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.

Receipt date:6/3/2021  acceptance date:4/5/2021 Publication date:31/31/2021

This work is licensed under a Creative Commons Attribution 4.0 International License.

The research in the role of variables contact for non-state actors have become more influential in the current of contemporary events, that related with the reality of seeking services and providing all of that in favor of maintaining the social peace, and ensuring its empowerment in order to make peace and stability outcomes as a real fa

This research is concerned with documenting and chronicling the art of NFTs art in the Saudi artistic cultural scene, the importance of which stems from the lack of scientific sources that document this field until the preparation of this research and aims to trace historically the emergence of the field of NFTs art in the Kingdom of Saudi Arabia in the arts sector through the experiences of Saudi artists. The most prominent events for the culture, arts and technology sector, and other Saudi sectors. The research dealt with the history of the emergence of the field of NFTs art, which extends from the history of digital arts, and reviewed the most famous works of NFTs art.
As a result of the technical revolution and the artistic move

The chromatographic behaviour of liquid crystalline compounds benzylidene-p-aminobenzoic acid and 4-(p-methyl benzylidene)-p-aminobenzoic acid as stationary phases for the separation of dimethylphenol isomers was investigated. These isomers were analysed on benzylidene-p-aminobenzoic acid within a nematic range of 169-194 ◦C with a temperature interval of 5 ◦C. Better peak resolution was at a column temperature of 190 ◦C. The analysis was repeated on a 4-(p-methyl benzylidene)-p-aminobenzoic acid column at a nematic temperature of 256 ◦C, which represented the end of the nematic range, and gave the optimum peak resolution. It was found that isomer better separation was obtained at 20% loading for both liquid crystal materials. Other

Three groups of subjects have been divided (25/group): healthy normotensive non-pregnant women (Group A), normal normotensive pregnant women (Group B), and women with preeclampsia (Group C).The levels of serum alanine aminotransferase (ALT), aspartate aminotransferase (AST), total bilirubin , creatinine , blood urea nitrogen, triglyceride , total cholesterol and glucose have been estimated in all subjects. All measured parameters were determined by spectrophotometric analysis. The results showed a significant(P<0.05) increase in serum ALT, AST, blood urea nitrogen, triglyceride and total cholesterol levels in group B as compared to group A. However creatinine, total bilirubin and glucose levels did not show any statistical significant alt

Analysis the economic and financial phenomena and other requires to build the appropriate model, which represents the causal relations between factors. The operation building of the model depends on Imaging conditions and factors surrounding an in mathematical formula and the Researchers target to build that formula appropriately. Classical linear regression models are an important statistical tool, but used in a limited way, where is assumed that the relationship between the variables illustrations and response variables identifiable. To expand the representation of relationships between variables that represent the phenomenon under discussion we used Varying Coefficient Models