相关论文: A proof of Sendov's conjecture

We show the Graceful Tree Conjecture holds.

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

We prove the Invariant Subspace Conjecture for separable Hilbert spaces.

We provide new sufficient conditions under which Ryser's conjecture holds.

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

In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].

A proof of Smale's mean value conjecture from 1981 is given.

In this short note, we prove Hadwiger's conjecture for strongly monotypic polytopes.

The Sendov conjecture asserts that if $p(z) = \prod_{j=1}^{N}(z-z_j)$ is a polynomial with zeros $|z_j| \leq 1$, then each disk $|z-z_j| \leq 1$ contains a zero of $p'$. Our purpose is the following: Given a zero $z_j$ of order $n \geq 2$,…

This is a survey on Sarnak's Conjecture

A simple proof of Atanassov's Conjecture is presented. Atanassov's Conjecture is a generalization of Sperner's Lemma, a lemma which has been used to prove Brouwer's Fixed Point Theorem, among other fixed point theorems. The proof of…

We present a short proof of the Alexandrov-Fenchel inequalities for mixed volumes of convex bodies.

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

An technically interesting proof of a known theorem.

A very simple but useful almost sure convergence theorem of probability is given.

Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.

Kolmogorov's invariant torus theorem is proved using a simple fixed point theorem.

In this paper we give an elementary proof for Bertrand's postulate also known as Bertrand-Chebyshev theorem.

We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.