Related papers: Comment on "Two notes on imbedded prime divisors"
In this note we present a characterisation of all unary and binary patterns that do not only contain variables, but also reversals of their instances. These types of variables were studied recently in either more general or particular…
In this short note, we prove the claim of the title.
In this short note we explain how one can use established results to prove various versions of the positive mass theorem for initial data sets with boundary, in dimensions less than 8.
In this paper, we explain how some basic facts about valuation can help clarify many questions about divisibility in integral domains.
We show, under some natural restrictions, that some semigroup orbits of polynomials cannot contain too many elements of small multiplicative order modulo a large prime $p$, extending previous work of Shparlinski (2017).
The Lueders postulate is reviewed and implications for the distinguishability of observables are discussed. As an example the distinguishability of two similar observables for spin-1/2 particles is described. Implementation issues are…
In this note, we find a new way to prove several properties of 2-alternating capacities.
In the first part of this article, we consider ruled surfaces defined over a finite field; we introduce invariants for them, and describe some explicit contructions that illustrate possible behaviour of these invariants. In the second part,…
We give lower bounds on the case of worst inhomogeneous approximation.
The first part of this paper consists of lecture notes which summarize the machinery of filtered root invariants. A conceptual notion of "homotopy Greek letter element" is also introduced, and evidence is presented that it may be related to…
We show that for any $\varepsilon > 0$, prime $q$ sufficiently large with respect to $1 / \varepsilon$ and residue class $(a,q) = 1$, there exist two integers $m, n \leq q^{5/2 + \varepsilon}$ with $m \equiv n \equiv a \pmod{q}$ such that…
In a recent paper of the first author and I. M. Isaacs it was shown that if m = m(G) is the maximal order of an abelian subgroup of the finite group G, then |G| divides m! ([AI18, Thm. 5.2]). The purpose of this brief note is to improve on…
We review the validity of the several representations of the two-level approximation
This note is an addendum to the paper ''Mahler's method in several variables and finite automata''. It strengthens part (i) of Theorem 1.1 of the aforementioned paper.
Due to the omission of a hypothesis from an elementary lemma in the author's paper "Gleason parts and point derivations for uniform algebras with dense invertible group", some of the proofs presented in that paper are flawed. We prove here…
This note is a response to [7] in which it is claimed that [13, Proposition 11] is false. We demonstrate here that this assertion in [7] is false, and is based on a misreading of the notion of set membership in [13, Proposition 11]. We…
We provide new sufficient conditions under which Ryser's conjecture holds.
In this paper we propose necessary upper bounds for the second, third and fourth smallest prime divisors of friends of 10 based on the number of distinct prime divisors of it.
We discuss some problems with the indefinite integral notation and the way of teaching of integrals in Calculus. Based on the discussion, and in order to avoid mistakes, we propose another notation for indefinite integrals.
It has been pointed out to the author by David Glickenstein that the proof of the (closely related) Lemmas 1.2 and 3.2 in the title paper is incorrect. The statements of both Lemmas are correct, and the purpose of this note is to give a…