In this research we have been studied the 3rd order spherical aberration for an optical system consisted of obscured circular aperture with non central circular obscuration through the calculation of point spread function (P.S.F) in presence of the obscuration in the center and comparing the obtained results with that results of moving obscuration far away from the center, where the results showed significant improvement for(P.S.F) value. The study was done of different obscurities ratios in addition to the different 3rd order spherical aberration values (W40=0.25 ,0.5 ,0.75 ,1 ).

The Electrical power system has become vast and more complex, so it is subjected to sudden changes in load levels. Stability is an important concept which determines the stable operation of the power system. Transient stability analysis has become one of the significant studies in the power system to ensure the system stability to withstand a considerable disturbance. The effect of temporary occurrence can lead to malfunction of electronic control equipment. The application of flexible AC transmission systems (FACTS) devices in the transmission system have introduced several changes in the power system. These changes have a significant impact on the power system protection, due to differences inline impedance, line curre

The study aims at finding out the effect of the lead time strategy on the first intermediate class pupils' achievement in geography The partial experimental design of two groups, experimental and control, with pre-post tests is used. The sample is represented in (73) female pupils. The sample is divided into two groups (37) experimental group and (36) control one. The sam ple is selected from first intermediate class pupils ( Al Batol intermediate school for girls) Baghdad Al-karkh-3, for academic year 2015-2016 The researcher has equalized the two groups in several variables: the previous achievement tests, intelligence, age in months, the scores of geography test of first course

In this paper, a discretization of a three-dimensional fractional-order prey-predator model has been investigated with Holling type III functional response. All its fixed points are determined; also, their local stability is investigated. We extend the discretized system to an optimal control problem to get the optimal harvesting amount. For this, the discrete-time Pontryagin’s maximum principle is used. Finally, numerical simulation results are given to confirm the theoretical outputs as well as to solve the optimality problem.

in this paper fourth order kutta method has been used to find the numerical solution for different types of first liner

Krawtchouk polynomials (KPs) and their moments are promising techniques for applications of information theory, coding theory, and signal processing. This is due to the special capabilities of KPs in feature extraction and classification processes. The main challenge in existing KPs recurrence algorithms is that of numerical errors, which occur during the computation of the coefficients in large polynomial sizes, particularly when the KP parameter (p) values deviate away from 0.5 to 0 and 1. To this end, this paper proposes a new recurrence relation in order to compute the coefficients of KPs in high orders. In particular, this paper discusses the development of a new algorithm and presents a new mathematical model for computing the

In 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 .