A p.c.f. self-similar set with no self-similar energy

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2017-01-26 DOI:10.4171/jfg/82

Roberto Peirone

引用次数: 3

Abstract

A general class of finitely ramified fractals is that of P.C.F. self-similar sets. An important open problem in analysis on fractals was whether there exists a self-similar energy on every P.C.F. self-similar set. In this paper, I solve the problem, showing an example of a P.C.F. self-similar set where there exists no self-similar energy.

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一个没有自相似能的p.c.f.自相似集

有限分支分形的一个一般类别是P.C.F.自相似集。分形分析中一个重要的开放问题是是否存在一个自相似能在每一个P.C.F.自相似集合上。本文解决了这一问题，给出了一个不存在自相似能量的P.C.F.自相似集的例子。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.