In this paper the modified trapezoidal rule is presented for solving Volterra linear Integral Equations (V.I.E) of the second kind and we noticed that this procedure is effective in solving the equations. Two examples are given with their comparison tables to answer the validity of the procedure.

A computational investigation has been carried out on the design and properties of the electrostatic mirror. In this research, we suggest a mathematical expression to represent the axial potential of an electrostatic mirror. The electron beam path under zero magnification condition had been investigated as mirror trajectory with the aid of fourth – order – Runge – Kutta method. The spherical and chromatic aberration coefficients of mirror has computed and normalized in terms of the focal length. The choice of the mirror depends on the operational requirements, i.e. each optical element in optical system has suffer from the chromatic aberration, for this case, it is use to operate the mirror in optical system at various values

    In this paper, the finite difference method is used to solve fractional hyperbolic partial differential equations, by modifying the associated explicit and implicit difference methods used to solve fractional  partial differential equation. A comparison with the exact solution is presented and the results are given in tabulated form in order to give a good comparison with the exact solution

The objective of this study was to assess the nutritional status of childs of nurseries in Baghdad city so that an early detection of malnutrition cases could be carried out. The results revealed that the daily consumption of food calories, protein, fat and carbohydrate were 1180.5 calories, 27.2gm, 38gm and 180gm, respectively, which were less than the RDA values and the percentages of these nutrients supplied by the food intake were 90.8, 83.7, 87.3 and 90.3%, respectively. It was also demonstrated that the highest percentages of stunting, underweight and wasting, which amounted to 32, 22.7 and 1.5%, respectively, were among those childs who obtained inadequate calories, while the percentages of the forementioned malnutrition cases amon

Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

In this work, a simple and new method is proposed to simultaneously improve the physical layer security and the transmission performance of the optical orthogonal frequency division multiplexing system, by combining orthogonal frequency division multiplexing technique with chaotic theory principles. In the system, a 2-D chaotic map is employed. The introduced system replaces complex operations such as matrix multiplication with simple operations such as multiplexing and inverting. The system performance in terms of bit error rate (BER) and peak to average ratio (PAPR) is enhanced. The system is simulated using Optisystem15 with a MATLAB2016 and for different constellations. The simulation results showed that the  BE

ABSTRACT Planetary Nebulae (PN) distances represent the fundamental parameter for the determination the physical properties of the central star of PN. In this paper the distances scale to Planetary Nebulae in the Galactic bulge were calculated re- lated to previous distances scales. The proposed distance scale was done by recalibrated the previous distance scale technique CKS/D82. This scale limited for nearby PN (D ≤ 3.5 kpc), so the surface fluxes less than other distance scales. With these criteria the results showed that the proposed distance scale is more accurate than other scales related to the observations for adopted sample of PN distances, also the limit of ionized radius (Rio) for all both optically thick and optically thin in

          In the present research, a crane frame has been investigated by using finite element method. The damage is simulated by reducing the stiffness of assumed elements with ratios (10% and 20 %) in mid- span of the vertical column in crane frame. The cracked beam with a one-edge and non-propagating crack has been used. Six cases of damage are modeled for crane frame and by introducing cracked elements at different locations with ratio of depth of crack to the height of the beam (a/h) 0.1, 0.20. A FEM program coded in Matlab 6.5 was used to model the numerical simulation of the damage scenarios. The results showed a decreasing in the five natural frequencies from undamaged beam which means

Based on the diazotization reaction of 4-aminoacetophenone with sodium nitrite in acid medium to form diazonium salt, which was coupled with Methyldopa to form a violet reddish soluble azo dye with maximum absorbance at 560 nm,a batch procedure had been developed for the estamination of Methyldopa. Under optimum experimental parameters affecting on the development and stability of the colored product, Beer´s law obeyed in the range (0.5-45) ?g.ml-1 with a correlation coefficient (0.9979).The proposed method was successfully applied to the determination of Methyldopa in either pure form and in commercial brands of pharmaceuticals, no interference was observed from common excipients in the formulations. The analytical results obtained by app

     Today, the use of iris recognition is expanding globally as the most accurate and reliable biometric feature in terms of uniqueness and robustness. The motivation for the reduction or compression of the large databases of iris images becomes an urgent requirement. In general, image compression is the process to remove the insignificant or redundant information from the image details, that implicitly makes efficient use of redundancy embedded within the image itself. In addition, it may exploit human vision or perception limitations to reduce the imperceptible information.
     This paper deals with reducing the size of image, namely reducing the number of bits required in representing the