Related papers: Some Structures arising from the Farey Fractal
Some aspects of analysis on disconnected open subsets of the plane with connected fractal boundary are discussed.
We introduce a variational structure for the Fourier-Cattaneo (FC) system which is a second-order hyperbolic system. This variational structure is inspired by the large-deviation rate functional for the Kac process which is closely linked…
We present a new structure theorem for finite fields of odd order that relates multiplicative and additive structure in an interesting way. This theorem has several applications, including an improved understanding of Dickson and Chebyshev…
Partial cubes are isometric subgraphs of hypercubes. Structures on a graph defined by means of semicubes, and Djokovi\'{c}'s and Winkler's relations play an important role in the theory of partial cubes. These structures are employed in the…
The present work aims to exploit the interplay between the algebraic properties of rings and the graph-theoretic structures of their associated graphs. We introduce commutatively closed graphs and investigate properties of commutatively…
The thesis deals with applications of fractional calculus to fractals. It introduces the notion of local fractional derivative (LFD). Fractal and multifractal functions have been studied in the thesis using LFD. New kind of equations are…
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…
This paper presents a new Lie theoretic approach to fractal calculus, which in turn yields such new results as a Fractal Noether's Theorem, a setting for fractal differential forms, for vector fields, and Lie derivatives, as well as…
We present some results about the number of rational points on a certain family of curves defined over a finite field. In a small number of cases the curves have more rational points than expected. Fibonacci numbers make an appearance, as…
We construct first a class of Moran fractals in R^d with countably many generators and non-stationary contraction rates; at each step n, the contractions depend on n-truncated sequences, and are related to asymptotic letter frequencies. In…
We exhibit a characteristic structure of the class of all regular graphs of degree d that stems from the spectra of their adjacency matrices. The structure has a fractal threadlike appearance. Points with coordinates given by the mean and…
Motivated by a fundamental geometrical object, the cut locus, we introduce and study a new combinatorial structure on graphs.
In this paper we consider the algebraic structures related to invariants of topological structures introduced respectively in [CEKL22] and [ADEM19]. Our main results is to show how all these structures are closely related to each other…
Some binary quadratic operads are endowed with anticyclic structures and their characteristic functions as anticyclic operads are determined, or conjectured in one case.
We introduce vortex configurations with fractional topological charges where one unicolor or colorful intersection of two perpendicular vortex pairs contributes to the topological charge of the configurations. Using both, the overlap and…
We study some number theory problems related to the harmonic analysis (Fourier bases) of the Cantor set introduced by Jorgensen and Pedersen in \cite{JP98}.
Pairs of graded graphs, together with the Fomin property of graded graph duality, are rich combinatorial structures providing among other a framework for enumeration. The prototypical example is the one of the Young graded graph of integer…
Fractional supersymmetry denotes a generalisation of supersymmetry which may be constructed using a single real generalised Grassmann variable, $\theta = \bar{\theta}, \, \theta^n = 0$, for arbitrary integer $n = 2, 3, ...$. An explicit…
Computations of the Julia and Mandelbrot sets of the Riemann zeta function and observations of their properties are made. In the appendix section, a corollary of Voronin's theorem is derived and a scale-invariant equation for the bounds in…
Aperiodic algebras are infinite dimensional algebras with generators corresponding to an element of the aperiodic set. These algebras proved to be an useful tool in studying elementary excitations that can propagate in multilayered…