Results 31 to 40 of about 127 (112)
The Hausdorff dimension and exact Hausdorff measure of random recursive sets with overlapping
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 1, Page 11-21, 2002., 2002 We weaken the open set condition and define a finite intersection property in the construction of the random recursive sets. We prove that this larger class of random sets are fractals in the sense of Taylor, and give conditions when these sets have positive and finite Hausdorff measures, which in certain extent generalize some of the known results ...
Hongwen Guo, Dihe Hu
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Abstract and Applied AnalysisMSC2020 Classification: 28A80, 47H10, 54E50 ...
A. Herminau Jothy +3 more
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Strongly nonlinear potential theory on metric spaces
Abstract and Applied Analysis, Volume 7, Issue 7, Page 357-374, 2002., 2002 We define Orlicz‐Sobolev spaces on an arbitrary metric space with a Borel regular outer measure, and we develop a capacity theory based on these spaces. We study basic properties of capacity and several convergence results. We prove that each Orlicz‐Sobolev function has a quasi‐continuous representative. We give estimates for the capacity of balls when
Noureddine Aïssaoui
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A Unified Framework Linking Entropy, Fractal Dimension, and Lyapunov Exponents in Chaotic Dynamics
Complexity, Volume 2026, Issue 1, 2026.This study presents a universal operator framework predicting critical transitions in nonlinear systems through the intrinsic nexus of entropy, fractal geometry, and chaos. We derive a unified model (Equation 4) that integrates fractal dimension (Dᵓ), Lyapunov exponents (λᵢ), and entropy (S) into a single predictive equation, justified through ...
Elio Quiroga Rodríguez, Naoki Masuda
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Fractal multiwavelets related to the cantor dyadic group
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 2, Page 307-314, 1998., 1997 Orthogonal wavelets on the Cantor dyadic group are identified with multiwavelets on the real line consisting of piecewise fractal functions. A tree algorithm for analysis using these wavelets is described. Multiwavelet systems with algorithms of similar structure include certain orthogonal compactly supported multiwavelets in the linear double‐knot ...
W. Christopher Lang
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Intermediate Value Property for the Assouad Dimension of Measures
Analysis and Geometry in Metric Spaces, 2020 Hare, Mendivil, and Zuberman have recently shown that if X ⊂ ℝ is compact and of non-zero Assouad dimension dimA X, then for all s > dimA X, X supports measures with Assouad dimension s. We generalize this result to arbitrary complete metric spaces.
Suomala Ville
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Journal of Function Spaces, Volume 2026, Issue 1, 2026.In this paper, we study Riemann–Liouville fractional calculus of nonlinear hidden variable recurrent fractal interpolation function (HVRFIF) constructed based on Rakotch contraction, which is a generalization of Banach contraction. First, we prove that Riemann–Liouville fractional integral and derivative of HVRFIF based on Rakotch contraction are also ...
Chung-Il Ro +4 more
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International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 1, Page 97-106, 1995., 1993 We define the coordinate d‐dimension print to distinguish sets of same fractal dimension, and investigate its geometrical properties.
Hung Hwan Lee, In Soo Baek
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Moments of the weighted Cantor measures
Demonstratio Mathematica, 2019 Based on the seminal work of Hutchinson, we investigate properties of α-weighted Cantor measures whose support is a fractal contained in the unit interval.
Harding Steven N. +1 more
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Analysis of Fractal Complex Differential Equations Using the Homotopy Analysis Method
Journal of Mathematics, Volume 2026, Issue 1, 2026.This study investigates fractal complex differential equations using the homotopy analysis method (HAM). The method provides an effective analytical approach. The fundamental concepts of fractal complex calculus and the theoretical framework of HAM are briefly presented.
Muhammed Emin Batuhan +2 more
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