Related papers: A refinement of a theorem by Franks

We present a short and self-contained proof of the choosability version of Brooks' theorem.

In the paper are proved theorems, which amplify the results of my paper "On the difference equation of Poincare type (Part 3)", Max-Plank-Institut fuer Mathematik, Bonn, Preprint Series, 2004, 09, 1-34.

The proof of Theorem 11 of the paper M. Scheepers, Remarks on countable tightness, Topology and its Applications 161 (2014), 407 - 432 relies on Lemma 10 of that paper. The offered proof of Lemma 10 had shortcomings, and I was recently…

It is discussed that Zeeman's theorem can be directly obtained from Liouville's theorem if we assume sufficient differentiability.

For functions of two quaternionic variables that are regular in the sense of Fueter, we establish a result similar in spirit to the Hanges and Tr\`eves theorem. Namely, we show that a ball contained in the boundary of a domain is a…

We prove Faltings Finiteness Theorem using Rieffel's classification of the noncommutative tori.

We give a refinement of the local class field theory of Serre and Hazewinkel. This refinement allows the theory to treat extensions that are not necessarily totally ramified. Such a refinement was obtained and used in the authors' paper on…

We generalize and prove a result which was first shown by Zippin, and was explicitly formulated by Benyamini.

We present a self-contained elementary and detailed exposition of Mertens' own proof of his theorem on the divergence of the series of the reciprocals of the primes and compare it with the modern proofs. His proof contains explicit…

In this paper, we prove a fine condensation theorem. This is quite similar to condensation theorems for pure extender mice in the literature, except that condensation for iteration strategies has been added to the mix.

In this article we present Pickands theorem and his double sum method. We follow Piterbarg's proof of this theorem. Since his proof relies on general lemmas we present a complete proof of Pickands theorem using Borell inequality and Slepian…

We give four new proofs of the directed version of Brook's Theorem and an NP-completeness result.

We provide a complete proof of an optimal version of the Marcinkiewicz multiplier theorem.

Recently the ``Fluctuation theorem'' has been criticized and incorrect incorrect contents have been atributed to it. Here I reestablish and comment the original statements.

This note relies mainly on a refined version of the main results of the paper by F. Catrina and D. Costa (J. Differential Equations 2009). We provide very short and self-contained proofs. Our results are sharp and minimizers are obtained in…

This article corrects two mistakes in the article "Coarse homology theories" [math.AT/0106183].

This work is motivated by a paper of Davenport and Schmidt, which treats the question of when Dirichlet's theorems on the rational approximation of one or of two irrationals can be improved and if so, by how much. We consider a…

In this paper, using Pesin theory and Liao theory, we give a positive solution to a conjecture of A. Katok.

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.