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FRACTAL DIMENSION OF PRODUCT OF CONTINUOUS FUNCTIONS WITH BOX DIMENSION
Fractals, 2023This paper investigates fractal dimension of product of continuous functions with Box dimension on [Formula: see text]. For two continuous functions with different Box dimensions, the Box dimension of their product has been proved to be the larger one. Furthermore, the Box dimension of product of two continuous functions with the same Box dimension may
Liu, Peizhi, Du, Yumeng, Liang, Yongshun
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Learning boxes in high dimension
Algorithmica, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Beimel, A., Kushilevitz, E.
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BOX DIMENSIONS OF α-FRACTAL FUNCTIONS
Fractals, 2016The box dimension of the graph of non-affine, continuous, nowhere differentiable function [Formula: see text] which is a fractal analogue of a continuous function [Formula: see text] corresponding to a certain iterated function system (IFS), is investigated in the present paper.
Akhtar, Md. Nasim +2 more
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2019
The main goal of this chapter is to generalize the classical box dimension in the broader context of fractal structures. We state that whether the so-called natural fractal structure (which any Euclidean subset can be always endowed with) is selected, then the box dimension remains as a particular case of the generalized fractal dimension models.
Manuel Fernández-Martínez +3 more
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The main goal of this chapter is to generalize the classical box dimension in the broader context of fractal structures. We state that whether the so-called natural fractal structure (which any Euclidean subset can be always endowed with) is selected, then the box dimension remains as a particular case of the generalized fractal dimension models.
Manuel Fernández-Martínez +3 more
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Box-counting dimensions of popcorn subsets
Journal of Mathematical Analysis and Applications, 2023Let \(S\) be a subset of \(\mathbb N\).
Du, Yali, Wei, Chun, Wen, Shengyou
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Box dimension of Neimark–Sacker bifurcation
Journal of Difference Equations and Applications, 2014In this paper we show how a change of a box dimension of orbits of two-dimensional discrete dynamical systems is connected to their bifurcations in a nonhyperbolic fixed point. This connection is already shown in the case of one-dimensional discrete dynamical systems and Hopf bifurcation for continuous systems.
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Network Box Counting Dimension
2020In this chapter we begin our detailed study of fractal dimensions of a network \(\mathbb {G}\). There are two approaches to calculating a fractal dimension of \(\mathbb {G}\). One approach, applicable if \(\mathbb {G}\) is a spatially embedded network, is to treat \(\mathbb {G}\) as a geometric object and apply techniques, such as box counting or ...
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On the Box Dimension of Typical Measures
Monatshefte f�r Mathematik, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Myjak, Józef, Rudnicki, Ryszard
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BOX DIMENSION OF BILINEAR FRACTAL INTERPOLATION SURFACES
Bulletin of the Australian Mathematical Society, 2018Bilinear fractal interpolation surfaces were introduced by Ruan and Xu in 2015. In this paper, we present the formula for their box dimension under certain constraint conditions.
QING-GE KONG, HUO-JUN RUAN, SHENG ZHANG
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BOX-COUNTING DIMENSION COMPUTED BY α-DENSE CURVES
Fractals, 2017We introduce a method to reduce to the real case the calculus of the box-counting dimension of subsets of the unit cube [Formula: see text], [Formula: see text]. The procedure is based on the existence of special types of [Formula: see text]-dense curves (a generalization of the space-filling curves) in [Formula: see text] called [Formula: see text ...
García Macías, Gonzalo +2 more
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