南方科技大学知识苑(SUSTech KC): ON SELF-SIMILARITY OF QUADRANGLE

题名	ON SELF-SIMILARITY OF QUADRANGLE
作者	Xu, Jiajun 1; Xi, Jinghua 2; Jiang, Kan 1
通讯作者	Jiang, Kan
发表日期	2024-06-01
DOI	10.1142/S0218348X24500968
发表期刊	FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY 影响因子和分区
ISSN	0218-348X
EISSN	1793-6543
摘要	Wen [Some problems in fractal geometry, in Report in Chinese Conference on Fractal Geometry and Dynamical Systems, 2023] posed the following questions: when a quadrangle is a self-similar set with the open set condition (OSC). It is well known that any convex quadrangle is a self-similar set. For the concave quadrangles, this case is more complicated. Loosely speaking, some concave polygons may be not self-similar. In this paper, we prove two results. First, we give a necessary and sufficient condition such that a concave quadrangle is a self-similar set. Moreover, we also give a necessary condition for a concave quadrangle to be a self-similar set with the OSC. For the convex quadrangle, we investigate the trapezoid. We show under some condition that the trapezoid is a self-similar set with the OSC. In particular, for any trapezoid, if the ratio of the lengths of two bases is rational, then the trapezoid is a self-similar set with the OSC.
关键词	Self-Similar Set Open Set Condition Trapezoid Concave Quadrangle
相关链接	[来源记录]
收录类别	SCI ; EI
语种	英语
学校署名	其他
资助项目	National Natural Science Foundation of China["11701302","12171259","11831007","11771226"]
WOS研究方向	Mathematics ; Science & Technology - Other Topics
WOS类目	Mathematics, Interdisciplinary Applications ; Multidisciplinary Sciences
WOS记录号	WOS:001258103200002
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
ESI学科分类	MATHEMATICS
来源库	Web of Science
引用统计
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/783866
专题	理学院_数学系
作者单位	1.Ningbo Univ, Sch Math & Stat, Ningbo, Peoples R China 2.Southern Univ Sci & Technol, Dept Math, Shenzhen, Peoples R China
推荐引用方式 GB/T 7714	Xu, Jiajun,Xi, Jinghua,Jiang, Kan. ON SELF-SIMILARITY OF QUADRANGLE[J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY,2024.
APA	Xu, Jiajun,Xi, Jinghua,&Jiang, Kan.(2024).ON SELF-SIMILARITY OF QUADRANGLE.FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY.
MLA	Xu, Jiajun,et al."ON SELF-SIMILARITY OF QUADRANGLE".FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY (2024).