Related papers: A merry-go-round with the circle map, primes and p…
The chronicle of prime numbers travel back thousands of years in human history. Not only the traits of prime numbers have surprised people, but also all those endeavors made for ages to find a pattern in the appearance of prime numbers has…
In this article, we study the structure of the graph implied by a given map on the set $S_p=\{1,2,\dots,p-1\}$, where $p$ is an odd prime. The consecutive applications of the map generate an integer sequence, or in graph theoretical context…
We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral…
In this work we classify the at-point regularities of set-valued mappings into two categories and then we analyze their relationship through several implications and examples. After this theoretical tour, we use the subregularity properties…
Regular hypermaps with underlying simple hypergraphs are analysed. We obtain an algorithm to classify the regular embeddings of simple hypergraphs with given order, and determine the automorphism groups of regular embedding of simple…
The present work aims to exploit the interplay between the algebraic properties of rings and the graph-theoretic structures of their associated graphs. We introduce commutatively closed graphs and investigate properties of commutatively…
The $k$-coprime graph of order $n$ is the graph with vertex set $\{k, k+1, \ldots, k+n-1\}$ in which two vertices are adjacent if and only if they are coprime. We characterize Hamiltonian $k$-coprime graphs. As a particular case, two…
We study singularities of constant positive Gaussian curvature surfaces and determine the way they bifurcate in generic 1-parameter families of such surfaces. We construct the bifurcations explicitly using loop group methods. Constant…
In this expository article we provide an elegant proof of the one-sided Ingham-Karamata Tauberian theorem. As an application, we present a short deduction of the prime number theorem.
A characterization is completed for finite groups acting arc-transitively on maps with square-free Euler characteristic, associated with infinite families of regular maps of square-free Euler characteristic presented. This is based on a…
For a positive linear map F and a normal matrix N, we show that |F(N)| is bounded by some simple linear combinations in the unitary orbit of F(|N|). Several elegant sharp inequalities are derived, especially for the Schur product.
Let $\widehat{\Gamma}$ be the natural map given in \cite[\S1]{Oh12}. Here, we construct a deformation $B_q$ of a Poisson algebra $B_1$ and a prime ideal $P$ of $B_q$ such that $\widehat{\Gamma}(P)$ is not a Poisson prime ideal of $B_1$.
We study the set of periods of degree 1 continuous maps from sigma into itself, where sigma denotes the space shaped like the letter sigma (i.e., a segment attached to a circle by one of its endpoints). Since the maps under consideration…
We define a natural ensemble of trace preserving, completely positive quantum maps and present algorithms to generate them at random. Spectral properties of the superoperator Phi associated with a given quantum map are investigated and a…
The problem of representing a class of maps in a form suited for application of normal form methods is revisited. It is shown that using the methods of Lie series and of Lie transform a normal form algorithm is constructed in a…
We prove that the Neron-Severi groups of several complex Fermat surfaces are generated by lines. Specifically, we obtain these new results for all degrees up to 100 that are relatively prime to 6. The proof uses reduction modulo a…
The action of ring automorphisms of the polynomial ring in two variables over the real numbers on real plane curves is considered. The orbits containing degree-three polynomials are computed, with one representative per orbit being…
In the conference paper we construct analouge to Pascal's triangle that characterize primes with additional fascinating properties.
A formula for the radii and positions of four circles in the plane for an arbitrary linearly independent circle configuration is found. Among special cases is the recent extended Descartes Theorem on the Descartes configuration and an…
Some examples of naturally arising multisum $q$-series which turn out to have representations as fermionic single sums are presented. The resulting identities are proved using transformation formulas from the theory of basic hypergeometric…