Related papers: A geometric construction for fractal sets and rela…
We have built a new kind of manifolds which leads to an alternative new geometrical space. The study of the nowhere differentiable functions via a family of mean functions leads to a new characterization of this category of functions. A…
Algorithmic fractal dimensions -- constructs of computability theory -- have recently been used to answer open questions in classical geometric measure theory, questions of mathematical analysis whose statements do not involve computability…
We give a geometric characterisation of plus-one generated projective line arrangements that are next-to-free. We present new succinct proofs, via associated line bundles, for some properties of plus-one generated projective line…
We provide a rigorous study on dimensions of fractal interpolation function defined on a closed and bounded interval of $\mathbb{R}$ which is associated to a continuous function with respect to a base function, scaling functions and a…
Gauging is a ubiquitous tool in many-body physics. It allows one to construct highly entangled topological phases of matter from relatively simple phases and to relate certain characteristics of the two. Here we develop a gauging procedure…
In this paper, we extend the principles of Nambu mechanics by incorporating fractal calculus. This extension introduces Hamiltonian and Lagrangian mechanics that incorporate fractal derivatives. By doing so, we broaden the scope of our…
Kaluza-Klein theory in which the geometry of an additional dimension is fractal has been considered. In such a theory the mass of an elementary electric charge appears to be many orders of magnitude smaller than the Planck mass, and the…
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…
This paper provides a summary of the fractal calculus framework. It presents higher-order homogeneous and nonhomogeneous linear fractal differential equations with $\alpha$-order. Solutions for these equations with constant coefficients are…
By examining arithmetic operations between decimal numbers in a given base m we uncover fractal structures that generalize the Sierpinski triangle
We describe a new way to construct finite geometric objects. For every k we obtain a symmetric configuration E(k-1) with k points on a line. In particular, we have a constructive existence proof for such configurations. The method is very…
There are many research papers dealing with fractal dimension of real-valued fractal functions in the recent literature. The main focus of the present paper is to study fractal dimension of complex-valued functions. This paper also…
A process of extending sets which can be used as foundation for an alternative organization for Differential and Integral Calculus is presented.
We review the theoretical framework that establishes a crucial bridge between the general Steiner-type formula of Hug, Last, and Weil and the theory of complex (fractal) dimensions of Lapidus et all. Two novel families of geometric…
This paper seeks to build on the extensive connections that have arisen between automata theory, combinatorics on words, fractal geometry, and model theory. Results in this paper establish a characterization for the behavior of the fractal…
This paper provides an alternative description for the fixed points of the fractal operator associated with a mixed possibly infinite iterated function system via a canonical projection type function. Some visual aspects of our results are…
Modern SAT solvers have experienced a remarkable progress on solving industrial instances. Most of the techniques have been developed after an intensive experimental testing process. Recently, there have been some attempts to analyze the…
In this paper we present a method for constructing the continuous best fractal approximation in the space of bounded functions. We construct the finite-dimensional subspace of the space of bounded functions whose base consists of the…
Fracton topological phases host fractionalized excitations that are either completely immobile or only mobile along certain lines or planes. We demonstrate how such phases can be understood in terms of two fundamentally different types of…
In this study the general formula for differential and integral operations of fractional calculus via fractal operators by the method of cumulative diminution and cumulative growth is obtained. The under lying mechanism in the success of…