The method of operational matrices is based on the Bernoulli and Shifted Legendre polynomials which is used to solve the Falkner-Skan equation. The nonlinear differential equation converting to a system of nonlinear equations is solved using Mathematica®12, and the approximate solutions are obtained. The efficiency of these methods was studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as  increases. Moreover, the obtained approximate solutions are compared with the numerical solution obtained by the fourth-order Runge-Kutta method (RK4), which gives  a good agreement.

KE Sharquie, AA Noaimi, WK Al-Janabi, Journal of Cosmetics, Dermatological Sciences and Applications, 2013

A numerical method is developed for calculation of the wake geometry and aerodynamic forces on two-dimensional airfoil under going an arbitrary unsteady motion in an inviscid incompressible flow (panel method). The method is applied to sudden change in airfoil incidence angle and airfoil oscillations at high reduced frequency. The effect of non-linear wake on the unsteady aerodynamic properties and oscillatory amplitude on wake rollup and aerodynamic forces has been studied. The results of the present method shows good accuracy as compared with flat plate and for unsteady motion with heaving and pitching oscillation the present method also shows good trend with the experimental results taken from published data. The method shows good result

The current research included palynological study for nine ornamental cultivated species of Asteraceae family. The study included measurement the dimensions of pollen grains and there shape in polar view and equatorial view, sculpturing,colpi length and width, spines length and number of spines rows between colpiand exine thickness, the study showed variations in pollen grains characters forthe studied taxa

The Korteweg-de Vries equation plays an important role in fluid physics and applied mathematics. This equation is a fundamental within study of shallow water waves. Since these equations arise in many applications and physical phenomena, it is officially showed that this equation has solitary waves as solutions, The Korteweg-de Vries equation is utilized to characterize a long waves travelling in channels. The goal of this paper is to construct the new effective frequent relation to resolve these problems where the semi analytic iterative technique presents new enforcement to solve Korteweg-de Vries equations. The distinctive feature of this method is, it can be utilized to get approximate solutions for travelling waves of 

Voice studies are one of the sensory studies of their first association with auditory taste, which broadcasts its connection to the most sensory point contained in the physical corners, and in order to satisfy our conscience from these fundamental voices, we searched for in modern contexts, high proportions related to the words of Muhammadiyah, so we are looking for (events In the hadiths of the Prophet (peace be upon him), to settle our journey when the true adhkaar received from the Prophet, peace be upon him, and to control us start a journey through which we repeat between the cities of audio repetitions, sometimes we find ourselves have stood at the entrance of what corresponds to the sounds between the title of the Hadith and its t

Passive optical network (PON) is a point to multipoint, bidirectional, high rate optical network for data communication. Different standards of PONs are being implemented, first of all PON was ATM PON (APON) which evolved in Broadband PON (BPON). The two major types are Ethernet PON (EPON) and Gigabit passive optical network (GPON). PON with these different standards is called xPON. To have an efficient performance for the last two standards of PON, some important issues will considered. In our work we will integrate a network with different queuing models such M/M/1 and M/M/m model. After analyzing IPACT as a DBA scheme for this integrated network, we modulate cycle time, traffic load, throughput, utilization and overall delay

In this paper , the CO2 laser receiver system is designed and studied, with wavelength laser 10.6 ?m in room temperature , and to evaluate the performance and discussion it via the package of optical design (ZEMAX), from its output the Spot Diagram is measured through RMS ,and from the Ray fan plot , the aberrations is found which is the normal error for the best focus named (under corrected ) , the other output was the Geometric Encircled Energy in the spot diagram . and found that the radius of spot diagram at 80% (R80%) from the total energy ,and focal shift .The designed system have high efficiency and low cost .