Related papers: A note on an Counter Example of Dacorogna

This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.

Explainable recommendation through counterfactual reasoning seeks to identify the influential aspects of items in recommendations, which can then be used as explanations. However, state-of-the-art approaches, which aim to minimize changes…

This short note deals with some applications of the Beta function

This letter is a comment on an article by T.C. Halsey and M.H. Jensen in Nature about using recurrence times as a reliable tool to estimate multifractal dimensions of strange attractors. Our aim is to emphasize that in the recent…

This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.

This short note delivers, via elementary calculations, a product representation of pi.

The purpose of this note is to correct an error in a paper of M. Cowling, G. Fendler and J.J.F. Fournier, and to give a counterexample to a conjecture of J.-L. Rubio de Francia.

We refute the conjecture that all negative translations are intuitionistically equivalent by giving two counterexamples. Then we characterise the negative translations intuitionistically equivalent to the usual ones.

This work summarises some of the attempts to explain the phenomenon of dark energy as an effective description of complex gravitational physics and the proper interpretation of observations. Cosmological backreaction has been shown to be…

In this paper, we propose a weak regularity principle which is similar to both weak K\"onig's lemma and Ramsey's theorem. We begin by studying the computational strength of this principle in the context of reverse mathematics. We then…

A recent Comment [arXiv:0811.2790] on the Letter 'Quantum Bounce and Cosmic Recall' by the authors is shown to arise from an incorrect understanding of the issues at hand and of our analysis. The conclusions of Bojowald's Comment are shown…

This note is a reaction to Conant and Kruckman's recent preprint `Three surprising instance of dividing'. It mainly consists of an erratum to the author's paper `Forking, imaginaries and other features of ACFG', in light of the results of…

We perform the a posteriori error analysis of residual type of a transmission problem with sign changing coefficients. According to [6] if the contrast is large enough, the continuous problem can be transformed into a coercive one. We…

This paper has been withdrawn by the author due to a misunderstanding.

This article aims to find explicit congruences between Dirichlet characters and gives various results on how to find some effectively on a computer. It ends with concrete examples putting those ideas in application.

A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.

We give a counterexample to the proof in the literature [K-Theory 25 (2002), 215-231] of the existence of linear representatives of higher Chow groups of number fields.

Either fibered knots supporting the tight contact structure are unique in their smooth concordance class or there exists a fibered counterexample to the Slice-Ribbon Conjecture.

In this article, the author provides full details of the proof of the concordance/isotopy problem. The first published proof, [5], accomplished this task only partially since there was an error, see the erratum [6], which damaged the main…

A conjecture regarding the structure of expander graphs is discussed.