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

In this research (100* 40* 4 cm) solar cell panel was used in Baghdad at autumn season (2010), to get best solar cell panel angles experimentally, and then a mirror (40*50 cm) is use to concentrate incident sunlight intensity on a panel. At first case we get (Tilt angle ?P =60°and Surface Azimuth angle ?P =36°E) is the best angles and other case, we add a mirror at angle = 120° at bottom of panel, then we get output power (27.48watt) is bigger than without using a mirror (25.16watt). We can benefit from these cases in variety applications.

We propose an intraguild predation ecological system consisting of a tri-trophic food web with a fear response for the basal prey and a Lotka–Volterra functional response for predation by both a specialist predator (intraguild prey) and a generalist predator (intraguild predator), which we call the superpredator. We prove the positivity, existence, uniqueness, and boundedness of solutions, determine all equilibrium points, prove global stability, determine local bifurcations, and illustrate our results with numerical simulations. An unexpected outcome of the prey's fear of its specialist predator is the potential eradication of the superpredator.

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

Differences in transversal sections and activities of geomorphological operations led to forming geomorphological shapes as river turns and river isles in watercourse in the area of study. The study showed three river turns that are Sindia turn with length 4723m, turn wave 3599 average width 267.6, Zanbour turn length 11374m, turn wave 7110 average width 307.5m,and Dojama turn with length 5876m, turn wave 4982m average width 313.4m. This difference is caused by the activity of erosion and sedimentation that led to the appearance of the length rivers turn.
The study showed that the turn of Dojama is the only corresponding turn, whereas the phenomena of corresponding never appeared in other turns in the area of study. The study also sho