Related papers: The Marker-Steinhorn Theorem
We prove new results on the derivative of the Minkowski question mark function. Some of our theorems are non-improvable.
This short note present a "proof" of $P\neq NP$. The "proof" with double quotation marks is to indicate that we do not know whether the proof is correct or not (We're confused because we do know in which we make the mistakes).
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…
We give a short proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis. The part of the proof which is my own (not Pin's) is a complete replacement of the same part in an earlier version of this paper.
This is an introductory article to the theory of multiple gaps.
We present a simple extension of Lindeberg's argument for the Central Limit Theorem to get a general invariance result. We apply the technique to prove results from random matrix theory, spin glasses, and maxima of random fields.
We give a rigorous proof for the linear stability of the Skyrmion. In addition, we provide new proofs for the existence of the Skyrmion and the GGMT bound.
We survey the classical results of the Dirichlet Approximation Theorem.
A short proof of the Mazur-Ulam theorem concerning isometries of real normed spaces.
We show that Thompson's $A\times B$-Lemma can be obtained as a consequence of the Brauer pair version of Brauer's Third Main Theorem.
Doob's theorem provides guarantees of consistent estimation and posterior consistency under very general conditions. Despite the limitation that it only guarantees consistency on a set with prior probability 1, for many models arising in…
We give an elementary proof to Hasse theorem.
We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.
In [3, Theorem 6.7B], the authors use the Main Theorems of Brauer to give a proof of Burnside's Normal $p$-complement Theorem. Unfortunately, the proof contains an error. We take this opportunity to give a proof along similar lines,…
The article presents the proof of Casas-Alvero conjecture.
We prove existence of an invariant measure on a hypergroup.
We revisit Ahlfors theory of covering surfaces thanks to Stokes theorem.
In this paper, we prove common fixed point results for a self-mappings satisfying an implicit function which is general enough to cover a multitude of known as well as unknown contractions. Our results modify, unify, extend and generalize…
This note contains a complete proof of the Abhyankar-Moh-Suzuki theorem (in characteristic zero case).
We extract the Abhyankar-Moh-Suzuki theorem from the Lin-Zaidenberg theorem.