Related papers: On the Cotlar-Stein lemma
We give again the proof of several classical results concerning the cyclotomic approach to Fermat's last theorem using exclusively class field theory (essentially the reflection theorems), without any calculations. The fact that this is…
The aim of this article is to give an elementary proof of the fact that the Schwarz-Pick Lemma follows from the Ahlfors-Schwarz-Pick Lemma.
We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.
We consider M systems (each an electron in a long square cylinder) uniformly arranged on a ring and with Coulomb interactions. Exact straightforward numerical time-dependent perturbation calculation of a single N-level ($\lesssim 7$)…
In this expository note we give proof of the Weierstrass gap theorem in Cohomology terminology. We analyze gap sequence for finding possible gaps and non-gaps on X.
This paper shows an elementary and direct proof of the Fundamental Theorem of Algebra, via Bolzano-Weierstrass Theorem on Minima and the Binomial Formula, that avoids: any root extraction other than the one used to define the modulus…
In this continuation paper we will address the problem of tunneling. We will show how to settle this phenomenon within our classical interpretation. It will be shown that, rigorously speaking, there is no tunnel effect at all.
We consider Brouwer's fixed point theorem and Sperner's lemma in one dimension. We present a proof of the Brouwer theorem using the Sperner lemma, and vice versa. However, we also show that they are not equivalent, because the Sperner lemma…
When introduced in a 2018 article in the American Mathematical Monthly, the omega integral was shown to be an extension of the Riemann integral. Although results for continuous functions such as the Fundamental Theorem of Calculus follow…
We introduce a theorem proving algorithm that uses practically no domain heuristics for guiding its connection-style proof search. Instead, it runs many Monte-Carlo simulations guided by reinforcement learning from previous proof attempts.…
We strengthen the Free Will Theorem, which proved the spontaneity of particles, based on the free will of the experimenter. The new result is unconditional, and does not require the experimenter's free will to prove the particles'…
We expose here a short proof of Cramer's theorem in R based on convex duality.
In a recent paper we introduced a new framework for the study of call by need computations to normal form and root-stable form in term rewriting. Using elementary tree automata techniques and ground tree transducers we obtained simple…
It is shown theoretically that the speed of light cannot depend on direction.
The goal of the paper is to present two simple proofs of the Lagrange Inversion Formula for formal power series. Both proofs are non-external in the sense that they use concepts that do not go beyond the scope of formal power series…
The proof of Brouwer's fixed-point theorem based on Sperner's lemma is often presented as an elementary combinatorial alternative to advanced proofs based on algebraic topology. The goal of this note is to show that: (i) the combinatorial…
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.
We prove a power series ring analogue of the Dedekind-Mertens lemma. Along the way, we give limiting counterexamples, we note an application to integrality, and we correct an error in the literature.
A nonconstructive proof can be used to prove the existence of an object with some properties without providing an explicit example of such an object. A special case is a probabilistic proof where we show that an object with required…
We show that there is a point on a computable arc that does not belong to any computable rectifiable curve. We also show that there is a point on a computable rectifiable curve with computable length that does not belong to any computable…