Related papers: The Sharkovsky Theorem

We obtain some results related to Romanoff's theorem.

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

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

We prove new results on the derivative of the Minkowski question mark function. Some of our theorems are non-improvable.

All the already known results on self descriptive numbers, together with the demonstration of the uniqueness for bases greater than 6, are here obtained through a systematic scheme of proof and not trial and error. The proof is also…

Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.

The recent non-calculus proof of Kepler's first law succeeds because of an obscure, but valid property of the ellipse.

We survey the classical results on the prime number theorem

The import of Bell's Theorem is elucidated. The theorem's proof is illustrated both heuristically and in mathematical detail in a pedagogical fashion. In the same fashion, it is shown that the proof is correct mathematically, but it doesn't…

We give a new proof for Godel's second incompleteness theorem, based on Kolmogorov complexity, Chaitin's incompleteness theorem, and an argument that resembles the surprise examination paradox. We then go the other way around and suggest…

This report presents a formalization of May's theorem in the proof assistant Coq. It describes how the theorem statement is first translated into Coq definitions, and how it is subsequently proved. Various aspects of the proof and related…

A recently proposed axiom system for Andr\'e's central translation structures is improved upon. First, one of its axioms turns out to be dependent (derivable from the other axioms). Without this axiom, the axiom system is indeed…

The authors study the classical Lagrange inversion theorem--an antecedent of the modern implicit function theorem--in the smooth case. Examples are given to show that the result is sharp.

This paper provides a rigorous and gap-free proof of the index theorem used in the theory of regular economy. In the index theorem that is the subject of this paper, the assumptions for the excess demand function are only several usual…

This paper is purely expository. We present short elementary proofs of * the Gauss Theorem on constructibility of regular polygons; * the existence of a cubic equation unsolvable in real radicals; * the existence of a quintic equation…

Iterated reflection principles have been employed extensively to unfold epistemic commitments that are incurred by accepting a mathematical theory. Recently this has been applied to theories of truth. The idea is to start with a collection…

We explore possibilities and limitations of a purely topological approach to the Dvoretzky Theorem.

The content of this review is summarized here through the titles of its sections, as follows: 1. Introduction: Schwarzschild's original solution and the ``Schwarzschild solution''. 2. The wrong arrow of time of Hilbert's manifold is at the…

Kronecker's 1856 paper contains a solvability theorem that is useful to construct unsolvable algebraic equations. We show how Kronecker's solvability theorem can be derived naturally via a polynomial complete decomposition method. This…

We present an alternative proof of Perron's theorem, which is probabilistic in nature. It rests on the representation of the Perron eigenvector as a functional of the trajectory of an auxiliary Markov chain.