Related papers: Quasi-fractal sets in space

Some aspects of analysis on disconnected open subsets of the plane with connected fractal boundary are discussed.

The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…

In this paper we define a new class of weighted complex networks sharing several properties with fractal sets, and whose topology can be completely analytically characterized in terms of the involved parameters and of the fractal dimension.…

Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…

This article was prepared in connection with the 2009 Barnett lecture at the University of Cincinnati, and deals with various classes of fractal sets and analysis on them.

The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…

Extremal elements and a h-hull of sets in the n-dimensional hypercomplex space are investigated. Introduced a class of H-quasiconvex sets including strongly hypercomplex convex sets and being closed with respect to intersections.

In this note, we extend the quasi-projective dimension of finite (that is, finitely generated) modules to homologically finite complexes, and we investigate some of homological properties of this dimension.

In this talk, we touch upon the chaotic and fractal aspects of the Universe.

The soft topological spaces and some their related concepts have stud- ied in [7]. In this paper, we introduce and study the notions of soft connected topological spaces after a review of preliminary definitions.

In the present article, topological, metric, and fractal properties of certain sets are investigated. These sets are images of sets whose elements have restrictions on using digits or combinations of digits in own s-adic representations,…

The paper presents mathematical models of quasicrystals with particular attention given to cut-and-project sets. We summarize the properties of higher-dimensional quasicrystal models and then focus on the one-dimensional ones. For the…

In this paper, a class of fractals, called quadrilateral labyrinth fractals, are introduced and studied. They are a special kind of fractals on any quadrilateral on the plane. This type of fractal is motivated by labyrinth fractal on the…

We construct field theories in $2+1$ dimensions with multiple conformal symmetries acting on only one of the spatial directions. These can be considered a conformal extension to "subsystem scale invariances", borrowing the language often…

Here we look at (collections of) semimetrics and seminorms, including their ultrametric versions. In particular, we are concerned with geometric properties related to connectedness and topological dimension 0.

This is a brief survey which reviews some traditional themes in harmonic analysis and some more recent areas of activity, connected to "analysis on fractals" in particular.

The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…

We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several…

This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…

The main purpose of this paper is to study complex valued metric-like spaces as an extension of metric-like spaces, complex valued partial metric spaces, partial metric spaces, complex valued metric spaces and metric spaces. In this…