Related papers: On bivariate fractal approximation
We improve both dimension compression and expansion bounds for homeomorphisms with $p$-exponentially integrable distortion. To the first direction we also introduce estimates for the compression multifractal spectra, which will be used to…
Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in problems of mathematics, statistics and natural sciences. In this article we start considering the case of a Gauss hypergeometric…
We develop a theory of bounded variation functions and Besov spaces in abstract Dirichlet spaces which unifies several known examples and applies to new situations, including fractals.
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless.…
Computations in high-dimensional spaces can often be realized only approximately, using a certain number of projections onto lower dimensional subspaces or sampling from distributions. In this paper, we are interested in pairs of…
An order theoretic and algebraic framework for the extended real numbers is established which includes extensions of the usual difference to expressions involving $-\infty$ and/or $+\infty$, so-called residuations. Based on this,…
We present and study approximate notions of dimensional and margin complexity, which correspond to the minimal dimension or norm of an embedding required to approximate, rather then exactly represent, a given hypothesis class. We show that…
Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets…
This paper presents a study of generalized polyhedral convexity under basic operations on multifunctions. We address the preservation of generalized polyhedral convexity under sums and compositions of multifunctions, the domains and ranges…
An approach is proposed which, given a family of linearly independent functions, constructs the appropriate biorthogonal set so as to represent the orthogonal projector operator onto the corresponding subspace. The procedure evolves…
This paper provides an unique dual representation of set-valued lower semi-continuous quasiconvex and convex functions. The results are based on a duality result for increasing set valued functions.
The input to the distant representatives problem is a set of $n$ objects in the plane and the goal is to find a representative point from each object while maximizing the distance between the closest pair of points. When the objects are…
In this article, for a certain subset $\mathcal{X}$ of the extended set of rational numbers, we introduce the notion of {\it best $\mathcal{X}$-approximations} of a real number. The notion of best $\mathcal{X}$-approximation is analogous to…
The method of self-similar factor approximants is completed by defining the approximants of odd orders, constructed from the power series with the largest term of an odd power. It is shown that the method provides good approximations for…
The notions of fractal and essentially fractal algebras of approximation sequences and of the Arveson dichotomy have proved extremely useful for several spectral approximation problems. The purpose of this short note is threefold: to…
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…
Our research proposes a novel method for reducing the dimensionality of functional data, specifically for the case where the response is a scalar and the predictor is a random function. Our method utilizes distance covariance, and has…
We obtain a result concerning the stability under the interpolation with functional parameter method for the approximation spaces of Lorentz-Marcinkiewicz type and also for the approximation spaces generated by symmetric norming functions…
We describe new families of random fractals, referred to as "V-variable", which are intermediate between the notions of deterministic and of standard random fractals. The parameter V describes the degree of "variability" : at each…
In the present work, the notion of Super Fractal Interpolation Function (SFIF) is introduced for finer simulation of the objects of the nature or outcomes of scientific experiments that reveal one or more structures embedded in to another.…