An optimization calculation is made to find the optimum properties of combined quadrupole lens which consists of electrostatic and magnetic lens. Both chromatic and spherical aberration coefficients are reduced to minimum values and the achromatic aberration is found for many cases. These calculations are achieved with the aid of transfer matrices method and using rectangular model of field distribution, where the path of charged-particles beam traversing the field has been determined by solving the trajectory equation of motion and then the optical properties for lens have been computed with the aid of the beam trajectory along the lens axis. The computations have been concentrated on determining the chromatic and spher

Various simple and complicated models have been utilized to simulate the stress-strain behavior of the soil. These models are used in Finite Element Modeling (FEM) for geotechnical engineering applications and analysis of dynamic soil-structure interaction problems. These models either can't adequately describe some features, such as the strain-softening of dense sand, or they require several parameters that are difficult to gather by conventional laboratory testing. Furthermore, soils are not completely linearly elastic and perfectly plastic for the whole range of loads. Soil behavior is quite difficult to comprehend and exhibits a variety of behaviors under various circumstances. As a result, a more realistic constitutive model is

The optimization calculations are made to find the optimum properties of combined quadrupole lens consist of electrostatic and magnetic lenses to produce achromatic lens. The modified bell-shaped model is used and the calculation is made by solving the equation of motion and finding the transfer matrices in convergence and divergence planes, these matrices are used to find the properties of lens as the magnification and aberrations coefficients. To find the optimum values of chromatic and spherical aberrations coefficients, the effect of both the excitation parameter of the lens (n) and the effective length of the lens into account as effective parameters in the optimization processing

Various simple and complicated models have been utilized to simulate the stress-strain behavior of the soil. These models are used in Finite Element Modeling (FEM) for geotechnical engineering applications and analysis of dynamic soil-structure interaction problems. These models either can't adequately describe some features, such as the strain-softening of dense sand, or they require several parameters that are difficult to gather by conventional laboratory testing. Furthermore, soils are not completely linearly elastic and perfectly plastic for the whole range of loads. Soil behavior is quite difficult to comprehend and exhibits a variety of behaviors under various circumstances. As a result, a more realistic constitutive model is

Gypseous soil covers approximately 30% of Iraqi lands and is widely used in geotechnical and construction engineering as it is. The demand for residential complexes has increased, so one of the significant challenges in studying gypsum soil due to its unique behavior is understanding its interaction with foundations, such as strip and square footing. This is because there is a lack of experiments that provide total displacement diagrams or failure envelopes, which are well-considered for non-problematic soil. The aim is to address a comprehensive understanding of the micromechanical properties of dry, saturated, and treated gypseous sandy soils and to analyze the interaction of strip base with this type of soil using particle image

The study aimed to reveal the level to which the international issues are integrated into the books of Saudi public education social studies and citizenship in the light of the principles of international education, and to know the level of continuity and integration of these issues in the books, to build a range and sequence matrix of international issues through it. The study followed the descriptive and analytical method that used the content analysis card as a tool for study when the tool achieved the necessary validity and reliability characteristics. The data of this study has been processed using the SPSS statistical program according to a set of appropriate methods of descriptive and inferential statistics.

 The resu