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We give a short proof for the Hartogs's extension theorem on (n-1)-complete complex spaces.

In this note we exhibit a very simple proof of McNaughton Theorem, almost right out of the definitions, and at the same time we observe that this theorem does not depend of Chang's completeness theorem.

In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.

We obtain simple proofs of certain inequalites for bivariate means.

The Bollob\'as-Varopoulos theorem is an analogue of Hall's matching theorem on non-atomic measure spaces. Here we prove a finite version with a completely constructive proof.

We present a proof of Moessner's theorem by double induction, using only basic rules of arithmetic. No prerequisite knowledge is assumed. Familiarity with summation is advised.

We give a new proof of Dunn's additivity for the little $n$-cubes operads $C_n$, which has the advantage of being considerably shorter than the ones in the literature. At the end we remark on how our proof can be adjusted to work for the…

A generalization of the law of total covariance is presented and proved.

We give a proof of a result of Bonet, Engli\v{s} and Taskinen filling in several details and correcting some flaws.

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

In this article, we prove a limit theorem for an observable on the torus with a singularity of type $x^{-a}$, where $0<a<1$.

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.

A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and linear algebra.

This note contains a complete proof of the Abhyankar-Moh-Suzuki theorem (in characteristic zero case).

This is just a short proof of Kruskal's theorem regarding uniqueness of expressions for tensors, phrased in geometric language.

In this note we prove a converse of Bohr's equivalence theorem for Dirichlet series under some natural assumptions.

In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.

By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.

We give a relatively short and self contained proof of Ratner's theorem in the special case of SL(2,R)-invariant measures.

We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.