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.

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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.

The goal of the research is to find the optimization in the test of the appropriate cross-over design for the experiment that the researcher is carrying out (under assumption that there are carry-over effects of the treatments) to posterior periods after the application period (which is often assumed to be the first period). The comparison between the double cross-over design and the cross-over design with extra period. The similarities and differences between the two designs were studied by measuring the Relative Efficiency (RE) of the experiment.

Background: Arterial stiffness is related with atherosclerosis and cardiovascular disease events. Patients with atherosclerotic disease show to have larger diameters, reduced arterial compliance and lower flow velocities. Aim of study : To compare between patients of two age groups with concomitant diseases diabetes and hypertension in regard to intima media thickness and blood flow characteristics in order to estimate the blood perfusion to the brain via the common and internal carotid arteries. Subject and Methods : 40 patients with (diabetic and hypertension) diseases were enrolled , they were classified according to age. Color Doppler and B mode ultrasound was used to determine lumen Diameter (D), Intima – media thickness (IMT)

This paper deals  with constructing mixed probability distribution  from exponential with scale parameter (β) and also Gamma distribution with (2,β), and the mixed proportions are (  .first of all, the probability density function (p.d.f) and also cumulative distribution function (c.d.f) and also the reliability function are obtained. The parameters of mixed distribution, ( ,β)  are estimated by three different methods, which are  maximum likelihood, and  Moments method,as well proposed method (Differential Least Square Method)(DLSM).The comparison is done using simulation procedure, and all the results are explained in tables.

Volterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained