Related papers: The multifractal box dimensions of typical measure…
Explicit expressions and computational approaches are given for the Fortet-Mourier distance between a positively weighted sum of Dirac measures on a metric space and a positive finite Borel measure. Explicit expressions are given for the…
Algorithmic fractal dimensions quantify the algorithmic information density of individual points and may be defined in terms of Kolmogorov complexity. This work uses these dimensions to bound the classical Hausdorff and packing dimensions…
The light scattering experiment establishes a relationship between refractive index fluctuations and fractal dimension in weakly scattering tissue-like media. Based on the box-counting approach, an analytical model is developed and shows…
Multiplicative invariance is a well-studied property of subsets of the unit interval. The theory in the complex plane is less developed. This paper introduces an analogous definition for multiplicative invariance in the complex plane…
Porosity and dimension are two useful, but different, concepts that quantify the size of fractal sets and measures. An active area of research concerns understanding the relationship between these two concepts. In this article we will…
Let $(X,d,\mu)$ be an Ahlfors metric measure space. We give sufficient conditions on a closed set $F\subseteq X$ and on a real number $\beta$ in such a way that $d(x,F)^\beta$ becomes a Muckenhoupt weight. We give also some illustrations to…
We estimate the upper and lower bounds of the Hewitt$\textbf{-}$Stromberg dimensions. In particular, these results give new proofs of theorems on the multifractal formalism which is based on the Hewitt$\textbf{-}$Stromberg measures and…
In the context of general iterated function systems (IFSs), we introduce bilinear fractal interpolants as the fixed points of certain Read-Bajraktarevi\'{c} operators. By exhibiting a generalized "taxi-cab" metric, we show that the graph of…
The fractal structure of real world objects is often analyzed using digital images. In this context, the compression fractal dimension is put forward. It provides a simple method for the direct estimation of the dimension of fractals stored…
We show that under quite general conditions, various multifractal spectra may be obtained as Legendre transforms of functions $T\colon \RR\to \RR$ arising in the thermodynamic formalism. We impose minimal requirements on the maps we…
We estimate the growth of the canonical integral of Hadamard-Weierstrass of measure of finite order on the complex plane by the type of counting function or average counting function of this measure
In this paper, we prove central limit theorems for bias reduced estimators of the structure function of several multifractal processes, namely mutiplicative cascades, multifractal random measures, multifractal random walk and multifractal…
A multifractal analysis is performed on a three-dimensional grayscale image associated with a complex system. First, a procedure for generating 3D synthetic images (2D image stacks) of a complex structure exhibiting multifractal behaviour…
We compute the Hausdorff, upper box and packing dimensions for certain inhomogeneous Moran set constructions. These constructions are beyond the classical theory of iterated function systems, as different nonlinear contraction…
We consider the class of multiple Fourier series associated with functions in the Dirichlet space of the polydisc. We prove that every such series is summable with respect to unrestricted rectangular partial sums, everywhere except for a…
One of the goals of this article is to define a an unified setting adapted to the description of means (normalized integrals or invariant means) on an infinite product of measured spaces with infinite measure. We first remark that some…
The classical Stein--Tomas theorem extends the theory of linear Fourier restriction estimates from smooth manifolds to fractal measures exhibiting Fourier decay. In the multilinear setting, transversality allows for Fourier extension…
We describe a parametrization of the box variety (variety of cuboids) by theta functions. This will imply that the box variety is a modular variety. Actually this parametrization can be defined over the Gauss number field.
We invent the notion of a {\it dimension of a variety} $V$ as the cardinality of all its proper {\it derived} subvarieties (of the same type). The dimensions of varieties of lattices, varieties of regular bands and other general algebraic…
Let $K \subset \mathbb{R}^{2}$ be a rotation and reflection free self-similar set satisfying the strong separation condition, with dimension $\dim K = s > 1$. Intersecting $K$ with translates of a fixed line, one can study the $(s -…