Related papers: The Sharkovsky Theorem
This paper is withdrawn. The current main theorem can be proved by using a simple field theory. The main theorem is to placed by another theorem, shortly.
We study how to extend Sanov theorem to the quantum setting. Although a quantum version of the Sanov theorem was proposed in Bjelakovic et al (Commun. Math. Phys., 260, p.659 (2005)), the classical case of their statement is not the same as…
The better title is "Yet another FALSE proof of the 4-colour theorem." Please consider all versions of this paper as historical material on the way to a non-computer proof of the 4-colour theorem. Interpreted as proofs, all versions are…
We give an endorsement for Cornacchia's famous algorithm. Thus we do not claim anything new but an approach which is supposed to be simpler than those of previous works written with the same aim.
We present a simpler way than usual to deduce the completeness theorem for the second-oder classical logic from the first-order one. We also extend our method to the case of second-order intuitionistic logic.
We generalize certain arguments in Zariski's irregularity theorem on cyclic multiple planes.
Oftentimes, Stokes' theorem is derived by using, more or less explicitly, the invariance of the curl of the vector field with respect to translations and rotations. However, this invariance -- which is oftentimes described as the curl being…
This article provides a simple proof of the quadratic formula, which also produces an efficient and natural method for solving general quadratic equations. The derivation is computationally light and conceptually natural, and has the…
Using a Zariski topology associated to a finite field extensions, we give new proofs and generalize the primitive and normal basis theorems.
The main objective of this paper is to study the existence of solutions to some basic fractional difference equations. The tools employed are Krasnosel'skii fixed point theorem which guarantee at least two positive solutions.
A formal theory of experimentation will be presented. Such a theory presents the necessary & sufficient conditions a world must satisfy in order to admit the use of the scientific method.
An alternative form of Fermats equation[1] is proposed. It represents a portion of the identity that includes three terms of Fermats original equation. This alternative form permits an elementary and compact proof of the first case of…
The proof of the Independence Theorem for Kim-independence in positive thick NSOP$_1$ theories from (Dobrowolski and Kamsma, 2022) contains a gap. The theorem is still true, and in this corrigendum we give a different proof.
We show that some mathematical results and their negations are both deducible. The derived contradictions indicate the inconsistency of current mathematics. This paper is an updated version of arXiv:math/0606635v3 with additional results…
An elementary proof of Bertrand's theorem is given by examining the radial orbit equation, without needing to solve complicated equations or integrals.
We present Korovkin approximation theorems that incorporate summability methods. These result allows us to obtain a unified treatment of several previous results, focusing on the underlying structure and the properties that a summability…
A new generalization of the classical separate algebraicity theorem is suggested and proved.
An technically interesting proof of a known theorem.
By addressing a long-standing open problem, listed in a highly regarded collection of open questions in the field and described as a "worthwhile research project", this note extends Markov's theorem (Markoff, Math. Ann., 27:177-182, 1886)…
This paper has been withdrawn by the author due to an error in an inequality in the proof of Theorem 1.1.