Related papers: Minkowski Measurability and Exact Fractal Tube For…
The dual formulation of the compact U(1) lattice gauge theory in three spacetime dimensions allows to finely study the squared width and the profile of the confining flux tube on a wide range of physical interquark distances. The results…
Fractal is an intriguing geometry with self-similarity and non-integer dimensions, the elastic-wave topological phase based on fractal structures has not been revealed up to now. In this work, elastic-wave higher-order topological states in…
We calculate dimensional reduction of gravitational flux tube solutions in the scheme of Kaluza-Klein theory. The fifth dimension is compacified to a region of Planck size. Assuming the width of the tube to be also Planck size we obtain…
This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its…
Fibonacci word fractals are a class of fractals that have been studied recently, though the word they are generated from is more widely studied in combinatorics. The Fibonacci word can be used to draw a curve which possesses…
The problem of detecting and measuring the repetitiveness of one-dimensional strings has been extensively studied in data compression and text indexing. Our understanding of these issues has been significantly improved by the introduction…
The area-perimeter scaling can be employed to evaluate the fractal dimension of urban boundaries. However, the formula in common use seems to be not correct. By means of mathematical method, a new formula of calculating the boundary…
The general volume of a star body, a notion that includes the usual volume, the $q$th dual volumes, and many previous types of dual mixed volumes, is introduced. A corresponding new general dual Orlicz curvature measure is defined that…
We study the spectrum of the Fibonacci Hamiltonian and prove upper and lower bounds for its fractal dimension in the large coupling regime. These bounds show that as $\lambda \to \infty$, $\dim (\sigma(H_\lambda)) \cdot \log \lambda$…
We study a class of 2-variable polynomials called exact polynomials which contains $A$-polynomials of knot complements. The Mahler measure of these polynomials can be computed in terms of a volume function defined on the vanishing set of…
The $L_p$ chord Minkowski problem was recently introduced by Lutwak, Xi, Yang and Zhang, which seeks to determine the necessary and sufficient conditions for a given finite Borel measure such that it is the $L_p$ chord measure of a convex…
The $L_p$ chord Minkowski problem based on Chord measures and $L_p$ chord measures introduced firstly by Lutwak, Xi, Yang and Zhang [38] is a very important and meaningful geometric measure problem in the $L_p$ Brunn-Minkowski theory. Xi,…
We give a direct, pointwise proof for the tube formula of Lapidus-Pearse for self-similar fractals, where we allow non-convex, non-Steiner-like generators.
We revisit the problem of characterizing the eigenvalue distribution of the Dirichlet-Laplacian on bounded open sets $\Omega\subset\mathbb{R}$ with fractal boundaries. It is well-known from the results of Lapidus and Pomerance \cite{LapPo1}…
A general construction of Laakso-type fractal spaces was recently introduced by the first two authors. In this paper, we establish a simple condition characterizing when the Ahlfors regular conformal dimension of a symmetric Laakso-type…
Since the recent dissertation by Steffen Winter, for certain self-similar sets $F$ the growth behaviour of the Minkowski functionals of the parallel sets $F_\varepsilon := \{x\in \mathbb R^d : d(x,F)\leq \varepsilon\}$ as $\varepsilon…
The notion of $s$--fractional $L^p$ polar projection bodies, recently introduced by Haddad and Ludwig (Math.\ Ann.\ \textbf{388}:1091--1115, 2024), provides a bridge between fractional Sobolev theory and convex geometry. In this manuscript,…
This work proposes to obtain novel fractal descriptors from gray-level texture images by combining information from interior and boundary measures of the Minkowski dilation applied to the texture surface. At first, the image is converted…
While numerous examples of fractal spaces may be found in various fields of science, the flow of time is typically assumed to be one-dimensional and smooth. Here we present a metamaterial-based physical system, which can be described by…
We examine the scaling properties of an evolving network of strings in Minkowski spacetime and study the evolution of length scales in terms of a 3-scale model proposed by Austin, Copeland and Kibble (ACK). We find good qualitative and some…