Related papers: The Sharkovsky Theorem
The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…
The aim of this note is to give a proof of the Schottky theorem in general domains in $\mathbb{C}^n$. The proof is short and works for the cases $n = 1$ and $n > 1$ at the same time.
The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper I describe a technique for simplifying automated proofs. Hopefully this discussion will stimulate interest in the…
We prove a version of Hrushovski's socle lemma for rigid groups in an arbitrary simple theory.
Kotlarski's theorem (see H. Kotlarski. Bounded Induction and Satisfaction Classes. Mathematical Logic Quarterly, vol. 32, 31-34, 1986, P. 531--544.) formalized in $WKL_0$.
An elementary proof of the two-sidedness of the matrix-inverse is given using only linear independence and the reduced row-echelon form of a matrix. In addition, it is shown that a matrix is invertible if and only if it is row-equivalent to…
A proof of Sendov's conjecture is given.
We present an accurate detailed exposition of the proof of existence of the Alexander-Conway polynomial (of links in 3-dimensional space). Other proofs were given by J. Alexander, J. Conway, V. Mantourov and L. Kauffman.
This note is an (exact) copy of the report of Jaak Peetre, "Generalizing Ovchinnikov's Theorem". Published as Technical Report, Lund (1981). Some more recent general references have been added, some references updated though (in italics)…
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.
Tchakaloff's Theorem establishes the existence of a quadrature rule of prescribed degree relative to a positive, compactly supported measure that is absolutely continuous with respect to Lebesgue measure on $\mathbb{R}^{d}$. Subsequent…
There exists an extensive and fairly comprehensive discrete analytic function theory which is based on circle packing. This paper introduces a faithful discrete analogue of the classical Schwarzian derivative to this theory and develops its…
Ramsey Theorem [6] for pairs is intuitionistically but not classically provable: it is equivalent to a subclassical principle [2]. In this note we show that Ramsey may be restated in an intuitionistically provable form, which is informative…
This is an elementary geometrical proof of Birkhoff theorem. It is hardly important, but the pictures behind are quite nice.
The ain of this note is to make available the unpublished proof of Scorichenko of the isomorphism between stable K-theory and functor homology for polynomial coefficients over an arbitrary ring.
We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.
Several recent results bring into focus the superintuitionistic nature of most notions of proof-theoretic validity, but little work has been done evaluating the consequences of these results. Proof-theoretic validity claims to offer a…
The purpose of this note is to provide a detailed proof of Nazarov's inequality stated in Lemma A.1 in Chernozhukov, Chetverikov, and Kato (2017, Annals of Probability).
This paper is partly a historical survey of various approaches and methods in the fractional calculus, partly a description of the Kipriyanov extraordinary theory in comparison with the classical one. The significance and outstanding…
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.