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.

Background The Transportation Problem (TP) is a detailed model in operations study with applications in logistics, supply chain management, and resource allocation. The classical IBFS methods including North-West Corner, Least Cost and Vogel’s Approximation have competitive computational efficiency, but they are very sensitive to the structure of the problem and usually lead to a solution that is far from the global optimum. Classic enhancement strategies like the Generalized Distribution (MODI) and Stepping-Stone (SS) approaches have low computational complexity but may fall into a local optimum quickly, which makes them ineffective in large-scale or unbalanced problems. Methods We propose the first generic hybrid algorithm, calle

The research includes an introduction on Unmarried as one of the most dangerous phenomena's in Arab society in general and Iraqi society in specific especially after last decades wars that ruined the country and enlarged the number of unmarried women. First chapter dealt with the research problem that was increasing day after another while the percentage of unmarried women became 85% due to embargo and wars made by ex-regime that led to kill many Iraqis and decreasing marriage chances.

The research aims to recognize the reasons behind that and tries to find solutions by using quest ways and tools to get rid of old habits that represent obstacle marriage. The research dealt with unmarried in Arab countries where National Instituti

This is a search for Al-Rwandiyah and its heretical deviant sects, and its destructive goals that targeted the Arab nation, and its true Islamic religion in order to exhale poisons of demolition and sabotage, leading to its racist, populist goals ( ) that the Magi aspire to to restore the so-called ancient Persian glories, and undermine the Abbasid caliphate.
Al-Biruni said: (And that a person will emerge who will restore the Magian state and seize all the land, and remove the king of the Arabs) (), and among the indications of Ibn Al-Nadim is that a populist man called Muhammad bin Al-Hussein who was turned into Zaidan () was (claiming... the transition of the Islamic state to a state Persia ..... and their religion, which is the rel

This review highlights the importance of photodynamic therapy in periodontology. It can be confirmed that the photodynamic therapy as adjunct to classical scaling and root planing can be recommended as treatment option, which can by no means replace the classical therapy concepts. But even over an observation period of six months a slightly higher improvement of the clinical parameters was achieved than with SRP alone.

In recent times, many of those who practice the professions of Koranic treatment away from the legal controls, which dragged Muslims a lot of sedition and inflicted many in heresies and irregularities, and even spoiled the doctrines of many people making them relate to the causes and forget the Lord of the causes.
    For this reason it was incumbent upon the scholars to show the right from falsehood in this section, and because of the importance of the subject of jetting in Ruqyah and others, and how it is related, I chose the subject (jets and its jurisprudence), for all this I called on God to help me to show the right from wrong with regard to jetting And its provisions.