Related papers: Fractal Interpolation over Nonlinear Partitions
In this paper, a class of fractals, called quadrilateral labyrinth fractals, are introduced and studied. They are a special kind of fractals on any quadrilateral on the plane. This type of fractal is motivated by labyrinth fractal on the…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
Flux reconstruction provides a framework for solving partial differential equations in which functions are discontinuously approximated within elements. Typically, this is done by using polynomials. Here, the use of radial basis functions…
The paper presents analytical solution for hydraulic fracture driven by a non-Newtonian fluid and propagating under plane strain conditions in cross sections parallel to the fracture front. Conclusions are drawn on the influence of the…
In the present work, the notion of Cubic Spline Super Fractal Interpolation Function (SFIF) is introduced to simulate an object that depicts one structure embedded into another and its approximation properties are investigated. It is shown…
For the interpolation of graph signals with generalized shifts of a graph basis function (GBF), we introduce the concept of positive definite functions on graphs. This concept merges kernel-based interpolation with spectral theory on graphs…
A fractal approach to numerical analysis of electromagnetic space-time crystals, created by three standing plane harmonic waves with mutually orthogonal phase planes and the same frequency, is presented. Finite models of electromagnetic…
In this paper, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating nonlinearities onto approximation spaces defined with the help of finite elements, the…
Fractal geometry deals mainly with irregularity and captures the complexity of a structure or phenomenon. In this article, we focus on the approximation of set-valued functions using modern machinery on the subject of fractal geometry. We…
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a…
We present a generalisation of the theory of iterated function systems and associated fractals to the setting of noncommutative geometry. Along the way, we discuss some ideas surrounding locally compact noncommutative metric spaces.
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
In this article, we prove the following interpolation problem: if the composition of a function and a regular map between affine varieties is a regular function, then there exists a global regular function of the target variety that…
We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is…
Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this…
Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum…
We employ density functional theory to study in detail the crystallization of super-paramagnetic particles in two dimensions under the influence of an external magnetic field that lies perpendicular to the confining plane. The field induces…
A simple, yet unifying method is provided for the construction of tilings by tiles obtained from the attractor of an iterated function system (IFS). Many examples appearing in the literature in ad hoc ways, as well as new examples, can be…
Interpolation Theory gives techniques for constructing spaces from two initial Banach spaces. We provide several conditions under which the restriction of a holomorphic map $f:X_0+X_1 \rightarrow Y_0+Y_1$ to the interpolated spaces (using…
Motivated by applications in data science, we study partial differential equations on graphs. By a classical fixed-point argument, we show existence and uniqueness of solutions to a class of nonlocal continuity equations on graphs. We…