Related papers: Correction: Root extraction in one-relator groups …
This paper contains a survey of recent developments in investigation of word equations in simple matrix groups and polynomial equations in simple (associative and Lie) matrix algebras along with some new results on the image of word maps on…
The aim of this note is to point out some inaccuracies in our paper \cite{HD} and to fix them. Some new notions are introduced and properties of them are investigated.
The aim of this note is to present the simple observation that a slight refinement of the Contraction Mapping Principle allows one to recover the precise convergence rate in the Picard-Lindel\"of Theorem.
We provide a short and self-contained argument for the existence of Cartan-Iwahori-Matsumoto decompositions for reductive groups.
Here we give a reformulation of a key lemma in the paper [2], "Spaces of Topological Complexity One", which is necessary due to an oversight.
Although sloppy interpretation is usually accounted for by theories of ellipsis, it often arises in non-elliptical contexts. In this paper, a theory of sloppy interpretation is provided which captures this fact. The underlying idea is that…
We give a description of non-growing subsets in linear groups, which extends the Product theorem for simple groups of Lie type. We also give an account of various related aspects of growth in linear groups.
The growing demand for structured knowledge has led to great interest in relation extraction, especially in cases with limited supervision. However, existing distance supervision approaches only extract relations expressed in single…
The extension of the singular perturbative approach to the second order is presented in this paper. The general expansion to the second order is derived. The second order expansion is considered as a small correction to the first order…
In 1977, Adleman, Manders and Miller had briefly described how to extend their square root extraction method to the general $r$th root extraction over finite fields, but not shown enough details. Actually, there is a dramatic difference…
In this paper, we give a counter-example, in the general case, Kronecker theorem will derive contradiction. Kronecker theorem be correct after removing some conditions.
This note corrects conditions in Proposition 3.4 and Theorem 5.2(ii) and comments on imprecisions in Propositions 4.2 and 4.4 in Fissler and Ziegel (2016).
An appeal for symmetry is made to build established notions of specific representation and specific nonlinearity of measurement (often called model error) into a canonical linear regression model. Additive components are derived from the…
A short proof is given that the graphs with proper interval representations are the same as the graphs with unit interval representations.
This paper is concerned with minimal-length representatives of equivalence classes of words in F_2 under Aut F_2. We give a simple inequality characterizing words of minimal length in their equivalence class. We consider an operation that…
This note provides an alternate account of Calegari's rationality theorem for stable commutator length in free groups.
I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
A slip on a paper concerning near-vector spaces is fixed. New characterization of near-vector spaces determined by finite fields is provided and the number (up to the isomorphism) of these spaces is exhibited.