Related papers: A Short Proof of the Poincar\'e Conjecture

The article provides a counterexample to a conjecture by Blocki-Zwonek.

The recently developed proof of Fermat's Last Theorem is very lengthy and difficult, so much so as to be beyond all but a small body of specialists. While certainly of value in the developments that resulted, that proof could not be, nor…

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

We prove a conjecture due to Gica (Fibonacci Quarterly, 2008). Our proof is simple, uses only elementary abstract algebra, and generalizes to other recursive sequences.

We produce a new, shorter construction of a minor-universal planar graph.

Error in proof of theorem 10.

The article presents the proof of Casas-Alvero conjecture.

The paper presents a counterexample to the Hodge conjecture.

We present an alternative proof of Perron's theorem, which is probabilistic in nature. It rests on the representation of the Perron eigenvector as a functional of the trajectory of an auxiliary Markov chain.

In this short communication, we present a new proof for the Korn inequality in a n-dimensional context. The results are based on standard tools of real and functional analysis. For the final result the standard Poincar\'{e} inequality plays…

We report the results of our empirical investigations on the Bateman-Horn conjecture. This conjecture, in its commonly known form, produces rather large deviations when the polynomials involved are not monic. We propose a modified version…

Analogue of Springer's formula for the Poincar\'e series of the algebra invariants of ternary form is found.

The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…

In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.

We give a new proof of the existence of designs, which is much shorter and gives better bounds.

This is an appendix to our paper "An update of the Hirsch Conjecture" (arXiv:0907.1186), containing proofs of some of the results and comments that were omitted in it.

We will give a simple proof of the ambiguous class number formula.

This paper has been withdrawn by the author due to the version of [A complete proof of Hamilton's conjecture] at arXiv:1008.1576

In this paper, we obtained an equivalent proposition of Brennan`s conjecture. And given two lower bound estimation of the conjecture one of them connected with Schwarzian derivative. The present study also verified the correctness of the…

A short and elementary proof is given of a celebrated eigenvalue-perturbation result due to Alfred Brauer.