Fractal dimension for fractal structures
TLDR
A new definition in order to compute the fractal dimension of a subset respect to any fractal structure, which completes the theory of classical box-counting dimension and allows to classify and distinguish a much larger number of topological spaces than the classical definition.About:
This article is published in Topology and its Applications.The article was published on 2014-02-15 and is currently open access. It has received 66 citations till now. The article focuses on the topics: Fractal & Fractal dimension.read more
Citations
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Structure, Fractality, Mechanics and Durability of Calcium Silicate Hydrates
TL;DR: In this paper, the main product of hydrated products of cement-based materials is calcium silicate hydrate (C-S-H) gels that are considered as the binding phase of cement paste.
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Fractal dimension for fractal structures: A Hausdorff approach revisited
TL;DR: In this article, a new approach to the Hausdorff dimension from both continuous and discrete points of view has been proposed, based on the fractal structure of Euclidean spaces.
Journal ArticleDOI
Cryptocurrency market efficiency in short- and long-term horizons during COVID-19: An asymmetric multifractal analysis approach
Shinji Kakinaka,Ken Umeno +1 more
TL;DR: In this paper, the authors investigated asymmetric multifractality and market efficiency of the major cryptocurrencies during the COVID-19 pandemic while accounting for different investment horizons, and showed that the outbreak affected the efficiency property of price behaviors differently between short and long-term horizons.
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Chaotic evolution of prisoner's dilemma game with volunteering on interdependent networks
TL;DR: It is showed that voluntary participation could effectively promote the density of co-operation, that is also greatly affected by interdependent strength between two coupled networks and found that an intermediate interdependence would play a bigger role on the evolution of dynamics.
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Evaluation of Floor Water Inrush based on Fractal Theory and an Improved Analytic Hierarchy Process
TL;DR: A new evaluation model based on fractal theory and an improved analytic hierarchy process (IAHP) was developed to predict the potential for water inrush in Lu-an mining area.
References
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Book
The Fractal Geometry of Nature
TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.
Book
Fractal Geometry: Mathematical Foundations and Applications
TL;DR: In this article, a mathematical background of Hausdorff measure and dimension alternative definitions of dimension techniques for calculating dimensions local structure of fractals projections of fractality products of fractal intersections of fractalities.
Journal ArticleDOI
Partial Metric Topology
TL;DR: This paper presents a symmetric generalised metric for such topologies, an approach which sheds new light on how metric tools such as Banach's Theorem can be extended to non‐Hausdorff topologies.
Book ChapterDOI
Generalized Metric Spaces
TL;DR: The notion of generalized metric spaces as mentioned in this paper is a generalization of metric spaces that is closely related to what is known as metrization theory and can be used to characterize the images or pre-images of the metric spaces under certain kinds of mappings.