The aim of this book is to present a method for solving high order ordinary differential equations with two point boundary condition of the different kind, we propose semi-analytic technique using two-point osculatory interpolation to construct polynomial solution. The original problem is concerned using two-points osculatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] . Also, we discussion the existence and uniqueness of solutions and many examples are presented to demonstrate the applicability, accuracy and efficiency of the methods by compared with conventional method .i.e. VIDM , Septic B-Spline , , NIM , HPM, Haar wavelets on one hand and to confirm the order convergence on the other

The study of biomechanical indicators in the arc of the run and the upgrading stage is one of the important variables that affect the nature of the upgrading and thus affect the result of the race due to the importance of these stages and the consequent variables during the last steps. That’s why, the jump-trainings based on assistant means or body weight positively affect the step-time for each of the three steps in the acceleration arc. As well as, it focuses on the momentary strength of each step at this stage. It also significantly affects the speed of motor performance to suit the activity in which the runner needs to perform perfect steps with high flow in order to convert the horizontal speed to a vertical one. This is achieved thr

The reinforced fiberglass in cement slurry reflects the effect on its properties compared to usual additives. Fiberglass is typically used in cement slurry design for one or another of the following goals: (Earth earthquake, bearing storage, and with differential stresses, to enhance cement durability and increase its compressive strength). The main goal is to use glass fiber and ground fiberglass to improve the tensile strength and moderate compressive strength significantly. On the other hand, the use of glass fibers led to a slight increase in the value of thickening time, which is a desirable effect. Eleven glass fiber samples and milled glass fiber were used to show these materials' effect on Iraqi cement with (0.125, 0.25, 0.5

The biosorption of Pb (II), Cd (II), and Hg (II) from simulated aqueous solutions using baker’s yeast biomass was investigated. Batch type experiments were carried out to find the equilibrium isotherm data for each component (single, binary, and ternary), and the adsorption rate constants. Kinetics pseudo-first and second order rate models applied to the adsorption data to estimate the rate constant for each solute, the results showed that the Cd (II), Pb (II), and Hg (II) uptake process followed the pseudo-second order rate model with (R2) 0.963, 0.979, and 0.960 respectively. The equilibrium isotherm data were fitted with five theoretical models. Langmuir model provides the best fitting for the experimental results with (R2) 0.992, 0

The application of low order panel method with the Dirichlet boundary condition on complex aircraft configuration have been studied in high subsonic and transonic speeds. Low order panel method has been used to solve the case of the steady, inviscid and compressible flow on a forward swept wing – canard configuration with cylindrical fuselage and a vertical stabilizer with symmetrical cross section. The aerodynamic coefficients for the forward swept wing aircraft were calculated using measured wake shape from an experimental work on same model configuration. The study showed that the application of low order panel method can be used with acceptable results

In this work, oral lesions belong to 17 patients, 7 males and 10 females. Their ages range between 15 and 45 years. Follow up was conducted after one day, 7 days, 14 days, one month, and finally 3 months postoperatively. The study lasted for 1.5 year. Surgical diode laser with wavelength of 810 ± 20 nm, with two power levels of 10 and 15 W were used in contact and in non-contact mode via optical fiber. The postoperative outcome revealed; greater haemostatic capability, dry, sealed wound and noticeable lack in pain sensation

Broyden update is one of the one-rank updates which solves the unconstrained optimization problem but this update does not guarantee the positive definite and the symmetric property of Hessian matrix.

In this paper the guarantee of positive definite and symmetric property for the Hessian matrix will be established by updating the vector  which represents the difference between the next gradient and the current gradient of the objective function assumed to be twice continuous and differentiable .Numerical results are reported to compare the proposed method with the Broyden method under standard problems.

The primary components of successful engineering projects are time, cost, and quality. The use of the ring footing ensures the presence of these elements. This investigation aims to find the optimum number of geogrid reinforcement layers under ring footing subjected to inclined loading. For this purpose, experimental models were used. The parameters were studied to find the optimum geogrid layers number, including the optimum geogrid layers spacing and the optimum geogrid layers number. The optimum geogrid layers spacing value is 0.5B. And as the load inclination angle increased, the tilting and the tilting improvement percent for the load inclination angles (5°,10°,15°) are (40%,28%, and 5%) respectively. The reduction percent o