Related papers: Shape Preserving Zipper Hidden Variable Fractal In…
We find that multifractal scaling is a robust property of a large class of continuous stochastic processes, constructed as exponentials of long-memory processes. The long memory is characterized by a power law kernel with tail exponent…
We study a wide class of fractal interpolation functions in a single platform by considering the domains of these functions as general attractors. We obtain lower and upper bounds of the box dimension of these functions in a more general…
The aim of this paper is to construct a fractal with the help of a finite family of generalized F-contraction mappings, a class of mappings more general than contraction mappings, defined in the setup of b-metric space. Consequently, we…
We consider an optical diffraction grating in which the spatial distribution of open slits forms a fractal set. The Fraunhofer diffraction patterns through the fractal grating are obtained analytically for the simplest triad Cantor type and…
Formerly the geometry was based on shapes, but since the last centuries this founding mathematical science deals with transformations, projections and mappings. Projective geometry identifies a line with a single point, like the perspective…
The paper introduces a technique that decomposes the dynamics of a nonlinear system about an equilibrium into low order components, which then can be used to reconstruct the full dynamics. This is a nonlinear analogue of linear modal…
Amorphous metal-organic frameworks are an important emerging materials class that combine the attractive physical properties of the amorphous state with the versatility of metal-organic framework (MOF) chemistry. The structures of amorphous…
We study locally constant skew-product maps over full shifts of finite symbols with arbitrary compact metric spaces as fiber spaces. We introduce a new criterion to determine the density of leaves of the strong unstable (and strong stable)…
Integrating high-level context information with low-level details is of central importance in semantic segmentation. Towards this end, most existing segmentation models apply bilinear up-sampling and convolutions to feature maps of…
We propose a transformation algorithm for a class of Linear Parameter-Varying (LPV) systems with functional affine dependence on parameters, where the system matrices depend affinely on nonlinear functions of the scheduling varable, into…
In a previous paper, dealing with "Applications in $\mathbb{R}^1$," the authors developed a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS and studied some applications…
Video frame interpolation(VFI) has witnessed great progress in recent years. While existing VFI models still struggle to achieve a good trade-off between accuracy and efficiency: fast models often have inferior accuracy; accurate models…
In the paper we unify two extensions of the classical Hutchinson--Barnsley theory - the topological and the fuzzy-set approaches. We show that a fuzzy iterated function system (fuzzy IFS) on a Tychonoff space $X$ which is contracting w.r.t.…
While free fermion topological crystalline insulators have been largely classified, the analogous problem in the strongly interacting case has been only partially solved. In this paper, we develop a characterization and classification of…
We show that many important convex matrix functions can be represented as the partial infimal projection of the generalized matrix fractional (GMF) and a relatively simple convex function. This representation provides conditions under which…
An integrated photonic circuit architecture to perform a modified-convolution operation based on the Discrete Fractional Fourier Transform (DFrFT) is introduced. This is accomplished by utilizing two nonuniformly-coupled waveguide lattices…
A novel focusing structure with fractal properties is presented. It is a photon sieve in which the pinholes are appropriately distributed over the zones of a fractal zone plate. The focusing properties of the fractal photon sieve are…
We analyze generalizations of two dimensional topological insulators which can be realized in interacting, time reversal invariant electron systems. These states, which we call fractional topological insulators, contain excitations with…
For fractals on Riemannian manifolds, the theory of iterated function systems often does not apply well directly, as fractal sets are often defined by relations that are multivalued or non-contractive. To overcome this difficulty, we…
The class of radial fuzzy systems is introduced. The fuzzy systems in this class use radial functions to implement membership functions of fuzzy sets and exhibit a shape preservation property in antecedents of their rules. The property is…