The presentwork is a theoretical study in the field of charged particle optics. It concentrates on the design of electrostatic enzil lens for focusing charge particles beams, using inverse method in designingthe electrostatic lens. The paraxial ray equation was solved to obtain the trajectory of the particles, the optical properties such as the focal length and spherical and chromatic aberration coefficients were determined. The shape of the electrode of the electrostatic lens were determined by solving poison equation and the results showed low values of spherical and chromatic aberrations, which are considered as good criteria for good design.

The charge transfer at C23H17F8N8O2PRu, C44H30BF4N5O4Ru, C56H52CL5N5OOsP2 and C76H88F80N24O11P10Ru4 nitrosyl complexes are investigation and studies theoretically using the quantum consideration. Charge transfer behavior largely rely to the electric properties of nitrosyl complexes system whose depending on the main important parameters for the transmission rate constant such that: orientation transition energy, overlapping coupling coefficient, driving force energy, height barrier and Temperature T (K). Data results have been evaluated using a MATLAB program. Results show that rate of charge transfer increases due to increases the orientation transition energy.

Water flow into unsaturated porous media is governed by the Richards’ partial differential equation expressing the mass conservation and Darcy’s laws. The Richards’ equation may be written in three forms,where the dependent variable is pressure head or moisture content, and the constitutive relationships between water content and pressure head allow for conversion of one form into the other. In the present paper, the “moisture-based" form of Richards’ equation is linearized by applying Kirchhoff’s transformation, which
combines the soil water diffusivity and soil water content. Then the similarity method is used to obtain the analytical solution of wetting front position. This exact solution is obtained by means of Lie’s

New complexes of the type [ML2(H2O)2] ,[FeL2(H2O)Cl] and [VOL2] were M=Co(II),Ni(II) and Cu(II) ,L=4-(2-methyl-4-oxoquinazoline-3(4H)-yl) benzoic acid were synthesized and characterized by element analysis, magnetic susceptibility ,molar conductance ,FT-IR and UV-visible. The studies indicate that the L acts as doubly monodentate bridge for metal ions and form mononuclear complexes. The complexes are found to be octahedral except V(IV) complex is square pyrimde shape . The structural geometries of compounds were also suggested in gas phase by theoretical treatments, using Hyper chem-6 program for the molecular mechanics and semi-empirical calculations, addition heat of formation(?Hf ?) and binding energy (?Eb)for the free ligan

This paper deals with an analytical study of the flow of an incompressible generalized Burgers’ fluid (GBF) in an annular pipe. We discussed in this problem the flow induced by an impulsive pressure gradient and compare the results with flow due to a constant pressure gradient. Analytic solutions for velocity is earned by using discrete Laplace transform (DLT) of the sequential fractional derivatives (FD) and finite Hankel transform (FHT). The influences of different parameters are analyzed on a velocity distribution characteristics and a comparison between two cases is also presented, and discussed in details. Eventually, the figures are plotted to exhibit these effects.

A simple straightforward mathematical method has been developed to cluster grid nodes on a boundary segment of an arbitrary geometry that can be fitted by a relevant polynomial. The method of solution is accomplished in two steps. At the first step, the length of the boundary segment is evaluated by using the mean value theorem, then grids are clustered as desired, using relevant linear clustering functions. At the second step, as the coordinates cell nodes have been computed and the incremental distance between each two nodes has been evaluated, the original coordinate of each node is then computed utilizing the same fitted polynomial with the mean value theorem but reversibly.

The method is utilized to predict

Linear attenuation coefficient of polymer composite for beta particles and bremsstrahlung ray were investigated as a function of the absorber thickness and energy. The attenuation coefficient were obtained using NaI(Tl) energy selective scintillation counter with ⁹⁰Sr/⁹⁰Y beta source having an energy range from 0.1-1.1 MeV. The present results show the capability of this composite to absorber beta particles and bremsstrahlung ray that yield from it. That’s mean it is useful to choice this composite for radiation shielding of beta ray with low thickness.

In this research، a comparison has been made between the robust estimators of (M) for the Cubic Smoothing Splines technique، to avoid the problem of abnormality in data or contamination of error، and the traditional estimation method of Cubic Smoothing Splines technique by using two criteria of differentiation which are (MADE، WASE) for different sample sizes and disparity levels to estimate the chronologically different coefficients functions for the balanced longitudinal data which are characterized by observations obtained through (n) from the independent subjects، each one of them is measured repeatedly by group of  specific time points (m)،since the frequent measurements within the subjects are almost connected an