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基于拓扑指数和熵测度通过回归模型对二氧化硅进行分析。

On analysis of silicon dioxide based on topological indices and entropy measure via regression model.

作者信息

Huang Rongbing, Hanif Muhammad Farhan, Siddiqui Muhammad Kamran, Hanif Muhammad Faisal, Gegbe Brima

机构信息

School of Computer Science, Chengdu University, Chengdu, China.

Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan.

出版信息

Sci Rep. 2024 Sep 28;14(1):22478. doi: 10.1038/s41598-024-73163-8.

Abstract

The construction sector accounts for around 95% of the commercial usage of silicon dioxide (sand), for example, in the making of concrete. There are several uses for quartz, however in order to get a purer material, chemical processing is needed. Graph theory proved to be very beneficial for other research, especially in the applied sciences. In particular, graph theory has greatly influenced the field of chemistry. To do this, a transformation is needed to produce a graph with the vertices representing the atoms in the chemical compound and the edges indicating the bonds between the atoms. This graph then represents a chemical network or structure. In a graph, a vertex's valency (or degree) is determined by the number of edges that are incident to it. The entropy of a probability quantifies a system's level of uncertainty. In this article, we compute Zagreb-type indices and then compute the entropy measure. In order to evaluate the relevance of each kind, this article builds several edge degree-based entropies that link to the indices and establish how to adjust them. We also create the logarithmic regression model between indices and entropy.

摘要

例如,建筑业约占二氧化硅(沙子)商业用途的95%,用于制造混凝土。石英有多种用途,然而,为了获得更纯净的材料,需要进行化学处理。事实证明,图论对其他研究非常有益,尤其是在应用科学领域。特别是,图论对化学领域产生了极大的影响。为此,需要进行一种变换,以生成一个图,其中顶点代表化合物中的原子,边表示原子之间的键。然后,这个图代表一个化学网络或结构。在一个图中,顶点的价(或度)由与之关联的边的数量决定。概率的熵量化了系统的不确定程度。在本文中,我们计算了 Zagreb 型指标,然后计算了熵测度。为了评估每种类型的相关性,本文构建了几个基于边度的熵,这些熵与指标相关联,并确定如何对其进行调整。我们还建立了指标与熵之间的对数回归模型。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/522b/11439057/1a40fd3c3451/41598_2024_73163_Fig1_HTML.jpg

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