Related papers: Problems on spherical maximal functions
In the present article, the main attention is given to fractal sets whose elements have certain restrictions on using digits or combinations of digits in own nega-P-representation. Topological, metric, and fractal properties of images of…
Using a generalized cut vertex expansion we introduce the concept of an extended fracture function for the description of semi-inclusive deep inelastic processes in the target fragmentation region. Extended fracture functions are shown to…
We investigate the existence of the meromorphic extension of the spectral zeta function of the Laplacian on self-similar fractals using the classical results of Kigami and Lapidus (based on the renewal theory) and new results of Hambly and…
In this paper, we consider a generalization of the Stirling number sequence of both kinds by using a specialization of a new family of symmetric functions. We give combinatorial interpretations for this symmetric functions by means of…
We study the statistical fluctuations (such as the variance) of causal set quantities, with particular focus on the causal set action. To facilitate calculating such fluctuations, we develop tools to account for correlations between causal…
We present an Expectation-Maximization algorithm for the fractal inverse problem: the problem of fitting a fractal model to data. In our setting the fractals are Iterated Function Systems (IFS), with similitudes as the family of…
In this paper, we propose two methods of calculating theoretically maximal metamer mismatch volumes. Unlike prior art techniques, our methods do not make any assumptions on the shape of spectra on the boundary of the mismatch volumes. Both…
In this paper we study analogues of the perfect splines for weighted Sobolev classes of functions defined on the half-line. Maximally oscillating splines play important role in the solution of certain extremal problems. In particular, using…
A fractal construction shows that, for any beta>0, the beta-skeleton of a point set can have arbitrarily large dilation. In particular this applies to the Gabriel graph.
Recently, attempts have been made to take into account the fractal properties of seismicity when mapping the long-term rate of earthquakes. The paper touches upon the theoretical aspects of fractality and provides a critical analysis of its…
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…
We study algorithmic problems on subsets of Euclidean space of low fractal dimension. These spaces are the subject of intensive study in various branches of mathematics, including geometry, topology, and measure theory. There are several…
In this paper, we explore some significant properties associated with a fractal operator on the space of all continuous functions defined on the Sierpi\'nski Gasket (SG). We also provide some results related to constrained approximation…
We study an optimal partition problem on the sphere, where the cost functional is associated with the fractional $Q$-curvature in terms of the conformal fractional Laplacian on the sphere. By leveraging symmetries, we prove the existence of…
We develop an effective model to describe the dynamics of a system of particle moving in circular configurations around a central mass, by considering the continuum limit of the angular distribution, to obtain the stable configurations for…
We evaluate the shattering dimension of various classes of linear functionals on various symmetric convex sets. The proofs here relay mostly on methods from the local theory of normed spaces and include volume estimates, factorization…
Orbital fuzzy iterated function systems are obtained as a combination of the concepts of iterated fuzzy set system and orbital iterated function system. It turns out that, for such a system, the corresponding fuzzy operator is weakly…
We study the size and regularity properties of level sets of continuous functions with bounded upper-scaled and lower-scaled oscillation.
We study the question of the existence of a dual extremal function for a bounded matrix function on the unit circle in connection with the problem of approximation by analytic matrix functions. We characterize the class of matrix functions,…
We give a new characterization of the space of functions of bounded variation in terms of a pointwise inequality connected to the maximal function of a measure. The characterization is new even in Euclidean spaces and it holds also in…