{"title":"WEAK TANGENTS ON CLOSED POPCORN GRAPHS","authors":"Haipeng Chen, Lixuan Zheng","doi":"10.1142/s0218348x23500731","DOIUrl":null,"url":null,"abstract":"Given [Formula: see text], we study the Assouad dimension and weak tangents of closed [Formula: see text]-popcorn graphs. For all [Formula: see text], we prove that [Formula: see text] is a weak tangent of the closed [Formula: see text]-popcorn graphs by using some arguments on prime numbers. For all [Formula: see text], we first show that the Assouad dimension of the closed [Formula: see text]-popcorn graphs is 1, and then prove that [Formula: see text] is a weak tangent of them. We also discuss some specific weak tangents of closed [Formula: see text]-popcorn graphs when [Formula: see text] and [Formula: see text].","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":" ","pages":""},"PeriodicalIF":3.3000,"publicationDate":"2023-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0218348x23500731","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 1
Abstract
Given [Formula: see text], we study the Assouad dimension and weak tangents of closed [Formula: see text]-popcorn graphs. For all [Formula: see text], we prove that [Formula: see text] is a weak tangent of the closed [Formula: see text]-popcorn graphs by using some arguments on prime numbers. For all [Formula: see text], we first show that the Assouad dimension of the closed [Formula: see text]-popcorn graphs is 1, and then prove that [Formula: see text] is a weak tangent of them. We also discuss some specific weak tangents of closed [Formula: see text]-popcorn graphs when [Formula: see text] and [Formula: see text].
期刊介绍：
The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development and applications in the past decades. For this relatively short time, geometrical and/or temporal scaling have been shown to represent the common aspects of many processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry, economics, engineering and technology, and human behavior. As a rule, the complex nature of a phenomenon is manifested in the underlying intricate geometry which in most of the cases can be described in terms of objects with non-integer (fractal) dimension. In other cases, the distribution of events in time or various other quantities show specific scaling behavior, thus providing a better understanding of the relevant factors determining the given processes.
Using fractal geometry and scaling as a language in the related theoretical, numerical and experimental investigations, it has been possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iterative functions, colloidal aggregation, biological pattern formation, stock markets and inhomogeneous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality.
The main challenge of the journal devoted exclusively to the above kinds of phenomena lies in its interdisciplinary nature; it is our commitment to bring together the most recent developments in these fields so that a fruitful interaction of various approaches and scientific views on complex spatial and temporal behaviors in both nature and society could take place.
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