Research
Research
Research
Research
69+ open-access research outputs.
We prove that a finitely generated virtually RFRS group of cohomological dimension at most $2$ is coherent if and only if its second $L^{2}$-Betti number vanishes if and only if it is virtually free-b…
Let $f(x)=(x^{k}+c)^{m}-ax^{n}\in\mathbb{Z}[x]$ be an irreducible polynomial over $\mathbb{Q}$, where $k,m,n\in\mathbb{N}$ with $km>n$, and let $K=\mathbb{Q}(\theta)$, where $\theta$ is a root of $f(x…
How many natural numbers below $X$ can be written as a sum of $k$ units of the ring of integers of a given number field? We give the asymptotics as $X$ gets large for quadratic number fields. This sol…
In this follow-up paper, we again inspect a surprising relationship between the set of fixed points of a polynomial map $\varphi_{d, c}$ defined by $\varphi_{d, c}(z) = z^d + c$ for all $c, z \in \mat…
In this note we show that the nonnegative part of a proper complex toric variety has the homeomorphism type of a sphere, and consequently that the nonnegative part has a natural structure of a cell co…
We introduce a class of convolutions on arithmetical functions that are regular in the sense of of Narkiewicz, homogeneous in the sense of Burnett et al, and bounded, in the sense that there exists a …
We respond briefly to the recent comment by Jay Lawrence, Marcin Markiewicz and Marek \'{Z}ukowski [arXiv:2210.09025 and Found. Phys. \textbf{54}, 45 (2024)] regarding our work defending RQM against t…
In this follow-up paper, we again inspect a surprising connection between the set of fixed points of a polynomial map $\varphi_{d,c}$ defined by $\varphi_{d,c}(z) = z^d + c$ for all $c, z \in \mathcal…
This paper provides an iterative procedure for constructing hyperbolic Coxeter groups that virtually fiber over $\mathbb{Z}$ that is flexible enough to yield infinitely many isomorphism classes in eac…
In this first article of a multi-part series, we inspect a surprising relationship between the set of fixed points of a polynomial map $\varphi_{d, c}$ defined by $\varphi_{d, c}(z) = z^d + c$ for all…
The randomized online-LOCAL model captures a number of models of computing; it is at least as strong as all of these models: - the classical LOCAL model of distributed graph algorithms, - the quan…
We provide geometric methods to give bounds on the large-scale dimension of CAT(0) cube complexes quasiisometric to a given group $G$. In situations where these bounds conflict we obtain obstructions …
We study the distribution of families of multiplicative functions among the coprime residue classes to moduli varying uniformly in a wide range, obtaining analogues of the Siegel--Walfisz Theorem for …
We prove that the triangle Artin group $\mathrm{Art}_{23M}$ splits as a graph of free groups if and only if $M$ is greater than $5$ and even. This answers two questions of Jankiewicz \cite[Question 2.…
The accelerated method in solving optimization problems has always been an absorbing topic. Based on the fixed-time (FxT) stability of nonlinear dynamical systems, we provide a unified approach for de…
In this paper, for any nonic number field $K$ generated by a root $\alpha$ of a monic irreducible trinomial $F(x)=x^9+ax+b \in \mathbb{Z}[x]$ and for every rational prime $p$, we characterize when $p$…
A 1957 conjecture by Zdzislaw Melzak, that the unit volume polyhedron with least edge length was a triangular right prism, with edge length $2^{2/3}3^{11/6}$. We present a variety of necessary local c…
This paper describes Adam Mickiewicz University's (AMU) solution for the 4th Shared Task on SlavNER. The task involves the identification, categorization, and lemmatization of named entities in Slavic…
Let $K=\Q(\theta)$ be an algebraic number field with $\theta$ a root of an irreducible quadrinomial $f(x) = x^6+ax^m+bx+c\in\Z[x] $ with $m\in\{2,3,4,5\}$. In the present paper, we give some explicit …
In this paper, we deal with the problem of monogenity of number fields defined by monic irreducible trinomials $F(x)=x^{12}+ax^m+b\in \mathbb{Z}[x]$ with $1\leq m\leq11$. We give sufficient conditions…
Free open-access publishing with Google Scholar indexing.
Submission Guide →