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.

For any group G, we define G/H (read” G mod H”) to be the set of left cosets of H in G and this set forms a group under the operation (a)(bH) = abH. The character table of rational representations study to gain the K( SL(2,81)) and K( SL(2, 729)) in this work.

A factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure. In this paper, the factor groups K(SL(2,121)) and K(SL(2,169)) computed for each group from the character table of rational representations.

The road networks is considered to be one of the determinants that controls to specify the areas of human activities, which it depend on to specify the arrival cost , in addition it is useful to achieve the connectivity for interaction and human activities , and shorten the distance and time between the population and places of service. The density of the road network in any space directly affected by the density of population and the type of economic activities and administrative functions performed by the space. On this basis, the subject of this study is reflected in the quantitative analysis of the roads network in the Governorate of Karbala. The study consists the quantitative analysis for the roads network and the Urban Nodes in th

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