent of their actual practice of breast self-examination before the diagnosis of the disease.  The examined variables included the age of the patients, marital status, education, occupation, smoking habit, family history of cancer, frequency of gravidity, parity and abortions. Results: The age of patients ranged from (24-70) years with a mean age of 48 years. The highest frequency of the examined sample

The current study included the anatomical structure of the metatarsal bone in sheep in terms of the traditional structural description of the bone, as it was found that the metatarsal bone in the fore and hind limbs of adult sheep had no visible differences between it and animals, especially ruminants. The metacarpal \tarsal bone No. 3 was cylindrical in shape, with the presence of the metacarpal \tarsal bones 2 and 4 declines, articulated from the proximal end with the metacarpal and metatarsal bones whereas from the distal part with the fetlock joint and the first phalanx bone. The aim of the study is to determine whether the environment and its changes in Iraq have affected the animals and their bones in terms of length, thicknes

  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

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