The present work represents a theoretical study for the correction of spherical aberration of an immersion lens of axial symmetry operating under the effect of space charge, represented by a second order function and preassigned magnification conditions in a focusing of high current ion beams. The space charge depends strongly on the value of the ionic beam current which is found to be very effective and represents an important factor effecting the value of spherical aberration .The distribution of the space charge was measured from knowing it's density .It is effect on the trajectory of the ion beam was studied. To obtain the trajectories of the charged particles which satisfy the preassined potential the axial electrostatic potential was represented by a fourth order polynomial function . To measure the optical properties of the lens and to obtain the electrode shape of the electrostatic lens we have solved Poissonequation
The increase in obesity and the many accompanying diseases is attributed to the increased production and consumption of foods made of non-nutritive sweeteners without regard to the risks of consuming additional calories, and this in turn leads to hormonal imbalance and metabolic disorders and the resulting imbalance and ill health that have spread to all segments of society. During the research, 0.01, 0.02, 0.03, 0.04 and 0.05 % of stevia sweetener was added to the cream instead of the sugar used. Physical and chemical tests were performed for the stevia extract and the microbial content in the cream, as well as the sensory evaluation. It was noted that fortifying the cream with calorie-free stevia sugar led to the production of
... Show MoreIn this paper, we study the growth of solutions of the second order linear complex differential equations insuring that any nontrivial solutions are of infinite order. It is assumed that the coefficients satisfy the extremal condition for Yang’s inequality and the extremal condition for Denjoy’s conjecture. The other condition is that one of the coefficients itself is a solution of the differential equation .
(15)
(8)
(15)
(8)
Basically, this study aims to identify the extent to which Iraqi secondary school students use writing strategies and how proficiency level and students gender could affect writing strategy use. The study also examines the relationship between writing achievement and writing strategy use among Iraqi secondary school students. For this purpose, 140 Iraqi secondary school students were selected randomly from six different schools. Petric and Czarl’s questionnaire (2003) was adopted in the study as an instrument to collect the needed data. A software of SPSS used to analyze the collected data. The findings revealed that secondary school students appeared as low users of writing strategies; low proficient students do not show a sta
... Show MoreAO Dr. Ali Jihad, Journal of Physical Education, 2021
(7)
(3)
The aim of this study was to propose and evaluate an eco-epidemiological model with Allee effect and nonlinear harvesting in predators. It was assumed that there is an SI-type of disease in prey, and only portion of the prey would be attacked by the predator due to the fleeing of the remainder of the prey to a safe area. It was also assumed that the predator consumed the prey according to modified Holling type-II functional response. All possible equilibrium points were determined, and the local and global stabilities were investigated. The possibility of occurrence of local bifurcation was also studied. Numerical simulation was used to further evaluate the global dynamics and the effects of varying parameters on the asymptotic behavior of
... Show More