Indexes of topological play a crucial role in mathematical chemistry and network theory, providing valuable insights into the structural properties of graphs. In this study, we investigate the Resize graph of G2(3), a significant algebraic structure arising from the exceptional Lie group (G2) over the finite field F3. We compute several well-known topological indices, including the Zagreb indices, Wiener index, and Randić index, to analyze the graph's connectivity and complexity. Our results reveal intricate relationships between the algebraic structure of G2(3) and its graphical properties, offering a deeper understanding of its combinatorial and spectral characteristics. These findings contribute to the broader study of algebraic graph t

This paper considers approximate solution of the hyperbolic one-dimensional wave equation with nonlocal mixed boundary conditions by improved methods based on the assumption that the solution is a double power series based on orthogonal polynomials, such as Bernstein, Legendre, and Chebyshev. The solution is ultimately compared with the original method that is based on standard polynomials by calculating the absolute error to verify the validity and accuracy of the performance.

The purpose of this resesrh know (the effectiveness of cooperative lerarning implementation of floral material for calligraphy and ornamentation) To achieve the aim of the research scholar put the two zeros hypotheses: in light of the findings of the present research the researcher concluded a number of conclusions, including: -
1 - Sum strategy helps the learner to be positive in all the information and regulations, monitoring and evaluation during the learning process.
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Physics and applied mathematics form the basis for understanding natural phenomena using differential equations depicting the flow in porous media, the motion of viscous liquids, and the propagation of waves. These equations provide a thorough study of physical processes, enhancing the understanding of complex applications in engineering, technology, and medicine. This paper presents novel approximate solutions for the Darcy-Brinkmann-Forchheimer moment equation, the Blasius equation and the FalknerSkan equation with initial / boundary conditions by using two iterative methods: the variational iteration method and the optimal variational iteration method. The variational iteration method is effectively developed by adding a control paramete

     The primary objective of the current paper is to suggest and implement effective computational methods (DECMs) to calculate analytic and approximate solutions to the nonlocal one-dimensional parabolic equation which is utilized to model specific real-world applications. The powerful and elegant methods that are used orthogonal basis functions to describe the solution as a double power series have been developed, namely the Bernstein, Legendre, Chebyshev, Hermite, and Bernoulli polynomials. Hence, a specified partial differential equation is reduced to a system of linear algebraic equations that can be solved by using Mathematica®12. The techniques of effective computational methods (DECMs) have been applied to solve some s

The concern of this article is the calculation of an upper bound of second Hankel determinant for the subclasses of functions defined by Al-Oboudi differential operator in the unit disc. To study special cases of the results of this article, we give particular values to the parameters A, B and λ

Learning the vocabulary of a language has great impact on acquiring that language. Many scholars in the field of language learning emphasize the importance of vocabulary as part of the learner's communicative competence, considering it the heart of language. One of the best methods of learning vocabulary is to focus on those words of high frequency. The present article is a corpus based approach to the study of vocabulary whereby the research data are analyzed quantitatively using the software program "AntWordprofiler". This program analyses new input research data in terms of already stored reliable corpora. The aim of this article is to find out whether the vocabularies used in the English textbook for Intermediate Schools in Iraq are con