Related papers: Some simplifications in the proof of the Sims conj…

The Andrews-Curtis conjecture claims that every balanced presentation of the trivial group can be reduced to the standard one by a sequence of ``elementary transformations" which are Nielsen transformations augmented by arbitrary…

In this paper, we get an elementary and important lemma(See Lemma 3.2) which is about pushout and pullback of modules. And we prove a weak form of a long open conjecture on vanishing of group cohomology for blocks.

In this paper we shall prove that any $2$-transitive finitely homogeneous structure with a supersimple theory satisfying a generalized amalgamation property is a random structure. In particular, this adapts a result of Koponen for binary…

We show how minimal elements of a stopping time $\sigma$-algebra can be expressed in terms of the minimal elements of the $\sigma$-algebra of the underlying filtration. This facilitates an intuitive interpretation of stopping time…

In this article, we generalise a result of Pottmeyer from the multiplicative group of the algebraic numbers to almost split semiabelian varieties defined over number fields. This concerns a consequence of R\'emond's generalisation of…

By using a general formalism, we expose a simplified proof of the convergence of the B\'ezier polynomials attached to a continuous function defined in arbitrary dimensional simplex. We obtain an error estimate that contains the error in…

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.

Simion had a unimodality conjecture concerning the number of lattice paths in a rectangular grid with the Ferrers diagram of a partition removed. Hildebrand recently showed the stronger result that these numbers are log concave. Here we…

In the paper we complete a case by case proof of Reeder's Conjecture started in our previous work, proving the conjecture for simple Lie algebras of type $D$ and for the exceptional cases.

We present an astonishingly simple and elegant proof of the celebrated Basel problem.

We give a simple construction involving partial actions which permits us to obtain an easy proof of a weakened version of L. O'Carroll's theorem on idempotent pure extensions of inverse semigroups.

We explain a conjecture relating the monster simple group to an algebraic variety that was discovered in a non-monstrous context.

We state and prove a Lemma in 1 variable Calculus, that justifies some arguments previously used to ilustrate non-uniqueness of some generalized physical quantities.

The main result can be given a short and elementary proof which has been incorporated into Lemma 3.2 of arXiv:1206.5775

We prove a discretized Product Theorem for general simple Lie groups, in the spirit of Bourgain's Discretized Sum-Product Theorem.

This note offers an elementary proof of the Siegel-Walfisz theorem for primes in arithmetic progressions.

We give an elementary proof to Hasse theorem.

We suggest a modified and briefer version for the proof of Higman's embedding theorem stating that a finitely generated group can be embedded in a finitely presented group if and only if it is recursively presented. In particular, we…

We give a new proof of the fundamental theorem of algebra. It is entirely elementary, focused on using long division to its fullest extent. Further, the method quickly recovers a more general version of the theorem recently obtained by…

Green [Geometric and Functional Analysis 15 (2005), 340--376] established a version of the Szemer\'edi Regularity Lemma for abelian groups and derived the Removal Lemma for abelian groups as its corollary. We provide another proof of his…