Related papers: Another proof of M. Kontsevich formality theorem
In this paper, we give a detailed account of Goldfeld's proof of Siegel's theorem. Particularly, we present complete proofs of the nontrivial assumptions made in his paper.
The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.
A version of Kontsevich Formality theorem is proven for smooth DG algebras. As an application of this, it is proven that any quasiclassical datum of noncommutative unfolding of an isolated surface singularity can be quantized.
This paper describes a formalism that subsumes Peterson's intermediate quantifier syllogistic system, and extends the ideas by van Eijck on Aristotle's logic. Syllogisms are expressed in a concise form making use of and extending the…
Work in progress concerning alternative formalizations of arithmetic.
A variation on the splitting principle
Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems
We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.
This article offers different proofs of ten inequalities from those already published. So that the readers can see for themselves, the tasks specified in the condition of the source and classical inequalities which used in previously…
We present an alternative proof of the Alexander-Hirschowitz Theorem in dimension 3 using degenerations of toric varieties.
In his famous paper entitled "Operads and motives in deformation quantization", Maxim Kontsevich constructed (in order to prove the formality of the little d-disks operad) a topological operad, which is called in the literature the…
Continued fractions are used to give an alternate proof of $e^{x/y}$ is irrational.
This short note gives an elementary alternative proof for a theorem of Danilov and Koshevoy on Minkowski summation and unimodularity in discrete convex analysis. It is intended to disseminate this fundamental theorem and make its proof…
The following paper follows on from work by Kamae, and gives a rigorous proof of the Ergodic Theorem, using nonstandard analysis.
In this paper a new conjecture equivalent to Collatz conjecture is presented. In particural, showing that (all) the solution(s) of newly introduced iterative functional equation(s) have a given property is equivalent to prove Collatz…
The first and second representation theorems for sign-indefinite, not necessarily semi-bounded quadratic forms are revisited. New straightforward proofs of these theorems are given. A number of necessary and sufficient conditions ensuring…
This paper has been withdrawn by the author due to an error in an inequality in the proof of Theorem 1.1.
We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.
We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.
We give the mathematical theory of duality computer in the density matrix formalism. This result complements the mathematical theory of duality computer of Gudder in the pure state formalism.