Related papers: An Elementary proof for Bertrand's Postulate

Pusey, Barrett and Rudolph (PBR) have recently proven an important new theorem in the foundations of quantum mechanics. Here we propose alternative experimental protocols which lead to the PBR result for a special case and a weaker PBR-like…

In this note we give two proofs of Brooks' Theorem. The first is obtained by modifying an earlier proof and the second by combining two earlier proofs. We believe these proofs are easier to teach in Computer Science courses.

There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of…

We provide a new short proof for the Birman--Solomyak theorem for Hilbert--Schmidt operators and give an application to a Schr\"odinger--Poisson system.

We give a counterexample to a recently conjectured variant of the Penrose inequality.

Wedderburn's theorem on the structure of finite dimensional semisimple algebras is proved by using minimal prerequisites.

We discuss an alternative non-perturbative proof of Bertrand's theorem that leads in a concise way directly to the two allowed fields: the newtonian and the isotropic harmonic oscillator central fields.

There are several extensions of the classical Banach Fixed Point Theorem in technical literature. A branch of generalizations replaces usual contractivity by weaker but still effective assumptions. Our note follows this stream, presenting…

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

The purpose of this letter is to point out an argument which may ultimately lead to a rigorous proof of the Penrose inequality in the general case. The argument is a variation of Geroch's original proposal for a proof of the positive energy…

The aim of this article is to give a new proof of Cohen-Gabber theorem in the equal characteristic $p>0$ case.

Building on the concept of pretentious multiplicative functions, we give a new and largely elementary proof of the best result known on the counting function of primes in arithmetic progressions.

Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.

A vector variational principle is proved.

In this note we give a detailed proof of a theorem of Aubin.

We use Beltrami's theorem as an excuse to present some arguments from parabolic differential geometry without any of the parabolic machinery.

We give an elementary introduction to the theory of supermembranes.

A family of exact upper bounds interpolating between Chebyshev's and Cantelli's is presented.

This article describes a new proof of the equality condition for the Brunn-Minkowski inequality.

In this note we investigate the Cheltsov--Rubinstein conjecture. We show that this conjecture does not hold in general and some counterexamples will be presented.