Related papers: A geometric construction for fractal sets and rela…
This article emphasizes an extension of the study of metric and par- tition dimension to hypergraphs. We give a sharp lower bounds for the metric and partition dimension of hypergraphs in general and give exact values under specified…
Context. A porous and/or fractal description can generally be applied where particles have undergone coagulation into aggregates. Aims. To characterise finite-sized, porous and fractal particles and to understand the possible limitations of…
This paper discusses some topics of enquiry concerning fractals, functions on them, and so on.
We have developed a simulation technique that uses non-linear finite element analysis and elastic fracture mechanics to compute physically plausible motion for three-dimensional, solid objects as they break, crack, or tear. When these…
A well studied family of random fractals called fractal percolation is discussed. We focus on the projections of fractal percolation on the plane. Our goal is to present stronger versions of the classical Marstrand theorem, valid for almost…
Self-similar sets with open set condition, the linear objects of fractal geometry, have been considered mainly for crystallographic data. Here we introduce new symmetry classes in the plane, based on rotation by irrational angles. Examples…
We study the formation of fractal structure in one-dimensional many-body systems with attractive power-law potentials. Numerical analysis shows that the range of the index of the power for which fractal structure emerges is limited.…
We describe the construction of the slice fibration of a given one.
In the present article, the main attention is given to fractal sets whose elements have certain restrictions on using digits or combinations of digits in own nega-P-representation. Topological, metric, and fractal properties of images of…
This review aims to provide a very short and pedestrian introduction to some of the basics of extra-dimensional physics. The hope is to facilitate access and to be, in some respects, complementary to the many already existing reviews on…
The algebraic expression $3 + 2 + 6$ can be evaluated to $11$, but it can also be partially evaluated to $5 + 6$. In categorical algebra, such partial evaluations can be defined in terms of the $1$-skeleton of the bar construction for…
These are the lecture notes for a course at the Summer School on "Applied Analysis" at the Technical University Chemnitz in September 2011. We start with the definition of a fractal algebra and show that the fractal property is enormously…
Differential systems with a Fuchsian linear part are studied in regions including all the singularities in the complex plane of these equations. Such systems are not necessarily analytically equivalent to their linear part (they are not…
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…
This article describes a natural piecewise Euclidean bi-simplicial cell structure for the space of $n$-element multisets in a fixed Euclidean rectangle. In particular, we highlight some connections with spaces of complex polynomials and…
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…
Fractals are ubiquitous natural emergences that have gained increased attention in engineering applications, thanks to recent technological advancements enabling the fabrication of structures spanning across many spatial scales. We show how…
An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut
We present a new idea to understand the structure of nuclei, which is comparing to the liquid drop model. After discussing the probability that the nuclear system may be a fractal object with the characteristic of self-similarity, the…
A fractal construction shows that, for any beta>0, the beta-skeleton of a point set can have arbitrarily large dilation. In particular this applies to the Gabriel graph.