Pure and doped barium titanate with Mg2+ ion at two molar ratios x= (5%, 10%) mol. has been synthesized by solid state reaction technique. The powders sintered at two temperatures (1000 °C and 1400 °C). An XRD technique was used in order to study the crystal structure of pure and doped barium titanate, which confirmed the formation of the tetragonal phase of BaTiO3, and then calculate the lattice parameters of pure and doped barium titanate, the addition of magnesium ion Mg2+ can lead to decreases lattice parameters.

This study presents a mathematical model describing the interaction of gut bacteria in the participation of probiotics and antibiotics, assuming that some good bacteria become harmful through mutations due to antibiotic exposure. The qualitative analysis exposes twelve equilibrium points, such as a good-bacteria equilibrium, a bad-bacteria equilibrium, and a coexisting endemic equilibrium in which both bacteria exist while being exposed to antibiotics. The theory of the Sotomayor theorem is applied to study the local bifurcation around all possible equilibrium points. It’s noticed that the transcritical and saddle-node bifurcation could occur near some of the system’s equilibrium points, while pitchfork bifurcation cannot be accrued at

   The research aims to identify the importance of using the style of the cost on the basis of activity -oriented in time TDABC and its role in determining the cost of products more equitably and thus its impact on the policy of allocation of resources through the reverse of the changes that occur on an ongoing basis in the specification of the products and thus the change in the nature and type of operations . The research was conducted at the General Company for Textile Industries Wasit / knitting socks factory was based on research into the hypothesis main of that ( possible to calculate the cost of activities that cause the production through the time it takes to run these activities can then be re- distributed product cost