Related papers: Apology of Euclid

This is an expository note to give a brief review of classical elastica theory, mainly prepared for giving a more detailed proof of the author's Li--Yau type inequality for self-intersecting curves in Euclidean space. We also discuss some…

This article, written in honor of Fritz Rohrlich, briefly surveys the role of topology in physics.

This paper has been withdrawn by the author due to an error in the proof.

Aristotle's discussions on modal syllogistic have often been viewed as error-prone and have garnered significant attention in the literature due to historical and philosophical interests. However, from a contemporary standpoint, they also…

We give a simple rigourous treatment of the classical results of the abelian sandpile model. Although we treat results which are well-known in the physics literature, in many cases we did not find complete proofs in the literature. The…

Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…

This note is devoted to a combinatorial proof of a Schmidt type theorem due to Andrews and Paule. A four-variable refinement of Andrews and Paule's theorem is also obtained based on this combinatorial construction.

We give a short proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis. The part of the proof which is my own (not Pin's) is a complete replacement of the same part in an earlier version of this paper.

We present a simple method based on the stability and duality of the properties of sampling and interpolation, which allows one to substantially simplify the proofs of some classical results.

Ontology engineering is a hard and error-prone task, in which small changes may lead to errors, or even produce an inconsistent ontology. As ontologies grow in size, the need for automated methods for repairing inconsistencies while…

In this talk, some aspects of duality symmetries are presented.

The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…

This paper has been withdrawn by the author due to a crucial error.

We describe two distinct simple, short and self contained proofs of the composition lemma.

The calculus of looping sequences is a formalism for describing the evolution of biological systems by means of term rewriting rules. We enrich this calculus with a type discipline to guarantee the soundness of reduction rules with respect…

In this largely expository paper, we will present a list of En -operads and give complete, and in some cases new, proofs of the equivalences between these operads.

We obtain simple proofs of certain inequalites for bivariate means.

This paper has been withdrawn by the author due to a crucial argument error at p.10.

We characterise the canonical elements, in the sense of Burstall--Rawnsley \cite{BurRaw90}, of a compact semisimple Lie algebra and discuss the case of $\mathfrak{so}(n)$ in detail. In so doing, we correct two errors in Burstall et al.…

This article provides a brief introductory account of the theory of aperiodic order.