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

Topological indices provide important insights into the structural characteristics of molecular graphs. The present investigation proposes and explores a creative graph on a finite group G, which is known as the RIG. This graph is designated as ΓRS G2(4) indicating a simple undirected graph containing elements of G. Two distinct ertices are regarded as nearly the same if and only if their sum yields a non-trivial involution element in G. RIGs have been discovered in various finite groups. We examine several facets of the RIG by altering the graph through the conjugacy classes of G. Furthermore, we investigate the topological indices as applications in graph theory applying the distance matrix of the G2(4) group.

The research included making a bibliography of the jurisprudential books available in the reference section of the central library at the University of Al-Mustansiriya. From this research, and I also saw that one of its objectives was to classify these books scientifically according to what was included in the Contemporary Islamic Fiqh Library of sections that were classified on its basis, according to what has settled in the custom of contemporary jurists, and according to the researcher’s view and his humble diligence, so the research was organized into an introduction and three topics. Each topic contained approximately five demands that included the sections of the contemporary jurisprudential lib

Contrary to deconstruction and its destructive pursuit, the concept of undermining the familiar seeks to refute the constants and its known limitations. It is done through the process of receiving and what is imposed by the formation of the word or text or the structural and design structure in general, along with the Arabic calligraphy in particular. This is based on the recipient's understanding and interpretation of the dual phenomenon and the content's manifestation. More accurately, the disclosure of its reality through its expressive phenomenology; for that sake, the research was devoted to studying “undermining the familiar and embodiment content in Arabic calligraphy” including four chapters. The first chapter comprised

يشكل السياق جانبا مهماً في فهم الخطاب والمقصود هنا العرض المسرحي، من خلال ما يمده السياق للمتلقي من مؤشرات، يتم الاعتماد عليها في استكمال المعنى الظاهر بالمعنى المستتر، فالسياق يعتمد في الاصل على المحيط المادي الاجتماعي الذي يتم فيه التواصل وفيه يتعرف المرسل والمتلقي أحدهما على الآخر وتتبلور الصورة التي يحملها الطرفان أحدهما عن الآخر، الى جانب كونه يمثل الاحداث التي سبق لهما أن عاشاها والتبادل القولي

August Wilson’s major concern is to communicate the African American cultural awareness; to establish a counter-culture based on self-confidence and assertiveness. He advocates an encouraging attitude to elevate the African Americans’ spiritual consciousness and to teach them how to sublimate their aims in life. He aspires to win the everlasting battle against racial discrimination, oppression, injustice, and identity confusion. Sublimation, as a defense mechanism, will be Wilson’s new ammunition to re-read and to re-interpret the psychic constitution of his people, to help them get out of their self-imposed fences and this is the core of Wilson’s new culture. Sublimation is the process in which the psyche directs the negative drive

Digital literacy is crucial in the modern workforce, where technology plays an integral role in daily operations. This abstract explores the significance of digital literacy in enhancing productivity, efficiency, and competitiveness in the workplace. Digital literacy encompasses the ability to use and navigate digital tools and platforms effectively, including software, applications, and online communication tools. In today's digital age, employers increasingly value candidates with strong digital skills, as they are better equipped to adapt to rapidly evolving technologies. This abstract highlights the importance of digital literacy in empowering employees to perform tasks more efficiently, collaborate seamlessly, and innovate effecti