Related papers: Contractive function systems, their attractors and…
This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff's concepts of fractional dimension geometry. The…
In this thesis, we study connections between metric and combinatorial graphs from a Dirichlet space point of view.
A recently developed viewpoint on the fundamentals of density-functional theory for finite interacting spin-lattice systems that centers around the notion of degeneracy regions is presented. It allows for an entirely geometrical description…
A way to add an extra dimension is briefly discussed.
The Theory of Functional Connections (TFC) is a functional interpolation framework founded upon the so-called constrained expression: a functional that expresses the family of all possible functions that satisfy some user-specified, linear…
In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…
Static vortices close together are studied for two different models in 2-dimen- sional Euclidean space. In a simple model for one complex field an expansion in the parameters describing the relative position of two vortices can be given in…
We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1$ $$ < $$ $$h$$ $$ <$$ $$ 2$, a fractal distribution…
The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. A textural fractal can be employed to explain the scale-free property of regional boundaries such as border lines,…
We initiate the study of pseudofiniteness in continuous logic. We introduce a related concept, namely that of pseudocompactness, and investigate the relationship between the two concepts. We establish some basic properties of…
There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…
We review a formulation of the entanglement entropy of a quantum scalar field in terms of its spacetime two-point correlation functions. We discuss applications of this formulation to studying entanglement entropy in various settings in…
Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…
We describe a class of fractal attractors induced by \beta-shifts. We use a coding by these shifts to show that the systems are mixing with topological entropy log \beta and have an ergodic measure of full entropy. Moreover we determine 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…
We propose a measure of shape which is appropriate for the study of a complicated geometric structure, defined using the topology of neighborhoods of the structure. One aspect of this measure gives a new notion of fractal dimension. We…
Here, we investigate the fractal-lattice Hubbard model using various numerical methods: exact diagonalization, the self-consistent diagonalization of a (mean-field) Hartree-Fock Hamiltonian and state-of-the-art Auxiliary-Field Quantum Monte…
The intention of this article is to introduce a generalization of Proinov-type contraction via simulation functions. We name this generalized contraction map as Proinov-type Z-contraction. This article establishes the existence and…
The role of projectors associated with Poisson brackets of constrained Hamiltonian systems is analyzed. Projectors act in two instances in a bracket: in the explicit dependence on the variables and in the computation of the functional…
In this work, we provide an overview of the recent investigations on the non-extensive Tsallis statistics and its applications to high energy physics and astrophysics, including physics at the Large Hadron Collider (LHC), hadron physics,…