相关论文: Fractal algebras of discretization sequences

Fractal functions that produce smooth and non-smooth approximants constitute an advancement to classical nonrecursive methods of approximation. In both classical and fractal approximation methods emphasis is given for investigation of…

The theory of finitely supported algebraic structures is related to Pitts theory of nominal sets (by equipping finitely supported sets with finitely supported internal algebraic laws). It represents a reformulation of Zermelo Fraenkel set…

In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…

In 2009, the first author introduced a new class of zeta functions, called `distance zeta functions', associated with arbitrary compact fractal subsets of Euclidean spaces of arbitrary dimension. It represents a natural, but nontrivial…

We introduce the fractal expansions, sequences of integers associated to a number. We show that these sequences characterize the O-sequences and encode some information on lex segment ideals. Moreover, we introduce a numerical functions…

We introduce the concept of fractels for functions and discuss their analytic and algebraic properties. We also consider the representation of polynomials and analytic functions using fractels, and the consequences of these representations…

We give a unified interpretation of confluences, contiguity relations and Katz's middle convolutions for linear ordinary differential equations with polynomial coefficients and their generalization to partial differential equations. The…

In this paper, we introduce the concept of the $\alpha$-fractal function and fractal approximation for a set-valued continuous map defined on a closed and bounded interval of real numbers. Also, we study some properties of such fractal…

Our main goal in this long survey article is to provide an overview of the theory of complex fractal dimensions and of the associated geometric or fractal zeta functions, first in the case of fractal strings (one-dimensional drums with…

We consider three notions of divisibility in the Cuntz semigroup of a C*-algebra, and show how they reflect properties of the C*-algebra. We develop methods to construct (simple and non-simple) C*-algebras with specific divisibility…

Following \cite{Visintin}, we exploit the fractional perimeter of a set to give a definition of fractal dimension for its measure theoretic boundary. We calculate the fractal dimension of sets which can be defined in a recursive way and we…

We forge connections between the theory of fractal sets obtained as attractors of iterated function systems and process calculi. To this end, we reinterpret Milner's expressions for processes as contraction operators on a complete metric…

We develop a new definition of fractals which can be considered as an abstraction of the fractals determined through self-similarity. The definition is formulated through imposing conditions which are governed the relation between the…

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…

An important problem in the analysis of experimental data showing fractal properties, is that such samples are composed by a set of points limited by an upper and a lower cut off. We study how finite size effect due to the discreteness of…

Abstrct: In this note, by considering fractionally linear functions over a finite field and consequently developing an abstract sequence, we study some of its properties.

A fractal function is a function whose graph is the attractor of an iterated function system. This paper generalizes analytic continuation of an analytic function to continuation of a fractal function.

In this manuscript, fractal and fuzzy calculus are summarized. Fuzzy calculus in terms of fractal limit, continuity, its derivative, and integral are formulated. The fractal fuzzy calculus is a new framework that includes fractal fuzzy…

By appropriate choices of elements in the underlying iterated function system, methodology of fractal interpolation entitles one to associate a family of continuous self-referential functions with a prescribed real-valued continuous…

This article discusses the notion of convergence of sequences of iterated function systems. The technique of iterated function systems is one of the several methods to construct objects with fractal nature, and the fractals obtained with…