An interpretation of second-order neighborhood Harmonic index

IF 2.4 3区数学 Q1 MATHEMATICS Journal of Applied Mathematics and Computing Pub Date : 2024-08-16 DOI:10.1007/s12190-024-02213-1

A. Bharali, Monjit Chamua, Jibonjyoti Buragohain, Tarun Boruah

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Abstract

The Topological index serves as a powerful mathematical descriptor, capturing the intricate structural features of molecules and providing insightful analysis in the field of chemical sciences. This communication studies the higher-order Neighborhood Harmonic index (\(NH_{\alpha }\)) and presents an alternative perspective on the correlation of the second-order Neighborhood Harmonic index (\(NH_{2}\)) with the normal boiling point of straight-chain Alkanes and Octane Isomers. Based on the findings of this study, it can be observed that with an increase in the molecular weight of an straight-chain alkane, there is a concurrent elevation in both the normal boiling point and the collective involvement of \(NH_{2}\) along all conceivable internal C–C–C routes. As all the isomers of Octane possess the same molecular weights, we first categorize the isomers into distinct groups and then establish a meaningful connection with their respective normal boiling points. In case of normal boiling point (computed using modified Frost-Kalkwarf equation), it is found that, the proposed index i.e., Second-Order Neighborhood Harmonic index has good predictive ability with a probability of \(90\%\) for absolute relative errors of less than \(6.29\%\). Further, some important mathematical properties of the (\(NH_{2}\)) are also presented in the paper.

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二阶邻域谐波指数的解释

摘要拓扑指数是一种强大的数学描述符，它捕捉了分子错综复杂的结构特征，并在化学科学领域提供了富有洞察力的分析。本文研究了高阶邻域谐波指数（\(NH_{\alpha }\），并从另一个角度探讨了二阶邻域谐波指数（\(NH_{2}\）与直链烷烃和辛烷异构体的正常沸点的相关性。根据这项研究的结果，我们可以发现，随着直链烷烃分子量的增加，正常沸点和 \(NH_{2}\) 沿所有可想象的内部 C-C-C 路线的集体参与都会同时升高。由于正辛烷的所有异构体都具有相同的分子量，我们首先将这些异构体分为不同的组别，然后将它们与各自的常沸点建立有意义的联系。在正常沸点方面（使用改进的弗罗斯特-卡尔克沃夫方程计算），我们发现所提出的指数，即二阶邻近谐波指数具有良好的预测能力，绝对相对误差小于（6.29%）时的概率为（90%）。此外，本文还介绍了（\(NH_{2}\)）的一些重要数学特性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Applied Mathematics and Computing Mathematics-Computational Mathematics

CiteScore

4.20

自引率

4.50%

发文量

131

期刊介绍： JAMC is a broad based journal covering all branches of computational or applied mathematics with special encouragement to researchers in theoretical computer science and mathematical computing. Major areas, such as numerical analysis, discrete optimization, linear and nonlinear programming, theory of computation, control theory, theory of algorithms, computational logic, applied combinatorics, coding theory, cryptograhics, fuzzy theory with applications, differential equations with applications are all included. A large variety of scientific problems also necessarily involve Algebra, Analysis, Geometry, Probability and Statistics and so on. The journal welcomes research papers in all branches of mathematics which have some bearing on the application to scientific problems, including papers in the areas of Actuarial Science, Mathematical Biology, Mathematical Economics and Finance.