Related papers: Clifford-Valued Fractal Interpolation
Uniform interpolation properties are defined for equational consequence in a variety of algebras and related to properties of compact congruences on first the free and then the finitely presented algebras of the variety. It is also shown,…
This paper is primarily intended as an introduction for the mathematically inclined to some of the rich algebraic combinatorics arising in for instance CFT. It is essentially self-contained, apart from some of the background motivation and…
Extending and unifying concepts extensively used in the literature, we introduce the notion of approximable interpolation sets for algebras of functions on locally compact groups, especially for weakly almost periodic functions and for…
This paper presents a new approach of constructing $\alpha$-fractal interpolation functions (FIFs) using neural network operators, integrating concepts from approximation theory. Initially, we construct $\alpha$-fractals utilizing neural…
Our central observation is that unbounded additive recurrence establishes a homomorphism between $\mathbb{N}$ and Modus Ponens in a constructive sense. By finding sums of nonconsecutive Fibonacci indices, each inference step corresponds to…
We consider the numerical homogenization of a class of fractal elliptic interface problems inspired by related mechanical contact problems from the geosciences. A particular feature is that the solution space depends on the actual fractal…
We provide a general framework to construct fractal interpolation surfaces (FISs) for a prescribed countably infinite data set on a rectangular grid. Using this as a crucial tool, we obtain a parameterized family of bivariate fractal…
Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…
Fractal Interpolation has been proposed in the literature as an efficient way to construct closure models for the numerical solution of coarse-grained Navier-Stokes equations. It is based on synthetically generating a scale-invariant…
Fractional dissipation is a powerful tool to study non-local physical phenomena such as damping models. The design of geometric, in particular, variational integrators for the numerical simulation of such systems relies on a variational…
This is an introduction to geometric algebra, an alternative to traditional vector algebra that expands on it in two ways: 1. In addition to scalars and vectors, it defines new objects representing subspaces of any dimension. 2. It defines…
We introduce a new multiplication for the polytope algebra, defined via the intersection of polytopes. After establishing the foundational properties of this intersection product, we investigate finite-dimensional subalgebras that arise…
We construct a class of super-reflexive complementably minimal spaces, and study uniformly convex distortions of the norm on Hilbert space by using methods of complex interpolation.
Using valuation rings and valued fields as examples, we discuss in which ways the notions of "topological IFS attractor" and "fractal space" can be generalized to cover more general settings.
This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with…
Dimension theory lies at the heart of fractal geometry and concerns the rigorous quantification of how large a subset of a metric space is. There are many notions of dimension to consider, and part of the richness of the subject is in…
Expansion of higher transcendental functions in a small parameter are needed in many areas of science. For certain classes of functions this can be achieved by algebraic means. These algebraic tools are based on nested sums and can be…
The geometric product, defined by Graf on the space of differential forms, endows the sections of the exterior bundle by a structure that is necessary to construct a Clifford algebra. The Graf product is introduced and revisited with a…
Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.
We construct Lagrange interpolating polynomials for a set of points and values belonging to the algebra of real quaternions $H\simeq R_{0,2}$, or to the real Clifford algebra $R_{0,3}$. In the quaternionic case, the approach by means of…