Results 221 to 230 of about 135,666 (260)

On the Intermediate Values of the Box Dimensions

Siberian Mathematical Journal, 2023
The box dimension \(\dim_B X\) of a metric compactum \((X,\rho)\) is defined by the formula \[ \dim_B X=\lim_{\varepsilon\to 0}\frac{\log N(X,\varepsilon)}{-\log\varepsilon}, \] where \(N(X,\varepsilon)\) denotes the least number of closed balls of radius \(\varepsilon\) needed to cover \(X\).
openaire   +2 more sources

Learning boxes in high dimension

Algorithmica, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amos Beimel, Eyal Kushilevitz
openaire   +2 more sources

On the Box Dimension of Typical Measures

Monatshefte f�r Mathematik, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Myjak, Józef, Rudnicki, Ryszard
openaire   +2 more sources

BOX DIMENSION AND MINKOWSKI CONTENT OF THE CLOTHOID

Fractals, 2009
We prove that the box dimension of the standard clothoid is equal to d = 4/3. Furthermore, this curve is Minkowski measurable, and we compute its d-dimensional Minkowski content. Oscillatory dimensions of component functions of the clothoid are also equal to 4/3.
Županović, Vesna, Žubrinić, Darko, Korkut, Luka   +2 more
openaire   +2 more sources

BOX DIMENSIONS OF α-FRACTAL FUNCTIONS

Fractals, 2016
The 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, Prasad, M. Guru Prem, Navascués, M. A.   +2 more
openaire   +2 more sources

Box dimension of Neimark–Sacker bifurcation

Journal of Difference Equations and Applications, 2014
In 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.
openaire   +3 more sources

Box Dimension Type Models

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, Juan Luis García Guirao, Miguel Ángel Sánchez-Granero, Juan Evangelista Trinidad Segovia   +3 more
openaire   +1 more source

Box and packing dimensions of projections and dimension profiles

Mathematical Proceedings of the Cambridge Philosophical Society, 2001
For E a subset of ℝn and s ∈ [0, n] we define upper and lower box dimension profiles, B-dimsE and B-dimsE respectively, that are closely related to the box dimensions of the orthogonal projections of E onto subspaces of ℝn. In particular, the projection of E onto almost all m-dimensional subspaces has upper box dimension B-dimmE and lower box ...
openaire   +2 more sources

Box and Packing Dimensions of Typical Compact Sets

Monatshefte f�r Mathematik, 2000
Let \((X,\rho)\) be a complete metric space. For a set \(A\subset X\), the number \[ \text{sl-}\overline\dim A= \inf\{\overline\dim(B(x, r)\cap A): x\in A, r> 0\} \] is called the smallest local upper box dimension of \(A\), where \(\overline\dim\) is the upper box dimension of the corresponding set and \(B(r,x)\) is the ball of radius \(r\) centred at
Myjak, Józef, Rudnicki, Ryszard
openaire   +1 more source

BOX DIMENSION OF BILINEAR FRACTAL INTERPOLATION SURFACES

Bulletin of the Australian Mathematical Society, 2018
Bilinear 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
openaire   +1 more source