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The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…
These notes present some elements of causality theory. While they are not as complete as other treatments of the topic, there is some originality in that the whole approach is based on a definition of causal curves which allows to simplify…
This paper has been withdrawn by the author due to an error in the main proof (thanks to Carlos D'Andrea)
We fix a gap in the proof of a result in our earlier paper arXiv:1908.09548
In this note we correct two errors in our paper "On the Homology of Completion and Torsion", arXiv:1010.4386, that appeared in Algebras and Representation Theory (2014).
We adapt a construction taken from `L. Motto Ros and B. Semmes, A new proof of a theorem of Jayne and Rogers, Real Anal. Exchange 35(1) (2009/2010), 195-204' in order to correct a mistake contained in the first part of the same paper. As a…
In this article we construct a large family of $R$-matrices for various extensions of small quantum groups by grouplike elements. The extensions are in correspondence to lattices between root and weight lattice and admit $R$-matrices in…
A critical analysis of the relativistic formulation of matter reveals some surprising inconsistencies and paradoxes. Corrections are discovered which lead to the long-sought-after equality of the gravitational and inertial masses, which are…
The paper is a short survey of recent developments in the area of first order descriptions of linear groups. It is aimed to illuminate the known results and to pose the new problems relevant to logical characterizations of Chevalley groups…
Recent neural models for relation extraction with distant supervision alleviate the impact of irrelevant sentences in a bag by learning importance weights for the sentences. Efforts thus far have focused on improving extraction accuracy but…
Here we prove that for dilatation structures linearity (see arXiv:0705.1440v1) is equivalent to a statement about the inverse semigroup generated by the family of dilatations of the space. The result is new for Carnot groups and the proof…
The original version of this paper contains an error; when this is corrected the basic conclusion changes. A revised manuscript will be submitted shortly.
We correct one erroneous statement made in our recent paper "Medial axis and singularities".
Based on a reduction processing, we rewrite a hypergeometric term as the sum of the difference of a hypergeometric term and a reduced hypergeometric term (the reduced part, in short). We show that when the initial hypergeometric term has a…
Forms are a common type of document in real life and carry rich information through textual contents and the organizational structure. To realize automatic processing of forms, word grouping and relation extraction are two fundamental and…
This paper has been withdrawn by the author due to an error in the proof of Theorem 1.
The purpose of this erratum and addendum is to correct the errors in [1]. It consists of five components: 1. Lemma 7.1 and Proposition 7.2 are wrong and discarded; 2. A new proof of existence $\lambda(\xi)$ in (7.1) without Proposition 7.2;…
The property 4 in Proposition 2.3 from the paper "Some remarks on Davie's uniqueness theorem" is replaced with a weaker assertion which is sufficient for the proof of the main results. Technical details and improvements are given.
In this short note we give counterexamples to several results related to extension theorems published recently.
In this short note we introduce a new metric on certain finite groups. It leads to a class of groups for which the element orders satisfy an interesting inequality. This extends the class CP_2 studied in our previous paper [16].