Results 61 to 70 of about 3,079 (209)
Progress on Fractal Dimensions of the Weierstrass Function and Weierstrass-Type Functions
Fractal and FractionalThe Weierstrass function W(x)=∑n=1∞ancos(2πbnx) is a function that is continuous everywhere and differentiable nowhere. There are many investigations on fractal dimensions of the Weierstrass function, and the investigation of its Hausdorff dimension is ...
Yue Qiu, Yongshun Liang
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A Note on Sobolev‐Lorentz Capacity and Hausdorff Measure
Mathematische Nachrichten, EarlyView.ABSTRACT In this paper, we give an elementary proof that sets of zero p,1$p,1$‐Sobolev‐Lorentz capacity are Hn−p$\mathcal {H}^{n-p}$‐null sets, independently of nonlinear potential theory. We further show that there exists a set of Sobolev‐Lorentz‐(p,1)$(p,1)$ capacity equal to zero with Hausdorff dimension equal n−p$n-p$.
Daniel Campbell
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We develop a unified mathematical framework extending classical moment theory from discrete integer orders to a continuous spectrum of real orders f>0$$ f>0 $$, providing a systematic statistical characterization of complex systems exhibiting power‐law behavior.
Farrukh A. Chishtie
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Numerical estimates of Hausdorff dimension [PDF]
Journal of Computational Physics, 1982 Numerical methods for estimating Hausdorff dimension, useful in the analysis of turbulence, are explained and applied to a specific example. In particular, methods involving rescaling and approximation by Cantor sets are discussed.
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On the Existence of Solutions of Dynamic Equations on Time Scales in Banach Spaces
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT In this paper we address the question of solvability of dynamic equations on time scales in Banach spaces. In particular, our main theorem extends the result for classical differential equations in Banach spaces of Banaś and Goebel established in [5], to an arbitrary time scale.
Dušan Oberta
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On the Dimension of Paracompact Hausdorff Spaces [PDF]
Nagoya Mathematical Journal, 1955 This short note gives the generalized sum theorem for Lebesgue dimension of paracompact Hausdorff spaces. Our theorem, though it is a generalization of Mr. Morita’s sum theorem for fully normal spaces [3, Theorem 3. 2] which is essentially based on his generalized sum theorem for normal spaces [3, Theorem 3.1], is obtained by very brief arguments ...
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Computational aspects of the Hausdorff distance in unbounded dimension
Journal of Computational Geometry, 2014 We study the computational complexity of determining the Hausdorff distance oftwo polytopes given in halfspace- or vertex-presentation in arbitrary dimension.
Stefan König
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Renormalization techniques for inflation systems and some of their applications
Acta Crystallographica Section A, EarlyView.In this work, renormalization methods for quantities related to the diffraction of inflation systems are surveyed.Exact renormalization techniques are important and powerful, particularly for inflation‐generated systems. We review recent results in this direction.
Michael Baake +4 more
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On the Billingsley dimension of Birkhoff average in the countable symbolic space
Comptes Rendus. Mathématique, 2020 We compute a lower bound of Billingsley–Hausdorff dimension, defined by Gibbs measure, of the level set related to Birkhoff average in the countable symbolic space $\mathbb{N}^{\mathbb{N}}$.
Attia, Najmeddine, Selmi, Bilel
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Fractal properties of particle paths due to generalised uncertainty relations
European Physical Journal C: Particles and Fields, 2022 We determine the Hausdorff dimension of a particle path, $$D_\textrm{H}$$ D H , in the recently proposed ‘smeared space’ model of quantum geometry. The model introduces additional degrees of freedom to describe the quantum state of the background and ...
Matthew J. Lake
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