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Exploring the Edge Hyper-Zagreb Index of Graphs: Applications and Predictions of Thermodynamic Properties for Organic Linear Acenes Molecules 探索图形的边缘超萨格勒布索引：有机线性烯分子热力学性质的应用与预测
arXiv - MATH - General Mathematics Pub Date : 2024-06-07 DOI: arxiv-2406.16916
Z. Aliannejadi, S. Shafiee Alamoti
{"title":"Exploring the Edge Hyper-Zagreb Index of Graphs: Applications and Predictions of Thermodynamic Properties for Organic Linear Acenes Molecules","authors":"Z. Aliannejadi, S. Shafiee Alamoti","doi":"arxiv-2406.16916","DOIUrl":"https://doi.org/arxiv-2406.16916","url":null,"abstract":"The paper discusses the edge hyper-Zagreb index of a graph, which is\u0000calculated by replacing vertex degrees with edge degrees. The degree of an edge\u0000is determined by adding up the degrees of the end vertices of the edge and\u0000subtracting 2. We examine the edge hyper-Zagreb index of the Cartesian product\u0000and join of graphs, and also calculate it for organic linear Acenes molecules\u0000with the formula (C4n+2H2n+4). We establish a correlation between topological\u0000indices based on the number of rings and predict thermodynamic properties of\u0000Acenes family, such as electron affinity, bond, heat of formation and gap\u0000energy, using the Topological Indices Method (T IM).","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141531665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Formulas of special polynomials involving Bernoulli polynomials derived from matrix equations and Laplace transform 从矩阵方程和拉普拉斯变换得出的涉及伯努利多项式的特殊多项式公式
arXiv - MATH - General Mathematics Pub Date : 2024-05-31 DOI: arxiv-2406.08503
Ezgi Polat, Yilmaz Simsek
{"title":"Formulas of special polynomials involving Bernoulli polynomials derived from matrix equations and Laplace transform","authors":"Ezgi Polat, Yilmaz Simsek","doi":"arxiv-2406.08503","DOIUrl":"https://doi.org/arxiv-2406.08503","url":null,"abstract":"The main purpose and motivation of this article is to create a linear\u0000transformation on the polynomial ring of rational numbers. A matrix\u0000representation of this linear transformation based on standard fundamentals\u0000will be given. For some special cases of this matrix, matrix equations\u0000including inverse matrices, the Bell polynomials will be given. With the help\u0000of these equations, new formulas containing different polynomials, especially\u0000the Bernoulli polynomials, will be given. Finally, by applying the Laplace\u0000transform to the generating function for the Bernoulli polynomials, we derive\u0000some novel formulas involving the Hurwitz zeta function and infinite series.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fibonacci sequence and Pythagorean triples in the composition of functions for integer solutions from certain operator 某些算子的整数解的函数组成中的斐波那契数列和毕达哥拉斯三元组
arXiv - MATH - General Mathematics Pub Date : 2024-05-31 DOI: arxiv-2405.21039
Pablo José Vega Esparza
{"title":"Fibonacci sequence and Pythagorean triples in the composition of functions for integer solutions from certain operator","authors":"Pablo José Vega Esparza","doi":"arxiv-2405.21039","DOIUrl":"https://doi.org/arxiv-2405.21039","url":null,"abstract":"The following article summarizes research where theorems and their respective\u0000demonstrations are postulated based on quadratic equations with special\u0000properties given by the Pythagorean triplets and the Fibonacci sequence given\u0000the second order of equations where integer solutions are found an environment\u0000in number theory and its applications to calculus.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141258757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Integration Formulas Involving Fibonacci and Lucas Numbers 涉及斐波那契和卢卡斯数的积分公式
arXiv - MATH - General Mathematics Pub Date : 2024-05-30 DOI: arxiv-2406.00064
Kunle Adegoke, Robert Frontczak
{"title":"Integration Formulas Involving Fibonacci and Lucas Numbers","authors":"Kunle Adegoke, Robert Frontczak","doi":"arxiv-2406.00064","DOIUrl":"https://doi.org/arxiv-2406.00064","url":null,"abstract":"We present a range of difficult integration formulas involving Fibonacci and\u0000Lucas numbers and trigonometric functions. These formulas are often expressed\u0000in terms of special functions like the dilogarithm and Clausen's function. We\u0000also prove complements of integral identities of Dilcher (2000) and Stewart\u0000(2022). Many of our results are based on a fundamental lemma dealing with\u0000differentiation of complex-valued Fibonacci (Lucas) functions.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141259051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Building the Butterfly Fractal: The Eightfold Way 构建蝴蝶分形八正道
arXiv - MATH - General Mathematics Pub Date : 2024-05-30 DOI: arxiv-2406.00068
Indubala I Satija
{"title":"Building the Butterfly Fractal: The Eightfold Way","authors":"Indubala I Satija","doi":"arxiv-2406.00068","DOIUrl":"https://doi.org/arxiv-2406.00068","url":null,"abstract":"The hierarchical structure of the butterfly fractal -- the Hofstader\u0000butterfly, is found to be described by an octonary tree. In this framework of\u0000building the butterfly graph, every iteration generates sextuplets of\u0000butterflies, each with a tail that is made up of an infinity of butterflies.\u0000Identifying {it butterfly with a tale} as the building block, the tree is\u0000constructed with eight generators represented by unimodular matrices with\u0000integer coefficients. This Diophantine description provides one to one mapping\u0000with the butterfly fractal, encoding the magnetic flux interval and the\u0000topological quantum numbers of every butterfly. The butterfly tree is a\u0000generalization of the ternary tree describing the set of primitive Pythagorean\u0000triplets.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141258748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic behavior of the Manhattan distance in $n$-dimensions: Estimating multidimensional scenarios in empirical experiments n$维曼哈顿距离的渐近行为：在实证实验中估计多维场景
arXiv - MATH - General Mathematics Pub Date : 2024-05-30 DOI: arxiv-2406.15441
Ergon Cugler de Moraes Silva
{"title":"Asymptotic behavior of the Manhattan distance in $n$-dimensions: Estimating multidimensional scenarios in empirical experiments","authors":"Ergon Cugler de Moraes Silva","doi":"arxiv-2406.15441","DOIUrl":"https://doi.org/arxiv-2406.15441","url":null,"abstract":"Understanding distance metrics in high-dimensional spaces is crucial for\u0000various fields such as data analysis, machine learning, and optimization. The\u0000Manhattan distance, a fundamental metric in multi-dimensional settings,\u0000measures the distance between two points by summing the absolute differences\u0000along each dimension. This study investigates the behavior of Manhattan\u0000distance as the dimensionality of the space increases, addressing the question:\u0000how does the Manhattan distance between two points change as the number of\u0000dimensions n increases?. We analyze the theoretical properties and statistical\u0000behavior of Manhattan distance through mathematical derivations and\u0000computational simulations using Python. By examining random points uniformly\u0000distributed in fixed intervals across dimensions, we explore the asymptotic\u0000behavior of Manhattan distance and validate theoretical expectations\u0000empirically. Our findings reveal that the mean and variance of Manhattan\u0000distance exhibit predictable trends as dimensionality increases, aligning\u0000closely with theoretical predictions. Visualizations of Manhattan distance\u0000distributions across varying dimensionalities offer intuitive insights into its\u0000behavior. This study contributes to the understanding of distance metrics in\u0000high-dimensional spaces, providing insights for applications requiring\u0000efficient navigation and analysis in multi-dimensional domains.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141531666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability of additive-quadratic functional equation in modular space 模块空间中加法二次函数方程的稳定性
arXiv - MATH - General Mathematics Pub Date : 2024-05-29 DOI: arxiv-2406.15436
Abderrahman Baza, Mohamed Rossafi, Choonkil Park
{"title":"Stability of additive-quadratic functional equation in modular space","authors":"Abderrahman Baza, Mohamed Rossafi, Choonkil Park","doi":"arxiv-2406.15436","DOIUrl":"https://doi.org/arxiv-2406.15436","url":null,"abstract":"Using the direct method, we prove the generalised Hyers-Ulam stability of the\u0000following functional equation begin{equation} phi(x+y, z+w)+phi(x-y, z-w)-2\u0000phi(x, z)-2 phi(x, w)=0 end{equation} in modular space satisfying the Fatou\u0000property or $Delta_2$-condition.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141531667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unifying trigonometric and hyperbolic function derivatives via negative integer order polylogarithms 通过负整数阶多项式统一三角函数和双曲函数导数
arXiv - MATH - General Mathematics Pub Date : 2024-05-28 DOI: arxiv-2405.19371
Andrew Ducharme
{"title":"Unifying trigonometric and hyperbolic function derivatives via negative integer order polylogarithms","authors":"Andrew Ducharme","doi":"arxiv-2405.19371","DOIUrl":"https://doi.org/arxiv-2405.19371","url":null,"abstract":"Special functions like the polygamma, Hurwitz zeta, and Lerch zeta functions\u0000have sporadically been connected with the nth derivatives of trigonometric\u0000functions. We show the polylogarithm $text{Li}_s(z)$, a function of complex\u0000argument and order $z$ and $s$, encodes the nth derivatives of the cotangent,\u0000tangent, cosecant and secant functions, and their hyperbolic equivalents, at\u0000negative integer orders $s = -n$. We then show how at the same orders, the\u0000polylogarithm represents the nth application of the operator $x frac{d}{dx}$\u0000on the inverse trigonometric and hyperbolic functions. Finally, we construct a\u0000sum relating two polylogarithms of order $-n$ to a linear combination of\u0000polylogarithms of orders $s = 0, -1, -2, ..., -n$.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"122 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141197274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Multi-resolution Low-rank Tensor Decomposition 多分辨率低阶张量分解
arXiv - MATH - General Mathematics Pub Date : 2024-05-27 DOI: arxiv-2406.18560
Sergio Rozada, Antonio G. Marques
{"title":"A Multi-resolution Low-rank Tensor Decomposition","authors":"Sergio Rozada, Antonio G. Marques","doi":"arxiv-2406.18560","DOIUrl":"https://doi.org/arxiv-2406.18560","url":null,"abstract":"The (efficient and parsimonious) decomposition of higher-order tensors is a\u0000fundamental problem with numerous applications in a variety of fields. Several\u0000methods have been proposed in the literature to that end, with the Tucker and\u0000PARAFAC decompositions being the most prominent ones. Inspired by the latter,\u0000in this work we propose a multi-resolution low-rank tensor decomposition to\u0000describe (approximate) a tensor in a hierarchical fashion. The central idea of\u0000the decomposition is to recast the tensor into emph{multiple}\u0000lower-dimensional tensors to exploit the structure at different levels of\u0000resolution. The method is first explained, an alternating least squares\u0000algorithm is discussed, and preliminary simulations illustrating the potential\u0000practical relevance are provided.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141531668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Soft convex structures 软凸结构
arXiv - MATH - General Mathematics Pub Date : 2024-05-26 DOI: arxiv-2405.19367
José Sanabria, Adolfo Pimienta, Semiramis Zambrano
{"title":"Soft convex structures","authors":"José Sanabria, Adolfo Pimienta, Semiramis Zambrano","doi":"arxiv-2405.19367","DOIUrl":"https://doi.org/arxiv-2405.19367","url":null,"abstract":"In this manuscript the idea of soft convex structures is given and some of\u0000their properties are investigated. Also, soft convex sets, soft concave sets\u0000and soft convex hull operator are defined and their properties are studied.\u0000Moreover, the concepts of soft convexly derived operator and soft convex base\u0000are studied and their relationship to convex structures are explored.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141197278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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