Related papers: Diminished Fermat-type arrangements and unexpected…
Our paper is devoted to several problems from the field of modified divisors: namely exponential and infinitary divisors. We study the behaviour of modified divisors, sum-of-divisors and totient functions. Main results concern with the…
In accordance with recent progress of fracton topological phases, unusual topological phases of matter hosting fractionalized quasiparticle excitations with mobility constraints, new type of symmetry is studied -- multipole symmetry,…
A new family of maximal curves over a finite field is presented and some of their properties are investigated.
We relate the total curvature and the isoperimetric deficit of a curve $\gamma$ in a two-dimensional space of constant curvature with the area enclosed by the evolute of $\gamma$. We provide also a Gauss-Bonnet theorem for a special class…
Motivated by some applications in applied mathematics, biology, chemistry, physics and engineering sciences, new tight Tur\'an type inequalities for modified Bessel functions of the first and second kind are deduced. These inequalities…
In this paper we are concerned with the existence of invariant curves of planar twist mappings which are almost periodic in a spatial variable. As an application of this result to differential equations we will discuss the existence of…
We study a special case of the configuration model, in which almost all the vertices of the graph have degree $2$. We show that the graph has a very peculiar and interesting behaviour, in particular when the graph is made up by a vast…
We extend the classical Enriques-Petri Theorem to $s$-subcanonical projectively normal curves, proving that such a curve is $(s+2)$-gonal if and only if it is contained in a surface of minimal degree. Moreover, we show that any Fermat…
In this article we improve the upper bound for the arithmetic self-intersection number of the dualizing sheaf of the minimal regular model for the Fermat curves $F_p$ of prime exponent.
We investigate the occurrence of additive and multiplicative structures in random subsets of the natural numbers. Specifically, for a Bernoulli random subset of $\mathbb{N}$ where each integer is included independently with probability…
We investigate space curves with large cohomology. To this end we introduce curves of subextremal type. This class includes all subextremal curves. Based on geometric and numerical characterizations of curves of subextremal type, we show…
We compare the asymptotic grows of the number of rational points on modular varieties of D-elliptic sheaves over finite fields to the grows of their Betti numbers as the degree of the level tends to infinity. This is a generalization to…
In this paper we study the concept of characteristic numbers and Chern slopes in the context of curve configurations in the real and complex projective plane. We show that some extremal line configurations inherit the same asymptotic…
This is the first in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we study theories of supercommutative algebras…
This note examines the infinite divisibility of density-based transformations of normal random variables. We characterize a class of density-based transformations of normal variables which produces non-infinitely divisible distributions. We…
This paper aims to introduce high school students to the intriguing world of continued fractions, a mathematical concept that provides a unique representation of numbers. The study focuses on the exploration and development of the…
The presented paper is devoted to study the curvature and torsion of slant Frenet curves in 3-dimensional normal almost paracontact metric manifolds. Moreover, in this class of manifolds, properties of non- Frenet slant curves (with null…
Elliptic functions considered by Dixon in the nineteenth century and related to Fermat's cubic, $x^3+y^3=1$, lead to a new set of continued fraction expansions with sextic numerators and cubic denominators. The functions and the fractions…
We develop a new approach for constructing normalized differentials on hyperelliptic curves of infinite genus and obtain uniform asymptotic estimates for the distribution of their zeros.
In a three-dimensional Fermi liquid, quasiparticles near the Fermi surface may possess a Berry curvature. We show that if the Berry curvature has a nonvanishing flux through the Fermi surface, the particle number associated with this Fermi…